Introduction

Most nonlinear experiments using hollow-core PCF rely on the intrinsic third-order nonlinearity of the filling gas, which has vanishingly small values of second-order susceptibility χ(2). If however a dc electric field is applied, the centrosymmetry can be broken and an effective χ(2) induced. This process has been studied in conventional step-index fibres, for example by direct electric field poling [Kazansky (1997)]. In this project, we have demonstrated electric field-induced second harmonic generation (EFISH) using external electrodes to induce a second-order nonlinearity in gas-filled HC-PCF.

This project is an on-going collaboration with Prof. Jean-Michel Menard at the University of Ottawa, supported by the Max Planck-uOttawa Centre for Extreme and Quantum Photonics.

EFISH in gas-filled HC-PCF

EFISH was investigated by pumping a Xe-filled kagomé-PCF with nanosecond optical pulses at ~1 µm [Menard (2015)]. Phase-matching between LP01 pump and LP02 SH modes could be obtained over a broad range of pump wavelengths, simply by changing the gas pressure. The SH modal profile appeared in the LP02 mode, and the gas pressure required to achieve phase matching was accurately predicted by a theoretical model based on a modified capillary waveguide. We also showed that the EFISH pulse energy follows a quadratic dependence on both the pump pulse energy and the voltage applied to the electrodes. The results are in good agreement with an analytical model obtained by solving the coupled nonlinear wave equations. At the highest voltage across the electrodes, we achieved a maximum conversion efficiency of ~0.02 and a SH pulse energy of 430 pJ.

(a) Schematic of the experimental set-up. (b) Measured near-field intensity distribution (linear scale) of the SH signal in the LP02 mode. The SEM image of the fibre core structure is superimposed for reference. (c) Pulse energy of the SH in the LP02 mode as function of the pump pulse energy for 300-fs-long pump pulses. The measurements (blue circles) follow the quadratic dependence of the SHG process (black line).

Broadband EFISH with ultrashort pulses

With 300 fs pump pulses, spectral broadening due to self-phase modulation was observed at the highest peak powers [Menard (2016)]. This caused a slight departure between the measured SH signal and the quadratic dependence predicted by the simple theoretical model. We monitored the SH spectrum as a function of launched pump pulse energy (figure left). At low peak energies, the SH spectrum has a Gaussian-like distribution centred at 515 nm with a full width half maximum (FWHM) of ~3 nm. As the pump power increases, the spectrum gradually broadens, reaching a maximum bandwidth of ~10 nm FWHM. Surprisingly, symmetric spectral broadening of the pump pulse spectrum due to self-phase modulation (SPM) creates an asymmetric SH spectrum with pronounced features on the short-wavelength side. Due to its lower group velocity, the generated SH pulse is delayed with respect to the pump pulse. Therefore, the SH pulse experiences parametric gain on the trailing edge of the pump pulse, where SPM creates higher frequencies. The broad linewidth of the SH signal confirms that the gas-filled HC-PCF is suitable for efficient three-wave mixing of ultrashort pulses. The detected bandwidth corresponds to the FWHM spectral linewidth of a ~100 fs transform-limited pulse. Furthermore, the electrode length, which was 16 cm, could easily be shortened or lengthened so as to adjust the nonlinear phase-matching bandwidth and potentially allow conversion of optical pulses of any duration.

Periodically patterned electrodes were used to generate a SH signal in the LP01 mode by quasi-phase matching (QPM). Upon applying a voltage across the electrodes and scanning the gas pressure, two prominent SH peaks were consistently recorded. The first one was at a Xe pressure of 3.9 bar, corresponding to the LP02 mode as described above. A second peak was seen at different pressures depending on the QPM period L (figure right). For example, at a Xe pressure of 4.1 bar for L = 1.82 mm (dark blue curve) the second SH signal was always in the LP01 mode. Since χ(3) scales linearly with gas pressure, a stronger SH signal is generated for smaller QPM periods because the phase-matching pressure is higher. The dependence of SH power on the gas pressure is quadratic, but saturates above 10 bar as a result of group velocity walk-off between the pump and SH pulses.

(a) Spectrum of the EFISH signal as a function of launched pump pulse energy. At low pump energies, the SH spectrum is Gaussian-like, centred at 515 nm with a full-width-half-maximum of ?3 nm. With increasing pump energy, the spectrum gradually broadens, reaching a maximum bandwidth of 10 nm. (b) SH signals in the LP01 mode are generated at gas pressures that vary with the period L of the QPM electrode. At 3.9 bar, the LP02 mode generated by intermodal phase matching is observed for all L.

Measuring fibre loss

The set-up provides a convenient non-destructive means of measuring propagation loss at the SH wavelength, which might require an expensive and complex laser system to access. For example, by applying a voltage sequentially to few-cm-long electrodes placed at different positions along the fibre and then measuring the SH output signal, it is straightforward after data processing to extract the propagation loss at the SH. Used in combination with a tunable pump laser, the system would allow characterization over a broad bandwidth of the loss of the LP01 mode (and some higher modes), in any type of hollow-core PCF that guides at the pump and SH frequencies. This application is especially interesting in the deep and vacuum ultraviolet.