Thresholdless deep and vacuum ultraviolet Raman frequency conversion in hydrogen-filled photonic crystal fiber: supplementary material

This document provides supplementary information to “Thresholdless deep and vacuum ultraviolet Raman frequency conversion in hydrogen-filled photonic crystal fiber,” https://doi.org/10.1364/OPTICA.6.000731 . Here we give further details on the experimental set-up, fiber dispersion and the numerical simulations of the evolution of light pulses inside hydrogen-filled hollow-core photonic crystal fibers. In addition, we also discuss the spectral purity of the generated coherence waves, the influence of the pump energy on the UV conversion efficiency and the modeling of the UV performance of kagomé-type photonic crystal fibers.

Here we give further details on the experimental set-up, fiber dispersion and the numerical simulations of the evolution of light pulses inside hydrogen-filled hollow-core photonic crystal fibers. In addition, we also discuss the spectral purity of the generated coherence waves, the influence of the pump energy on the UV conversion efficiency and the modeling of the UV performance of kagomé-type photonic crystal fibers.

Experimental set-up
Laser source.-We employed an injection-seeded Nd:YAG laser delivering 1064 nm, 3.2 ns pulses at 3 kHz repetition rate. As the inter-pulse separation of ~0.33 ms is much longer than the typical dephasing time of the Raman coherence (~1 ns), we can disregard any pulse-to-pulse effects. By frequency-doubling the laser pulses in a Potassium-Titanyl-Phosphate (KTP) crystal, we obtained the green pump source at 532 nm. The 266 nm mixing beam was then obtained by another frequency-doubling stage of the 532 nm pump in a Beta-Barium-Borate (BBO) crystal. An uncoated planoconvex CaF2 lens with focal length 100 mm was used to launch both the pump and the mixing beam into the fiber. To mitigate the in-coupling mismatch of the two wavelengths due to chromatic aberration, we used two telescopes placed in the optical paths of both beams-before the dichroic mirror (see Fig. 2(a) in main text). The use of this arrangement resulted in independent control of the beam diameters of both beams, which facilitated their simultaneous coupling into the fiber.
Gas system.-The hollow-core photonic crystal fiber (HC-PCF) is placed in two 8-cm-long gas-cells connected by a hollow metallic tube. Light enters and exits the gas-cells through 3 mm thick and 10 mm in diameter MgF2 optical windows. The pressure in the gascells was manually regulated with a very fine step size of ~50 mbar. This was made possible by the combined action of a number of gas-flow components: a coarse self-venting pressure regulator, a needle valve and a metering valve. The metering valve, when completely closed, played a key role in providing the minimum gas flow with additional control being provided by the needle valve.

Dispersion landscape of kagomé-type HC-PCF
The wavelength-dependent propagation constant β ij (λ) for the LPij-like modes of a gas-filled kagomé-style hollow-core photonic crystal fiber is analytically calculated using the modified Marcatili-Schmelzer model [1]  where ij u is the j-th root of the i-th order Bessel function of the first kind, with (i, j) being also the azimuthal and radial mode orders, gas n p λ is the pressure, p, and wavelength-dependent refractive index of the filling gas, and a is the area-preserving core radius. Note that this model disregards the influence of loss bands caused by anticrossings between the core mode and modes in the glass walls surrounding the core, which are irrelevant in our experimental conditions as we have discussed in the main text.

Details of the numerical simulations
The evolution of the electric fields of the Raman sidebands, as well as the molecular coherence triggered by the green pump are modeled through a set of coupled Maxwell-Bloch equations involving several fiber modes [2]. As in the experiment, we considered a fiber length of 40 cm and core radius a = 22 µm. The material dispersion of hydrogen gas is adopted from [3]. Based on the experimental observations, only the fundamental, LP01-like, and two-lobed or ring, LP11-like, higher-order modes (HOM) were considered for the pump, mixing beam and their sidebands.

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