## Abstract

I respond to a comment on [Appl. Opt. **42**, 4152 (2003)] and discuss some unusual features that arise in a plane-wave-inspired analysis of the virtually imaged phased-array spectral disperser.

© 2012 Optical Society of America

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### Equations (9)

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(1)
$$2kL[\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{i}]=2m\pi ,$$
(2)
$$\frac{{E}_{\text{out}}}{{E}_{\text{in}}}={t}_{1}{t}_{2}{e}^{-j\delta /2}\sum _{m=0}^{\infty}{({r}_{1}{r}_{2}{e}^{-j\delta})}^{m},$$
(3)
$$\frac{{I}_{\text{out}}}{{I}_{\text{in}}}=\frac{(1-{R}_{1})(1-{R}_{2})}{1+{R}_{1}{R}_{2}-2{r}_{1}{r}_{2}\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\delta}.$$
(4)
$$\frac{{E}_{\text{out}}}{{E}_{\text{in}}}={t}_{2}{e}^{-j\delta /2}\sum _{m=0}^{\infty}{({r}_{1}{r}_{2}{e}^{-j\delta})}^{m}=\frac{{t}_{2}{e}^{-j\delta /2}}{1-{r}_{1}{r}_{2}{e}^{-j\delta}}.$$
(5)
$$\frac{{I}_{\text{out}}}{{I}_{\text{in}}}=\frac{(1-{R}_{2})}{1+{R}_{1}{R}_{2}-2{r}_{1}{r}_{2}\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\delta}.$$
(6)
$$\frac{{I}_{\text{out}}}{{I}_{\text{in}}}=\frac{1-{R}_{2}}{{(1-{r}_{1}{r}_{2})}^{2}}.$$
(7)
$$\frac{{I}_{\text{out}}}{{I}_{\text{in}}}=\frac{1+{r}_{2}}{1-{r}_{2}}.$$
(8)
$${\u3008\frac{{I}_{\text{out}}}{{I}_{\text{in}}}\u3009}_{\delta}=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}\frac{{I}_{\text{out}}}{{I}_{\text{in}}}\mathrm{d}\delta =\frac{1-{R}_{2}}{1-{R}_{1}{R}_{2}}.$$
(9)
$${\u3008\frac{{I}_{\text{out}}}{{I}_{\text{in}}}\u3009}_{\delta}=1.$$