Researching | Ultrabroadband second-harmonic generation via spatiotemporal-coupled phase matching

Journals >Chinese Optics Letters >Volume 22 >Issue 1 >Page 011901 > Article

Chinese Optics Letters
Vol. 22, Issue 1, 011901 (2024)

Ultrabroadband second-harmonic generation via spatiotemporal-coupled phase matching

Yudong Tao¹, Wentao Zhu¹, Yanfang Zhang¹, Jingui Ma¹, Jing Wang^1、*, Peng Yuan^1、**, Hao Zhang², Heyuan Zhu², and Liejia Qian^1、3

Author Affiliations

¹Key Laboratory for Laser Plasma, Shanghai Jiao Tong University, Shanghai 200240, China

²Key Laboratory of Micro and Nano Photonic Structures, Fudan University, Shanghai 200433, China

³Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China

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DOI: 10.3788/COL202422.011901 Cite this Article Set citation alerts

Yudong Tao, Wentao Zhu, Yanfang Zhang, Jingui Ma, Jing Wang, Peng Yuan, Hao Zhang, Heyuan Zhu, Liejia Qian. Ultrabroadband second-harmonic generation via spatiotemporal-coupled phase matching[J]. Chinese Optics Letters, 2024, 22(1): 011901 Copy Citation Text

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Abstract

We propose a spatially chirped quasi-phase-matching (QPM) scheme that enables ultrabroadband second-harmonic-generation (SHG) by using a fan-out QPM grating to frequency-convert a spatially chirped fundamental wave. A “zero-dispersion” 4f system maps the spectral contents of ultrabroadband fundamental onto different spatial coordinates in the Fourier plane, where the fundamental is quasi-monochromatic locally in picosecond duration, fundamentally canceling high-order phase mismatch. A fan-out QPM grating characterized by a linear variation of the poling period along the transverse direction exactly supports the QPM of the spatially chirped beam. We theoretically demonstrate the SHG of an 810-nm, 12.1-fs pulse into a 405-nm, 10.2-fs pulse with a conversion efficiency of 77%.

Keywords

few-cycle pulse nonlinear optics second-harmonic generation

a_{1 ω}^{in} (x, ω) = a_{0} \exp (- \frac{x^{2}}{2 D^{2}}) \exp [- \frac{ω^{2}}{2 {(Δ ω)}^{2}}],

(1)

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a_{1 ω}^{G_{1}} (x, ω) = a_{0} \exp (- \frac{x^{2}}{2 D^{2}}) \exp [- \frac{ω^{2}}{2 {(Δ ω)}^{2}}] \exp (i k_{1} β_{1} ω x),

(2)

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a_{1 ω}^{FP} (x, ω) = a_{1} \exp (- \frac{i k_{1}}{2 f} x^{2}) \exp (- \frac{i k_{1} β_{1}^{2} ω^{2} f}{2}) \exp [- \frac{ω^{2}}{2 {(Δ ω)}^{2}}] \exp (- i k_{1} β_{1} ω x) \exp [- \frac{{(x + β_{1} f ω)}^{2}}{2 σ^{2}}],

(3)

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ζ_{1} = \frac{d x}{d ω} = - β_{1} f .

(4)

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Δ ω_{1}^{FP} = \frac{σ}{| ζ_{1} |} = - \frac{1}{k_{1} β_{1} D} = - \frac{Δ θ_{1 ω}}{β_{1}},

(5)

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A_{1 ω}^{FP} (x, t) = A_{1} \exp [- \frac{x^{2}}{2 {(ζ_{1} Δ ω)}^{2}}] \exp [- \frac{t^{2}}{2 {(k_{1} β_{1} D)}^{2}}] \exp (\frac{- i x t}{ζ_{1}}),

(6)

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a_{2 ω}^{FP} (x, ω) = a_{2} \exp (- \frac{i k_{2}}{2 f} x^{2}) \exp [- \frac{i k_{2} β_{2}^{2} {(2 ω)}^{2} f}{2}] \exp [- \frac{ω^{2}}{4 {(Δ ω)}^{2}}] \exp [- i k_{2} β_{2} (2 ω) x] \exp {- \frac{{[x + β_{2} f (2 ω)]}^{2}}{σ^{2}}},

(7)

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a_{2 ω}^{G_{2}} (x, ω) = a_{3} \exp (- \frac{x^{2}}{D^{2}}) \exp [- \frac{ω^{2}}{4 {(Δ ω)}^{2}}] \exp (- i 2 k_{2} β_{2} ω) .

(8)

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a_{2 ω}^{out} (x, ω) = a_{3} \exp (- \frac{x^{2}}{D^{2}}) \exp [- \frac{ω^{2}}{4 {(Δ ω)}^{2}}] .

(9)

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Δ k_{Q} (x, λ) = k_{2} (x, λ / 2) - 2 k_{1} (x, λ) - \frac{2 π}{Λ (x)} .

(10)

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\frac{\partial A_{2 ω}}{\partial z} + \sum_{n = 1}^{3} \frac{{(- i)}^{n - 1}}{n!} k^{(n)} \frac{\partial A_{2 ω}}{\partial t} = - i \frac{ω_{2} d_{eff}}{n_{2} c π} A_{1 ω}^{2} e^{i Δ k_{Q} (x) z},

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\frac{\partial A_{1 ω}}{\partial z} + \sum_{n = 1}^{3} \frac{{(- i)}^{n - 1}}{n!} k^{(n)} \frac{\partial A_{1 ω}}{\partial t} = - i \frac{2 ω_{1} (x) d_{eff}}{n_{1} c π} A_{1 ω}^{*} A_{2 ω} e^{- i Δ k_{Q} (x) z},

(11b)

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Λ_{\max} = \frac{2 π}{k_{2} (x, \frac{λ_{\max}}{2}) - 2 k_{1} (x, λ_{\max})},

(12a)

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Λ_{\min} = \frac{2 π}{k_{2} (x, \frac{λ_{\min}}{2}) - 2 k_{1} (x, λ_{\min})} .

(12b)

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I_{2 ω} (x, L) = \frac{32 L^{2} d_{eff}^{2}}{n_{1}^{2} n_{2} λ_{2}^{2} c ε_{0}} I_{1 ω}^{2} {sinc}^{2} [\frac{Δ k_{Q} (0, λ) L}{2}] .

(13)

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| Δ k_{Q} (λ_{0} \pm Δ λ_{local}) L | = 2 π .

(14)

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ω_{1} (x) = ω_{0} - \frac{x}{β_{1} f},

(15)

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Λ_{opt} (x) = \frac{2 π}{k_{2} - 2 k_{1}} = \frac{π c}{(n_{2} - n_{1}) ω_{0}} \times \frac{1}{1 - \frac{x}{β_{1} f ω_{0}}} .

(16)

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Λ (x) \approx \frac{π c}{(n_{20} - n_{10}) ω_{0}} \times (1 + \frac{x}{β_{1} f ω_{0}}),

(17)

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θ_{tilt} = \arctan {\frac{N_{v} [Λ_{\max} - Λ_{\min}]}{2 (x_{\max} - x_{\min})}},

(18)

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References (21)

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Yudong Tao, Wentao Zhu, Yanfang Zhang, Jingui Ma, Jing Wang, Peng Yuan, Hao Zhang, Heyuan Zhu, Liejia Qian. Ultrabroadband second-harmonic generation via spatiotemporal-coupled phase matching[J]. Chinese Optics Letters, 2024, 22(1): 011901

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