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Computation of diffracted fields for the case of high numerical aperture using the angular spectrum method.

Tomasz Kozacki1, Konstantinos Falaggis, Malgorzata Kujawinska

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The angular spectrum method faces limitations with high numerical apertures. A new modified algorithm using the Wigner distribution offers accurate and efficient field computation, overcoming conventional method constraints.

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Area of Science:

  • Computational electromagnetics
  • Wave propagation modeling
  • Numerical methods in physics

Background:

  • The angular spectrum (AS) method accurately solves the Helmholtz Equation without approximations.
  • High numerical aperture (NA) scenarios pose challenges for the conventional AS method due to extensive zero-padding requirements.
  • These requirements lead to impractical memory and computational demands.

Purpose of the Study:

  • To derive novel criteria for sampling requirements in AS method using the Wigner distribution (WD).
  • To address the limitations of the conventional AS method in high NA cases.
  • To propose an efficient and accurate alternative for field computation.

Main Methods:

  • Derivation of new sampling criteria utilizing the Wigner distribution (WD).
  • Development of a modified angular spectrum (AS) algorithm that selectively evaluates non-zero field components.
  • Comparative analysis of the modified AS algorithm against the conventional AS method.

Main Results:

  • The Wigner distribution (WD) analysis reveals impractical zero-padding needs for conventional AS in high NA scenarios.
  • The modified AS algorithm effectively bypasses the need for excessive zero-padding by processing only essential field components.
  • The proposed method demonstrates accurate and computationally efficient field computation for challenging high NA cases.

Conclusions:

  • The conventional AS method is computationally prohibitive for high NA applications due to sampling requirements.
  • The modified AS algorithm, guided by WD criteria, provides a practical and efficient solution for accurate field computation.
  • This advancement enables wider applicability of AS method in demanding optical and electromagnetic simulations.