Meep Tutorial/Local density of states
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| - | In this example, we will investigate the Purcell enhancement of the local density of states (LDOS), computed in two different ways, for a microcavity. A lossless localized mode yeilds a δ-function spike in the LDOS, whereas a <i>lossy</i> (arising from either small absorption or radiation) localized mode -- a <i>resonant cavity mode</i> -- leads to a Lorentzian peak. The large enhancement in the LDOS at the resonant peak is known as a [[w: Purcell effect]], named after Purcell's proposal for enhancing spotaneous emission of an atom in a cavity (analogous to a microwave antenna resonating in a metal box). | + | In this example, we will investigate the Purcell enhancement of the local density of states (LDOS), computed in two different ways, for a microcavity. The LDOS is a measure of how much the harmonic modes of a system overlap with the source point (proportional, as well, to the radiation resistance of a dipole antenna) and is a key quantity in electromagnetism due to the fact that the <i>same</i> current radiates a <i>different</i> amount of power depending on the surrounding geometry. The LDOS is of central importance not only for understanding classical dipole sources, but also in many physical phenomena that can be understood semiclassically in terms of dipole currents -- for example, the spontaneous emission rate of atoms (key to fluorescence and lasing phenomena) is proportional to the LDOS. For a more mathematical treatment of the theory behind the LDOS, we refer you to the relevant discussion in chapter 4 of our upcoming book. A lossless localized mode yields a δ-function spike in the LDOS, whereas a <i>lossy</i> (i.e. arising from either small absorption or radiation) localized mode -- a <i>resonant cavity mode</i> -- leads to a Lorentzian peak. The large enhancement in the LDOS at the resonant peak is known as a [[w: Purcell effect|Purcell effect]], named after Purcell's proposal for enhancing spontaneous emission of an atom in a cavity (analogous to a microwave antenna resonating in a metal box). The LDOS is related to the |
Revision as of 01:09, 24 July 2012
In this example, we will investigate the Purcell enhancement of the local density of states (LDOS), computed in two different ways, for a microcavity. The LDOS is a measure of how much the harmonic modes of a system overlap with the source point (proportional, as well, to the radiation resistance of a dipole antenna) and is a key quantity in electromagnetism due to the fact that the same current radiates a different amount of power depending on the surrounding geometry. The LDOS is of central importance not only for understanding classical dipole sources, but also in many physical phenomena that can be understood semiclassically in terms of dipole currents -- for example, the spontaneous emission rate of atoms (key to fluorescence and lasing phenomena) is proportional to the LDOS. For a more mathematical treatment of the theory behind the LDOS, we refer you to the relevant discussion in chapter 4 of our upcoming book. A lossless localized mode yields a δ-function spike in the LDOS, whereas a lossy (i.e. arising from either small absorption or radiation) localized mode -- a resonant cavity mode -- leads to a Lorentzian peak. The large enhancement in the LDOS at the resonant peak is known as a Purcell effect, named after Purcell's proposal for enhancing spontaneous emission of an atom in a cavity (analogous to a microwave antenna resonating in a metal box). The LDOS is related to the
