Supercontinuum generation and soliton self-compression in &#x03C7;<sup>(2)</sup>-structured KTiOPO<sub>4</sub>

Anne-Lise Viotti; Robert Lindberg; Andrius Zukauskas; Rimantas Budriunas; Dainius Kucinskas; Tomas Stanislauskas; Fredrik Laurell; Valdas Pasiskevicius

doi:10.1364/OPTICA.5.000711

Optica
Vol. 5,
Issue 6,
pp. 711-717
(2018)
•https://doi.org/10.1364/OPTICA.5.000711

Supercontinuum generation and soliton self-compression in χ⁽²⁾-structured KTiOPO₄

Anne-Lise Viotti, Robert Lindberg, Andrius Zukauskas, Rimantas Budriunas, Dainius Kucinskas, Tomas Stanislauskas, Fredrik Laurell, and Valdas Pasiskevicius

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Anne-Lise Viotti, Robert Lindberg, Andrius Zukauskas, Rimantas Budriunas, Dainius Kucinskas, Tomas Stanislauskas, Fredrik Laurell, and Valdas Pasiskevicius, "Supercontinuum generation and soliton self-compression in χ⁽²⁾-structured KTiOPO₄," Optica 5, 711-717 (2018)

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Abstract

Ultrafast sources in the mid-IR are indispensable research tools for spectroscopic and medical applications and can also potentially be used to generate attosecond pulses. We investigated a route to directly achieve self-compressed supercontinuum pulses with an octave-exceeding spectrum extending into the mid-IR by employing self-defocusing nonlinearities obtained through cascaded $χ^{(2)}$ interactions in domain-structured ferroelectrics. A model was developed based on a single-wave nonlinear envelope equation that accounts for cascaded $χ^{(2)}$ nonlinearities, the native Kerr response from the third-order nonlinear polarization, and the delayed Raman response. Experimental validation of the model was carried out by using an in-house fabricated, periodically poled, Rb-doped ${KTiOPO}_{4}$ crystal with a period of 36 μm. A supercontinuum spectrum spanning from 1.1 to 2.7 μm was achieved, as well as self-compression down to 18.6 fs, from a 128 fs pump pulse at 1.52 μm. Using the actual pump pulse and sample parameters, excellent agreement was reached between the model and the experimental results, thus proving the validity of the model. As periodically poled ${KTiOPO}_{4}$ can be obtained with large apertures, this approach is energy scalable and hence promising for future development in the field.

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Fig. 1. (a) Group index for

c

polarization (dashed line) and group velocity dispersion (solid line) as a function of the wavelength for KTP. The horizontal black solid line represents zero GVD. (b) KTP third-order dispersion (TOD). (c) Phase mismatch (dashed line) and

n_{2}^{casc}

spectrum for KTP (solid line); the vertical dotted red line in (a) and (b) highlights the zero GVD wavelength. (d) Zoomed-in plot of the

n_{2}^{casc}

spectrum for the region of interest.

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Fig. 2. (a) Calculated spectral evolution along the 10 mm PPKTP crystal, (b) calculated temporal evolution of the femtosecond pulse, (c) output supercontinuum spectrum after the 10 mm long PPKTP crystal, (d) temporal comparison of input pump pulse and output supercontinuum pulse for

f_{R T} = 0.5

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Fig. 3. Schematic of the SHG-FROG/SFG-XFROG setup.

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Fig. 4. (a) SHG-FROG retrieved spectrum and spectral phase of the pump beam centered at 1.52 μm, (b) the temporal profile of the input pump pulse. The FWHM is 128 fs. The FROG error was calculated to be 0.48%.

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Fig. 5. (a) Measured SFG-XFROG trace and (b) retrieved SFG-XFROG trace of the supercontinuum pulse. The time axes are reversed, and the color bars represent the normalized spectrogram amplitude in log scale. (c) Retrieved spectrum and spectral phase of the supercontinuum pulse. A long-pass filter cuts away wavelengths shorter than 1.1 μm.

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Fig. 6. (a) Calculated spectral distribution and (b) the calculated temporal evolution of the pump pulse along the 11 mm long PPRKTP crystal. The Raman coefficient

f_{R T}

was set to 0.5.

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Fig. 7. Comparison of (a) output temporal profiles and (b) output supercontinuum spectra for both the numerical model (blue solid curves) and the experimental results (orange solid curves). The experimentally obtained spectrum starts above 1 μm because a long-pass filter was used in the SFG-XFROG setup, cutting away shorter wavelengths.

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Tables (1)

Table 1. Parameters Used for the Simulations of Raman Delayed Response Including Two Resonances for KTP from [23,24]

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Equations (7)

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\frac{\partial A}{\partial Z} + (i D - α) A = - i \frac{χ^{(2)} ω_{0}^{2}}{4 β_{0} c^{2}} (1 - \frac{i}{ω_{0}} \frac{\partial}{\partial t^{'}}) [\begin{array}{l} A^{2} e^{i ω_{0} t^{'} - i (β_{0} - β_{1} ω_{0}) Z} \\ + 2 {| A |}^{2} e^{- i ω_{0} t^{'} + i (β_{0} - β_{1} ω_{0}) Z} \end{array}] + i γ (ω_{0}) (1 - \frac{i}{ω_{0}} \frac{\partial}{\partial t^{'}}) A \int_{- \infty}^{+ \infty} R (t) {| A (Z, t^{'} - t) |}^{2} d t,

FT [i D - α] = i (k (ω) - β_{0} - β_{1} (ω - ω_{0})) - α (ω),

χ^{(2)} = d_{33} sign (\cos (\frac{2 π Z}{Λ})),

γ (ω_{0}) = \frac{1}{2} ω_{0} n (ω_{0}) ϵ_{0} n_{2}^{nat},

R (t) = (1 - f_{R T}) δ (t) + \sum_{j = 1}^{N} f_{R j} \frac{τ_{1 j}^{2} + τ_{2 j}^{2}}{τ_{1 j} τ_{2 j}^{2}} H (t) e^{- \frac{t}{τ_{2 j}}} \sin (\frac{t}{τ_{1 j}}),

n_{2}^{casc} = \frac{2 ω_{p} d_{33}^{2}}{n_{ω_{p}}^{2} n_{2 ω_{p}} c^{2} ϵ_{0} Δ k} (\sin c (Δ k L) - 1),

Δ k = k (2 ω_{p}) - 2 k (ω_{p}) - K_{g},

Material	$τ_{11}$ (fs)	$τ_{12}$ (fs)	$f_{R 1}$	$τ_{21}$ (ps)	$τ_{22}$ (ps)	$f_{R 2}$	$f_{R T}$
KTP	20	7.6	0.13	7.4	1.2	0.37	0.5