UV Laser Source
4.5 Set-up of the Cavity
4.6.2 Set-up of the Feedback Loops
where we the interference terms between carrier and sidebands can-cel each other and terms withδ2 were dropped.
We see that the phase modulation of the input field gets converted into amplitude modulation in the output.
The RF signal of the photodiode is mixed (electronically multiplied) Mixer with the signal of the local oscillator, which is phase-locked to the
laser modulation signal, and is then send through a low-pass filter.
Sweeping the phase relation between the local oscillator and the modulation signal we obtain either the sine (absorption) or the cosine (dispersion) term. In any case the signal changes its sign when the carrier frequency passes the resonance. Therefore the
signal is called error signal and gives direct information whether Error signal the carrier is below or above the resonance of the cavity. The error
signal is used in a feedback loop to control either the laser frequency or the cavity length to retain resonance.
The phase between the local oscillator and the demodulated photo-diode output is chosen to be ∆Φ = 0: on resonance, the error signal then shows the steepest gradient and thus provides the highest ef-ficiency of the feedback loop. The capture range of the feedback loop is twice the modulation frequency.
4.6.2 Set-up of the Feedback Loops
For both frequency locks the phase-modulation technique of Pound, Drever, and Hall [95] is used. The light reflected from the incou-pling mirror is spectrally decomposed via a diffraction grating and detected by fast radio frequency photodetectors (typeFND100), as shown in Fig. 4.12.
To stabilize the cavity to the 532 nm light, the master oscillator is Modulation frequencies phase modulated at 3.2 MHz via a piezotransducer mounted on the
Nd:YAG crystal. Due to the non-resonant set-up of the frequency doubling, this modulation is transferred to the 532 nm light. Phase modulation of the diode laser frequency is obtained by modulation of the diode current at 20 MHz using a bias-tee input connector directly at the diode laser head.
To achieve stable locks it is important to maximize the bandwidth Optimizing gain
& bandwidth of the feedback loops for efficient correction of fast disturbances on
313 nm
phase lock
phase lock
mixer
mixer
1064 nm 532 nm
760 nm
piezo actuator
optical grating
servo
servo modulation
modulation
local oscillator
local oscillator
frequency control
slow (grating) fast (current)
Nd:YAG
Diode laser (ECL)
SHG PPLN (6 cm)
PD2 PD1
Mod.
Mod.
LBO
Figure 4.12: Set-up of the lasers and the feedback circuits of the doubly-resonant SFG apparatus. Lenses and waveplates are skipped for simplicity. PD: RF photodiodes (type FND 100).
the one side, and to provide a high gain at low frequencies to com-pensate slow drifts on the other side. The servos of both frequency locks contain an integrator circuit, which provides high (theoreti-cally infinite) gain to compensate slow (static) drifts.
However, if the gain of the feedback loop is too high above a certain frequency, the feedback loop starts oscillating. The maximal pos-sible bandwidth is limited by the mechanical and electronic prop-erties of the controlled module. A piezoelectric transducer (e. g.
either the one that controls the cavity length, or the one that
con-4.6 Stabilization 93
trols the diode laser frequency via the grating) shows resonances at certain frequencies. The first significant resonance usually limits the maximum bandwidth (unless a notch filter is used to suppress the resonance). Mechanical stabilization of the cavity and adding additional metal plates to the mirror mount in particular helps to shift the first resonances to at least well above 10 kHz. A measure-ment of amplitude and phase response of our cavity piezo is shown in Fig. 4.13.
frequency [Hz]
amplitude[dB] phase [°]
500 -110
-90 -70 -50 -30
0 90
-90 -180 180
1000 10000 40000
frequency [Hz]
500 1000 10000 40000
Figure 4.13: Transfer function of the piezo controlling the cavity length Apart from the amplitude response, the phase response can be used to judge the behavior more quantitatively. An oscillation of the feedback loop occurs if the total phase shift of the feedback loop at a certain frequency fcritical is more than 180◦ and the gain at fcritical is higher than 1. Then, any small disturbances atfcriticalwill be “compensated” by the feedback loop with delay of 180◦ which causes enhancement instead of suppression of the disturbance, and the loop starts oscillating.
Balancing the piezo mount with heavy weights in our particular set-up could shift the first resonance frequency from 8 kHz to 18 kHz.
Furthermore, to damp environmental disturbances the top sides of the cavity mirror mounts are attached to each other via metal bars.
Pictures of the cavity before and after mechanical stabilization are shown in Fig. 4.14.
The bandwidth of the integrating cavity length servo is 10 kHz. Bandwidth
Figure 4.14: Pictures of the bow-tie cavity, compare figure 4.7. Since the intensity of the green light (and the human eye’s sensitivity) is con-siderably higher than the other colors, the path of the light in the cavity appears green. Left: Set-up before mechanical stabilization seen from the top. Right: Side view after mechanical stabilization.
The frequency of the diode laser is controlled by two circuits: a Two feedback
channels acting on the diode laser
slow, integrating channel with high gain at low frequencies acting upon the external grating (bandwidth 3 kHz) (→4.4.2), and a fast channel acting directly upon the current of the diode (bandwidth 200 kHz).
The wiring of the diode laser set-up is rather extensive. The diode laser is controlled by four sources.
• Main DC supply.
To avoid output power noise this source is filtered using a large capacity, and is hence not suitable to add a fast modulation.
• Phase modulation input.
This input is coupled into the diode current using a bias-tee.
• Fast feedback on the diode current for the frequency lock.
This input is attached to the gate of a field-effect transistor, which is connected parallel to the diode. The voltage applied to the gate makes the FET shunt some of the current from the diode.
• The piezo controlling the external grating.
To obtain a wide tunability, the diode current needs to be cor-rected when the grating is tilted. Therefore a certain amount of the voltage applied to the piezo is fedforward to the diode current. This is achieved via the DC input, since a large bandwidth is not of concern.
More about feedback circuits is found in [68, 98, 99, 100]