Upper bound on the diffraction efficiency of phase-only fanout elements

Area of Science:

• Optics and Photonics
• Diffractive Optics
• Holography

Background:

• Fanout gratings are crucial optical elements for beam splitting.
• Understanding the theoretical limits of diffraction efficiency is essential for device design.
• Previous research has explored efficiency limits for various grating types.

Purpose of the Study:

• To determine the upper bounds on diffraction efficiency for one-dimensional (1D) binary-phase and continuous-phase fanout elements.
• To analyze these bounds for fanout numbers ranging from 2 to 25.
• To investigate the impact of phase quantization on achievable diffraction efficiency.

Main Methods:

• Optimization of array phase to establish an upper bound on diffraction efficiency for a coherent array.
• Imposition of specific phase restrictions for binary-phase gratings (0, pi) and (0, non-pi).
• Calculation of theoretical efficiency limits for continuous and quantized phase fanout elements.

Main Results:

• For fanouts greater than 5, the upper bound for continuous phase fanouts is 97-98%.
• The upper bound for (0, pi) binary-phase fanouts is 83-84%.
• The upper bound for (0, non-pi) binary-phase fanouts is 87-88%.

Conclusions:

• Theoretical upper bounds for diffraction efficiency have been established for various 1D fanout grating types.
• Continuous phase fanout elements offer higher potential diffraction efficiency compared to binary-phase elements.
• The findings provide critical benchmarks for the design and performance evaluation of diffractive optical elements.