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

Area of Science:

• Optics and Photonics
• Wave Phenomena
• Diffraction Gratings

Background:

• Fabry-Perot cavities are crucial optical resonators.
• Coupling to these cavities often involves reflective or transmissive elements.
• Understanding the behavior of multi-port gratings is key to advanced optical system design.

Purpose of the Study:

• To analyze an optical three-port reflection grating using scattering matrix formalism.
• To derive amplitude and phase relations for the three diffraction orders.
• To investigate the application of such gratings as couplers to Fabry-Perot cavities.

Main Methods:

• Scattering matrix formalism applied to a three-port reflection grating.
• Derivation of input-output relations for a grating-coupled Fabry-Perot cavity.
• Analysis of interference effects within the coupled cavity system.

Main Results:

• Amplitude and phase relations among the three diffraction orders were derived.
• The three-port grating functions as an all-reflective, low-loss coupler.
• Distinct properties were identified in the three-port grating coupled cavity compared to two-port systems.
• Destructive interference at an additional cavity port was demonstrated.

Conclusions:

• The three-port reflection grating is a versatile optical component.
• It enables the creation of low-loss, all-reflective Fabry-Perot cavities.
• By controlling interference, it can emulate standard transmissive two-port coupled cavities.