## Abstract

We present a theoretical and experimental analysis of nonlinear microwave photonic filters. Far from the conventional condition of low modulation index commonly used to neglect high-order terms, we have analyzed the harmonic distortion involved in microwave photonic structures with periodic and non-periodic frequency responses. We show that it is possible to design microwave photonic filters with reduced harmonic distortion and high linearity even under large signal operation.

© 2012 OSA

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### Equations (6)

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(1)
$${e}_{IN}(t)=\frac{1}{\sqrt{2\pi}}{\displaystyle \sum _{n=-\infty}^{+\infty}\left\{{\displaystyle \underset{-\infty}{\overset{+\infty}{\int}}{s}_{n}({V}_{o})\cdot {E}_{s}^{}\left(\omega \right)}\cdot {e}^{j\left(\omega +n\Omega \right)t}\cdot d\omega \right\}}$$
(2)
$${e}_{OUT}(t)=\frac{1}{\sqrt{2\pi}}{\displaystyle \sum _{n=-\infty}^{+\infty}\left\{{\displaystyle \underset{-\infty}{\overset{+\infty}{\int}}{s}_{n}{E}_{s}^{}\left(\omega \right)}\cdot {H}_{opt}^{}\left(\omega +n\Omega \right){e}^{j\left(\omega +n\Omega \right)t}\cdot d\omega \right\}}$$
(3)
$${V}_{RF}^{OUT}(t)=\Re \u3008{\left|{e}_{OUT}(t)\right|}^{2}\u3009\cdot {Z}_{o}$$
(4)
$${V}_{RF}^{OUT}(t)=\frac{{V}_{o}}{2}{\displaystyle \sum _{k=-\infty}^{+\infty}{H}_{k}^{RF}\left(\Omega \right)\cdot {e}^{jk\Omega t}}+c.c.$$
(5)
$${H}_{opt}^{}\left(\omega \right)={e}^{-j\beta \left(\omega \right)L}\begin{array}{ccc}& with& \end{array}\beta \left(\omega \right)={\beta}_{o}\left({\omega}_{o}\right)+{\beta}_{1}\left(\omega -{\omega}_{o}\right)+\frac{1}{2}{\beta}_{2}{\left(\omega -{\omega}_{o}\right)}^{2}.$$
(6)
$${H}_{k}^{RF}(\Omega )=\frac{\Re {P}_{o}\cdot {Z}_{o}}{\pi {V}_{o}}\cdot {e}^{j{\beta}_{1}L\left(k\Omega \right)}\underset{CSE}{\underset{\u23b5}{{\displaystyle \sum _{n=-\infty}^{+\infty}{s}_{n}^{}{s}_{n-k}^{*}}{e}^{-j\frac{1}{2}{\beta}_{2}L\left(k-2n\right){\Omega}^{2}}}}\cdot \frac{{\displaystyle \underset{-\infty}{\overset{+\infty}{\int}}{\left|E\left(\omega \right)\right|}^{2}\cdot {e}^{j{\beta}_{2}L\left(\omega -{\omega}_{o}\right)\left(k\Omega \right)}\cdot d\omega}}{{\displaystyle \underset{-\infty}{\overset{+\infty}{\int}}{\left|E\left(\omega \right)\right|}^{2}\cdot d\omega}}$$