Semiconductor lasers stabilized to spectral holes in rare earth crystals to a part in 1013 and their...

Journal of Luminescence 98 (2002) 309–315

Semiconductor lasers stabilized to spectral holes inrare earth crystals to a part in 1013 and

their application to devices and spectroscopy

G.J. Prydea, T. B .ottgera,*, R.L. Conea, R.C.C. Wardb

aPhysics Department and The Spectrum Lab, Montana State University, Bozeman, MT 59717 USAbClarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK

Abstract

Single-frequency diode lasers have been stabilized to 200Hz at 1.5 mm and independently to 20Hz at 793 nm over

10-ms integration times using narrow spectral holes in the absorption lines of Er3+- and Tm3+-doped cryogenic crystals

as frequency references. Kilohertz stability over 100-s integration times is provided by these techniques, and that

performance should be extendable to long integration times with further development. The achieved frequency

stabilization provides ideal lasers for high-resolution spectroscopy in the time and frequency domains, real time analog

optical signal processing based on spatial-spectral holography, interferometry, and other applications requiring ultra-

narrow-band light sources or coherent detection. The stabilized lasers have enabled demonstrations of analog optical

signal processing in Er3+ materials at 0.5GHz bandwidths at temperatures of 4.2K, and they will be important

for electromagnetically induced transparency and quantum information demonstrations. r 2002 Elsevier Science B.V.

All rights reserved.

PACS: 42.60.Lh; 42.62.Fi; 06.30.Ft

Keywords: Spectral hole burning; Laser stabilization; Rare earth; Er3+; 1.5mm wavelength

1. Introduction

The concept of a spectral hole as a frequencyreference for a stabilized laser finds its mostobvious realization with persistent spectralholes. Demonstrations of diode laser frequencystabilization have been made to persistent holes in

Er3+- or Tm3+-doped CaF2:D� and provide

stabilities of 700Hz for integration times of100ms–10 s [1,2].

For SHB device applications using materialsoptimized for correlators or memories, stable lasersources are required at specific wavelengthsand with stability over material-dependent timescales. We have demonstrated that frequencyreferences meeting these requirements are auto-matically provided by using a spectral hole in aseparate piece of the SHB correlator or memorymaterial to provide the frequency reference for

*Corresponding author. Tel.: +1-406-994-2443; fax: +1-

406-994-4452.

E-mail address: [email protected]

(T. B .ottger).

0022-2313/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 0 2 2 - 2 3 1 3 ( 0 2 ) 0 0 2 8 5 - 5

laser stabilization. Regenerative transient (lifetimelimited) spectral holes with kHz widths in anumber of Er3+- and Tm3+-doped materialshave provided excellent performance [3–7], andlasers stabilized to Tm3+:YAG and Er3+:Y2SiO5

have been successfully transferred to SHB corre-lator devices at The Spectrum Lab. These materi-als have produced stabilities as good as 20Hz [3].Our latest results for Er3+:KTP are presentedbelow.

These transient SHB materials provide a funda-mentally different type of frequency referencefrom Fabry–Perot cavities or isolated atomicreferences, because the laser can modify thespectral hole reference. This interplay ofthe dynamics of materials and the stabilizationprocess has been investigated numerically andexperimentally, and these results have been usedto optimize the system performance. Thehole width, hole lifetime and rate of spectraldiffusion govern performance of the referencein different noise regimes and over differentintegration times. In particular, the hole lifetimetypically dictates the integration time scale of beststability and the performance over long integra-tion times. For integration times shorter than thehole lifetime, the hole width is the criticalparameter.

Gated SHB materials for portable secondaryfrequency standards are under development. Someof those developments are described in anotherpaper in this volume [8]. Photoemission spectro-scopy has been used to locate the sharp rare earthlevels relative to the host valence and conductionbands, in order to optimize design of systems fortwo-photon photoionization gating. Materialparameters for persistent hole burning materialslike deuterated CaF2 are being optimized [9].Likewise, development of better hole burningmaterials for time domain analog optical signalprocessing improves performance of regenerativehole burning frequency references.

Stabilization to spectral holes is applicable todistributed feedback lasers and other types oflasers and to other transducers like acousto-opticor electro-optic frequency shifters. Mode lockedlasers may also be stabilized to a comb of spectralholes.

2. Laser stabilization to spectral holes in

Er3+:KTP

Potassium titanyl phosphate, KTiOPO4 (KTP),is an important nonlinear electro-optic materialprimarily used as a frequency doubling crystal andfor optical waveguides. Here we report theachievement of 200Hz laser stabilization utilizingEr3+:KTP with an Er3+ concentration of0.004 at% as a spectral hole burning frequencyreference. The crystal was grown at the ClarendonLaboratory of the University of Oxford and wasoriented with its a-axis parallel to an externalmagnetic field and its b-axis parallel to the laserk-vector. The lowest energy 4I15/2-

4I13/2 Er3+

transition has been observed to exhibit six distinctsites near 1537 nm [10]. The site with the strongestabsorption, located at 1536.87 nm (6506.69 cm�1),exhibits transient spectral hole burning by popula-tion storage in the excited state of the opticallyactive Er3+ ion; laser stabilization experimentswere performed using the absorption transitionbetween the lowest Zeeman split levels. Fig. 1ashows the transmission through the B2GHz(FWHM) wide inhomogeneously broadened linefor a magnetic field of B ¼ 0:25T and temperatureT ¼ 1:9K. The origin of the shoulder appearing athigher frequency is most likely due to absorptionfrom a spectrally similar site, as indicated byfluorescence decay experiments. A narrow spectralhole, indicated by an arrow, has been prepared bya second laser and can be placed anywhere withinthe inhomogeneously broadened line. The homo-geneous line width has been characterized usingtwo pulse photon echoes measured as a function ofdelay time between the two excitation pulses. Themeasured dephasing time corresponds to a homo-geneous line width of 2–3 kHz for small magneticfields below B ¼ 0:4T [10].

The experimental setup is similar to that used inprevious demonstrations [1–7]. Two externalcavity lasers in the Littman–Metcalf configurationequipped with quantum well InGaAsP/InP single-angled faceted laser diodes have been stabilizedusing the conventional Pound–Drever–Hall tech-nique [11]. The lasers were modulated withmodulation index MB0:4 at 27 and 30MHz,respectively, values greatly exceeding the spectral

G.J. Pryde et al. / Journal of Luminescence 98 (2002) 309–315310

hole width. The error signal was derived from thespectral hole transmission exploiting frequencymodulation (FM) spectroscopy. Fig. 1b shows thetransmission through a spectral hole burnedby a second laser and Fig. 1c the correspondingdemodulated FM error signal probed witha phase-modulated laser; detector signal and localoscillator are in phase. For active laser frequencystabilization the error signal is applied to afast servo loop providing rapid modulation ofthe injection current of the laser diode whereasa slow servo loop makes corrections to thepiezoelectrically driven feedback prism plate

of the external laser cavity. To obtain a goodsignal-to-noise ratio in the detection underlow laser locking irradiance, it is beneficial tochoose a large frequency reference crystal. Crystaldimensions were 12.87mm along a, 14.89mmalong c, with a 5.18mm optical path along b;both lasers were locked to the same crystal. Toavoid spatial overlap or interaction of the twoindependently locked laser beams, a mask withseparated 4mm apertures was placed over thecrystal. A small magnetic field of BB0:25Thas been conveniently applied by sandwichingthe sample holder between two permanent Nd–Fe–B magnet disks of diameter 2.5 cm, greatlysimplifying the experimental apparatus. Themounted crystal was immersed in liquid heliumat T ¼ 1:9K. The entire two-laser optical setup,including the cryostat, fit on a 30 � 40 opticalbreadboard, which was placed on vibrationdamping foam on a commercially availablepneumatically floated optical table. An acousticalisolation enclosure box [12] made of mediumdensity fiberboard lined with 3/400 thick polyesterembossed sound control mat covered the experi-ment to provide passive acoustical isolation fromambient acoustic noise.

The laser irradiance of B100 mW/cm2 at thecrystal was split from the laser beam using a l/2-plate/prism–polarizer combination, leaving mostof the laser output power to be used for experi-ments requiring a stabilized source or to saturatean Erbium-doped fiber amplifier for higher powerapplications. Using higher irradiance at the lock-ing crystal leads to a deeper spectral hole, which inturn becomes broader since there is less saturationof material absorption in the wings of a hole thanat the center. During active stabilization, eachlaser burns a spatially and spectrally separatedtransient spectral hole into the inhomogeneouslybroadened absorption profile. Error signal feed-back to each laser leads to a continuous regenera-tion of the transient spectral hole until a balancebetween spontaneous hole relaxation and holeburning occurs.

Relative frequency stability of the two stabilizedlasers was characterized by the statistical Allanstandard deviation [13] of the optical beat fre-quency since no absolute frequency reference was

Fig. 1. (a) Transmission spectrum of 0.004% Er3+:KTP at

1537 nm showing the entire inhomogeneously broadened4I15/2-

4I13/2 optical absorption scanned by a diode probe

laser. The arrow indicates a spectral hole, which has been

burned by a second laser. (b) Transmission of a phase-

modulated probe laser through a single-spectral hole created

by a second laser, using an applied magnetic field of B ¼ 0:25T.(c) Demodulated FM-error signal derived from the spectral

hole in (b).

G.J. Pryde et al. / Journal of Luminescence 98 (2002) 309–315 311

available. The beat signal from a photodiode wasmeasured with a frequency counter and recordedover time with a computer at 50ms time intervals.Allan deviations for integration times up to 50mswere directly measured with the frequency counter,whereas for longer integration times the Allandeviation was calculated from the recorded hetero-dyne beat frequency data.

The joint Allan deviation for the free runninglasers and actively stabilized lasers is shown inFig. 2. With the laser locked to transient spectralholes in Er3+:KTP an improvement in the Allandeviation over the free running lasers to 250Hzhas been achieved for integration times between1 and 100ms, demonstrating the potential ofEr3+:KTP at the current stage of system develop-ment. During quiet periods, Allan deviationsof 200Hz at 10ms integration time have beenmeasured. The structure of the Allan deviationcurve is reproducible. Long-term linear drift of thelaser evidenced by an upturn of the Allandeviation at longer integration times has beengreatly reduced by choosing an intermediate phasesetting at the mixer between detector signaland local oscillator. This technique combines the

excellent short-term stability of the spectralhole with the good long-term stability of theinhomogeneous line [4]; long-term drift of the beatfrequency between the two lasers has beensuppressed to B10 kHz/min. The demonstratedshort-term stability shows a clear improvementcompared to the previously reported results usingtransient spectral holes in Er3+:Y2SiO5 [4] andis the best result achieved in Er3+-doped com-pounds. As in the case of Er3+:Y2SiO5, spectraldiffusion plays a significant role in the achievedperformance [6]. Even though the transientspectral hole provides a narrow (few kHz wide)reference, the narrow hole width cannot befully exploited over longer periods because ofthe T1-limited hole lifetime. In addition, the strongEr3+ ion magnetic moments are perturbed by localfield fluctuations due to electron spin flips ofnearby Er3+ ions in the ground state. Theseperturbations lead to a broadening of the homo-geneous line width over time. The small appliedmagnetic field of B ¼ 0:25T slows this spectraldiffusion process by thermally depopulating theupper Zeeman component of the Er3+-ion groundstate but does not eliminate it completely.

Technical limitations are also set by reflectionsinside the electro-optic modulators, temperature-dependent residual amplitude modulation at theelectro-optic modulators, and voltage offsetscreated in the electronic servo loop. Since atransient spectral hole is a dynamic reference,any voltage offsets introduced to the error signalbaseline cause the lock frequency to shiftand consequently introduce long-term laser driftsince the laser is modifying its own reference.Further improvements can be expected frompassive and active temperature stabilization inorder to minimize and stabilize voltage offsets.Environmental disturbances due to vibration andacoustical noise sources have been partiallyaddressed by floating the optical table and cover-ing the experiment by the acoustical enclosure. The250Hz improvement in stabilization performancefor Er:KTP relative to Er3+:Y2SiO5 [4] is due to acombination of three factors: extra vibrational andacoustical isolation, reduced noise in systemcomponents such as electronics, and the subtledifferences in regenerative hole burning materials.

Fig. 2. Allan deviation for the heterodyne beat frequency

between two lasers: lasers free-running (squares), independently

locked to transient spectral holes in the 4I15/2-4I13/2 transition

in Er3+:KTP at 1537 nm (triangles) and model prediction of

stabilization in Er3+:KTP (circles) based on the measured

spectral noise density.


Materials studies to date suggest that the lastcontribution is minor.

3. Modeling of spectral hole burning frequency

references

Spectral hole burning frequency references usingregenerative or persistent spectral holes are quali-tatively different from other references, such asFabry–Perot cavities or gas absorption cells, sincethe reference hole can, in general, be modified bythe laser probing it. This dynamic interplaybetween the reference and the laser cannot bedescribed by the traditional frequency-domaintechniques of feedback control theory [14,15],since the hole spectrum may be time dependent.

A hybrid time- and frequency-domain numericalmodel and a more complicated time-domainnumerical model have been developed [16] toinvestigate the dependence of the laser stabilityon materials and system parameters and to speedoptimization of the experimental demonstrations.These simulations use rate equations and theoptical Bloch equations, respectively, to representthe interaction of the material with the opticalfield. In these models, stochastic and deterministicnoise are provided as inputs, along with thematerial parameters and varying degrees of systemdetail, such as the frequency- or time-dependentservo response. The input noise can either bemathematically generated or derived from themeasured spectral noise density of the experimen-tal system. The stability of the system, character-ized by the Allan deviation or spectral noisedensity, is examined as material or system para-meters are varied in turn. Furthermore, the outputof the simulations can be used as an input forother spectroscopic or optical processing models,such as the simulation of coherent transient pulsesequences.

Stabilization of lasers to regenerative spectralholes—where the hole lifetime is of the order of theoptical T1—has been of particular interest, since todate, the lowest experimental Allan deviationshave been achieved in this regime. It has beenfound that the hole width, governed by acombination of homogeneous line width and the

probing Rabi frequency, dictates the stability overshort integration times, while the stability mea-sured over integration times longer than the holelifetime is governed by the hole lifetime or rate ofspectral diffusion, parameters that serve to char-acterize the memory time of the reference [7]. Byemploying the time-domain model, which de-scribes the material in terms of the optical Blochequations, it was possible to obtain the frequency-dependent response of the error signal. This isshown in Fig. 3, where it is compared with theresponse of a Fabry–Perot cavity of the samespectral width and with the experimentally mea-sured spectrum for the regenerative hole burningmaterial Er3+:Y2SiO5. The experimental resultwas obtained by probing a regenerative spectralhole with the stabilized laser. Phase-modulationsidebands were swept over the frequency range ofinterest and the phase-modulation spectrum re-corded. This spectrum was scaled by a factorproportional to the inverse modulation frequency,for comparison with the calculated responses forthe hole and cavity, since the latter assumefrequency modulation rather than phase modula-tion. Since the phase-modulation signal goes tozero at DC, the signal-to-noise ratio imposes a

Fig. 3. Frequency response of the error signal generated from a

regenerative spectral hole frequency reference: experimental

measurement in Er3+:Y2SiO5 (solid line) and using the model

(open circles), compared with the calculated response of a

Fabry–Perot cavity with the same line width (dashed line), with

the Fabry–Perot gain scaled for comparison.


lower limit on the measurable error signal re-sponse. The low frequency response of the holecan be inferred beyond this limit by taking theratio of the spectral noise density measuredrelative to the regenerative spectral hole and thatmeasured relative to a static reference, in this case,a 150MHz FWHM inhomogeneous line in iso-topically purified Er3+:LiYF4. This measurementis the source of the experimental data in Fig. 3 atfrequencies below 300Hz. The narrow features inthe low frequency error signal response areartifacts of this technique.

Over the range of the measurement, the modeland experiment agree, and they are both incoincidence with the response of a Fabry–Perotcavity. It is clear that the high-frequency rolloff isclose to 20 dB/decade, which is ideal for servodesign since the accumulated phase shift from thereference is limited to 901. At lower frequencies,the predicted rolloff of the gain is observed,consistent with the idea that the system is losingits memory as a frequency reference because of thelimited hole lifetime. In principle, this can bepartially compensated by servo gain and the issuesassociated with compensation are presently underinvestigation.

The hybrid model was used to compute thepredicted Allan deviation for locking inEr3+:KTP, based on the measured spectral noisedensity of the unstabilized laser and the knownmaterials and system parameters. The resultsof this computation are compared with theexperimentally measured Allan deviation inFig. 2. It can be seen that there is good agreementbetween the computed and measured valuesfor shorter and longer integration times. Overthe range of integration times from 1 to 100ms,where the measured Allan deviation is a minimum,there is some divergence of the computed valuesfrom the measured values. This deviationis attributed to a reduced spectral noise densityof the unstabilized laser, over the relevant integra-tion times, at the time that it was recorded,compared to the time that the directly measuredAllan deviation was acquired. The narrow(B5 kHz) spectral hole in Er3+:KTP resultsin high gain, leading to excellent suppressionof the noise over short integration times.

Over longer integration times, the limited lifetimeof the hole causes the reference to lose itsfrequency memory and the effects of drift andother slow fluctuations begin to dominate theAllan deviation curve. The effective hole lifetimeused in the modeling is 10ms, which is inagreement with our experiments.

The modeling has led to understanding of theprocess of stabilization to regenerative spectralholes and identification of the ideal hole burningmaterial–one with long-lived, narrow spectralholes and no spectral diffusion. In addition, itallows investigation of the effect of varying lockingsystem parameters for a given spectral holefrequency reference, leading to optimization ofthe stabilization experiments.

4. Summary

Lasers have been stabilized to spectral holes in avariety of Er3+ and Tm3+ materials. The goal is toprovide compact and portable secondary opticalfrequency standards and ultra-stable laser sourcesfor a variety of applications including otherspectral hole burning devices. Gated spectralholes, persistent spectral holes, and transientregenerative spectral holes all have application tolaser stabilization. Regenerative spectral holeshave produced the highest level of stabilization,20Hz, so far. New materials of all three types areunder development to extend the range of practicaldevice applications.

Acknowledgements

We thank G. Reinemer and Y. Sun for spectro-scopic information on Er3+:KTP, P.B. Sellin,Jun Ye, and J.L. Hall for valuable discussions,G.C. Dodge, G.W. Switzer, K.R. Repasky,J.L. Carlsten, and N. Williams for assistingwith laser design and construction, Steve Kellyfor assistance with the feedback electronicsand Wavelength Electronics for donated equip-ment.

This research was supported by US AirForce Office of Scientific Research Grant


Nos. F49620-98-1-0171, and F49620-99-1-0202,and F49620-00-1-0314 and the Montana StateUniversity Spectrum Lab. R.L. Cone’s emailaddress is [email protected].

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