Frequency stabilization of the non resonant wave of a continuous-wave singly resonant optical parametric oscillator
aa r X i v : . [ phy s i c s . op ti c s ] M a r Frequency stabilization of the non resonant wave of a continuous-wave singly resonantoptical parametric oscillator
Aliou Ly , Benjamin Szymanski , and Fabien Bretenaker ∗ Laboratoire Aim´e Cotton, CNRS-ENS Cachan-Universit´e Paris Sud 11, 91405 Orsay Cedex, France Blue Industry & Science, 208 bis rue la Fayette, 75010 Paris, France (Dated: July 11, 2018)We present an experimental technique allowing to stabilize the frequency of the non resonantwave in a singly resonant optical parametric oscillator (SRO) down to the kHz level, much belowthe pump frequency noise level. By comparing the frequency of the non resonant wave with areference cavity, the pump frequency noise is imposed to the frequency of the resonant wave, and isthus subtracted from the frequency of the non resonant wave. This permits the non resonant waveobtained from such a SRO to be simultaneously powerful and frequency stable, which is usuallyimpossible to obtain when the resonant wave frequency is stabilized.
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I. INTRODUCTION
Continuous – wave (CW) optical parametric oscilla-tors (OPOs) are versatile sources of coherent light. Theypermit to reach single – frequency operation on a verybroad wavelength tuning range, and multi-Watt outputpower, which makes them well suited for applications toatomic physics [1, 2] and high resolution molecular spec-troscopy [3], among other applications [4]. Concerningtheir output power, singly resonant OPOs (SROs) havelong been sought for their high efficiency, as predictedby earliest theoretical studies [5, 6]. Indeed, in the planewave approximation, a 100 % conversion efficiency is pre-dicted for pumping at ( π/ times above the oscillationthreshold. This theoretical limit was almost reached witha CW SRO based on a periodically poled lithium niobate(PPLN) crystal for which the authors reported 93 % ofpump depletion [7]. In most cases, the optimization ofthe output power depends on the choices of the crys-tal length and mirror reflectivities for a given availablepump power. A recent example shows that a low thresh-old is not necessarily the best way to obtain a high outputpower, even for the non resonant beam (idler) [8].Besides, SROs are also extremely attractive for theirfrequency noise properties. In particular, it has beenshown that the frequency noise of the pump can bedumped to the wave which is not resonant inside thecavity [9]. By locking the frequency of the resonant waveat resonance with a high finesse resonator, this has al-lowed to stabilize this frequency down to the kHz level[10, 11], i. e., well below the linewidth of the pump laser.The problem then is that the output power obtained fromthe resonant wavelength is usually quite small, i. e. wellbelow 1 W for pump powers of several Watts. Indeed,the converted pump power is mostly extracted by thenon resonant wave which carries the pump noise. Thisproblem has received quite some attention. For exam- ∗ Electronic address: [email protected] ple, extracting some power from the wave resonant inthe cavity can be performed by using an optimized out-put coupler such as a dielectric coating mirror [2, 13] ora volume Bragg grating [14]. Another method consists ininserting a plate inside the cavity at an incidence angleclose to the Brewster angle in order to ensure a small butadjustable amount of output coupling [15].However, in spite of the partial success of these demon-strations, it would be extremely desirable to be ableto stabilize the frequency of the non resonating wave.This would allow us to benefit from the two main ad-vantages of SROs – efficient conversion and extremelysmall linewidth – in the same wave. To this aim, we ex-plore here the possibility to add to the resonant wave theamount of frequency noise that would allow it to mimicthe frequency fluctuations of the pump. Then, thanks toenergy conservation during the parametric process, thefrequency of the non resonant wave should be immune ofnoise. We thus describe in the following how we imple-mented such a stabilization technique and the obtainedresults.
II. PRINCIPLE OF THE FREQUENCYSTABILIZATION SCHEME
The principle of the frequency stabilization schemetested here is schematized in Fig. 1. In such a paramet-ric oscillator, the energy conservation between the threebeams reads ω p ( t ) = ω r ( t ) + ω nr ( t ) , (1)where ω p , ω r , and ω nr are the instantaneous frequenciesof the pump, the wave resonant in the cavity (which canbe the signal or the idler), and the non resonant wave(idler or signal, respectively). We suppose that thesefrequencies vary with time, i. e., contain noises, andthat the instantaneous frequencies of these noises are slowenough, compared to the OPO oscillation building time,for eq. (1) to be instantaneously satisfied. Now, the fre-quency of the resonant wave is constrained to be resonant PUMP
RESONANT
NON RESONANT
V(t)
PUMP
RESONANT
NON RESONANT
V(t)
PZT
PZT
STABILIZATION OF THE RESONANT WAVELENGTH
STABILIZATION OF THE NON RESONANT WAVELENGTH (a) (b)
FIG. 1: Principle of the stabilization of the frequency of aSRO. (a) The frequency of the resonant wave is stabilized andthe pump frequency noise is transferred to the non resonantone. (b) The frequency of the non resonant wave is stabilizedby imposing the pump frequency noise on the resonant one. in the cavity of optical length L , leading to: ω r ( t ) = 2 πp cL ( t ) , (2)where p is an integer.Let us then consider the configuration of Fig. 1(a),which corresponds to the stabilization scheme developedin Refs. [9, 10]. In order to stabilize the frequency ofthe resonant wave, the cavity length L in eq. (2) mustbe kept as stable as possible. According to eq. (1), thefrequency fluctuations δω p ( t ) of the pump are transferredto the non resonant wave only: δω nr ( t ) = δω p ( t ) , (3) δω r ( t ) = 0 . (4)As stated in the introduction, this scheme has been verysuccessful in stabilizing the frequency of the resonantsignal. However, the wave that carries the largest out-put power, i. e. the non resonant one, receives all thepump noise. Conversely, if now we want to stabilize thefrequency of the non resonant wave, as schematized inFig. 1(b), eqs. (3) and (4) become: δω nr ( t ) = 0 , (5) δω r ( t ) = δω p ( t ) . (6)Eq. (2) thus shows that some noise δL ( t ) must be intro-duced in the cavity length for the frequency noise of theresonant wave to mimic the pump one: δL ( t ) L = − δω r ( t ) ω r = − δω p ( t ) ω r . (7)This is the scheme which is implemented in the experi-ment described below. MgO:PPSLT
Pump
Idler
Signal
Reference level
Loop
Filter P ZT + - FP L HVA (1.2-1.4 µ m) DM Absorber (850-
950 nm)
BPF PM PD PM Etalon
FIG. 2: Experimental setup. HVA: high-voltage amplifier.PZT: piezoelectric transducer. PD: Photodiode. L: focusinglens. FP: Fabry-Perot cavity. DM: Dichroic Mirror. BPF:Bandpass Filter. NPBC: Non Polarizing Beamsplitter Cube.PM: Power Meter.
III. EXPERIMENTAL SETUP
The experimental setup is depicted in Fig. 2. TheOPO, which is similar to the one used in Ref. [10], ispumped at 532 nm by a cw 10 W single-frequency Co-herent Verdi laser and is based on a 30-mm long MgO-doped periodically poled stochiometric lithium tantalate(PPSLT) crystal ( d eff ≃
11 pm / V) manufactured andcoated by HC Photonics. This crystal contains a singlegrating with a period of 7.97 µ m and is anti-reflectioncoated for the pump, the signal, and the idler. It is de-signed to lead to quasi-phase matching conditions for anidler wavelength in the 1200-1400 nm range, dependingon the temperature. The OPO cavity is a 1.15-m longring cavity and consists in four mirrors. The two mirrorsthat sandwich the nonlinear crystal both have a 150 mmradius of curvature. The two other mirrors are planarwith one of them acting as an output coupler for theresonant wave. All mirrors are designed to exhibit a re-flectivity larger than 99.8 % between 1.2 µ m and 1.4 µ mand a transmission larger than 95 % at 532 nm and be-tween 850 nm and 950 nm. This allows the OPO to besingly resonant, with the resonant wave of Sec. II beingthe idler. The estimated waist of the idler beam at themiddle of the PPSLT crystal is 37 µ m. The pump beamis focused to a 53 µ m waist inside the PPSLT crystal.A 150 µ m thick uncoated Nd:YAG ´etalon is insertedin the second waist of the cavity to ensure stable single-frequency operation of the OPO. Heating the PPSLTcrystal at T=100 ◦ C, we measure, with a spectrometer(AvaSpec 2048-2) not represented here, an idler wave-length of 1213 nm and a signal wavelength of 947 nm. S i gn a l O u t pu t P o w e r ( W ) Pump Power (W)
FIG. 3: Measured evolution of the signal output power versuspump power.
The OPO threshold corresponds to an input pump power P (in)p = 500 mW. The evolution of the signal outputpower versus pump power is reproduced in Fig. 3. Onecan clearly see that the extracted pump power is mainlyconverted to non resonant signal, leading to an outputpower larger than 1 Watt.The OPO output beams are collimated with a 300 mmfocal length lens, not represented in Fig. 2. The dichroicmirror separates the pump from the signal beam. Thepump power P (out)p at the output of the OPO is measuredto evaluate the pump depletion η = 1 − P (out)p /P (in)p .Since the dichroic mirror is not perfect, we introduce abandpass filter centered at 950 nm, with a bandwith of10 nm, on the signal path, to make sure that only thesignal is sent into the Fabry-Perot cavity.In order to optimize the frequency locking of the OPO,we first perform a measurement of the frequency noisespectrum of the non resonant signal beam. To this aim,we use a low finesse Fabry-Perot cavity as a frequencyto intensity noise converter [9]. This first cavity has a750 MHz free spectral range and a finesse F = 28 at thesignal wavelength of 947 nm. The OPO signal frequencyis tuned the side of the transmission peak of this anal-ysis cavity, and the transmitted signal is recorded dur-ing 1 s using a deep memory oscilloscope. A fast Fouriertransform algorithm is then used to retrieve the frequencynoise spectrum of the non resonant signal, which is repro-duced in Fig. 4. This measurement has been obtained fora pump power P (in)p = 2 . η = 80 % and a signal power of the or-der of 800 mW. This spectrum reproduces fairly well thespectrum of the pump frequency noise [9], showing thatthe pump noise is transferred to the non resonant signal.Integrating this noise power spectral density over all fre-quencies, we obtain a RMS frequency noise of 1.3 MHz. Frequency (Hz) N o i s e PS D ( H z / H z ) Free running OPO
FIG. 4: Single-sided power spectral density of the frequencynoise of the non resonant signal obtained from the free runningSRO.
Moreover, we checked that the contributions of the de-tection noise and the signal intensity noise are negligi-ble. The spectrum of Fig. 4 shows that the frequencynoise essentially lies at low frequencies (below 1 kHz),thus validating the hypothesis of eq. (1). The plateauobserved above 1 kHz corresponds to the detection limit,which is pretty high due to the relatively poor linewidth( ≈
27 MHz) of the cavity.In order to stabilize the frequency of the non resonantsignal wave, we must apply the noise measured in Fig. 4to the cavity length, in order to satisfy eq. (7). To do thiswith a better signal-to-noise ratio than the one of Fig. 4,we turn to a Fabry-Perot cavity with a better linewidth.This reference cavity has a free spectral range of 1 GHzand a finesse F = 100 at 947 nm, leading to a linewidthof the order of 10 MHz. In order to build the error signalthat will drive the cavity length variations, the intensityat the output of the cavity is detected, and the corre-sponding signal is subtracted from a reference voltage.This reference voltage is adjusted in such a way that azero error signal corresponds to the situation where thesignal frequency is tuned half way between the minimumand the maximum transmission of the cavity, where thecavity response is almost linear and exhibits a maximumslope [16]. The error signal is filtered by a proportional-integral (PI) loop filter, amplified through a high-voltageamplifier, before being applied to a piezoelectric trans-ducer (Piezomechanik model PSt 150/10x10/2) carryingone the cavity planar mirrors (see Fig. 2).To lock the OPO signal frequency, we set the PI cor-ner frequency of the servo controller at 10 kHz. In theseconditions, once the loop is closed, we record the errorsignal during 1 s and process it in the same way as beforein order to retrieve the power spectral density of the fre-quency noise of the OPO signal. The result is reproducedin Fig. 5.By comparing Figs. 4 and 5, we see that the low fre-quency noise is reduced by 8 orders of magnitude whenthe SRO is locked. This leads to a nearly white frequency Frequency (Hz) N o i s e PS D ( H z / H z ) Locked OPO
FIG. 5: Single-sided power spectral density of the frequencynoise of the non resonant signal obtained from the frequencylocked SRO. noise in the considered frequency domain. The remainingsmall peaks, at frequencies between 100 Hz and 1 kHz,are probably due to electrical perturbations and/or tothe fluctuations of the pump frequency. However, thereis a remarkable peak around the 4 kHz frequency whichreaches almost 10 Hz / Hz. This peak probably comesfrom the fact that the loop becomes unstable at such fre-quencies, and could probably be suppressed by a bettermanagement of the servo-loop phase. By integrating thisnoise power spectral density from 1 Hz to 30 kHz, we ob-tain a RMS frequency noise of 7.3 kHz. This value hasto be compared with the value of 1.3 MHz obtained pre-viously for the pump laser and the spectrum of Fig. 4.The important conclusion of this result is that we wereable to dump the frequency noise of the pump into theresonant wave, as expected from eqs. (5,6).In order to have an idea of the signal linewidth, wehave also numerically calculated its spectrum when theOPO is in the free running mode and when it is locked.This is performed by neglecting the OPO intensity noiseand by calculating the auto-correlation of the field E ofthe OPO signal using the following expression [17]: R E ( τ ) ∝ exp (cid:20) − Z ∞−∞ S ν ( f ) 1 − cos(2 πf τ ) f d f (cid:21) , (8)where S ν ( f ) is the power spectral density of the fre-quency noise. By injecting the results of Figs. 4 and 5 intoeq. (8) and performing the Fourier transform of R E ( τ ),we obtain the laser spectra of Figs. 6 and 7, respectively.The spectrum of Fig. 7 has a Lorentzian lineshape,which is consistent with the fact that the correspond-ing frequency noise spectra is almost white (see Fig. 5).Moreover, we can see that by adding noise to the reso-nant wave, we have been able to decrease the linewidthof the non resonant signal by more than three orders ofmagnitude, down to the kHz domain. −6 −4 −2 0 2 4 600.10.20.30.40.50.60.70.80.91 Frequency(MHz) I n t e n s it y ( a . u . ) Free running OPO 3 MHz
FIG. 6: Lineshape of the non resonant signal of the SRO inthe free running mode. −100 −80 −60 −40 −20 0 20 40 60 80 10000.10.20.30.40.50.60.70.80.91
Frequency(kHz) I n t e n s it y ( a . u . )
13 kHzLocked OPO
FIG. 7: Lineshape of the non resonant signal of the SRO inthe locked mode.
IV. CONCLUSION
In conclusion, we have demonstrated, for the first timeto our knowledge, the possibility to lock the frequency ofthe non resonant wave of a singly resonant OPO down toa frequency noise much lower that the pump frequencynoise. This technique opens interesting potentialities inorder to obtain both high power and spectrally pure out-put, contrary to the use of the resonant wave which canprovide only much lower output powers. The presentexperiment, which aimed at demonstrating the validityof the approach, led to a power of the order of 1 Wattwith a relative noise corresponding to a linewidth of theorder of 10 kHz. Future steps will include the optimiza-tion of the OPO cavity losses in order to obtain severalWatts of output power, as evidenced in Ref. [18], togetherwith the development of a Pound-Drever-Hall stabiliza-tion scheme with a higher finesse cavity [10, 19, 20] inorder to reach the sub-kilohertz linewidth level for thenon resonant wave. [1] S. Zaske, D.-H. Lee, C. Becher, Appl. Phys. B: LasersOpt. , 729 (2010).[2] P. Gross, I. D. Lindsay, C. J. Lee, M. Nittmann, T.Bauer, J. Bartschke, U. Warring, A. Fischer, A. Keller-bauer, K.-J. Boller , Opt. Lett. , 820 (2010).[3] E. V. Kovalchuk, D. Dekorsy, A. I. Lvovsky, C. Brax-maier, J. Mlynek, A. Peters, S. Schiller, Opt. Lett. ,1430 (2001).[4] I. Breuning, D. Haertle, K. Buse, Appl. Phys. B: LasersOpt. , 99 (2011).[5] L.B. Kreuzer, in Proc. Joint Conf. Lasers and Opt.-Elect. (1969), p.52.[6] S.E. Harris, Proc. IEEE , 2096 (1969).[7] W.R. Bosenberg, A. Drobshoff, J.I. Alexander, L.E. My-ers, R.L. Byer, Opt. Lett. , 1336 (1996).[8] R. Sowade, I. Breunig, J. Kiessling, K. Buse, Appl. Phys.B: Lasers Opt. , 25 (2009).[9] O. Mhibik; T.-H. My, D. Pabœuf, F. Bretenaker, C.Drag, Opt. Lett. , 2364 (2010).[10] O. Mhibik, D. Pabœuf, C. Drag, F. Bretenaker, Opt.Express , 18047 (2011).[11] E. Andrieux, T. Zanon, M. Cadoret, A. Rihan, J.-J. Zondy, Opt. Lett. , 1212 (2011).[12] C.R. Phililips, M.M. Fejer, J. Opt. Soc. Am. B , 2687(2010).[13] G. K. Samanta, M. Ebrahim-Zadeh, Opt. Express ,6883 (2008).[14] M. Vainio, M. Siltanen, T. Hieta, L. Halonen, Opt. Lett. , 1527 (2010) .[15] D. Pabœuf, O. Mhibik, F. Bretenaker, C. Drag, Appl.Phys. B: Lasers Opt. , 289 (2012).[16] W. Vassen, C. Zimmermann, R. Kallenbach, T. W.H¨ansch, Opt. Commun. , 435 (1990).[17] N. Uehara, K. Ueda, Appl. Phys. B: Lasers Opt. , 9(1995).[18] T.-H. My, C. Drag, F. Bretenaker, Opt. Lett. , 1455(2008).[19] R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G.M. Ford, A. J. Munley, H. Ward: Appl. Phys. B: LasersOpt. , 97 (1983).[20] Ch. Salomon, D. Hils, J. L. Hall, J. Opt. Soc. Am. B5