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We analyze an optical 3-port reflection grating by means of a scatteringmatrix formalism. Amplitude and phase relations between the 3 ports, i.e. the 3orders of diffraction are derived. Such a grating can be used as anall-reflective, low-loss coupler to Fabry-Perot cavities. We derive the inputoutput relations of a 3-port grating coupled cavity and find distinctproperties not present in 2-port coupled cavities. The cavity relations furtherreveal that the 3-port coupler can be designed such that the additional cavityport interferes destructively. In this case the all-reflective, low-loss,single-ended Fabry-Perot cavity becomes equivalent to a standard transmissive,2-port coupled cavity.

Input-output relations for a 3-port grating coupled Fabry-Perot cavity