Approximate analytical description for the nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi></mml:mi> <mml:mi></mml:mi> </mml:math> -symmetric coupled-mode equations
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Bibliographic record
Abstract
Abstract In this paper, we present an approximate analytical description of the solutions dynamics of nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mi mathvariant="italic"></mml:mi> </mml:math> -symmetric coupled-mode equations which can be used to realize the nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mi mathvariant="italic"></mml:mi> </mml:math> -symmetric optical configuration. By the multiple-scale analysis, we construct the asymptotic solutions of the coupled-mode equations. In the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mi mathvariant="italic"></mml:mi> </mml:math> -symmetry unbroken region, there is a good agreement between the asymptotic solutions and exact numerical solutions, and the higher-order asymptotic series can yield a higher accuracy. However, in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mi mathvariant="italic"></mml:mi> </mml:math> -symmetry broken region, the asymptotic solutions become invalid quickly as z increases. Instead, we neglect one linear coupling term and obtain the approximate analytical solutions which, to some extent, describe the dynamics in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mi mathvariant="italic"></mml:mi> </mml:math> -symmetry broken region when z ≫ 1. This paper may be helpful for undergraduate and graduate students in physics to understand the nonlinear dynamics of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mi mathvariant="italic"></mml:mi> </mml:math> -symmetric systems.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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