Mixing Ince–Gaussian modes through sum-frequency generation

D. G. Pires; J. C. A. Rocha; M. V. E. C. da Silva; A. J. Jesus-Silva; E. J. S. Fonseca

doi:10.1364/JOSAB.401001

Journal of the Optical Society of America B
Vol. 37,
Issue 10,
pp. 2815-2821
(2020)
•https://doi.org/10.1364/JOSAB.401001

Mixing Ince–Gaussian modes through sum-frequency generation

D. G. Pires, J. C. A. Rocha, M. V. E. C. da Silva, A. J. Jesus-Silva, and E. J. S. Fonseca

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D. G. Pires, J. C. A. Rocha, M. V. E. C. da Silva, A. J. Jesus-Silva, and E. J. S. Fonseca, "Mixing Ince–Gaussian modes through sum-frequency generation," J. Opt. Soc. Am. B 37, 2815-2821 (2020)

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Table of Contents Category
- Nonlinear or High Field Optics
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About this Article
History
- Original Manuscript: June 23, 2020
- Revised Manuscript: August 6, 2020
- Manuscript Accepted: August 6, 2020
- Published: September 8, 2020

Abstract

We present a nonlinear mixing study of Ince–Gaussian (IG) beams in non-collinear sum-frequency generation, completing the fundamental analysis of all three families of paraxial wave equation solutions under this nonlinear process. Through theoretical and experimental results, we consider the nonlinear mixing of even and odd IG modes, and transition between the paraxial modes by controlling the eccentricity parameter $\epsilon$ and helical IG modes possessing arbitrary orbital angular momentum. Additionally, the selection rule of IG modes in the nonlinear mixing processes is determined. This work is important for optical communications and quantum protocols.

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Basis	Order	Selection Rule
${HG}_{n_{x} n_{y}}$	$N = n_{x} + n_{y}$	$n_{x} \leq n_{x}^{'} + n_{x}^{''}$ (mod 2)
		$n_{y} \leq n_{y}^{'} + n_{y}^{''}$ (mod 2)
${LG}_{nl}$	$N = 2 n + \| l \|$	$l = l^{'} + l^{''}$
		$n \leq n^{'} + n^{''} (l^{'} \cdot l^{''} > 0)$
		$n \leq P + n^{'} + n^{''} (l^{'} \cdot l^{''} \leq 0)$
${LG}_{nl}^{σ}$	$N = 2 n + \| l \|$	$l = {\| l^{'} - l^{''} \|, \| l^{'} + l^{''} \|}$
		$n \leq ((N^{'} + N^{''}) - l) / 2$
${IG}_{pm}^{σ}$	$N = p$	$p \leq p^{'} + p^{''}$ (mod 2)
		$m_{0} \leq m \leq p$ (mod 2)
${HIG}_{pm}^{\pm}$	$N = p$	$p \leq p^{'} + p^{''}$ (mod 2)
		$m_{0} \leq m \leq p$ (mod 2)
		$m_{Net} = m^{'} + m^{''}$

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