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We consider a system of first order coupled mode equations in $\mathbb{R}^d$ describing the envelopes of wavepackets in periodic media. Under the assumptions of a spectral gap and a generic assumption on the dispersion relation at the spectral edge, we prove the bifurcation of standing gap solitons of the coupled mode equations from the zero solution. The bifurcating solution is approximated in terms of a solution of an effective nonlinear Schrodinger equation. The proof is based on a decomposition in Fourier variables and a nested Banach fixed point argument. A numerical example in $\mathbb{R}^2$ is provided.

Bifurcation of Gap Solitons in Coupled Mode Equations in d Dimensions