## Abstract

We demonstrate a 2-D wavelength demultiplexer by using a virtually imaged phased array (VIPA) and a diffraction grating in bulk optics, which yields a hyperfine channel spacing 5 GHz (40 pm) with 1.75 GHz (14 pm) -3dB bandwidth, >20dB channel isolations, and a very large free spectral range. The 2-D wavelength demultiplexer is capable of having a very large number (≥1000) of hyperfine channels in the C-band (1530–1570 nm). We also present the first analytic theory for the 2-D demultiplexer.

© 2004 Optical Society of America

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### Equations (5)

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(1)
$${I}_{\mathit{out}}(x,y,\lambda )\propto {I}_{\mathit{in}}\left(\tilde{\omega}\right)\mathrm{exp}\left(-2\frac{{f}_{c}^{2}{x}^{2}}{{f}^{2}{W}^{2}}\right)\frac{1}{{\left(1-Rr\right)}^{2}+4\left(Rr\right){\mathrm{sin}}^{2}\left(\frac{k\Delta}{2}\right)}\mathrm{exp}\left[-\frac{{\left(y-\alpha \tilde{\omega}\right)}^{2}}{{{w}_{0}}^{2}}\right]$$
(2)
$${\lambda}_{p}-{\lambda}_{0}=-{\lambda}_{0}\left[\frac{\mathrm{tan}\left({\theta}_{\mathit{in}}\right)\mathrm{cos}\left({\theta}_{i}\right)}{{n}_{r}\mathrm{cos}\left({\theta}_{\mathit{in}}\right)}\frac{x}{f}+\frac{1}{2}\frac{1}{{{n}_{r}}^{2}}\frac{{x}^{2}}{{f}^{2}}\right]$$
(3)
$${\lambda}_{p}-{\lambda}_{0}=d\mathrm{cos}({\theta}_{{d}_{0}})\frac{y-{y}_{0}}{f}$$
(4)
$$\mathit{FWHM}{/}_{\mathit{frequency}}=\frac{c}{2\pi t{n}_{r}\mathrm{cos}\left({\theta}_{i}\right)}\frac{1-Rr}{\sqrt{Rr}},$$
(5)
$$\mathit{FWHM}{/}_{\mathit{wavelength}}=\frac{{{\lambda}_{0}}^{2}}{2\pi t{n}_{r}\mathrm{cos}\left({\theta}_{i}\right)}\frac{1-Rr}{\sqrt{Rr}},$$