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Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis.

Elias N Glytsis1

  • 1School of Electrical and Computer Engineering and Microelectronics Research Center, Georgia Institute of Technology, Atlanta 30332, USA. elias.glytsis@ece.gatech.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 6, 2002
PubMed
Summary

Scalar diffraction analysis is less accurate for 2-D gratings than 1-D. Accuracy decreases with higher refractive index, grating thickness, and asymmetry, and smaller feature sizes and period-to-wavelength ratios.

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Area of Science:

  • Optics and Photonics
  • Diffractive Optical Elements
  • Computational Electromagnetics

Background:

  • Scalar diffraction analysis is a common approximation for analyzing diffractive optical elements.
  • Its accuracy for complex, two-dimensionally-periodic structures like crossed gratings is not fully understood.
  • Rigorous Coupled-Wave Analysis (RCWA) provides exact solutions for comparison.

Purpose of the Study:

  • Quantify the range of validity for scalar diffraction analysis on 2-D periodic diffractive optical elements.
  • Compare scalar analysis predictions with rigorous analysis for various grating structures.
  • Identify key parameters influencing the accuracy of scalar diffraction analysis.

Main Methods:

  • Utilized Rigorous Coupled-Wave Analysis (RCWA) and scalar diffraction analysis.

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  • Analyzed three canonical 2-D grating unit cells: rectangular pillar, elliptical pillar, and arbitrarily pixellated multilevel.
  • Calculated and compared diffraction efficiencies from both methods.

    • Main Results:

    • Scalar diffraction analysis shows greater error for 2-D periodic elements compared to 1-D.
    • Accuracy degrades with increased grating refractive index, thickness, and unit cell asymmetry.
    • Accuracy also degrades with decreasing grating period-to-wavelength ratio and feature size.

    Conclusions:

    • Scalar diffraction analysis has limited validity for 2-D periodic diffractive optical elements.
    • RCWA is necessary for accurate analysis of complex 2-D gratings.
    • Design parameters significantly impact the reliability of scalar approximations.