Analysis of input-grating couplers having finite lengths

Area of Science:

• Photonics and Optical Engineering
• Integrated Optics
• Waveguide Devices

Background:

• Planar waveguide-grating couplers are essential components in integrated optical circuits.
• Understanding factors affecting input-coupling efficiency is crucial for device performance optimization.
• Previous analyses often assumed idealized conditions, neglecting finite length effects.

Purpose of the Study:

• To investigate the impact of finite grating length, incident beam size, and grating coupling length on input-coupling efficiency.
• To analyze how these finite lengths affect the angular range and shape of the coupling efficiency curve.
• To provide a general formula relating these characteristic lengths to normalized input-coupling efficiency.

Main Methods:

• Theoretical analysis of planar waveguide-grating couplers.
• Derivation of a general formula for normalized input-coupling efficiency.
• Experimental validation using two cases with short grating length and short coupling length.

Main Results:

• A general formula is presented to correlate grating length, beam size, and coupling length with input-coupling efficiency.
• When a characteristic length is significantly smaller than others, it primarily dictates the angular width and dependence of coupling efficiency.
• Experimental results confirm the theoretical predictions for short grating length and short coupling length scenarios.

Conclusions:

• Finite lengths of grating, incident beam, and coupling significantly influence waveguide-grating coupler performance.
• The dominant characteristic length determines the angular response of input coupling.
• The findings are crucial for designing and optimizing efficient planar waveguide-grating couplers.