David Shoemaker, Alain Brillet, C. Nary Man, and Olivier Cregut
Groupe de Recherches sur les Ondes de Gravitation, Bbtiment 104, Centre National de la Recherche Scientifique, 91405 Orsay, France
Graham Kerr
Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland
Received July 22, 1988; accepted March 30, 1989
We describe a frequency-stabilized diode-pumped Nd:YAG laser that is actively frequency stabilized relative to a
reference Fabry-Perot cavity using the Pound-Drever technique. We describe the servo loop and the measurement
of its noise and gain performance and demonstrate its ability to reduce the laser frequency noise close to the shot-
noise limit of 12.5 mHz/VIz. This corresponds to a linewidth of 1 mHz, well below the Schawlow-Townes limit of
0.13 Hz that applies for a free-running laser.
Laser sources exhibiting good short-term frequencystability are necessary in most schemes for the inter-ferometric detection of gravitational radiations 2 andin other precision metrology and spectroscopy experi-ments. The technique of stabilization to a referenceFabry-Perot cavity, either in transmissions or in re-flection4' 5 is well established and has been applied tovarious lasers (e.g., Ar,2 He-Ne,6 and dye7 lasers).Nd:YAG lasers showing good long-term passive stabil-ity have been demonstrated.8 We report here theapplication of the Pound-Drever technique toNd:YAG lasers and present a comparison between thecalculated and the measured signal-to-noise ratios forour system.
The laser consists of a linear cavity of 7.5 cm thatcontains the Nd:YAG crystal, an 6talon to select asingle longitudinal mode, a Brewster plate to select alinear polarization, and the output coupler. One endof the Nd:YAG crystal, which is pumped longitudinal-ly with a laser diode (SDL 2420), is coated for maxi-mum reflection at 1.06 Am and >90% transmission at807 nm (the pump wavelength); and other end is anti-reflection coated for 1.06 pm. The output coupler ismounted on a piezoelectric transducer to allow slowchanges in the length of the cavity to be corrected.The laser threshold is at 80 mW of pump power, andthe maximum single-frequency power at 1.06 ,gm is 20mW.
The fundamental source of laser frequency noise isspontaneous emission, which contributes a small butrandom phase jitter to the stimulated emission.9 Anestimate for the linear spectral density v measured inhertz/(hertz)1/2 of this white-noise source is given by'0
v = AV,42hvi/P, where Av, is the FWHM linewidth ofthe laser cavity, h is Planck's constant, v1 is the laserfrequency, and P is the total power lost from thecavity (output power plus losses). This is the Schaw-low-Townes limit for the frequency noise of a free-running laser. For the measurements presented hereone has v - 0.2 Hz/!Hz. For our research the linearspectral density of the frequency fluctuations is therelevant measure of this noise source, and it is also
the quantity most directly measured; however, to aidin comparison with other lasers one can calculate thelaser linewidth Av1 due to a white frequency noise,which is given byll Avi = Irp2. Thus, the laser fre-quency noise due to spontaneous emission can beexpressed as a total linewidth of the laser Avl - 0.13Hz.
The optical path for the frequency stabilization isindicated in Fig. 1. A Faraday isolator F is followedby an acousto-optic modulator AO, which serves as afast-frequency control element. An electro-opticmodulator EO impresses a 10-MHz phase modula-tion from the oscillator OSC onto the beam for thesystem of synchronous detection. A Fabry-Perotcavity FP is used as the frequency reference. Theincoming laser beam is closely matched to the TEMoomode of the reference cavity with lens L3. To reducethe coupling from transverse motions of the beaminto apparent frequency fluctuations the cavity iskept far from the degenerate case; thus excitation ofhigher-order modes in the cavity will not result in achange of the shape of the resonance curve (whichwould be possible if the cavity were close to, but notexactly, degenerate). The light reflected from thecavity is separated from the incoming beam with po-larization optics (polarizing beam splitter Pol andquarter-wave plate X/4) and falls onto the photodetec-tor PD.
YAG L1 F AO L2 EO L3 Pol X FP
, ~~~~~~~~~
2 H2 4
Fig. 1. Actively stabilized laser. Lenses L,, L2, and L3 arecollimating and matching lenses.
The calculated and the mlthe output of the mixer as a Iin frequency between the cincident laser light are show:cal form follows from a conence between the light direntrance mirror and the ligcavity. 4 "12 In normal operat:ity is used in the immediatnance. In this regime we clage at the output of the mixe
161 5,27Tv,= AP - iWM
7rc rjr 2
where Av is the difference belfrequency and the inciden2Fabry-Perot cavity has lengt](1 - rjr 2 ), the two mirrors hasof r1 and r2, and the entrancemission of T1. A fraction Amatched to the TEMoo modefunctions Jo(6) and J1(3) ha,phase-modulation strength acell. The photocurrent off rEthe net gain (in volts per anamplifier and the mixer MIXof the laser frequency fluctuaassumed that the frequency omuch greater than the cc/21, that the deviation frosmaller than Av,, and that hBessel function expansion ar
This sensitivity is to be cvoltage n,, resulting from the (todiode amplifier noise and ticurrent,
in = Gj/ 2e_(I
cn
(04-
en
M
-D
.50Ea-)0
2. 0
1. 0
0. 0
- 1. 0
-2. 0
- 40 - 20
F r-equen
Fig. 2. Error signal as a functThe solid curve is the superposeand the fitted analytical curve; ttinguishable. Also shown is a]pansion of the central part of thefitted analytical curve, and thedata points.
easured signal voltages of where e is the electron charge, lamp is the amplifierfunction of the difference noise expressed as an equivalent photocurrent, andavity resonance and the Imod is the photocurrent on resonance and with the 10-n in Fig. 2. The analyti- MHz modulation. The additional factor of a comes3ideration of the intefer- from the fact that the noise in the upper sideband andactly reflected from the the noise in the lower sideband are mixed down to the]ht stored in the optical same (positive) frequency and add incoherently.ion the Fabry-Perot cav- Fits to the experimental curves for both the demod-;e neighborhood of reso- ulated signal of Fig. 2 and the transmitted light inten-in derive the signal volt- sity allow an accurate determination of the experi-r, mental parameters rir 2 and I. To determine M the
(2VF\21 --1/2 transmitted light intensity for the TEMOO mode Ioo is'GlImax1 + , measured, as well as the sum all of the peaks E I,, of
the unwanted higher-order modes that are excited\thecvit/ resona when the laser frequency is scanned over one free
tween the cavity resonant spectral range of the reference cavity. Then M = Ioo/t light frequency. The (Ioo + L Imn), where typically 20 higher-order modesh 1 and finesse 5( = 7r/r 2 / make a measurable contribution. The photodiodeve amplitude reflectivities amplifier noise 'amp is determined by finding the zeromirror has a power trans- intercept of the linear relationship between the mea-l of the incident light is sured noise power (in volts squared per hertz) and theof the cavity. The Bessel photocurrent for a shot-noise-limited light source; theve as their argument the expected linear behavior is observed, ensuring that
impressed by the Pockels shot noise is correctly measured.esonance is Imax, and G, is For a typical measurement we have 1 = 0.18 m, M =ipere) of the photodiode 0.91, and rjr2 = 3.85 X 10-3 (and thus Y = 813, and AvP. The Fourier frequency = 1.1 MHz), 5 = 0.36, Imax = 0.614 mA, Imod = 0.279tions is VF. Here we have mA, and Iamp = 0.063 mA. Using the calculated values,f the phase modulation is for the signal and noise, one expects a unity signal-to-avity linewidth AvP = noise ratio for 12.5 mHz/!Hz.m resonance Av is much The sensitivity and noise can also be measured. Aigher-order terms in the calibrated frequency modulation at fhal = 50 kHz ise negligible. added to the voltage-controlled oscillator VCO (seecompared with the noise below), with the servo loops closed but with a unityquadratic sum of the pho- gain frequency of less than hal. This gives the sensi-ie shot noise of the photo- tivity in volts per hertz. To determine the noise the
light directly from the laser is put on the photodiode;d + lamp), the noise is measured at the mixer output for a photo-
mod amp X current equal to Imod* (An incandescent light sourcedrawing the same photocurrent Pmod gives the samenoise as the laser, indicating that the laser is shot-noise limited at 10 MHz.) This independent determi-nation of the unity signal-to-noise ratio yields a valueof 14.3 mHz/ Hz for the measurement above. Exten-sive experiments in which the finesse, the modulation,the matching, and the power were varied verify thatthe formulas for the signal and noise above describethe measurement system well. Special care has to betaken to ensure the linearity at every step of the detec-tion system in order to reach the close agreement ob-served (n 1.2 dB) between the calculated and the mea-sured signal-to-noise ratios.
The signal path for the servo system is indicated bythe solid curves in Fig. 2. Two loops are nested to
0. 0 20 40 obtain a combination of wide bandwidth and largedynamic range. The inner loop, consisting of the pho-
cy N nH z) todiode, the mixer, the amplifier GI, the filter H1, and
tion of the laser frequency. the voltage-controlled oscillator, uses the acousto-op-tion of the measured curve tic modulator as the control element; the principalhe two are effectively indis- limitation in the gain-bandwidth product of the servohundredfold horizontal ex- system is given by the delay T = 1.2 ,usec in this modu-curve; the dotted line is the lator. The outer loop takes its input from filter H,. Itcrosses are the measured consists of filter H2 and high-voltage amplifier G2 and
utilizes the piezoelectric transducer of the laser output
Fig. 3. Upper curve: the frequency noise, expressed as alinear spectral density, of the unstabilized laser. For fre-quencies greater than 10 kHz the noise is dominated by theSchawlow-Townes limit of 0.2 Hz/!Hz. Lower curve: thestabilized laser, measured at the error point of the servosystem.
coupling mirror as the control element. The laserfrequency can be controlled over approximately one-half free spectral range, or 500 MHz. Here the firstmechanical resonance of -3.3 kHz in the transducerlimits the gain-bandwidth product possible. The uni-ty-gain frequency of the inner loop is typically 120kHz, and the crossover frequency to the outer loop istypically 300 Hz. To take advantage of the limitedbandwidths available, the slope of the feedback net-work H, is 30 dB/octave at up to -1 kHz, and then it is18 dB/octave until the region of the unity-gain fre-quency, where it becomes 6 dB/octave; for H2 the slopeis maintained at 9 dB/octave. The gain of the com-bined loops at, for example, 1 kHz is of the order of 106(or 120 dB) and exceeds 109 at 10 Hz. The calculatedand the measured closed-loop transfer functions forfrequency fluctuations are in good agreement.
Figure 3 shows the frequency noise of the Nd:YAGlaser as measured at the error point of the servo sys-tem. The upper curve is the unstabilized noise; forthese measurements the shot-noise-limited noise floorof 12.5 mHz/!/z is indicated. Local mechanical andacoustic disturbances are responsible for the steep risefor frequencies less than -10 kHz. The relaxationoscillation results in a peak at -90 kHz. In the regionbetween 10 and 70 kHz the spontaneous-emission-induced laser frequency noise 0.2 Hz/!Hz dominates.The lower curve is the error point signal for the stabi-lized laser. While it is not an independent measure ofthe frequency fluctuations, this curve shows the sup-pression available with the servo system, which agreeswell with the predictions of the loop performance.The servo-loop performance is limited at frequenciesabove -10 kHz by the gain in the servo loop and atlower frequencies by the noise of the amplifier thatforms the summing junction for the servo loop. This
floor of 3 mHz! Hz is lower than the actual frequencynoise of the stabilized laser, which, for all frequencieslower than -40 kHz, cannot be less than the detectionnoise of 14.3 mHz/!Hz; however, the reduction of thenoise below the Schawlow-Townes limit of -200 mHz/Hz is perfectly feasible. If the frequency noise is
limited by the detection noise the resulting total laserlinewidth is of the order of Avl = 1 mHz.
The first steps toward a high-power, short-term,frequency-stable Nd:YAG laser have been made. Apractical system for a low-power reference oscillatorhas been demonstrated, which will be used to injectionlock13 a high-power Nd:YAG laser. The excellentagreement between the measured and the calculatedsignal-to-noise ratios for the detection system is reas-suring for the plans for laser-based gravitational wavedetectors and other critical applications of short-termstabilized lasers. Higher powers and narrower refer-ence-cavity linewidths will allow substantially bettershot-noise-limited performance if the gain bandwidthof the servo system is also increased; possible solutionsare the use of the electro-optic modulator for fastphase corrections 14 or the implementation of two cas-caded reference cavities.2
We thank R. Schilling of the Max-Planck-Institutfur Quantenoptik for his helpful comments concerningthe calculation of signal and noise. This research hasbeen partially sponsored by European EconomicCommunity stimulation grant ST2J-0093-2F.
References
1. R. Weiss, in Quarterly Progress Report, Research Lab-oratory of Electronics (Massachusetts Institute ofTechnology, Cambridge, Mass., 1972), Vol. 105, p. 54.
2. D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K.Maischberger, and A. Ruidiger, Phys. Rev. D 38, 423(1987).
3. D. Hils and J. Hall, Rev. Sci. Instrum. 58, 1406 (1988).4. A. Schenzle, R. DeVoe, and G. Brewer, Phys. Rev. A 25,
2606 (1982).5. R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A.
Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).6. C. Salomon, D. Hils, and J. Hall, J. Opt. Soc. Am. B 5,
1576 (1988).7. J. Helmcke, S. Lee, and J. Hall, Appl. Opt. 21, 1686
(1982).8. T. Kane, A. Nilsson, and R. Byer, Opt. Lett. 12, 175
(1987).9. A. Schawlow and C. Townes, Phys. Rev. 112, 1940
(1958).10. A. Yariv and W. Caton, IEEE J. Quantum Electron. QE-
10,509 (1974).11. F. Hartmann and F. Stoeckel, J. Phys. (Paris) 39, C1-32
(1978).12. M. Houssin, M. Jardino, B. Gely, and M. Desaintfuscien,
Opt. Lett. 13, 823 (1988).13. C. N. Man and A. Brillet, Opt. Lett. 9, 333 (1984).14. J. Hall and T. Hansch, Opt. Lett. 9, 502 (1984).
