Chromium Light Source
C.1.2 Cavity length stabilization
As illustrated in Figure C.2, Pound-Drever-Hall stabilization [111] is used to keep the fundamental laser light on resonance with a cavity mode. By applying feedback both to the cavity length on long timescales and to the laser fre-quency on short timescales, a locking bandwidth of about 1 MHz is achieved.
It is required to compensate for the various noise sources in a buffer-gas load-ing experiment, like acoustic interferences from pumps or mechanical impulses
Function generator 5MHz
phase lock
PZT
AC DC
R
L I
Optical system
Bias-T
Current FET
Frequencymodulation Fastfrequencyfeedback
HV loop amplifier P, I
-10V { 45V Low pass
160Hz
High BW amplifier P
Gain BW 30MHz¢
Figure C.2: Cavity locking scheme.
174 CHROMIUM LIGHT SOURCE
1 2 3 4 5 6 7 8 9 10
-180 -90 0 90 180
Phase[deg]
Frequency [kHz]
-95 -90 -85 -80 -75 -70 -65
Amplitude[dB]
7.11 kHz
Figure C.3:Frequency response of the cavity piezo. The curve was obtained from a network analyzer (SRS Model SR780) driving the piezo with a sine wave and letting the mounted mirror cut through a laser beam hitting a photodiode. Its signal, which then is a measure for the piezo’s expansion, is fed back into the network analyzer and processed to yield the above plot.
carried over the optical table from the ablation laser.
The Pound-Drever-Hall error signal is obtained by a modulation of the laser frequency at 5 MHz and subsequent phase-sensitive dedection of the cavity-reflected beat signal. After appropriate low-pass filtering, one part of the error signal is sent via a high voltage amplifier providing P and I gain to a piezoelectric transducer carrying one of the flat cavity mirrors to accordingly adjust the cavity length. The other part drives a high-bandwidth proportional amplifier (AD817) with a measured gain-bandwidth-product of 30 MHz. Its output is connected to a laser integrated FET current drain board, which allows to control the laser frequency with a maximum bandwidth of 20 MHz.
For a robust lock, the proper balancing of the individual gains is essential.
They set the cross-over point of the two feedback paths, which ideally should be close to the maximum piezo bandwidth. This is limited by its first mechanical resonance, where the phase response crosses the 90 degrees limit. To keep it as high as possible, the piezoelectric transducer has been glued into a massive, adjustable stainless steel holder. As Figure C.3 demonstrates, the first relevant resonance was thereby pushed to 7.11 kHz. Any higher frequency noise has thus to be taken out by the faster laser frequency feedback loop. The corresponding optimal gain adjustments are usually found experimentally.
PHASEMATCHING 175
C.2 Phasematching
The phasematching curve describes the dependence of the second-harmonic power on the crystal temperature. In the plane-wave limit, it ideally follows a sinc2-shape, which also can serve as a good approximation for Gaussian beams in a lot of cases.Phasematchingoccurs when the refractive indices of the employed nonlinear crystal are the same for the fundamental and the second-harmonic wave, so that they stay in phase over the complete length of the crystal. The conversion efficiency then is maximal. Deviations of the phasematching curve from the ideal shape are a very sensitive indicator to problems in the conversions process. They might originate from misalignment, corrupted optical surfaces, incorrect polarization, thermal effects in the crystal etc.
An experimental phasematching curve taken for this setup is shown in Figure C.4 along with a sinc2-fit to low output power values (P425 nm <2 mW). The data belongs to a fundamental power of 40 mW measured directly in front of the cavity at a wavelength of 851.1015 nm (11749.48 cm−1). Even though the changing temperature appreciably affects the position of the cavity modes, the cavity lock did not fail once during the whole data taking process.
While the fit reproduces the wings of the curve with considerable accuracy, the actual output power on phasematching stays behind the extrapolation by a factor of ∼2. This is expected to be a result of the deteriorating impedance matching, when the increasing efficiency of second-harmonic generation leads to a higher round-trip loss of the resonating fundamental wave in the cavity.
An additional effect might emerge from a local increase in crystal temperature through blue-light or blue-light induced infrared absorption (BLIIRA), that affects the phasematching condition at the position of the beam. This however would also cause an asymmetry in the phasematching curve, which has not been
1 2 3 4 5 6 7
0 1 2 3 4 5 6
Outputpower[mW]
Crystal temperature [Celsius]
Figure C.4: Experimental phasematching curve for SHG of 425 nm light.
176 CHROMIUM LIGHT SOURCE observed. Since also the second-harmonic powers are relatively low, thermal effects from absorption should thus be of minor importance here.
The fit yields a phasematching temperature of 4.00C, while predictions from published Sellmeier equations are in the range of 7C [124]. Again, the deviation might be explained with local heating of the crystal due to absorption of the fundamental or the second-harmonic wave. It is much more likely, though, that the calculated value suffers from an inaccuracy in the extension of the Sellmeier equation into this temperature region.
Residual fundamental light exiting the cavity leads to an offset of 0.43 mW in the measured second-harmonic powers. Its fraction is however further reduced on its way to the experimental cell to a negligible level by additional optics optimized for 425 nm.