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Exact iterative solution of second harmonic generation in quasi-phase-matched structures.

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Area of Science:

  • Nonlinear Optics
  • Computational Physics
  • Materials Science

Background:

  • Second harmonic generation (SHG) is crucial for frequency conversion in nonlinear optical (NLO) materials.
  • Modeling SHG with pump depletion in quasi-phase-matched (QPM) structures presents computational challenges.
  • Existing models may lack accuracy at high conversion efficiencies or for complex structures.

Purpose of the Study:

  • To develop a versatile and accurate numerical method for SHG with pump depletion.
  • To address the limitations of current models in handling high efficiencies and complex NLO structures.
  • To provide a robust tool for simulating nonlinear optical phenomena.

Main Methods:

  • A hybrid approach combining numerical iteration and the transfer-matrix method (TMM).
  • Derivation of iterative formulas from nonlinear coupled wave equations.
  • Obtaining intensity distributions of fundamental and second harmonic waves using TMM.

Main Results:

  • The method demonstrates rapid numerical convergence and perfect energy conservation.
  • Simulations align with the undepleted pump approximation at low SHG efficiencies (<15%).
  • Excellent agreement with the effective nonlinear susceptibility model at high conversion efficiencies (up to 100%).

Conclusions:

  • The developed method is highly accurate and versatile for SHG with pump depletion.
  • Applicable to diverse QPM structures including periodic, quasi-periodic, and aperiodic designs.
  • Suitable for photonic crystals and micro-cavities with complex linear and nonlinear susceptibility modulations.