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Frequency-Shifted Optical Feedback in a Pumping Laser Diode Dynamically Amplified by a Microchip Laser

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Frequency-Shifted Optical Feedback in a Pumping Laser Diode Dynamically Amplified by a Microchip Laser
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  Frequency-shifted optical feedback in a pumpinglaser diode dynamically amplified by a microchip laser Eric Lacot and Olivier Hugon Compared with conventional optical heterodyne detection, laser optical feedback imaging    LOFI   allowsfor a several orders of magnitude higher intensity modulation contrast. The maximum contrast ampli-fication is typically 10 3 for a diode laser in the gigahertz range and 10 6 for a microchip laser in themegahertz range. To take advantage of the wavelength tunability of a laser diode and of the lowerresonant detection frequency of a microchip laser, we used LOFI modulation induced by the frequency-shifted optical feedback in a laser diode as a modulated pumping power for a microchip laser for resonantdynamic amplification. In this way, we were able to transfer the optical feedback sensitivity of the laserdiode to the megahertz range. Application to telemetry is also reported. © 2004 Optical Society of  America OCIS codes:  120.3930, 120.4640, 120.5050, 120.5820, 140.3480, 180.3170. 1. Introduction Laser properties and behavior can be significantlyaffected and modified by optical feedback. 1 Sincethe discovery of lasers, parasitic coherent opticalfeedback has been the source of serious laser prob-lems, increasing noise and creating laser instabili-ties. 2,3 On the other hand, controlled opticalfeedback can be of practical use. 4 For example, line-width narrowing can be obtained with an externalcavity laser diode. 5 Potential applications are alsopossible, one of which is laser feedback interferome-try with which the steady-state intensity of a laser ismodified by coherent optical feedback from an exter-nal surface. 6,7 This phase-sensitive technique is de-pendent on the reflectivity, distance, and motion of the target.The remote characterization of noncooperative tar-gets such as diffuse surfaces is relevant for manyapplications. 8,9 Inthesecases,thereinjectedlightisonly partially coherent. The nature of such lightreduces drastically the interference contrast that oc-curs inside a laser cavity. To overcome this prob-lem,onesolutionisthentousethelaserdynamicthatis several orders of magnitude more sensitive to op-tical feedback than the laser steady-state proper-ties. 10,11 Nowadays, the dynamic sensitivity of lasers to frequency-shifted optical feedback is used inself-mixing laser Doppler velocimetry experi-ments 12,13 and in laser optical feedback imaging   LOFI   experiments. 14,15 Compared with conven-tionalopticalheterodynedetection,frequency-shiftedoptical feedback allows for a several orders of mag-nitude higher intensity modulation contrast   typi-cally 10 3 for a diode laser and 10 6 for a microchiplaser  . 10,13 The maximum of the modulation was ob-tained when the frequency shift was resonant withthe laser relaxation oscillation frequency   typically 1GHz for a diode laser and 1 MHz for a microchiplaser  .Here we have slightly modified our LOFI detectionsystem for highly sensitive telemetric sensing in themegahertz range. To take advantage of the wave-length tunability of a laser diode and of the lowerresonant detection frequency of a microchip laser, weused the LOFI modulation induced by the frequency-shifted optical feedback in a laser diode   i.e., directLOFImodulation  asamodulatedpumpingpowerfora microchip laser   indirect LOFI modulation  . Thispaper is organized as follows. In Section 2 we givetherateequationsthatgovernthedynamicsofalasersubmittedtodirectorindirectLOFImodulation. Bysolving the rate equations in a linear approximation,we determined the dynamic amplification gain pro- vided by the indirect LOFI modulation of a microchip E. Lacot   eric.lacot@ujf-grenoble.fr   and O. Hugon are with theLaboratoiredeSpectrome´triePhysique,Universite´ JosephFourierde Grenoble, Boite Postale 87, 38402 Saint Martin-d’He`res Cedex,France.Received 19 September 2003; revised manuscript received 16 April 2004; accepted 17 May 2004.0003-6935  04  254915-07$15.00  0 © 2004 Optical Society of America 1 September 2004    Vol. 43, No. 25    APPLIED OPTICS 4915  laser. In Section 3 we briefly describe the modifica-tion of the LOFI experiment that is necessary for theobservation of indirect optical feedback. The laseroutput power modulation induced by direct and indi-rect optical feedback is compared. In the megahertzrange, the contrast amplification is then determinedand compared to theoretical prediction. Phase-sensitive applications   distance and displacement  are also reported. 2. Theory   A. Basic Equations In the case of weak frequency-shifted optical feed-back, the dynamic behavior of a reinjected laser canbe described by the modified Lang–Kobayashi mod-el 16,17 :d  N   t  d t    1   N  0   N   t    BN   t    E  t   2 , (1a)d  E  t  d t   12    BN   t    c   E  t     e  cos   e t   c   e   t    t    e   E  t    e  , (1b)d  t  d t   12    BN   t    c     e  sin   e t   c   e   t    t    e   E  t    e   E  t   , (1c)where  N   t   is the population inversion,  E  t   and   t  are, respectively, the amplitude and the phase of thelaser electric field in reduced units   photon units  ,   c is the solitary laser frequency,  B  is the Einstein co-efficient,   1  N  0  is the pumping rate,   1  is the decayrate of the population inversion, and   c  is the lasercavity decay rate. In the laser diode, the linewidthenhancement factor     2–5   stems from the com-bined effect of the free-carrier plasma effect and thedetuning effect of lasing frequency from the sponta-neous emission peak   i.e., the Kramers–Kronig rela-tionship  . For a solid-state laser this phase-amplitude coupling parameter is generally neglected    0  .From a dynamic point of view, the periodic func-tions express the coherent interaction   beating    be-tween the lasing and the feedback electric fields.The laser cavity losses are then modulated at opticalfrequency shift    e . The optical feedback is alsocharacterized by two other parameters 14 : the first,   e    2 d  e  c  , is the photon round-trip time betweenthe laser and the target under investigation and thesecond,    e    c   R  e  , is the reinjection rate of thefeedback electric field. Parameters  d  e  and  R  e  are,respectively, the optical distance between the laseroutput and the target and the effective power reflec-tivity of the target.Without optical feedback   e  0  , the laser steady-state solutions are then given by  N   S   c   B , (2a)  I   S    E  S  2   I  sat   1  , (2b)where  I   S  is the stationary intensity of the laser fieldin photon units,  I  sat    E sat2   1   B  is the saturationintensity,and   BN  0   c isthenormalizedpumping rate. At this point we note that mean optical phase   S  of a laser does not appear in the steady-state solutions.This means that the phase is not determined or moreprecisely is randomly distributed over 2  . We cantherefore arbitrarily fix it to   S  2  . (2c) B. Direct Laser Optical Feedback Imaging Modulation For weak optical feedback    R  e    1  , the small laseroutput power modulation induced by cavity loss mod-ulation can be obtained by seeking an   0  1 periodicsolution of the form  N   t ,     R  e    N   S      R  e 1  N  1  t       R  e 2  N  2  t   . . . ,(3a)  E  t ,     R  e    E  S      R  e 1  E 1  t       R  e 2  E 2  t   . . . ,(3b)  t ,     R  e     S      R  e 1  1  t       R  e 2  2  t   . . . ,(3c)where  N   S ,  E  S , and   S  are given by Eqs.  2  . At firstorder,bysubstitutingEqs.  3  intoEqs.  1  andequat-ing to zero the coefficient of     R  e  leads to the follow-ing set of linearized equations:d  N  1  t  d t    1   B   E  S  2   N  1  t   2  BN   S  E  S  E 1  t  ,d  E 1  t  d t   12  BE  S  N  1  t    c  E  S  cos   e t   c   e  ,d  1  t  d t   12    BN  1   c  sin   e t   c   e  . (4)By solving Eqs.   4  , one obtains the standard LOFIsignal for relative modulation of the laser outputpower 18 :   P  t ,    e   P   2    R  e  E 1  t ,    e   E  S  2   e  12    e 2  1  2   R 2    e 2  2   12   e 2  1  2  cos   e t   c   e    R  , (5a)where  P    c  E  S 2 is the averaged photon output rate,   R    1  c    1  1  2 is the relaxation frequency of the laser,   1    1   is the damping rate of the relax- 4916 APPLIED OPTICS    Vol. 43, No. 25    1 September 2004  ation oscillations, and    R  is an additional dynamicphase shift defined bytan   R     e   R 2    e 2    1  2  1   R 2  .For phase-sensitive applications  profilometry, vibro-metry, telemetry, nanometric displacement, . . .  , tar-get distance  d  e  can be directly determined from theLOFI modulation phase:  d  e    c   e    R   c 2 d  e c     R . (5b)Hereafter, the laser output power modulation in-duced by frequency-shifted optical feedback is calledthe direct LOFI modulation.In Fig. 1 curves a and b represent the direct LOFImodulation versus the optical frequency shift   e  for alaser diode and for a microchip laser. For both la-sers, the normalized contrast of the laser outputpower modulation   1    R  e     P   P      exhibits a strong resonanceatlaserrelaxationfrequency   R withafullwidth at half-maximum given by   1   see Table 1  . At the resonance frequency   e   R  , the maximumrelative amplitude of the modulation is   P   R   P    2   e  1  2   c  1    R  e . (6)Compared with conventional heterodyne detection,an enhancement factor of    c   1  occurs in the LOFIexperiment. For a microchip laser, this factor is of the order of 10 6 with a resonant frequency in themegahertz range and is of the order of 10 3 and in thegigahertz range for a laser diode. The high sensitiv-ity of the direct LOFI detection technique comes fromthis resonant amplification of frequency-shifted opti-cal feedback. 14 The typical laser dynamic parame-ters are summarized in Table 1. C. Indirect Laser Optical Feedback Imaging Modulation For many LOFI applications such as telemetric sens-ing of a noncooperative target, the wavelength tun-ability of a laser diode is of practical use. 19 Incontrast, from a technical point of view, the highrelaxation frequency of a laser diode in the gigahertzrange is not of practical use. To lower the detectionfrequency while keeping a high amplification gain  i.e., a high sensitivity to optical feedback  , one solu-tion is to use the LOFI modulation induced by thefrequency-shifted optical feedback in a laser diode asa resonant modulated pump for a microchip laser.Hereafter, the microchip laser output power modula-tion induced by frequency-shifted optical feedback inthe pumping laser diode is called the indirect LOFImodulation.In these conditions, the pumping parameter rate of a microchip laser is then periodically modulated atoptical frequency shift    e :  1,   N  0,   t    1,   N  0,   1   d  cos   e t   d  , (7a)where modulation depth   d  is simply given by theLOFI modulation contrast of the laser diode outputpower   Eq.   5a  :  d   e ,  R  e     P d  P d  2  c , d    R  e  1, d 2    e 2  1  2   R , d 2    e 2  2   1, d 2   e 2  1  2 ,(7b)and where modulation phase shift  d  is simply givenby the LOFI modulation phase of a diode laser   Eq.  5c  :  d  d  e    c , d 2 d  e , d c     R , d . (7c)Nota bene: in Eqs.   7   and hereafter, indices  d  and  areused,respectively,toindicatethelaserdynamicparameters of the laser diode and of the microchiplaser.For weak modulated pumping    d    1  , the smallmicrochip laser output power modulation can be ob- Fig. 1. Normalized contrast of the laser output power modulation  1    R  e   P   P   versus frequency shift    e : a, laser diode withdirect frequency-shifted optical feedback   cavity loss modulation  ;b, microchip laser with direct frequency-shifted optical feedback  cavitylossmodulation  ;c,microchiplaserwithindirectfrequency-shifted optical feedback   pump modulation  . Table 1. Typical Laser Parameters Laser ParametersMicrochipLaserPumping Diode LaserLaser output power  P     10 mW 100 mWPumping parameters    1.8 4Cavity damping rate   c  8  10 9 s  1 5  10 11 s  1 Population damping rate   1  5  10 3 s  1 10 8 s  1 Relaxation frequency    R  2   0.9 MHz 1.95 GHzRelaxation damping rate   1  2   1.4 kHz 64 MHzLOFI enhancement factor   c   1  0.8  10 6 1.25  10 3 1 September 2004    Vol. 43, No. 25    APPLIED OPTICS 4917  tained by linearization of the set of Eqs.   1  . Byusing the modulated pumping rate given by Eqs.   7  and by taking    e ,   0  i.e., no optical feedback in themicrochiplaser  ,weobtainedtherelativemodulationof the indirect LOFI signal as   P   t ,    e   P    d   e ,  R  e  1,   c ,    R ,  2    e 2  2   1,  2   e 2  1  2  cos   e t   d  d  e     R ,   , (8a)where    R ,   is an additional phase shift defined bytan   R ,      e  1,      e 2    R ,  2  . As previously,the optical distance between the laser diode outputmirror and target  d  e , d  can be determined from theindirect LOFI modulation phase:    d  e    d  d  e     R ,    c , d 2 d  e , d c     R , d    R ,  .(8b)Curves a and c in Fig. 1 allow a direct comparisonof the direct LOFI modulation   laser diode modula-tion  and of the indirect LOFI modulation  microchiplaser modulation   versus optical frequency shift    e .When working at the microchip laser resonance fre-quency    e     R ,     1 MHz   i.e., far from the laserdiode relaxation frequency  , the direct LOFI modula-tion contrast of the laser diode   Fig. 1, curve a   islower than 3, and the indirect LOFI modulation  Fig.1, curve c   allows a contrast amplification of approx-imately 3 orders of magnitude:   P    R ,    P   P d   P d   R ,       c ,   1,  1      1  1.4  10 3 .(9)Finally, despite this amplification, the maximumgain brought by this technique   4    10 3   is compara-ble with the maximum gain brought by a semicon-ductor laser   2    10 3  . However, the mainadvantage is to lower the frequency at which thedetectionisdone  2GHzforalaserdiodedownloadto1MHzinthecaseofaNd:YAGmicrochiplaser  whilekeeping, for application sensing, the wavelength tun-ability of the laser diode. 3. Experimental Results  A. Experimental Setup The experimental setup is shown schematically inFig. 2. The laser is a Nd 3  :YAG microchip laserwith a cavity length of 800   m, lasing at a wave-length of 1061.34 nm. 20,21 The pumping laser is an810-nm laser diode. The typical laser parametersare listed in Table 1.For the direct LOFI modulation, the first part of the laser diode beam is frequency shifted and sent toa target under investigation mounted on a piezoelec-tric transducer   PZT  . In this way, we can controlthe optical phase between the laser cavity field andthe feedback electric field. The frequency shift isgenerated by means of two acousto-optic deflectors   AODs  . The first is supplied by a rf at 81.5 MHzand the diffracted beam   order   1   is sent into thesecond AOD, which is supplied by a rf at 81.5 MHz   F   e  2, where  F   e     e  2   is the frequency shift. Itsdiffracted beam   order   1   is therefore shifted by anoptical frequency of   F   e  2. The retroreflected light isreinjected inside the laser cavity after a second passthrough the frequency shifters. After this roundtrip the reinjected beam is then shifted by  F   e . Thisfrequency can be adjusted by means of a frequencysynthesizer. The amount of light coming back intothe diode laser cavity can be adjusted by use of a variable attenuator.For the indirect LOFI modulation, the second partof the laser diode beam is sent directly to the micro-chip laser to act as modulated pumping. A smallfraction of the output beams of the laser diode and of the microchip laser are sent to Si photodiodes loadedby a 50   resistor. The delivered voltages are ana-lyzed by means of a vectorial lock-in amplifier thatgives directly the amplitude and the phase compo-nents of the LOFI signal and  or by a spectrum ana-lyzer. All these signals are analog-to-digitalconverted and recorded by a PC for further analysisand  or imaging. B. Laser Optical Feedback Imaging Phase Signal FormanyLOFIapplications,suchastelemetricsens-ing of a noncooperative target, the wavelength tun-ability of the laser diode is of practical use. 19 Forlinear scanning of the laser optical frequency, thetarget–laser distance is simply obtained from the de-rivative of the LOFI phase   Eq.   5b   according tooptical frequency scanning    d : d  e , d  c 4  d  d . (10)Figure 3 shows a typical example of telemetricsensing of a scattering ceramic target   LabsphereSRS-99-010   by use of a 160-MHz frequency-shiftedoptical feedback  obtained by use of only one AOD  in Fig. 2. Schematic diagram of the LOFI experiment with a pump-ing laser diode: L 1 –L 4 , lenses; BS, beam splitter; AOD 1 , AOD 2 ,acousto-optic deflectors; rf, radio frequency generator;  F   e , fre-quency shift; VA, variable attenuator; PD 1 , PD 2 , photodiodes. 4918 APPLIED OPTICS    Vol. 43, No. 25    1 September 2004  a 35-mW power laser diode working at 685 nm   BlueSky Research PS107  . The laser optical frequencyscanning obtained with a diode current variation isdetermined by means of a low-finesse Fabry–Perotetalon with a free spectral range of 3.9644 GHz.Figure 3  a   shows the temporal response of theFabry–Perot etalon to the optical frequency scanning of the laser diode. A second-order polynomial fit al-lows us to calibrate the laser optical frequency vari-ation. Figures 3  b  and 3  c  show the time evolutionof the LOFI phase induced by optical frequency scan-ning the laser diode. The phase residual undulationis due to parasitic optical feedback from the focusing lens. Finally, Fig. 3  d   shows the unwrapped LOFIphase versus the calibrated optical frequency scan-ning. The slope of the graph gives an optical path of  d  e , d    1037.67 mm, in good agreement with the ex-perimental setup. For a phase measurement preci-sion of 2   100 and for a phase variation of 1500 rad,the relative distance precision is of the order of 4   10  5 .For weaker optical feedback   i.e., weaker effectivereflectivity  R  e  , the LOFI modulation contrast of thelaser diode   i.e., the signal-to-noise ratio   needs to beimproved. One potential solution is to increase thefrequency shift experimentally to work in the giga-hertz range   i.e., near the laser diode relaxation fre-quency  . From a technical point of view, thismethod is not of practical use. As predicted in Sec-tion 2 and Fig. 1, another possible solution is to usethe indirect LOFI modulation to work in the mega-hertz range.Our first step was to verify that the wavelengthtunability of the laser diode can be transferred to theoutput power modulation of a microchip laser. Forthe direct LOFI modulation of a pumping laser diode  SDL 5422-H1  and for the indirect LOFI modulationof a Nd 3  :YAG microchip laser, Fig. 4 shows the timeevolution of the LOFI phase induced by optical fre-quency scanning of the laser diode.In good agreement with Eqs.   7c   and   8b  , theLOFI phase variation of the laser diode and of themicrochip laser are well correlated. The correlatedswitchover in the linear evolutions of the direct andindirect LOFI phases seems to be due to laser diodemode hopping. This correlated switchover also indi-catesthatamicrochiplasercanbeusedasasensitivetool  a sort of photomultiplier  for the study of a diodelaser subjected to weak optical feedback.For a laser diode with a wavelength tunability of 2GHz  mA and a scanning speed of 0.016 mA   s, theslope of the linear part of the phase variation   1.325rad  s for the laser diode and 1.316 rad  s for the mi-crochip laser  allows us to determine in both cases anoptical feedback distance of the order of   d  e , d    1 m. Absolutetelemetricsensingisthereforepossiblewitha single-frequency cw microchip laser. C. Laser Optical Feedback Imaging Amplitude Signal Herewecompareexperimentallythemodulationcon-trast of both the direct and the indirect LOFI modu-lation in the megahertz range  i.e., far from the laserdiode relaxation frequency  . For direct LOFI mod-ulation   pumping laser diode   and for indirect LOFImodulation  microchiplaser  Fig.5showsapolarplotof the amplitude of the laser output power modula-tion versus the phase of the modulation. Experi-mentally the phase variation is induced by amicrometric displacement of the target mounted on aPZT. Far from the laser diode relaxation frequency,the direct LOFI modulation contrast is weak, and theindirect LOFI modulation shows a contrast amplifi- Fig. 3. LOFI telemetric sensing with a laser diode:   a  responseof a low-finesse Fabry–Perot etalon   free spectral range of 3.9644GHz   to the optical frequency scanning of a laser diode;   b   varia-tion of the LOFI phase   i.e., the optical phase   induced by opticalfrequency scanning of a laser diode;   c   small part of trace   b  ;   d  unwrapped LOFI phase    versus calibrated optical frequencyscanning    .Fig. 4. Time evolution of the phase of the output power modula-tion induced by optical frequency scanning of the laser diode: topcurve, microchip laser phase variation; bottom curve, pumping laser diode phase variation. 1 September 2004    Vol. 43, No. 25    APPLIED OPTICS 4919
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