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

TL;DR

This paper provides a detailed analysis of a 3-port reflection grating used as a low-loss, all-reflective coupler for Fabry-Perot cavities, revealing unique properties and potential for destructive interference.

Contribution

It introduces a scattering matrix formalism for 3-port gratings and derives their input-output relations, highlighting novel properties not seen in traditional 2-port cavities.

Findings

Derived amplitude and phase relations for the 3 ports.

Identified conditions for destructive interference at the additional port.

Showed that the 3-port cavity can mimic a 2-port cavity under certain conditions.

Abstract

We analyze an optical 3-port reflection grating by means of a scattering matrix formalism. Amplitude and phase relations between the 3 ports, i.e. the 3 orders of diffraction are derived. Such a grating can be used as an all-reflective, low-loss coupler to Fabry-Perot cavities. We derive the input output relations of a 3-port grating coupled cavity and find distinct properties not present in 2-port coupled cavities. The cavity relations further reveal that the 3-port coupler can be designed such that the additional cavity port 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.