Optical rectification of ultrafast Yb lasers: pushing power and bandwidth of terahertz generation in GaP

Jakub Drs; Norbert Modsching; Clément Paradis; Christian Kränkel; Valentin J. Wittwer; Olga Razskazovskaya; Thomas Südmeyer

doi:10.1364/JOSAB.36.003039

Optical rectification of ultrafast Yb lasers: pushing power and bandwidth of terahertz generation in GaP

Jakub Drs, Norbert Modsching, Clément Paradis, Christian Kränkel, Valentin J. Wittwer, Olga Razskazovskaya, and Thomas Südmeyer

Journal of the Optical Society of America B
Vol. 36,
Issue 11,
pp. 3039-3045
(2019)
•https://doi.org/10.1364/JOSAB.36.003039

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Jakub Drs, Norbert Modsching, Clément Paradis, Christian Kränkel, Valentin J. Wittwer, Olga Razskazovskaya, and Thomas Südmeyer, "Optical rectification of ultrafast Yb lasers: pushing power and bandwidth of terahertz generation in GaP," J. Opt. Soc. Am. B 36, 3039-3045 (2019)

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- Nonlinear or High Field Optics
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About this Article
History
- Original Manuscript: June 10, 2019
- Revised Manuscript: August 15, 2019
- Manuscript Accepted: August 27, 2019
- Published: October 16, 2019

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Abstract

We demonstrate broadband high-power terahertz (THz) generation at megahertz repetition rates by optical rectification in GaP driven by an ultrafast Yb-based thin-disk laser (TDL) oscillator. We investigate the influence of pulse duration in the range of 50–220 fs and thickness of the GaP crystal on the THz generation. Optimization of these parameters with respect to the broadest spectral bandwidth yields a gap-less THz spectrum extending to nearly 7 THz. We further tailor the driving laser and the THz generation parameters for the highest average power, demonstrating 0.3 mW THz radiation with a spectrum extending to 5 THz. This was achieved using a 0.5 mm thick GaP crystal pumped with a 95 fs, 20 W TDL, operating at 48 MHz repetition rate. We also provide a simple method to estimate the THz spectrum, which can be used for design and optimization of similar THz systems.

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Process	Equation	Ref.
IR ${\rm{sech}}^2$ ${s e c h}^{2}$ pulse intensity envelope, where ${\tau _{\rm laser}}\cdot1.76$ $τ_{l a s e r} \cdot 1.76$ corresponds to the FWHM pulse duration	$ {I_{{\rm{IR}}}}(t) = {{\mathop{\rm sech}\nolimits} ^2}( {\frac{t}{{{\tau _{{\rm{laser}}}}}}} ) $ $I_{I R} (t) = {sech}^{2} (\frac{t}{τ_{l a s e r}})$
Driving THz field, defined by second derivative of the driving pulse intensity envelope $ I_{\rm IR}$ $I_{I R}$ with respect to time	$ {E_{{{0}}\,{\rm{THz}}}}(\omega ) = {\cal F}( {\frac{{{d^2}{I_{{\rm{IR}}}}(t)}}{{d{t^2}}}} )(\omega ) $ $E_{0 T H z} (ω) = F (\frac{d^{2} I_{I R} (t)}{d t^{2}}) (ω)$	[33]
Sellmeier equation for refractive index of GaP	$ n_{{\rm{THz}}}^2 = 1 + \frac{{{B_{{1}}}\,{\lambda ^2}}}{{{\lambda ^2} - \lambda _1^2}} + \frac{{{B_2}\,{\lambda ^2}}}{{{\lambda ^2} - \lambda _2^2}}$ $n_{T H z}^{2} = 1 + \frac{B_{1} λ^{2}}{λ^{2} - λ_{1}^{2}} + \frac{B_{2} λ^{2}}{λ^{2} - λ_{2}^{2}}$ ,	[19]
	$B_1 = 2.064,\lambda _1 = 27.284 \,{\unicode{x00B5}{\rm m}}$ $B_{1} = 2.064, λ_{1} = 27.284 µ m$ ,
	${B_2} = 8.089$ $B_{2} = 8.089$ , ${\lambda _2} = 0.2707\,\,{\unicode{x00B5}{\rm m}}$ $λ_{2} = 0.2707 µ m$
PM condition for group velocity of the IR pulse and THz radiation phase velocity, where ${d_{\rm crystal}}$ $d_{c r y s t a l}$ determines thickness of the GaP crystal	$ {\rm{PM}}(\omega ) = \frac{{{e^{i\omega \delta (\omega )}} - 1}}{{i\omega \delta (\omega )}}$ $P M (ω) = \frac{e^{i ω δ (ω)} - 1}{i ω δ (ω)}$ , $ \delta(\omega) = \frac{{{n_{\rm{g}}}({\lambda _0}) - {n_{{\rm{THz}}}}(\omega )}}{{{c_{{\rm{light}}}}}}{d_{{\rm{crystal}}}}$ $δ (ω) = \frac{n_{g} (λ_{0}) - n_{T H z} (ω)}{c_{l i g h t}} d_{c r y s t a l}$ , ${n_{\rm{g}}}(1.03\,\;{\unicode{x00B5}\rm m}) = 3.31$ $n_{g} (1.03 µ m) = 3.31$	[28]
EOS response, determined byintensity envelope spectrum of the probing IR pulse	$ {\rm{EOS}}(\omega ) = {\cal F}( {{I_{{\rm{IR}}}}(t)} )(\omega ) $ $E O S (ω) = F (I_{I R} (t)) (ω)$	[34]
GaP absorption coefficient	$ k(\omega ) = {\mathop{\rm Im}\nolimits} \left( {{\varepsilon _{{\rm{el}}}} + \frac{{{{\rm{S}}_{{0}}}\,\omega _0^2}}{{\omega _0^2 - {\omega ^2} - i{\Lambda _0}\omega }}} \right)$ $k (ω) = Im (ε_{e l} + \frac{S_{0} ω_{0}^{2}}{ω_{0}^{2} - ω^{2} - i Λ_{0} ω})$ ,	[35]
	${\varepsilon _{{\rm{el}}}} = 8.7$ $ε_{e l} = 8.7$ , ${S_0} = 1.8$ $S_{0} = 1.8$ ,
	${\Lambda _0} = 0.126 \cdot {10^{12}}\,\,{\rm{rad/s}}$ $Λ_{0} = 0.126 \cdot 10^{12} r a d / s$ ,
	$\omega _0 = 69\cdot{10^{12}}\,\,{\rm{rad/s}}$ $ω_{0} = 69 \cdot 10^{12} r a d / s$
GaP transmission, based on Fresnel reflection and material absorption, where ${d_{\rm crystal}}$ $d_{c r y s t a l}$ determines thickness of the GaP crystal	${t_{{\rm{GaP}}}}(\omega ) = \frac{2}{{{n_{{\rm{THz}}}}(\omega ) + 1}}\cdot{e^{ - k \frac{{\omega \cdot{d_{{\rm{crystal}}}}}}{{{c_{{\rm{light}}}}}}}} $ $t_{G a P} (ω) = \frac{2}{n_{T H z} (ω) + 1} \cdot e^{- k \frac{ω \cdot d_{c r y s t a l}}{c_{l i g h t}}}$
Electro-optic coefficient $r_41$ $r_{4} 1$ of GaP	${r_{41}}(\omega ) = {d_{\rm{E}}}\left( {1 + \frac{{{C_0}\,\omega _0^2}}{{\omega _0^2 - {\omega ^2} - i{\Lambda _0}\omega }}} \right)$ $r_{41} (ω) = d_{E} (1 + \frac{C_{0} ω_{0}^{2}}{ω_{0}^{2} - ω^{2} - i Λ_{0} ω})$ ,	[35]
	${d_{\rm{E}}= 10^{ - 12}}\,\,{\rm{m/V}}$ $d_{E} = 10^{- 12} m / V$ , ${C_0} = - {{0.53}}$ $C_{0} = - 0.53$ ,
	${\Lambda _0} = 0.126\cdot{10^{12}}\,\,{\rm{rad/s,}}$ $Λ_{0} = 0.126 \cdot 10^{12} r a d / s,$ ,
	${\omega _0} = 69 \cdot{10^{12}}\,\,{\rm{rad/s}}$ $ω_{0} = 69 \cdot 10^{12} r a d / s$
Overall THz field estimate	${E_{{\rm{THz}}}} = {E_{{{0}}\,{\rm{THz}}}} \cdot {{\rm{PM}}_{{\rm{Det}}}} \cdot {{\rm{PM}}_{{\rm{Gen}}}} \cdot {\rm{EOS}} \cdot {t_{{\rm{GaP}}}} \cdot{r_{41}}$ $E_{T H z} = E_{0 T H z} \cdot {P M}_{D e t} \cdot {P M}_{G e n} \cdot E O S \cdot t_{G a P} \cdot r_{41}$
Dependence of THz average power on angle $\theta $ $θ$ of $\langle 110 \rangle $ $⟨ 110 ⟩$ -cut GaP crystal with respect to laser polarization	$ P( \theta ) \propto {\sin ^2}( {2\theta } ) + {\sin ^4}( \theta ) $ $P (θ) \propto \sin^{2} (2 θ) + \sin^{4} (θ)$	[33]

Norbert Modsching	https://orcid.org/0000-0001-6316-8810
Clément Paradis	https://orcid.org/0000-0003-2394-5659
Valentin J. Wittwer	https://orcid.org/0000-0003-1883-2393
Thomas Südmeyer	https://orcid.org/0000-0002-2425-1846

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