Hybrid nanowires for phase-matching of third-harmonic generation in hyperbolic metamaterial

Surawut Wicharn; Prathan Buranasiri; Prathan Buranasiri

doi:10.1364/AO.427283

Applied Optics
Vol. 60,
Issue 28,
pp. 8744-8755
(2021)
•https://doi.org/10.1364/AO.427283

Hybrid nanowires for phase-matching of third-harmonic generation in hyperbolic metamaterial

Surawut Wicharn and Prathan Buranasiri

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Surawut Wicharn and Prathan Buranasiri, "Hybrid nanowires for phase-matching of third-harmonic generation in hyperbolic metamaterial," Appl. Opt. 60, 8744-8755 (2021)

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Table of Contents Category
- Nonlinear Optics
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About this Article
History
- Original Manuscript: April 9, 2021
- Revised Manuscript: September 1, 2021
- Manuscript Accepted: September 5, 2021
- Published: September 24, 2021

Abstract

We propose a phase-matching technique for third-harmonic generation, called hyperbolic phase matching, that possibly can be achieved by optimal designing and engineering dispersion of hybrid-nanowire hyperbolic metamaterial. We demonstrate phase-matched conditions for two different third-harmonic interacting configurations, which can be created at two optimal incident angles of the pump field. Moreover, each composed hybrid nanowire can enhance third-harmonic generation by using strong field confinement along the metal/dielectric interface due to plasmonic resonance. Finally, conversion efficiencies of transmitted and reflected third-harmonic pulses as a function of incident angle and input pulse intensity are examined by numerical integration of nonlinear birefringent coupled-mode equations. The numerical results validate the idea that, using a combination of phase-matched conditions and pump field confinement, we can achieve a dramatic enhancement of conversion efficiencies of third-harmonic generation.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Case	FH	TH	THG Configuration	Phase-Matched Conditions
(I)	$o$ -wave	$o$ -wave	$o - o - o - o$	$n_{o} (ϖ_{0}) = n_{o} (3 ϖ_{0})$
(II)	$o$ -wave	$e$ -wave	$o - o - o - e$	$n_{o} (ϖ_{0}) = n_{e} (3 ϖ_{0})$
(III)	$e$ -wave	$o$ -wave	$e - e - e - o$	$n_{e} (ϖ_{0}) = n_{o} (3 ϖ_{0})$
(IV)	$e$ -wave	$e$ -wave	$e - e - e - e$	$n_{e} (ϖ_{0}) = n_{e} (3 ϖ_{0})$

$f$	$R e [ε_{xx} (ϖ_{0})]$	$R e [ε_{zz} (ϖ_{0})]$	$R e [ε_{xx} (3 ϖ_{0})]$	$R e [ε_{zz} (3 ϖ_{0})]$
0.1	3.192	−120.1	2.612	−1.053
0.2	4.027	−213.6	3.213	−1.872
0.3	5.146	−280.3	3.989	−2.456
0.4	6.725	−320.4	5.028	−2.807
0.5	9.119	−333.7	6.492	−2.924

Case	FH	TH	THG Configuration	Phase-Matched Conditions
(I)	$o$ -wave	$o$ -wave	$o - o - o - o$	$n_{o} (ϖ_{0}) = n_{o} (3 ϖ_{0})$
(II)	$o$ -wave	$e$ -wave	$o - o - o - e$	$n_{o} (ϖ_{0}) = n_{e} (3 ϖ_{0})$
(III)	$e$ -wave	$o$ -wave	$e - e - e - o$	$n_{e} (ϖ_{0}) = n_{o} (3 ϖ_{0})$
(IV)	$e$ -wave	$e$ -wave	$e - e - e - e$	$n_{e} (ϖ_{0}) = n_{e} (3 ϖ_{0})$

$f$	$R e [ε_{xx} (ϖ_{0})]$	$R e [ε_{zz} (ϖ_{0})]$	$R e [ε_{xx} (3 ϖ_{0})]$	$R e [ε_{zz} (3 ϖ_{0})]$
0.1	3.192	−120.1	2.612	−1.053
0.2	4.027	−213.6	3.213	−1.872
0.3	5.146	−280.3	3.989	−2.456
0.4	6.725	−320.4	5.028	−2.807
0.5	9.119	−333.7	6.492	−2.924

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