Photonics Papers and Abstracts

See also our main Papers and Publications page.

[1]

K. K. Lee, Y. Avniel, and S. G. Johnson, “Design strategies and rigorous conditions for single-polarization single-mode waveguides,” Optics Express, vol. 16, pp. 15170–15184, September 2008. [ bib | http ]

We establish rigorous necessary analytical conditions for the existence of single-polarization single-mode (SPSM) bandwidths in index-guided microstructured waveguides (such as photonic-crystal fibers). These conditions allow us to categorize designs for SPSM waveguides into four strategies, at least one of which seems previously unexplored. Conversely, we obtain rigorous sufficient conditions for the existence of two cutoff-free index-guided modes in a wide variety of microstructured dielectric waveguides with arbitrary periodic claddings, based on the existence of a degenerate fundamental mode of the cladding (a degenerate light line). We show how such a degenerate light line, in turn, follows from the symmetry of the cladding.

[2]

R. E. Hamam, M. Ibanescu, E. J. Reed, P. Bermel, S. G. Johnson, E. Ippen, J. D. Joannopoulos, and M. Soljačić, “Purcell effect in nonlinear photonic structures: a coupled mode theory analysis,” Optics Express, vol. 16, pp. 12523–12537, August 2008. [ bib | http ]

We develop a coupled mode theory (CMT) model of the behavior of a polarization source in a general photonic structure, and obtain an analytical expression for the resulting generated electric field; loss, gain and/or nonlinearities can also be modeled. Based on this treatment, we investigate the criteria needed to achieve an enhancement in various nonlinear effects, and to produce efficient sources of terahertz radiation, in particular. Our results agree well with exact finite-difference time-domain (FDTD) results. Therefore, this approach can also in certain circumstances be used as a potential substitute for the more numerically intensive FDTD method.

[3]

Z. Xu, X. Jiang, J. D. Joannopoulos, L. Torner, and M. Soljačić, “Nonlinear photonic crystals near the supercollimation point,” Optics Letters, vol. 33, pp. 1762–1764, August 2008. [ bib | DOI | .pdf ]

We uncover a strong coupling between nonlinearity and diffraction in a photonic crystal at the supercollimation point. We show that this is modeled by a nonlinear diffraction term in a nonlinear-Schrödinger-type equation in which the properties of solitons are investigated. Linear stability analysis shows solitons are stable in an existence domain that obeys the Vakhitov–Kolokolov criterium. In addition, we investigate the influence of the nonlinear diffraction on soliton collision scenarios.

[4]

A. F. Oskooi, L. Zhang, Y. Avniel, and S. G. Johnson, “The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers,” Optics Express, vol. 16, pp. 11376–11392, July 2008. [ bib | http ]

Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).

[5]

K. K. Y. Lee, Y. Avniel, and S. G. Johnson, “Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides,” Optics Express, vol. 16, pp. 9261–9275, June 2008. [ bib | DOI | http ]

We derive a sufficient condition for the existence of index-guided modes in a very general class of dielectric waveguides, including photonic-crystal fibers (arbitrary periodic claddings, such as “holey fibers”), anisotropic materials, and waveguides with periodicity along the propagation direction. This condition provides a rigorous guarantee of cutoff-free index-guided modes in any such structure where the core is formed by increasing the index of refraction (e.g. removing a hole). It also provides a weaker guarantee of guidance in cases where the refractive index is increased “on average” (precisely defined). The proof is based on a simple variational method, inspired by analogous proofs of localization for two-dimensional attractive potentials in quantum mechanics.

[6]

A. W. Rodriguez, J. D. Joannopoulos, and S. G. Johnson, “Repulsive and attractive Casimir forces in a glide-symmetric geometry,” Physical Review A, vol. 77, p. 062107, June 2008. [ bib | http ]

We describe a three-dimensional geometry in which both attractive and repulsive Casimir forces arise using ordinary metallic materials, as computed via an exact numerical method (no uncontrolled approximations). The geometry consists of a zipperlike, glide-symmetric structure formed of interleaved metal brackets attached to parallel platesābecause of the interleaving pattern, a net repulsive force can arise from a combination of attractive interactions. Depending on the separation, the perpendicular force between the plates and brackets varies from attractive (large separations) to repulsive (intermediate distances) and back to attractive (close separations), with one point of stable equilibrium in the perpendicular direction. This geometry was motivated by a simple intuition of attractive interactions between surfaces, and so we also consider how a rough proximity-force approximation of pairwise attractions compares to the exact calculations.

[7]

Y. D. Chong, X.-G. Wen, and M. Soljačić, “Effective theory of quadratic degeneracies,” Physical Review B, vol. 77, p. 235125, June 2008. [ bib | http ]

We present an effective theory for the Bloch functions of a two-dimensional square lattice near a quadratic degeneracy point. The degeneracy is protected by the symmetries of the crystal, and breaking these symmetries can either open a band gap or split the degeneracy into a pair of linear degeneracies that are continuable to Dirac points. A degeneracy of this type occurs between the second and third transverse magnetic bands of a photonic crystal formed by a square lattice of dielectric rods. We show that the theory agrees with numerically computed photonic band structures and yields the correct Chern numbers induced by parity breaking.

[8]

A. W. Rodriguez, A. P. McCauley, Y. Avniel, and S. G. Johnson, “Computation and visualization of photonic quasicrystal spectra via Bloch's theorem,” Physical Review B, vol. 77, p. 104201, March 2008. [ bib | http | .pdf ]

Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwell's equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Bloch's theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the higher-dimensional superspace with no additional computational cost. As a proof of concept, these general ideas are demonstrated for the simple case of one-dimensional quasicrystals, which can also be solved by simple transfer-matrix techniques.

[9]

S. J. Rahi, A. W. Rodriguez, T. Emig, R. L. Jaffe, S. G. Johnson, and M. Kardar, “Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders,” Physical Review A, vol. 77, p. 030101(R), March 2008. [ bib | http | .pdf ]

We analyze the Casimir force between two parallel infinite metal cylinders with nearby metal plates using two methods. Surprisingly, the attractive force between cylinders depends nonmonotonically on the separation from the plate(s), and the cylinder-plate force depends nonmonotonically on the separation of the cylinders. These multibody phenomenona do not follow from simple two-body force descriptions. We can explain the nonmonotonicity with the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders and their images on the nearby plate(s).

[10]

C. Kottke, A. Farjadpour, and S. G. Johnson, “Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods,” Physical Review E, vol. 77, p. 036611, March 2008. [ bib | http | .pdf ]

We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a “localized” coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking a limit in which a coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g. from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a sub-pixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.

[11]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light. Princeton University Press, second ed., February 2008. [ bib | http ]

Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications.

Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers.

[12]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Physical Review Letters, vol. 100, p. 013905, January 2008. [ bib | http | .pdf ]

We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D photonic crystals possessing Dirac point-derived band gaps, can appear in more general settings. We show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wave functions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is nonzero. In a square-lattice yttrium-iron-garnet crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects.

[13]

A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Efficient wireless non-radiative mid-range energy transfer,” Annals of Physics, vol. 323, pp. 34–48, January 2008. [ bib | DOI | .pdf ]

We investigate whether, and to what extent, the physical phenomenon of long-lifetime resonant electromagnetic states with localized slowly-evanescent field patterns can be used to transfer energy efficiently over non-negligible distances, even in the presence of extraneous environmental objects. Via detailed theoretical and numerical analyses of typical real-world model-situations and realistic material parameters, we establish that such a non-radiative scheme can strong coupling between two medium-range distant such states and thus could indeed be practical for efficient medium-range wireless energy transfer.

[14]

S. Zaheer, A. W. Rodriguez, S. G. Johnson, and R. L. Jaffe, “Optical-approximation analysis of sidewall-spacing effects on the force between two squares with parallel sidewalls,” Physical Review A, vol. 76, p. 063816, December 2007. [ bib | .pdf ]

Using the ray-optics approximation, we analyze the Casimir force in a two-dimensional domain formed by two metallic blocks adjacent to parallel metallic sidewalls, which are separated from the blocks by a finite distance h. For h>0, the ray-optics approach is not exact because diffraction effects are neglected. Nevertheless, we show that ray optics is able to qualitatively reproduce a surprising effect recently identified in an exact numerical calculation: the force between the blocks varies nonmonotonically with h. In this sense, the ray-optics approach captures an essential part of the physics of multibody interactions in this system, unlike simpler pairwise-interaction approximations such as proximity force approximations (PFA). Furthermore, by comparison to the exact numerical results, we are able to quantify the impact of diffraction on Casimir forces in this geometry.

[15]

M. Ghebrebrhan, M. Ibanescu, S. G. Johnson, M. Soljačić, and J. D. Joannopoulos, “Distinguishing zero-group-velocity modes in photonic crystals,” Physical Review A, vol. 76, p. 063810, December 2007. [ bib | .pdf ]

We examine differences between various zero-group-velocity modes in photonic crystals, including those that arise from Bragg diffraction, anticrossings, and band repulsion. Zero-group velocity occurs at points where the group velocity changes sign, and therefore is conceptually related to “left-hande” media, in which the group velocity is opposite to the phase velocity. We consider this relationship more quantitatively in terms of the Fourier decomposition of the modes, by defining a measure of how much the “average” phase velocity is parallel to the group velocity—an anomalous region is one in which they are mostly antiparallel. We find that this quantity can be used to qualitatively distinguish different zero-group-velocity points. In one dimension, such anomalous regions are found never to occur. In higher dimensions, they are exhibited around certain zero-group-velocity points, and lead to unusual enhanced confinement behavior in microcavities.

[16]

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Optics Express, vol. 15, pp. 16986–17000, December 2007. [ bib | http ]

Most photovoltaic (solar) cells are made from crystalline silicon (c-Si), which has an indirect band gap. This gives rise to weak absorption of one-third of usable solar photons. Therefore, improved light trapping schemes are needed, particularly for c-Si thin film solar cells. Here, a photonic crystal-based light-trapping approach is analyzed and compared to previous approaches. For a solar cell made of a 2 μm thin film of c-Si and a 6 bilayer distributed Bragg reflector (DBR) in the back, power generation can be enhanced by a relative amount of 24.0% by adding a 1D grating, 26.3% by replacing the DBR with a six-period triangular photonic crystal made of air holes in silicon, 31.3% by a DBR plus 2D grating, and 26.5% by replacing it with an eight-period inverse opal photonic crystal.

[17]

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Optics Express, vol. 15, pp. 16161–16176, November 2007. [ bib | http | .pdf ]

Nonlinear photonic-crystal microresonators offer unique fundamental ways of enhancing a variety of nonlinear optical processes. This enhancement improves the performance of nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic ultrafast integrated optical devices. Here, we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal microcavities. First, we discuss a system in which this enhancement has been successfully demonstrated both theoretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we show how nonlinear photonic crystal cavities can be also used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of materials can be strongly modified via the so-called Purcell effect, present in the resonant cavities under study.

[18]

J. Bravo-Abad, S. Fan, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Modeling nonlinear optical phenomena in nanophotonics,” Journal of Lightwave Technology, vol. 25, pp. 2539–2546, September 2007. Invited paper. [ bib | .pdf ]

In this paper, we review various numerical methods currently used to model nonlinear optical processes in nanophotonics. Among the different theoretical frameworks that have been used to study nonlinear photonic structures, we particularly focus on the application of both perturbation theory and coupled-mode theory to the analysis of complex nonlinear nanophotonic devices. This description is illustrated on several examples of how these techniques can be used to design photonic-crystal-based nonlinear devices. In addition, in all these examples, we show that the predictions made by the two mentioned techniques are in a good agreement with the numerical results obtained from a nonlinear finite-difference-time-domain approach to these problems.

[19]

A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical-electromagnetism techniques,” Physical Review A, vol. 76, p. 032106, September 2007. [ bib | .pdf ]

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising non-monotonic “lateral” force from the walls.

[20]

P. Bermel, A. Rodriguez, J. D. Joannopoulos, and M. Soljačić, “Tailoring optical nonlinearities via the Purcell effect,” Physical Review Letters, vol. 99, p. 053601, August 2007. [ bib | http | .pdf ]

We predict that the effective nonlinear optical susceptibility can be tailored using the Purcell effect. While this is a general physical principle that applies to a wide variety of nonlinearities, we specifically investigate the Kerr nonlinearity. We show theoretically that using the Purcell effect for frequencies close to an atomic resonance can substantially influence the resultant Kerr nonlinearity for light of all (even highly detuned) frequencies. For example, in realistic physical systems, enhancement of the Kerr coefficient by one to two orders of magnitude could be achieved.

[21]

A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: Nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Physical Review Letters, vol. 99, p. 080401, August 2007. [ bib | .pdf ]

We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a pistonlike problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate nonadditive and nonmonotonic changes in the force due to these lateral walls.

[22]

E. J. Reed, M. R. Armstrong, K. Kim, M. Soljačić, R. Gee, J. H. Glownia, and J. D. Joannopoulos, “Terahertz radiation from shocked materials,” Materials Today, vol. 10, pp. 44–50, July 2007. [ bib | DOI | .pdf ]

Distinct physical mechanisms for the generation of temporally coherent, narrow bandwidth optical radiation are few and rare in nature. Such sources, including lasers, have widespread applications ranging from spectroscopy to interferometry. We review the recent theoretical prediction of a new type of temporally coherent optical radiation source in the 1–100 THz frequency range that can be realized when crystalline polarizable materials like NaCl are subject to a compressive shock wave.

[23]

X. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Applied Physics Letters, vol. 91, p. 031105, July 2007. [ bib | http | .pdf ]

The authors theoretically and numerically investigate the beam propagation near the supercollimation frequency ω_n⁰ in a photonic crystal made of nonlinear material. Since the value and sign of the equal-frequency-contour curvature which dominates the beam behaviors can be nonlinearly tuned near ω_n⁰, a kind of nonlinear effect is generated. The envelope equation with unique form is also obtained. Beam-control mechanisms are theoretically predicted and observed in numerical experiments, such as tunable collimation, tunable beam-divergence angle, and self-lock of collimation. These mechanisms can be utilized to function as fiber, lens and coupler, or to design photonic devices.

[24]

A. Kurs, A. Karalis, R. Moffat, J. D. Joannopoulos, P. Fisher, and M. Soljačić, “Wireless power transfer via strongly coupled magnetic resonances,” Science, vol. 317, pp. 83–86, July 2007. [ bib | DOI ]

Using self-resonant coils in a strongly coupled regime, we experimentally demonstrated efficient nonradiative power transfer over distances up to 8 times the radius of the coils. We were able to transfer 60 watts with  40% efficiency over distances in excess of 2 meters. We present a quantitative model describing the power transfer, which matches the experimental results to within 5%. We discuss the practical applicability of this system and suggest directions for further study.

[25]

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Coupled-mode theory for general free-space resonant scattering of waves,” Physical Review A, vol. 75, p. 053801, May 2007. [ bib | http | .pdf ]

We present a universal coupled-mode-theory treatment of free-space scattering of waves from resonant objects. The range of applicability of the presented approach is fairly broad: it can be used for almost any linear wave system, as long as the resonant scatterer has either three-dimensional (3D) spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the resonant wavelength of the incident wave. The presented framework, while being intuitive and analytically simple, can nevertheless provide quantitatively very accurate modeling of scattering cross sections, absorption cross sections, and many other quantities of interest. We illustrate this approach by showing how it applies to the particular examples of scattering of light from spherically symmetric resonant objects and atoms, and scattering of neutrons off nuclei.

[26]

E. J. Reed, M. Soljačić, and J. D. Joannopoulos, “Maxwell equation simulations of coherent optical photon emission from shock waves in crystals,” Physical Review E, vol. 75, p. 056611, May 2007. [ bib | http | .pdf ]

We have predicted that weak coherent radiation in the 12013100 THz frequency regime can be emitted under some circumstances when a shock wave propagates through a polarizable crystal, like NaCl [Reed et al., Phys. Rev. Lett. 96, 013904 (2006)]. In this work, we present and analyze a new model of a shocked polarizable crystal that is amenable to systematic analytical study and direct numerical solution of Maxwell's equations to predict emitted coherent field amplitudes and properties. Our simulations and analysis indicate that the field amplitude of the effect decreases rapidly with increasing shock front rise distance. These models establish a fundamental limit of the ratio of emitted terahertz amplitude to the static polarization of a material. While this effect is treated classically in our previous work, we present a quantum perturbation analysis showing that it can also occur in the low-amplitude emission quantum limit.

[27]

O. Shapira, A. Stolyarov, N. D. Orf, K. Kuriki, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Towards dynamic surface-emitting fiber lasers,” Optics and Photonics News, vol. 18, pp. 26–31, May 2007. [ bib | http ]

The surface-emitting fiber laser combines characteristics of fiber lasers and VCSELs that could be translated into new and exciting applications in medicine, security and “smart” fabrics.

[28]

D.-Z. A. Chen, R. Hamam, M. Soljačić, J. D. Joannopoulos, and G. Chen, “Extraordinary optical transmission through subwavelength holes in a polaritonic silicon dioxide film,” Applied Physics Letters, vol. 90, p. 181921, May 2007. [ bib | http | .pdf ]

The authors present experimental data showing that extraordinary optical transmission occurs through subwavelength holes etched in an amorphous silicon dioxide film. The discrete frequency ranges of the enhanced transmission suggest the involvement of surface phonon-polaritons in mediating the transmission in a manner analogous to surface plasmons on metal films. Finite-difference time-domain simulations also predict the enhancement and correlate well with the experimental data. Both experimental and theoretical results show a fivefold increase in transmission through a perforated film versus a solid film.

[29]

E. J. Reed, M. Soljačić, R. Gee, and J. D. Joannopoulos, “Molecular dynamics simulations of coherent optical photon emission from shock waves in crystals,” Physical Review B, vol. 75, p. 174302, May 2007. [ bib | http | .pdf ]

We have previously predicted that coherent electromagnetic radiation in the 1–100 THz frequency range can be generated in crystalline polarizable materials when subject to a shock wave or solitonlike propagating excitation [E. J. Reed et al., Phys. Rev. Lett. 96, 013904 (2006)]. In this work, we present analysis and molecular dynamics simulations of shock waves in crystalline NaCl which expand upon this prediction. We demonstrate that the coherent polarization currents responsible for the effect are generated by a nonresonant, nonlinear effect that occurs at the shock front. We consider the effect of thermal noise and various shock pressures on the coherent polarization currents and find that the amplitude generally increases with increasing shock pressure and decreasing material temperature. Finally, we present calculations of the amplitude and distribution of emitted radiation showing that the radiation can be directed or undirected under various realistic conditions of the shape of the shock front.

[30]

A. Rodriguez, M. Soljačić, J. D. Joannopoulos, and S. G. Johnson, “χ⁽²⁾ and χ⁽³⁾ harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Optics Express, vol. 15, pp. 7303–7318, May 2007. [ bib | http | .pdf ]

We derive general conditions for 100% frequency conversion in any doubly resonant nonlinear cavity, for both second- and third-harmonic generation via χ⁽²⁾ and χ⁽³⁾ nonlinearities. We find that conversion efficiency is optimized for a certain “critical” power depending on the cavity parameters, and assuming reasonable parameters we predict 100% conversion using milliwatts of power or less. These results follow from a semi-analytical coupled-mode theory framework which is generalized from previous work to include both χ⁽²⁾ and χ⁽³⁾ media as well as inhomogeneous (fully vectorial) cavities, analyzed in the high-efficiency limit where down-conversion processes lead to a maximum efficiency at the critical power, and which is verified by direct finite-difference time-domain (FDTD) simulations of the nonlinear Maxwell equations. Explicit formulas for the nonlinear coupling coefficients are derived in terms of the linear cavity eigenmodes, which can be used to design and evaluate cavities in arbitrary geometries.

[31]

E. Lidorikis, S. Egusa, and J. D. Joannopoulos, “Effective medium properties and photonic crystal superstructures of metallic nanoparticle arrays,” Journal of Applied Physics, vol. 101, p. 054304, March 2007. [ bib | http ]

Using the finite-difference time-domain method we extract the effective optical constants of metallic nanoparticle arrays. We explore their behavior in the full range of filling fractions and find excellent agreement with the Maxwell-Garnett [Philos. Trans. R. Soc. London 203, 385 (1904)] effective medium theory for the effective dielectric constant. We also find that the resonance response of such systems exhibits an effective magnetic component, typically overlooked in standard effective medium theories. We verify that the description of these nanoarrays as an effective bulk medium is exact within numerical precision, at least in one-dimensional arrangements, by comparing with full simulations of more complex superlayer configurations. Finally, using the effective constants we study photonic crystal superstructures consisting of these arrays, demonstrating an interesting optical response where resonant absorption and reflection bands are separated by extremely sharp edges of almost 100% relative change per nanometer wavelength.

[32]

D. L. Chan, I. Celanovic, J. D. Joannopoulos, and M. Soljačić, “Emulating one-dimensional resonant Q-matching behavior in a two-dimensional system via Fano resonances,” Physical Review A, vol. 74, p. 064901, December 2006. [ bib | http | .pdf ]

Through detailed numerical and analytical studies, we establish that the significant enhancement of thermal emission via Q matching, which has been possible in one-dimensional (1D) systems only, can be extended to two-dimensional (2D) systems by means of Fano resonances in the 2D system. In particular, we show the existence of essentially 1D behavior in a 2D system—a case of reduced dimensionality. Moreover, we show how properties of these spectra can be controlled by changing the geometrical parameters of the 2D system.

[33]

A. F. Abouraddy, O. Shapira, M. Bayindir, J. Arnold, J. D. Joannopoulos, and Y. Fink, “Fabrics that “see”: Photosensitive fibers,” Optics and Photonics News, vol. 17, p. 21, December 2006. [ bib | http ]

We can now construct conformal detectors that allow us to have optically functional clothing.

[34]

S. A. Jacobs, B. Temelkuran, O. Weisberg, M. Ibanescu, S. G. Johnson, and M. Soljačić, “Hollow core fibers,” in Specialty Optical Fibers Handbook (A. Mendez and T. Morse, eds.), ch. 11, New York: Elsevier, December 2006. [ bib ]

[35]

M. Bayindir, A. F. Abouraddy, O. Shapira, J. Viens, D. S. Saygin-Hinczewski, F. Sorin, J. Arnold, J. D. Joannopoulos, and Y. Fink, “Kilometer-long ordered nanophotonic devices by preform-to-fiber fabrication,” IEEE J. Selected Topics in Quantum Electronics, vol. 12, pp. 1202–1213, November 2006. [ bib | DOI ]

A preform-to-fiber approach to the fabrication of functional fiber-based devices by thermal drawing in the viscous state is presented. A macroscopic preform rod containing metallic, semiconducting, and insulating constituents in a variety of geometries and close contact produces kilometer-long novel nanostructured fibers and fiber devices. We first review the material selection criteria and then describe metal–semiconductor–metal photosensitive and thermally sensitive fibers. These flexible, lightweight, and low-cost functional fibers may pave the way for new types of fiber sensors, such as thermal sensing fabrics, artificial skin, and large-area optoelectronic screens. Next, the preform-to-fiber approach is used to fabricate spectrally tunable photodetectors that integrate a photosensitive core and a nanostructured photonic crystal structure containing a resonant cavity. An integrated, self-monitoring optical-transmission waveguide is then described that incorporates optical transport and thermal monitoring. This fiber allows one to predict power-transmission failure, which is of paramount importance if high-power optical transmission lines are to be operated safely and reliably in medical, industrial and defense applications. A hybrid electron–photon fiber consisting of a hollow core (for optical transport by means of a photonic bandgap) and metallic wires (for electron transport) is described that may be used for transporting atoms and molecules by radiation pressure. Finally, a solid microstructured fiber fabricated with a highly nonlinear chalcogenide glass enables the generation of supercontinuum light at near-infrared wavelengths.

[36]

J. Bravo-Abad, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Photonic crystal optical waveguides for on-chip Bose-Einstein condensates,” Physical Review A, vol. 74, p. 053619, November 2006. [ bib | http | .pdf ]

We propose an on-chip optical waveguide for Bose-Einstein condensates based on the evanescent light fields created by surface states of a photonic crystal. It is shown that the modal properties of these surface states can be tailored to confine the condensate at distances from the chip surface significantly longer that those that can be reached by using conventional index-contrast guidance. We numerically demonstrate that by index-guiding the surface states through two parallel waveguides, the atomic cloud can be confined in a two-dimensional trap at about 1 μm above the structure using a power of 0.1 mW.

[37]

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, “Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials,” IEEE J. Selected Topics in Quantum Electronics, vol. 12, pp. 1345–1348, November 2006. [ bib | DOI | .pdf ]

A novel on-chip Bragg cladding waveguide is designed and fabricated using conventional CMOS techniques. This optical waveguide has a low refractive index core surrounded by high index-contrast cladding bilayers. Polysilicon (n = 3.5) and silicon nitride (n=2.0) are used for high index-contrast Bragg layers, where index difference is as high as 1.5. Our simulation shows that sharp bending in low index core materials can be achieved, which is not possible using index guiding mechanism. Within our approach, various on-chip applications are expected such as optical integration, high power transmission, biosensor/microelectromechanical system and so on.

[38]

B. Maes, M. Soljačić, J. D. Joannopoulos, P. Bienstman, R. Baets, S.-P. Gorza, and M. Haelterman, “Switching through symmetry breaking in coupled nonlienar micro-cavities,” Optics Express, vol. 14, pp. 10678–10683, October 2006. [ bib | http | .pdf ]

We describe stable symmetry-breaking states in systems with two coupled nonlinear cavities, using coupled-mode theory and rigorous simulations. Above a threshold input level the symmetric state of the passive Kerr system becomes unstable, and we show how this phenomenon can be employed for switching and flip-flop purposes, using positive pulses only. A device with compact photonic crystal microcavities is proposed by which we numerically demonstrate the principle.

[39]

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Physical Review A, vol. 74, p. 043818, October 2006. [ bib | http | .pdf ]

This paper demonstrates switching of a single signal photon by a single gating photon of a different frequency, via a cross-phase-modulation. This effect is mediated by materials exhibiting electromagnetically induced transparency (EIT), which are embedded in photonic crystals (PhCs). An analytical model based on waveguide-cavity QED is constructed for our system, which consists of a PhC waveguide and a PhC microcavity containing a four-level EIT atom. It is solved exactly and analyzed using experimentally accessible parameters. It is found that the strong coupling regime is required for lossless two-photon quantum entanglement.

[40]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Optics Letters, vol. 31, pp. 2972–2974, October 2006. [ bib | .pdf ]

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.

[41]

D. L. Chan, M. Soljačić, and J. D. Joannopoulos, “Direct calculation of thermal emission for three-dimensionally periodic photonic-crystal slabs,” Physical Review E, vol. 74, p. 036615, September 2006. [ bib | http | .pdf ]

We perform direct thermal emission calculations for three-dimensionally periodic photonic crystal slabs using stochastic electrodynamics following the Langevin approach, implemented via a finite-difference time-domain algorithm. We demonstrate that emissivity and absorptivity are equal, by showing that such photonic crystal systems emit as much radiation as they absorb, for every frequency, up to statistical fluctuations. We also study the effect of surface termination on absorption and emission spectra from these systems.

[42]

D. L. C. Chan and M. Soljačić, “Thermal emission and design in 2d-periodic metallic photonic crystal slabs,” Optics Express, vol. 14, pp. 8785–8796, September 2006. [ bib | http ]

We present a useful framework within which we can understand some of the physical phenomena that drive thermal emission in 2D-periodic metallic photonic crystal slabs, emphasizing phenomenology and physical intuition. Through detailed numerical calculations for these systems, we find that periodicity plays a key role in determining the types of physical phenomena that can be excited. We identify two structures as good candidates for thermal design, and conclude with a discussion of how the emissive properties of these systems can be tailored to our needs.

[43]

D. L. Chan, M. Soljačić, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Physical Review E, vol. 74, p. 016609, July 2006. [ bib | http | .pdf ]

We present a useful framework within which we can understand some of the physical phenomena that drive thermal emission in one-dimensional periodic metallic photonic crystals, emphasizing phenomenology and physical intuition. We perform detailed numerical calculations for these systems and find that polarization and periodicity play key roles in determining the types of physical phenomena that can arise. Two promising structures are identified as good candidates for thermal design. We conclude with a discussion of how the emissive properties of these systems can be tailored to our needs.

[44]

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Applied Physics Letters, vol. 88, p. 241920, June 2006. [ bib | http ]

Omnidirectional photonic band gaps opening at low values of refractive index contrast have been found for a nonspherical colloid-based photonic crystal structure. A mechanically stable design is described for the diamondlike photonic crystal composed of colloidal tetrahedra. The proposed tetrastack structure displays omnidirectional 2–3 band gap over a large range of filling fractions, refractive index contrasts, and building block orientations. The threshold refractive index for the inverted tetrastack structure was 1.94. A gap width of 25.3% relative to the center frequency was obtained for an inverted tetrastack with a 0.21 filling fraction of silicon.

[45]

A. F. Abouraddy, O. Shapira, M. Bayindir, J. Arnold, F. Sorin, D. S. Hinczewski, J. D. Joannopoulos, and Y. Fink, “Large-scale optical-field measurements with geometric fibre constructs,” Nature Materials, vol. 5, pp. 532–536, June 2006. [ bib | DOI ]

Optical fields are measured using sequential arrangements of optical components such as lenses, filters, and beam splitters in conjunction with planar arrays of point detectors placed on a common axis. All such systems are constrained in terms of size, weight, durability and field of view. Here a new, geometric approach to optical-field measurements is presented that lifts some of the aforementioned limitations and, moreover, enables access to optical information on unprecedented length and volume scales. Tough polymeric photodetecting fibres drawn from a preform are woven into light-weight, low-optical-density, two- and three-dimensional constructs that measure the amplitude and phase of an electromagnetic field on very large areas. First, a three-dimensional spherical construct is used to measure the direction of illumination over 4π steradians. Second, an intensity distribution is measured by a planar array using a tomographic algorithm. Finally, both the amplitude and phase of an optical wave front are acquired with a dual-plane construct. Hence, the problem of optical-field measurement is transformed from one involving the choice and placement of lenses and detector arrays to that of designing geometrical constructions of polymeric, light-sensitive fibres.

[46]

O. Shapira, K. Kuriki, N. D. Orf, A. F. Abouraddy, G. Benoit, J. F. Viens, A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, Y. Fink, and M. M. Brewster, “Surface-emitting fiber lasers,” Optics Express, vol. 14, pp. 3929–3935, May 2006. [ bib | http ]

All fiber lasers to date emit radiation only along the fiber axis. Here a fiber that exhibits laser emission that is radially directed from its circumferential surface is demonstrated. A unique and controlled azimuthally anisotropic optical wave front results from the interplay between a cylindrical photonic bandgap fiber resonator, anisotropic organic dye gain, and a linearly polarized axial pump. Low threshold (86nJ) lasing at nine different wavelengths is demonstrated throughout the visible and near-infrared spectra. We also report the experimental realization of unprecedented layer thicknesses of 29.5 nm maintained throughout meter-long fibers. Such a device may have interesting medical applications ranging from photodynamic therapy to in vivo molecular imaging, as well as textile fabric displays.

[47]

P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Physical Review B, vol. 73, p. 165125, April 2006. [ bib | http ]

A calculational scheme is presented to model the interaction of light with active dielectric media, represented by four-level atomic materials, surrounded by photonic crystals. Optically pumped lasing is studied in three model systems: a Fabry-Perot cavity, a line of defects in a two-dimensional square lattice of rods, and a cylindrical photonic crystal. Field profiles and conversion efficiencies are calculated for these systems. It is shown that high conversion efficiency can be achieved for large regions of active material in the cavity, as well as for a single fluorescent atom in a hollow-core cylindrical photonic crystal, suggesting designs for ultralow-threshold lasers and ultrasensitive biological sensors.

[48]

E. J. Reed, M. Soljačić, and J. D. Joannopoulos, “Comment on “explanation of the inverse Doppler effect observed in nonlinear transmission lines”,” Physical Review Letters, vol. 96, p. 069402, February 2006. [ bib | http | .pdf ]

A Comment on the Letter by Alexander B. Kozyrev and Daniel W. van der Weide, Phys. Rev. Lett. 94, 203902 (2005). The authors of the Letter offer a Reply.

[49]

C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler radiation emitted by an oscillating dipole moving inside a photonic band-gap crystal,” Physical Review Letters, vol. 96, p. 043903, February 2006. [ bib | .pdf ]

We study the radiation emitted by an oscillating dipole moving with a constant velocity in a photonic crystal, and analyze the effects that arise in the presence of a photonic band gap. It is demonstrated through numerical simulations that the radiation strength may be enhanced or inhibited according to the photonic band structure, and anomalous effects in the sign and magnitude of the Doppler shifts are possible, both outside and inside the gap. We suggest that this effect could be used to identify the physical origin of the backward waves in recent metamaterials.

[50]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre scale supercollimation in a large area 2d photonic crystal,” Nature Materials, vol. 5, pp. 93–96, February 2006. [ bib | .pdf ]

Diffraction, a fundamental process in wave physics, leads to spreading of the optical beams as they propagate. However, new photonic crystal (PhC) meta-materials can be nano-engineered to generate extreme anisotropy, resulting in apparent propagation of light without diffraction. This surprising phenomenon, called supercollimation, effectively freezes the spatial width of a light beam inside a PhC, observed over a few isotropic diffraction-lengths. However, using such experiments to predict the behaviour for longer propagation lengths is difficult, as a tiny error in a measured width can extrapolate to order unity uncertainty in the width at distances over hundreds of diffraction-lengths. Here, supercollimation is demonstrated in a macroscopic PhC system over centimetre-scale distances, retaining spatial width confinement without the need for waveguides or nonlinearities. Through quantitative studies of the beam evolution in a two-dimensional PhC, we find that supercollimation possesses unexpected but inherent robustness with respect to short-scale disorder such as fabrication roughness, enabling supercollimation over 600 isotropic diffraction-lengths. The effects of disorder are identified through experiments and understood through rigorous simulations. In addition, a supercollimation steering capability is proposed.

[51]

E. J. Reed, M. Soljačić, R. Gee, and J. D. Joannopoulos, “Coherent optical photons from shock waves in crystals,” Physical Review Letters, vol. 96, p. 013904, January 2006. [ bib | http | .pdf ]

We predict that coherent electromagnetic radiation in the 12013100 THz frequency range can be generated in crystalline materials when subject to a shock wave or solitonlike propagating excitation. To our knowledge, this phenomenon represents a fundamentally new form of coherent optical radiation source that is distinct from lasers and free-electron lasers. The radiation is generated by the synchronized motion of large numbers of atoms when a shock wave propagates through a crystal. General analytical theory and NaCl molecular dynamics simulations demonstrate coherence lengths on the order of mm (around 20 THz) and potentially greater. The emission frequencies are determined by the shock speed and the lattice constants of the crystal and can potentially be used to determine atomic-scale properties of the shocked material.

[52]

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced photonic band-gap confinement via Van Hove saddle point singularities,” Physical Review Letters, vol. 96, p. 033904, January 2006. [ bib | http ]

We show that a saddle point Van Hove singularity in a band adjacent to a photonic crystal band gap can lead to situations which defy the conventional wisdom that the strongest band-gap confinement is found at frequencies near the midgap. As an example, we present a two-dimensional square photonic crystal waveguide where the strongest confinement is close to the band edge. The underlying mechanism can also apply to any system that is described by a band structure with a gap. In general, the saddle point favors the appearance of a very flat band, which in turn results in an enhanced confinement at band-gap frequencies immediately above or below the flat band.

[53]

M. L. Povinelli, M. Lončar, E. J. Smythe, M. Ibanescu, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Enhancement mechanisms for optical forces in integrated optics,” Proc. SPIE, vol. 6326, p. 632609, 2006. [ bib | .pdf ]

We investigate the extension of optical micromanipulation to integrated optics. In particular, we consider whether propagating light signals can cause mechanical reconfiguration of a device. While such forces are intrinsically weak, we predict theoretically that significant displacements can be achieved using various enhancement mechanisms. These include the use of high-index materials, high-Q (cavity quality factor) enhancement, and slow light in photonic crystals. Silicon optical waveguides have a considerable refractive index contrast with the surrounding air, with a ratio of roughly 3.45/1 at optical communications wavelengths. We show that the strong confinement of light to silicon magnifies optical forces arising from overlap in the guided modes of neighboring waveguides. Silica microsphere resonators are known to have extremely high cavity quality factors, in excess of 108. We show that the quality factor of the resonator magnifies the optical force due to modal overlap between two neighboring spheres. Thirdly, we investigate slow-light enhancement of optical forces using photonic-crystal devices. We show that slow-light velocities give rise to larger forces for the same amount of signal power, enhancing optomechanical coupling effects. In addition to being of fundamental interest, our work suggests that optical manipulation may ultimately provide a route to all-optical conformational control and switching.

[54]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by sub-pixel smoothing in FDTD,” Proc. SPIE, vol. 6322, p. 63220G, 2006. [ bib | .pdf ]

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (“pixellization”). We show that accuracy can be significantly improved by using a sub-pixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory, and compare it to other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.

[55]

M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Tunable time delays in photonic-crystal waveguides,” Proc. SPIE, vol. 6128, p. 61280R, 2006. [ bib | .pdf ]

We study tunable time-delay devices in which the time delay is tuned by changing the group velocity of the propagating signal. The device is designed to place the operating frequency near a photonic band edge. This enhances the change in delay for a given tuning range of the device refractive index. Here we provide an extended explanation of mode symmetry, nomenclature, and the complete band structure of a sample, integrated device to aid the understanding of our previously published work.

[56]

M. Ibanescu, M. Soljačić, S. G. Johnson, and J. D. Joannopoulos, “Ultra-flat bands in two-dimensional photonic crystals,” Proc. SPIE, vol. 6128, p. 612808, 2006. Invited paper. [ bib | .pdf ]

We show that two-dimensional photonic crystals can be designed to have dispersion relations with an extended ultraflat cross-section, meaning that for a fixed wave vector wave vector component k_x the frequency of a band is almost constant when the other wave vector component k_y takes all possible values. these ultra-flat are the result of a non-trivial saddle point in the dispersion relation located in the interior of the Brillouin zone. Interesting consequences include 1D-like behavior, improved super-collimation, and enhanced density of states.

[57]

A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, and S. G. Johnson, “Disorder-immune confinement of light in photonic-crystal cavities,” Optics Letters, vol. 30, pp. 3192–3194, December 2005. [ bib | .pdf ]

We demonstrate by finite-difference time-domain simulations in 2D and 3D that optical cavities in realistic finite photonic crystals have lifetimes and modal volumes that are essentially insensitive to disorder (of various types, including surface disorder and randomized positions), even with unphysically large disorder. A lifetime Q=10⁸ is demonstrated in a 3D single-mode cavity with a half-wavelength mode diameter using only eight vertical periods of a disordered crystal.

[58]

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Optics Letters, vol. 30, pp. 3042–3044, November 2005. [ bib | .pdf ]

Forces arising from overlap between the guided waves of parallel, microphotonic waveguides are calculated. Both attractive and repulsive forces, determined by the choice of relative input phase, are found. Using realistic parameters for a silicon-on-insulator material system, we estimate that the forces are large enough to cause observable displacements. Our results illustrate the potential for a broader class of optically tunable microphotonic devices and microstructured artificial materials.

[59]

M. Skorobogatiy, S. A. Jacobs, S. G. Johnson, C. Anastassiou, and B. Temelkuran, “Heating of hollow photonic Bragg fibers from field propagation, coupling, and bending,” Journal of Lightwave Technology, vol. 23, pp. 3517–3525, November 2005. [ bib | .pdf ]

We investigate heating from field propagation, coupling, and bending, which are the potential failure mechanisms for an emerging new type of high-power radiation guides-hollow photonic Bragg fibers. Continuous wave (CW) and pulsed radiation sources are considered, assuming continuous operation of the laser source.

[60]

M. Bayindir, O. Shapira, D. Saygin-Hinczewski, J. Viens, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Integrated fibres for self-monitored optical transport,” Nature Materials, vol. 4, pp. 820–825, November 2005. [ bib | DOI ]

The ability to integrate distinct functional elements into a single device structure enables the realization of systems with higher-level functionality. Here we report on the design and fabrication of a fibre device structure that contains integrated optical, electrical and thermal elements for self-monitored optical transport. The fibre transmission element uses a hollow-core multilayer cylindrical photonic bandgap structure designed to guide high-power radiation at 10.6 μm along the fibre axis. Multiple thermal-detection elements are placed in the vicinity of the hollow core for the purpose of temperature monitoring along the entire fibre length. Metal wires bridged by a semiconductor layer extend along the length of the fibre and deliver an electrical response to the fibre ends on change in the fibre temperature. The multimaterial fibre is drawn at high speeds from a single preform to produce extended lengths of optically and thermally functional fibres. The exponential dependence on temperature of the electrical conductivity of the semiconducting material allows for the discrimination, in real time, between normal transmission conditions and those that are indicative of localized defect formation, thus enabling a self-monitoring high-power optical transmission line for failure prediction and prevention.

[61]

M. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators,” Optics Express, vol. 13, pp. 8286–8295, October 2005. [ bib | http | .pdf ]

We have calculated the optically-induced force between coupled high-Q whispering gallery modes of microsphere resonators. Attractive and repulsive forces are found, depending whether the bi-sphere mode is symmetric or antisymmetric. The magnitude of the force is linearly proportional to the total power in the spheres and consequently linearly enhanced by Q. Forces on the order of 100 nN are found for Q=108, large enough to cause displacements in the range of 1μm when the sphere is attached to a fiber stem with spring constant 0.004 N/m.

[62]

M. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Optics Express, vol. 13, pp. 7145–7159, September 2005. [ bib | http | .pdf ]

We propose the use of slow-light, band-edge waveguides for compact, integrated, tunable optical time delays. We show that slow group velocities at the photonic band edge give rise to large changes in time delay for small changes in refractive index, thereby shrinking device size. Figures of merit are introduced to quantify the sensitivity, as well as the accompanying signal degradation due to dispersion. It is shown that exact calculations of the figures of merit for a realistic, three-dimensional grating structure are well predicted by a simple quadratic-band model, simplifying device design. We present adiabatic taper designs that attain <0.1% reflection in short lengths of 10 to 20 times the grating period. We show further that cascading two gratings compensates for signal dispersion and gives rise to a constant tunable time delay across bandwidths greater than 100GHz. Given typical loss values for silicon-on-insulator waveguides, we estimate that gratings can be designed to exhibit tunable delays in the picosecond range using current fabrication technology.

[63]

S. N. Tandon, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2d-periodic photonic crystal slabs,” Photonics and Nanostructures, vol. 3, pp. 10–18, August 2005. [ bib | DOI | .pdf ]

The “superprism effect” is an effect observed in photonic crystal structures whereby the direction of light propagation is extremely sensitive to the wavelength and angle of incidence. To realize the superprism effect, new structures are presented which rely on the sensitivity of the phase velocity in a two-dimensional (2D) photonic crystal slab to observe angular magnification outside the photonic crystal medium. Constant frequency contour calculations for a photonic crystal slab of finite thickness are used to predict the phase velocity superprism effect. Further analysis using 2D finite-difference time-domain simulations indicate that a large area photonic crystal and wide excitation beam are necessary for clear observation of the superprism effect. A fabrication technique is demonstrated to achieve the structure's required nanometer-sized features over centimeter-scale areas.

[64]

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Physical Review Letters, vol. 95, p. 063901, August 2005. [ bib | http | .pdf ]

A class of axially uniform waveguides is introduced, employing a new mechanism to guide light inside a low-index dielectric material without the use of photonic band gap, and simultaneously exhibiting subwavelength modal size and very slow group velocity over an unusually large frequency bandwidth. Their basis is the presence of plasmonic modes on the interfaces between dielectric regions and the flat unpatterned surface of a bulk metallic substrate. These novel waveguides allow for easy broadband coupling and exhibit absorption losses limited only by the intrinsic loss of the metal.

[65]

S. G. Johnson, M. L. Povinelli, M. Soljačić, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Applied Physics B, vol. 81, pp. 283–293, July 2005. Invited paper, special issue on photonic crystals. [ bib | .pdf ]

We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic “volume-current method” (Green's functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.

[66]

G. Benoit, K. Kuriki, J.-F. Viens, J. D. Joannopoulos, and Y. Fink, “Dynamic all-optical tuning of transverse resonant cavity modes in photonic bandgap fibers,” Optics Letters, vol. 30, pp. 1620–1622, July 2005. [ bib | http ]

Photonic bandgap fibers for transverse illumination containing half-wavelength microcavities have recently been designed and fabricated. We report on the fabrication and characterization of an all-optical tunable microcavity fiber. The fiber is made by incorporating a photorefractive material inside a Fabry-Perot cavity structure with a quality factor Q>200 operating at 1.5 μm. Under short-wavelength transverse external illumination, a 2 nm reversible shift of the cavity resonant mode is achieved. Dynamic all-optical tuning is reported at frequencies up to 400 Hz. Experimental results are compared with simulations based on the amplitude and kinetics of the transient photodarkening effect measured in situ in thin films.

[67]

S. G. Johnson, M. Soljačić, and J. D. Joannopoulos, “Photonic crystals,” in Encyclopedia of Nonlinear Science (A. Scott, ed.), New York: Routledge, Taylor and Francis Group, July 2005. [ bib ]

[68]

D. L. Chan, E. Lidorikis, and J. D. Joannopoulos, “Point defect geometries in inverted opal photonic crystals,” Physical Review E, vol. 71, pp. 056602–056607, May 2005. [ bib | http ]

We study point defect geometries in inverted opal photonic crystals that can be easily fabricated by means of colloidal self-assembly. Two broad classes of defects are considered: substitutional and interstitial. Substitutional point defects are found to introduce a usable defect band into the photonic band gap. This can be done by using a silica sphere of radius between 0.33a and 0.35a (where a is the lattice constant). The state is triply degenerate. Reflectance and local density of states calculations are performed to verify the existence and frequency of this defect. The point defect can be made by precoating shrunk silica spheres with a thin layer of silicon. Such a defect can be used as a microcavity for localizing light at a point, with a quality factor Q that is limited primarily by the proximity of the defect to the surface of the photonic crystal and other such defects.

[69]

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, “Photonic band gaps and localization in the Thue–Morse structures,” Applied Physics Letters, vol. 86, p. 201110, May 2005. [ bib | http ]

Both theoretically and experimentally, we demonstrate that the photonic band gaps in Thue–Morse aperiodic systems can be separated into two flavors, the fractal gaps and the traditional gaps, distinguished by the presence or absence of fractal structure, respectively. The origin of two kind gaps is explained by the different interface correlations. This explanation is confirmed by the gap width behaviors. In addition, the eigenstates near the fractal gaps have a cluster-periodic form, while those near the traditional gaps have the Bloch wavelike form. Our detailed study of these differences is essential for understanding the spectra and light localization in aperiodic systems.

[70]

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Physical Review Letters, vol. 94, pp. 143902–143905, April 2005. [ bib | http ]

Virtually all electromagnetic waveguiding structures support a multiplicity of modes. Nevertheless, to date, an experimental method for unique decomposition of the fields in terms of the component eigenmodes has not been realized. The fundamental problem is that all current attempts of modal decomposition do not yield phase information. Here we introduce a noninterferometric approach to achieve modal decomposition of the fields at the output of a general waveguiding structure. The technique utilizes a mapping of the two-dimensional field distribution onto the one-dimensional space of waveguide eigenmodes, together with a phase-retrieval algorithm to extract the amplitudes and phases of all the guided vectorial modes. Experimental validation is provided by using this approach to examine the interactions of 16 modes in a hollow-core photonic-band gap fiber.

[71]

M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Applied Physics Letters, vol. 86, p. 171101, April 2005. [ bib | http | .pdf ]

Using analytical modeling and detailed numerical simulations, we investigate properties of hybrid systems of photonic crystal microcavities which incorporate a highly nonlinear ultraslow light medium. We demonstrate that such systems, while being miniature in size (order wavelength), and integrable, could enable ultrafast nonlinear all-optical switching at ultralow (even single photon) energy levels.

[72]

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Optics Letters, vol. 30, pp. 552–554, March 2005. [ bib | .pdf ]

We propose and demonstrate a mechanism for small-modal-volume high-Q cavities based on an anomalous uniform waveguide mode that has zero group velocity at a nonzero wave vector. In a short piece of a uniform waveguide with a specially designed cross section, light is confined longitudinally by small group-velocity propagation and transversely by a reflective cladding. The quality factor Q is greatly enhanced by the small group velocity for a set of cavity lengths that are separated by approximately π/k₀, where k₀ is the longitudinal wave vector for which the group velocity is zero.

[73]

M. Soljačić, E. Lidorikis, L. V. Hau, and J. D. Joannopoulos, “Enhancement of microcavity lifetimes using highly dispersive materials,” Physical Review E, vol. 71, pp. 026602–026606, February 2005. [ bib | http | .pdf ]

We show analytically and numerically that highly dispersive media can be used to drastically increase lifetimes of high-Q microresonators. In such a resonator, lifetime is limited either by undesired coupling to radiation, or by intrinsic absorption of the constituent materials. The presence of dispersion weakens coupling to the undesired radiation modes and also effectively reduces the material absorption.

[74]

E. J. Reed, M. Soljačić, M. Ibanescu, and J. D. Joannopoulos, “Reversed and anomalous Doppler effects in photonic crystals and other time-dependent periodic media,” Journal of Computer-Aided Materials Design, vol. 12, pp. 1–15, January 2005. [ bib | DOI | .pdf ]

We predict that reversed and anomalous non-relativistic Doppler shifts can be observed under some circumstances when light reflects from a shock wave front propagating through a photonic crystal, or material with a periodic modulation of the dielectric. This theoretical prediction is generalizable and applies to wave-like excitations in a variety of periodic media. An experimental observation of this effect has recently been made (Seddon, N. and Bearpark, T. Science, 302 (2003) 1537) and we provide a brief discussion of this experiment.

[75]

P. T. Rakich, H. Sotobayashi, J. T. Gopinath, S. G. Johnson, J. W. Sickler, C. W. Wong, J. D. Joannopoulos, and E. P. Ippen, “Nano-scale photonic crystal microcavity characterization with an all-fiber based 1.2–2.0 μm supercontinuum,” Optics Express, vol. 13, pp. 821–825, January 2005. [ bib | http | .pdf ]

The use of ultra-broadband supercontinuum generated by an all-fiber system to characterize high-index contrast photonic circuits over the wavelength range 1.2–2.0 μm is demonstrated. Efficient, broadband waveguide coupling techniques and sensitive normalized detection enable rapid and high-resolution measurements of nano-scale one-dimensional photonic crystal microcavities. Experimental mappings of bandgaps and cavity mode resonances with a wavelength resolution of 0.1 nm compare well with computer simulations.

[76]

P. T. Rakich, H. Sotobayashi, J. T. Gopinath, J. W. Sickler, C. W. Wong, S. G. Johnson, M. Qi, E. Lidorikis, H. I. Smith, J. D. Joannopoulos, and E. P. Ippen, “Broadband optical studies of 1-D and 3-D photonic crystals,” Proc. SPIE, vol. 6017, p. 601702, 2005. Invited paper. [ bib | .pdf ]

Supercontinuum based sources and measurement techniques are developed, enabling optical ultra-broadband studies of nano-scale photonic crystal devices and integrated photonic circuits over 1.2–2.0 μm wavelength range. Experiments involving 1-D periodic photonic crystal microcavity waveguides and 3-D periodic photonic crystals with embedded point defects are described. Experimental findings are compared with rigorous electromagnetic simulations.

[77]

M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “High-index-contrast, photonic-band-edge waveguides for tunable time delays,” Proc. SPIE, vol. 5926, p. 59260D, 2005. [ bib | .pdf ]

We describe the use of high-index-contrast, photonic-crystal wavegides for tunable time delays. The waveguide is designed such that the operating frequency is near a photonic band edge. In this slow light region, a small change in index yields a large change in group velocity, and consequently in time delay. Figures of merit for tunable time delay devices are introduced, including sensitivity, length, and dispersion. We show that a simple quadratic band model is a good predictor of the figures of merit for realistic, 3D, high-index-contrast structures. By cascading two grated waveguides, we can obtain a flat tunable time delay across the operating bandwidth.

[78]

C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal radiation from photonic crystals: A direct calculation,” Physical Review Letters, vol. 93, pp. 213905–213908, November 2004. [ bib | http ]

A classical simulation of equilibrium thermal emissivity from dispersive, lossy photonic crystals is presented. Normal emission results consistent with those assuming Kirchoff's law are obtained; i.e., a photonic crystal does not emit more than what a blackbody does. Significant enhancement, however, can be achieved over the radiation intensity from a uniform slab, indicating the potential usefulness of photonic crystals in incandescent lighting and thermal photovoltaic applications.

[79]

S. G. Johnson and J. D. Joannopoulos, “Photonic crystals: Electromagnetic theory,” in Encyclopedia of Modern Optics (B. D. Guenther, D. G. Steel, and L. Bayvel, eds.), pp. 120–127, Oxford: Elsevier, November 2004. [ bib | DOI ]

[80]

M. Bayindir, F. Sorin, A. F. Abouraddy, J. Viens, S. D. Hart, J. D. Joannopoulos, and Y. Fink, “Metal–insulator–semiconductor optoelectronic fibres,” Nature, vol. 431, pp. 826–829, October 2004. [ bib | DOI ]

The combination of conductors, semiconductors and insulators with well-defined geometries and at prescribed length scales, while forming intimate interfaces, is essential in most functional electronic and optoelectronic devices. These are typically produced using a variety of elaborate wafer-based processes, which allow for small features, but are restricted to planar geometries and limited coverage area. In contrast, the technique of fibre drawing from a preformed reel or tube is simpler and yields extended lengths of highly uniform fibres with well-controlled geometries and good optical transport characteristics. So far, this technique has been restricted to particular materials and larger features. Here we report on the design, fabrication and characterization of fibres made of conducting, semiconducting and insulating materials in intimate contact and in a variety of geometries. We demonstrate that this approach can be used to construct a tunable fibre photodetector comprising an amorphous semiconductor core contacted by metallic microwires, and surrounded by a cylindrical-shell resonant optical cavity. Such a fibre is sensitive to illumination along its entire length (tens of meters), thus forming a photodetecting element of dimensionality one. We also construct a grid of such fibres that can identify the location of an illumination point. The advantage of this type of photodetector array is that it needs a number of elements of only order N, in contrast to the conventional order N² for detector arrays made of photodetecting elements of dimensionality zero.

[81]

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, “On-chip Si-based Bragg cladding waveguide with high index contrast bilayers,” Optics Express, vol. 12, pp. 4775–4780, October 2004. [ bib | http ]

A new silicon based waveguide with full CMOS compatibility is developed to fabricate an on-chip Bragg cladding waveguide that has an oxide core surrounded by a high index contrast cladding layers. The cladding consists of several dielectric bilayers, where each bilayer consists of a high index-contrast pair of layers of Si and Si₃N₄. This new waveguide guides light based on omnidirectional reflection, reflecting light at any angle or polarization back into the core. Its fabrication is fully compatible with current microelectronics processes. In principle, a core of any low-index material can be realized with our novel structure, including air. Potential applications include tight turning radii, high power transmission, and dispersion compensation.

[82]

K. C. Huang, M. L. Povinelli, and J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Applied Physics Letters, vol. 85, pp. 543–545, July 2004. [ bib | http ]

We find that a two-dimensional photonic crystal composed of polaritonic materials behaves as an effective medium with negative permeability in the micron wavelength range. The resonance in μeff is due to the large values of ε(ω) attained near the transverse phonon frequency ω_T. The minimal wavelength for achieving an effective permeability less than -1 in a LiTaO₃ crystal, obtained by optimizing the rod size and the lattice constant, is around 12 μm, a range previously inaccessible using dielectric metamaterials. For certain dissipation levels, we find that other polaritonic media also exhibit a resonant effect with μeff < -1 for wavelengths ranging from 2 to ∼100 μm.

[83]

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Physical Review B, vol. 69, pp. 195111–195120, May 2004. [ bib | http ]

We examine the effects of absorption losses in photonic crystal structures composed of polar materials which exhibit transverse phonon-polariton excitations. In order to explore the Bloch states of such a system, we study the two subspaces of the complete set of complex (k,ω)states consisting of either real frequency, accessible through a frequency-domain method, or real-wave vector, which we determine using a frequency-dependent time-domain method. We describe analytically the conditions under which the imaginary frequency component of a real-wave-vector state is related to the imaginary-wave-vector component of a real-frequency state through a factor of the group velocity, and we present a one-dimensional lossy crystal as an example that satisfies these constraints. We also discover that the real-frequency states of a two-dimensional crystal bear little resemblance to the class of real-wave-vector states, due to interplay between the prohibitively large spatial decay of the states near the edge of the Brillouin zone and the existence of metalliclike states localized to the surrounding ambient dielectric region with much lower levels of loss. We then put these results in the context of possible experiments, including reflection of a plane-wave from a slab structure, and discuss the viability for observing the node switching and flux expulsion phenomena previously discovered in lossless crystals.

[84]

K. Kuriki, O. Shapira, S. Hart, G. Benoit, Y. Kuriki, J. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Optics Express, vol. 12, pp. 1510–1517, April 2004. [ bib | http ]

Here we report the fabrication of hollow-core cylindrical photonic bandgap fibers with fundamental photonic bandgaps at near-infrared wavelengths, from 0.85 to 2.28 μm. In these fibers the photonic bandgaps are created by an all-solid multilayer composite meso-structure having a photonic crystal lattice period as small as 260 nm, individual layers below 75 nm and as many as 35 periods. These represent, to the best of our knowledge, the smallest period lengths and highest period counts reported to date for hollow PBG fibers. The fibers are drawn from a multilayer preform into extended lengths of fiber. Light is guided in the fibers through a large hollow core that is lined with an interior omnidirectional dielectric mirror. We extend the range of materials that can be used in these fibers to include poly(ether imide) (PEI) in addition to the arsenic triselenide (As₂Se₃) glass and poly(ether sulfone) (PES) that have been used previously. Further, we characterize the refractive indices of these materials over a broad wavelength range (0.25 – 15 μm) and incorporated the measured optical properties into calculations of the fiber photonic band structure and a preliminary loss analysis.

[85]

C. Luo, M. Soljačić, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Optics Letters, vol. 29, pp. 745–747, April 2004. [ bib | http | .pdf ]

The superprism effect has been studied in the past by use of the anomalous group velocities of optical waves in photonic crystals. We suggest the possibility of realizing agile beam steering based on purely phase-velocity effects. We present designs of photonic crystal prisms that might make experimental observation of this effect possible.

[86]

E. Lidorikis, M. Soljačić, M. I. Y. Fink, and J. D. Joannopoulos, “Cutoff solitons in axially uniform systems,” Optics Letters, vol. 29, pp. 851–853, April 2004. [ bib | http | .pdf ]

The optical response of axially uniform nonlinear photonic bandgap fibers is studied theoretically. We observe gap-soliton-like generation and associated bistability, similar to what is typically found in periodically modulated nonlinear structures. This response stems from the nature of the guided-mode dispersion relations, which involve a frequency cutoff at zero wave vector. In such systems, solutions with zero group velocities and minimal coupling to radiation modes come in naturally. We term such solitons “cutoff solitons”; they provide an interesting alternative to gap solitons in periodically index-modulated fibers for in-fiber all-optical signal processing.

[87]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials, vol. 3, pp. 211–219, April 2004. [ bib | DOI | .pdf ]

The quest for all-optical signal processing is generally deemed to be impractical because optical nonlinearities are usually weak. The emerging field of nonlinear photonic crystals seems destined to change this view dramatically. Theoretical considerations show that all-optical devices using photonic crystal designs promise to be smaller than the wavelength of light, and to operate with bandwidths that are very difficult to achieve electronically. When created in commonly used materials, these devices could operate at powers of only a few milliwatts. Moreover, if these designs are combined with materials and systems that support electromagnetically induced transparency, operation at single-photon power levels could be feasible.

[88]

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Physical Review B, vol. 69, pp. 104202–104208, March 2004. [ bib | http ]

We studied analytically and numerically the complex properties of random lasing modes. Mode repulsion in frequency domain for inhomogeneously broadened gain media was confirmed by our numerical results. We constructed a coupled-mode model to explain the synchronized lasing behavior for modes whose frequency difference is less than the homogeneous gain width. The stability of coupled modes was investigated. The effective competition coefficient Ce for two modes with both gain competition and field coupling is obtained analytically. In our numerical experiments, we also found the coupled oscillations of two lasing modes. From the analytical derivation, we demonstrated that such oscillations could reveal the field-coupling strength between the random modes.

[89]

P. Bermel, J. D. Joannopoulos, Y. Fink, P. A. Lane, and C. Tapalian, “Properties of radiating pointlike sources in cylindrical omnidirectionally reflecting waveguides,” Physical Review B, vol. 69, pp. 035316–035322, January 2004. [ bib | http ]

The behavior of pointlike electric dipole sources enclosed by an axially uniform, cylindrically symmetric waveguide of omnidirectionally reflecting material is analyzed. It is found that the emission spectrum of a source inside the waveguide is strongly modified by features resembling one-dimensional Van Hove singularities in the local density of states (LDOS). Additionally, more than 100% of the power radiated by a dipole in vacuum can be captured at the end of the waveguide, owing to the overall enhancement of the LDOS (the Purcell effect). The effect of varying the positions and orientations of electric dipole sources is also studied.

[90]

D. Roundy, E. Lidorikis, and J. D. Joannopoulos, “Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry,” Journal of Applied Physics, vol. 96, pp. 7750–7752, 2004. [ bib | http ]

We demonstrate single-mode horizontal and vertical waveguides in a recently proposed photonic crystal having layered square symmetry. The vertical waveguide supports two degenerate polarizations, and thus light can be selectively steered into horizontal waveguides oriented at 90^o based on its polarization. We calculate the transmission of 90^o bends, both from horizontal waveguide to horizontal waveguide and from horizontal waveguide to vertical waveguide. In the case of the horizontal-horizontal bend, we show a transmission of 83% for a simple (“zero” radius of curvature) bend, and a peak transmission of 100% for a bend which has been optimized by moving one rod from the inner corner to the outer corner of the bend. For the vertical to horizontal bend, we find a transmission of 95% for the allowed polarization, but with a much smaller bandwidth than in the case of the optimized horizontal bend.

[91]

A. Karalis, S. G. Johnson, and J. D. Joannopoulos, “Discrete-mode cancellation mechanism for high-Q integrated optical cavities with small modal volume,” Optics Letters, vol. 29, pp. 2309–2311, 2004. [ bib | .pdf ]

A mechanism to reduce radiation loss from integrated optical cavities without a complete photonic bandgap is introduced and demonstrated. It is applicable to any device with a patterned substrate (including both low and high index-contrast systems), when it supports discrete guided or leaky modes through which power escaping the cavity can be channeled into radiation. One then achieves the associated increase in Q by designing the cavity such that the near-field pattern becomes orthogonal to these discrete modes, therefore canceling the coupling of power into them and thus reducing the total radiation loss. The method is independent of any delocalization mechanism and can be used to create high-Q cavities with small modal volume.

[92]

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Applied Physics Letters, vol. 85, pp. 1466–1468, 2004. [ bib | .pdf ]

We study the radiation pressure on the surface of a waveguide formed by omnidirectionally reflecting mirrors. In the absence of losses, the pressure goes to infinity as the distance between the mirrors is reduced to the cutoff separation of the waveguide mode. This divergence at constant power input is due to the reduction of the modal group velocity to zero, which results in the magnification of the electromagnetic field. Our structure suggests a promising alternative, microscale system for observing the variety of classical and quantum-optical effects associated with radiation pressure in Fabry–Perot cavities.

[93]

M. L. Povinelli, S. G. Johnson, E. Lidorikis, J. D. Joannopoulos, and M. Soljačić, “Effect of a photonic band gap on scattering from waveguide disorder,” Applied Physics Letters, vol. 84, pp. 3639–3641, 2004. [ bib | .pdf ]

We derive a general, analytical, coupled-mode theory for disorder-induced scattering in periodic systems that shows that in the experimentally relevant limit of weak disorder, the reflection in a photonic-crystal waveguide is just as low as in a comparable index-guided waveguide. Moreover, since the photonic band gap also blocks radiative loss, the total scattering loss is reduced, and the total transmission is higher. These general results are verified by direct numerical simulations in an example system.

[94]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature, vol. 429, pp. 538–542, 2004. [ bib | .pdf ]

Photonic crystals offer unprecedented opportunities for miniaturization and integration of optical devices. They also exhibit a variety of new physical phenomena, including suppression or enhancement of spontaneous emission, low-threshold lasing, and quantum information processing. Various techniques for the fabrication of three-dimensional (3D) crystals photonicsuch as silicon micromachining, wafer fusion bonding, holographic lithography, self-assembly, angled-etching, micromanipulation, glancing-angle deposition, auto-cloning, have been proposed and demonstrated with different levels of success. However, a critical step towards the fabrication of functional 3D devices, that is, the incorporation of microcavities or waveguides in a controllable way, has not been achieved at optical wavelengths. Here we present the fabrication of 3D photonic crystals that are particularly suited for optical device integration using a lithographic layer-by-layer approach. Point-defect microcavities are introduced during the fabrication process and optical measurements show they have resonant signatures around telecommunications wavelengths (1.3–1.5μm). Measurements of reflectance and transmittance at near-infrared are in good agreement with numerical simulations.

[95]

C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Applied Physics Letters, vol. 84, pp. 1242–1244, 2004. [ bib | .pdf ]

We report the design, device fabrication, and measurements of tunable silicon photonic band gap microcavities in optical waveguides, using direct application of piezoelectric-induced strain to the photonic crystal. We show, through first-order perturbation computations and experimental measurements, a 1.54 nm shift in cavity resonances at 1.56 μm wavelengths for an applied strain of 0.04%. The strain is applied through integrated piezoelectric microactuators. For operation at infrared wavelengths, we combine x-ray and electron-beam lithography with thin-film piezoelectric processing. This level of integration permits realizable silicon-based photonic chip devices, such as high-density optical filters, with active reconfiguration.

[96]

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5μm light in photonic crystals based on dielectric rods,” Applied Physics Letters, vol. 85, pp. 6110–6112, 2004. [ bib | .pdf ]

Photonic-crystal structures consisting of dielectric rods were designed, fabricated, and optically characterized. The combination of the high refractive-index-contrast GaAs/Al_xO_y material system with electron-beam lithography enabled the fabrication of structures suitable for the optical propagation of 1.5 μm light. Experimental transmission spectra were obtained for structures consisting of a two-dimensional array of rods and line-defect waveguides. Optical measurements confirmed the presence of a photonic band gap, as well as band gap guidance in the line-defect waveguide. A two-stage coupling scheme facilitated efficient optical coupling into the line-defect waveguide.

[97]

M. Soljačić, E. Lidorikis, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, “Optical bistability and cutoff solitons in photonic bandgap fibers,” Optics Express, vol. 12, pp. 1518–1527, 2004. [ bib | http | .pdf ]

We present detailed theoretical and numerical analysis of certain novel non-linear optical phenomena enabled by photonic bandgap fibers. In particular, we demonstrate the feasibility of optical bistability in an axially modulated nonlinear photonic bandgap fiber through analytical theory and detailed numerical experiments. At 1.55μm carrier wavelength, the in-fiber devices we propose can operate with only a few tens of mW of power, have a nearly instantaneous response and recovery time, and be shorter than 100μm. Furthermore, we predict existence of gap-like solitons (which have thus-far been described only in axially periodic systems) in axially uniform photonic bandgap fibers.

[98]

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Physical Review Letters, vol. 92, p. 063903, 2004. [ bib | .pdf ]

We show that modes of axially uniform waveguides of arbitrary cross section can be made to have anomalous dispersion relations resulting from strong repulsion between two modes. When the axial wave vector k is 0, the two modes have different TE/TM symmetry and thus can be brought arbitrarily close to an accidental frequency degeneracy. For nonzero k, the symmetry is broken causing the modes to repel. When the modes are sufficiently close together this repulsion leads to unusual features such as extremely flattened dispersion relations, backward waves, zero group velocity for nonzero k, atypical divergence of the density of states, and nonzero group velocity at k = 0.

[99]

Y. Sasaki, Y. Ohtera, S. G. Johnson, and S. Kawakami, “A reference analytical model of three-dimensional photonic crystal waveguides and their mode spectrum,” Trans. Inst. Elect. Info. Comm. Eng. C, vol. J87-C, no. 3, pp. 328–334, 2004. [ bib ]

[100]

Y. Tanaka, Y. Sugimoto, N. Ikeda, H. Nakamura, K. Asakawa, K. Inoue, and S. G. Johnson, “Group velocity depende