setup
A schematic diagram of the fibre-feedback bow-tie SPOPO ring cavity used in this work is shown in figure4.1. A ring cavity is better compared to a standing-wave cavity, since in a standing-wave arrangement with the fibre in one arm, launch losses, chromatic dispersion and potential nonlinear effects would be doubled due to the double pass of the signal pulses through the fibre. An MgO:PPLN piece (Covesion Ltd., United Kingdom) with dimensions of L = 40 mm, H = 10 mm and W = 1 mm and with five periodically poled gratings ranging from 29.5 µm to 31.5 µm was used. Each grating had a 1 mm× 1 mm wide aperture. The 40 mm length had a sufficient phase-matching bandwidth and minimal temporal walk-off for the involved wavelengths compared to the 100 ps pump pulses. The calculated GVM for a 1.5 µm signal and the 1.06 µm pump is 95 fs/mm, which leads to an acceptable walk-off of 3.8 ps along the entire crystal length. In order to eliminate any residual photo-refraction, the crystal was held in an oven at an elevated temperature of 150◦C.
Signal
Output Coupler (OC) Single-Mode
Fibre (~27m) Idler Pump MgO:PPLN Crystal Curved Mirror (CM1) Curved Mirror (CM2) L1 L2
FIGURE4.1: Schematic diagram of the fibre-feedback bow-tie SPOPO cavity. The curved mir- rors CM 1 and CM 2 have radii of curvature of −250 mm and the fibre coupling lenses L 1 and L 2 (aspherical) have focal lengths of 4.5 mm.
The two main criteria of the resonator design, namely obtaining large waist sizes to reduce the peak intensities and obtaining synchronism with the pump source repetition
Chapter 4. High-pulse-energy, compact, picosecond optical parametric oscillator 96 rate, were separated by choosing a free-space section of the resonator first in order to model the waist sizes (no fibre in the setup, but a plane “dummy” mirror model) and then removing the “dummy” mirror and inserting the fibre into the resonator, cut to the right length, to achieve synchronism.
Similar resonator design consideration as for the SPOPO in chapter3, i.e. (1) avoiding the physical clipping of the beams at the crystal clear aperture, (2) obtaining the largest possible beam waist radii to reduce the peak intensities and (3) considering the limita- tions due to the availability of curved mirrors with different radii of curvature, limited the design options to a signal waist radius around 100 µm. A Gaussian beam propaga- tion model and the well-known ABCD matrix formalism [14] were used to model the ring resonator, which resulted in calculated beam waist radii (1/e2-intensity) of the sig- nal in the centre of the MgO:PPLN of 99.4 µm and 98.0 µm (parallel and perpendicular to the resonator plane) using curved mirrors (CM 1, CM 2) with a radius of curvature of−250 mm. The signal waist asymmetry in the two orthogonal resonator planes was caused by astigmatism due to the bow-tie angle of 10.2◦, which was necessary because
of mechanical limits set by the physical dimensions of mirror and crystal mounts. The signal focusing parameter was ξs ≈ 0.45, which deviates significantly from the ideal
case of ξs= 1, but this was again accepted in favour of reducing the peak intensities to
a minimum. The cavity model produced a total free-space section of 1.35 m for a stable ring resonator with the≈ 99 µm signal waist resulting in an arbitrary repetition rate of 222 MHz when neglecting the fibre section (with dummy mirror in the model). In order to obtain a good match of the signal and the pump inside the nonlinear crystal, a telescope with a 150 mm and a 200 mm lens and a 250 mm focusing lens formed the pump beam to generate a waist of 104 µm.
The feedback fibre covering the majority of the 41.72 m ring cavity optical path length (corresponds to 7.19 MHz) was a standard single-mode fibre (SMF 28e, Corning Inc., USA) for the telecommunications C-band around 1.55 µm, which coincides with the typical signal wavelength range of this SPOPO. To obtain synchronism with the pump pulse repetition rate, the fibre was inserted in the resonator and must have a physi- cal length of 41.72 m minus the free-space section and divided by the group index of a signal pulse in silica at the correct wavelength. The two fibre ends were positioned at points between CM 1 and the OC close to where the dummy mirror of the model was located, so that a good fibre launch efficiency could be achieved taking the propagation of the signal beam in the resonator into account. The beam radius at these points (as calculated by the model) was 0.5 mm. For a good launch efficiency, the numerical aper- ture (NA) of the focused beam going into the fibre core should ideally be equal to the NA of the fibre core, which is approximately 0.14 and corresponds to an angle of 8.05◦. Using simple trigonometry, a lens with a focal length of≈ 3.6 mm or larger is required to achieve an NA that matches 0.14. Aspherical lenses with f = 4.5 mm were chosen
Chapter 4. High-pulse-energy, compact, picosecond optical parametric oscillator 97 (L 1, L 2). Both the fibre input / output ends and the aspherical lenses were mounted on three-axis translation stage assemblies to allow for launch alignment on the input side and for beam collimation on the output side. Fibre throughput efficiencies, including launch efficiency and fibre loss, were typically around 50% as measured for the pump beam after it had passed through the cavity to the fibre (see figure4.1). As a first ap- proximation, the launch efficiency of the resonating signal was assumed to be similar to this, because the cavity model delivers a beam radius at the fibre input of around 0.4 mm for the pump compared to 0.5 mm for the signal, where both numbers yield NAs of 0.11 and 0.09, respectively, well within the NA limit of 0.14 of the fibre. Since the fibre section is relatively long and vital to achieve synchronism, accurate values of the refractive indices n(λ, T ) and group indices
ng(λ, T ) = n(λ, T ) − λ
dn(λ, T )
dλ (4.1)
were calculated with the temperature-dependent Sellmeier equation of such a single- mode fibre (GeO2-doped SiO2 core and pure SiO2 cladding) as given in [15]. The dis-
persion curves at 20◦C are shown in figure4.2(a). With the exact fibre core group index
of ng,core(1.504 µm, 20◦C) = 1.481738, which reflects how fast a signal pulse travels in-
side the fibre at this centre wavelength (given by the MgO:PPLN grating), a fibre length of 27.24 m was calculated. 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.44 1.46 1.48 1.50 1.52 1.44 1.46 1.48 1.50 1.52 R e f r a c t i v e I n d e x n / G r o u p I n d e x n g Wavelength [µm] n core n cladding n g,core n g,cladding (a) -250 -200 -150 -100 -50 0 50 100 150 200 250 I n t e n s i t y [ a . u . ] Time Delay [ps] (b)
FIGURE4.2: (a)Refractive index n(λ, T ) and group index ng(λ, T ) as a function of wavelength of a silica fibre. The group velocity of a pulse propagating in the fibre can be determined with the group index. The SiO2core is doped with GeO2to raise the refractive index, the cladding is pure SiO2.(b)Time delay of the reflected and resonating pump pulse. The red curve shows only the input pulse, while the black curve shows both the input pulse and the resonating pulse. The time delay was ≈ 90 ps here. The cavity length had to be tuned to shift the resonating pulse towards the input pulse to achieve synchronism as indicated by the arrow.
Coarse spatial alignment of the cavity was undertaken by exploiting the low-level, non- phase-matched second harmonic of the pump beam generated in the MgO:PPLN. Fine tuning to achieve synchronism was carried out by directing the pump pulse reflected from the curved surface of CM 1 and the weak pump pulse transmitted through CM 1
Chapter 4. High-pulse-energy, compact, picosecond optical parametric oscillator 98 after completing one round trip in the cavity onto a 32 GHz InGaAs photodiode and observing their mutual time delay on a 50 GHz communication signal analyzer (CSA). In order to get similar intensities for both pulses on the detector, the reflected beam from CM 1 was intentionally misaligned away from the centre of the sensitive area of the detector. It has to be taken into account that the group delay of a signal pulse is different to the group delay of a pump pulse and hence the described procedure only helps to obtain synchronism of the resonating pump pulse. However, the difference in cavity length between a pump pulse at 1.06 µm and a signal pulse at 1.504 µm was only a few millimetres as determined from the dispersion curves in figure4.2(a)and can readily be covered by movement of the translation stages along the signal beam path. Typical CSA traces are shown in figure4.2(b), where the red curve shows only the input pulse reflected from CM 1 and the black curve shows both the input pulse and the resonating pulse. The time delay in this case was roughly 90 ps. Thus, the cavity length had to be tuned by the corresponding length of 2.7 cm to shift the resonating pulse towards the input pulse to achieve synchronism as indicated by the arrow. The MgO:PPLN input and output surfaces were broadband AR-coated for the signal wavelength range and the pump wavelength. The curved mirrors, based on CaF2 sub-
strates, were highly transmissive at the pump wavelength and in the MIR, which led to singly resonant operation additionally supported by the fact that the SMF 28e fibre does not transmit MIR wavelengths. A large signal OC transmission of 90% provided effi- cient output power extraction and also ensured that relatively low power levels were propagating in the feedback fibre to avoid unwanted nonlinear effects. Nevertheless, it has been found experimentally that the fibre input side must be placed in a heat sink arrangement to avoid gradual damage of the end facet. Furthermore, the coiled fibre was enclosed in a box to reduce the sensitivity to ambient temperature fluctuations. Lenses L 1 and L 2 also had broadband AR coatings for the pump and the signal range.