# Meep Tutorial/Near-to-far-field spectra

### From AbInitio

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In this example, we demonstrate the near-to-far-field transformation feature which requires Meep 1.3+. From the frequency-domain fields obtained using a "near" bounding surface inside the computational cell, we compute the resulting fields outside the computational cell using an analytical transformation. Note that this only works if the "near" surface and the "far" region lie in a single, homogeneous, non-periodic 2d or 3d medium. The analytical transformation is based on the principle of equivalence: given the Fourier-transformed tangential fields on the "near" surface, Meep computes equivalent currents and convolves them with the analytical Green's functions in order to compute the fields at any desired point in the "far" region. The use of the Fourier-transformed fields is similar to the flux and force spectra: we specify a set of desired frequencies, Meep accumulates the Fourier transforms, and then Meep computes the fields at each frequency for the desired far-field points. There are three steps to using the near-to-far-field feature: first, define the "near" surface(s) as a set of surfaces capturing all outgoing radiation in the desired direction(s); second, run the simulation, typically with a pulsed source, to allow Meep to accumulate the Fourier transforms on the near surface(s); third, tell Meep to compute the far fields at any desired points (optionally saving the far fields from a grid of points to an HDF5 file).

Here, we will compute the far field spectra of a resonant cavity mode in a holey waveguide as shown in a separate tutorial.