## Abstract

The main differences in nonlinear switching behavior between multicore versus multimode waveguide couplers are highlighted. By gradually decreasing the separation between the two cores of a dual-core waveguide and interpolating from a multicore to a multimode scenario, the role of the linear coupling, self-phase modulation, cross-phase modulation, and four-wave mixing terms are explored, and the key reasons are identified behind higher switching power requirements and lower switching quality in multimode nonlinear couplers.

© 2013 Optical Society of America

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### Equations (5)

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(1)
$$\frac{\partial {A}_{\mu}}{\partial z}=i\delta {\beta}_{\mu}{A}_{\mu}+i\left(\frac{{n}_{2}{\omega}_{0}}{c}\right)\sum _{\nu ,\kappa ,\rho =e,o}{f}_{\mu \nu \kappa \rho}{A}_{\nu}{A}_{\kappa}{A}_{\rho}^{\u2605},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mu =e,o,$$
(2)
$${f}_{\mu \nu \kappa \rho}={\int}_{-\infty}^{\infty}{F}_{\mu}{F}_{\nu}{F}_{\kappa}{F}_{\rho}dx,$$
(3)
$$\frac{\partial {\tilde{A}}_{j}}{\partial z}=i\delta {\beta}_{e}{\tilde{A}}_{{j}^{\prime}}+i\left(\frac{{n}_{2}{\omega}_{0}}{c}\right)\sum _{k,l,m=1,2}{f}_{jklm}{\tilde{A}}_{k}{\tilde{A}}_{l}{\tilde{A}}_{m}^{\u2605},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}j=1,{j}^{\prime}=2,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{or}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}j=2,\hspace{0.17em}\hspace{0.17em}{j}^{\prime}=1,$$
(4)
$$\begin{array}{l}{f}_{1111}={f}_{2222}=\left({f}_{eeee}+{f}_{oooo}+6{f}_{eeoo}\right)/4,\\ {f}_{1122}=\left({f}_{eeee}+{f}_{oooo}-2{f}_{eeoo}\right)/4,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{f}_{1112}={f}_{1222}=\left({f}_{eeee}-{f}_{oooo}\right)/4.\end{array}$$
(5)
$$\tau =\frac{1}{{\tilde{P}}^{2}}{\left|\sum _{i=1,2}{\tilde{A}}_{i}^{\u2605}(0){\tilde{A}}_{i}({L}_{c})\right|}^{2}=\frac{1}{{\tilde{P}}^{2}}{\left|\sum _{\mu =e,o}{A}_{\mu}^{\u2605}(0){A}_{\mu}({L}_{c})\right|}^{2},$$