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Updated: Jul 9, 2026
08:39
Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
Published on: January 28, 2019
Summary
This study introduces a reciprocity inequality for secondary sources, linking source size and angular spread. The lowest-order Hermite-Gaussian laser mode minimizes this product, optimizing spatial coherence and intensity distribution.
Area of Science:
- Optics and Photonics
- Statistical Optics
- Laser Physics
Background:
- Understanding the relationship between source characteristics and far-field properties is crucial in optics.
- The coherence state of a secondary source significantly influences its far-zone intensity distribution.
- Previous research has explored source size and angular spread independently.
Purpose of the Study:
- To derive a novel reciprocity inequality for statistically stationary, planar secondary sources.
- To investigate the influence of coherence state on the source size-angular spread product.
- To identify the optimal source type that minimizes this reciprocity product.
Main Methods:
- Mathematical derivation of a reciprocity inequality.
- Analysis of secondary sources with varying coherence states.
- Comparison of the reciprocity product for different source types, including Hermite-Gaussian modes.
Main Results:
- A general reciprocity inequality is established, connecting effective source size and far-zone angular spread.
- The product is shown to depend on the source's state of coherence.
- The fully spatially coherent, lowest-order Hermite-Gaussian laser mode yields the minimum reciprocity product.
Conclusions:
- The derived inequality provides a fundamental limit on the simultaneous control of source size and far-field angular spread.
- Spatially coherent sources, particularly the lowest-order Hermite-Gaussian mode, offer superior performance in minimizing the reciprocity product.
- This finding has implications for designing efficient optical sources and systems.
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