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Optics Communications 272 (2007) 425–430

Enhanced self-heterodyne performance usinga Nd-doped ceramic YAG laser

A. McKay *, P. Dekker, D.W. Coutts, J.M. Dawes

Centre for Lasers and Applications, Macquarie University, Sydney, NSW 2109, Australia

Received 29 March 2006; received in revised form 16 October 2006; accepted 21 November 2006

Abstract

Two-frequency operation in ceramic neodymium-doped yttrium aluminium garnet is demonstrated for 1.064 lm operation with a self-heterodyne beat-frequency tuning range in excess of 1.5 GHz. A 6 dB improvement of the peak-beat strength is seen in the ceramicmaterial over that of similar crystalline Nd:YAG lasers. Experimentally, the ceramic host material is shown to have substantially higherpolarization mode coupling constant, C = 0.72 ± 0.05, compared to crystalline Nd:YAG, C = 0.16 ± 0.05. The peak-beat strength isrelated to mode coupling. In general the Nd:ceramic YAG dual-frequency laser offers superior performance as a photonic-basedradio-frequency source over Nd:YAG.� 2006 Elsevier B.V. All rights reserved.

PACS: 42.70.Hj; 42.81.Gs; 42.55.Rz; 42.65.Sf

Keywords: Ceramic Nd:YAG; Dual polarization; Nonlinear mode coupling

1. Introduction

Dual-frequency lasers have been studied over the pastfew years for applications in the fields of microwave pho-tonics, optical interferometry and metrology, coherentsensing, stable tunable microwave sources, and radio-over-fibre communications systems [1–5]. We are studyingdual-frequency lasers in which the two frequencies ariseon two orthogonal polarizations in Nd:YAG and relatedlasers. The phenomenon of dual-frequency lasers arises inthese and other lasers [4–8] because of the quasi-isotropicnature of the gain medium and the relatively low intra-cav-ity polarization discrimination, which allows two eigen-polarizations to oscillate simultaneously. The two eigen-polarizations have slightly different optical frequencies,(m1 and m2) due mainly to the cold cavity resonances, orthe amount of birefringence experienced by each state.

0030-4018/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2006.11.059

* Corresponding author. Tel.: +61 2 9850 8964.E-mail address: aaron@ics.mq.edu.au (A. McKay).

Lamb’s mode-coupling analysis has been used to under-stand the mode interactions in more detail in two-modegas lasers [9] and in solid-state lasers [10–12].

Ceramic laser materials in recent years have surpassedthe quality [14,13] and high-power performance [15] oftheir crystalline counterparts. Ceramic Nd:YAG is formedfrom small (tens to hundreds of microns diameter), ran-domly oriented, Nd:YAG crystallites sintered into a singlepolycrystalline structure [16]. The scattering losses (whichhad been a limiting factor for the usefulness of the ceramicmaterials until recently) have been reduced to that of ahomogeneous crystal, reported to be less than 0.009 cm�1

[16–18]. Scattering sites such as grain boundaries and porevolume are key contributors to scattering losses. Grainboundaries have been reported to be less than 1 nm across,and pore volumes are comparable to those in crystallinematerials grown by the Czochralski method [19]. Morerecently highly doped (>4% doped Nd:YAG) ceramic gainmaterials have become commercially available with strongabsorption and better thermo-mechanical properties com-parable with those of equivalent Nd:YVO4 microchip

426 A. McKay et al. / Optics Communications 272 (2007) 425–430

lasers [13,18]. In this configuration, microcavities with sin-gle longitudinal mode operation and crystal lengths of lessthan 0.5 mm, are easily achieved. Importantly, ceramicYAG does not have a dominant gain axis, lasing readilyon any orientation and hence is very suitable for dual-fre-quency operation.

In this paper, we have chosen to investigate the dual-fre-quency (dual-polarization) operation and mode-couplingbehavior in ceramic YAG lasers. Here we compare theproperties of two very similar laser resonators, one basedon ceramic Nd:YAG and one using crystalline Nd:YAG.

2. Experimental methods

A standard linear cavity arrangement, as shown inFig. 1, was set up with two alternative gain materials toinvestigate and compare the beat-note properties of crystal-line and ceramic dual-polarization Nd:YAG lasers. Thecavity incorporated a dielectric input mirror with hightransmission (HT) at 808 nm and high reflectivity (HR)at 1064 nm, either a 5 mm long 1 at.% doped single crystalNd:YAG or a 5 mm long 1 at.% doped ceramic Nd:YAGcrystal, a 21 mm long z-cut LiNbO3 electro-optic crystaland a 0.5 mm thick 30% partially reflecting etalon to main-tain a single longitudinal mode. The output mirror was a97% HR with a radius of curvature (RoC) of 15 cm; theoverall cavity length was maintained in both cases toapproximately 5 cm and had a free spectral range (FSR)of 1.61 GHz.

The two laser crystal configurations were both pumpedby a fibre-coupled laser diode (maximum 2 W opticalpower and 100 lm core diameter) which was imaged intothe gain medium with a final spot diameter of approxi-mately 200 lm. The laser diode was temperature tuned tomatch the absorption peak of Nd:YAG near 808 nm. Adepolarizing prism was also inserted into a collimatedregion of the pump beam to eliminate possible pump polar-ization influence on the polarization dynamics of the laser[7,8].

In both configurations the two orthogonal polarizationswere tuned by applying an electric field across the lithium

V

HWP

PBS

Pinhole

Fast PIN diodeand RF analyzer

Fabry-Perot interferometer

1% dopedcrystalline or ceramic Nd:YAG 97% R output coupler

30% Retalon

Lithium niobate

5 cm

Incident pumpsource

Fig. 1. Cavity and measurement arrangement to investigate self-hetero-dyne properties of the Nd-doped ceramic and crystalline hosts.

niobate (LN) crystal to produce the orthogonally polarizedmodes aligned parallel and perpendicular to the electricfield lines in the LN crystal. The resulting relative fre-quency difference (dm = m2 � m1) between the orthogonalmodes is given simply by the optical path differencesbetween the ordinary and extra-ordinary polarization dueto the voltage-controlled birefringence, Dn(V). The fre-quency separation dm is given by [4]:

dm ¼ m0DnðV Þ LEO

L¼ m0n3

0r22

Vd

LEO

L; ð1Þ

where m0 is the laser center frequency, L is the cavity length,LEO, r22 and V/d are the lithium niobate crystal length,electro-optic coefficient of LN and the electric field appliedto the LN crystal respectively.

An extra-cavity half waveplate (HWP) was used toadjust the polarization modes to be at 45� to the axis ofan analyzing polarizing beam splitter (PBS) as shown inFig. 1. Half the resulting signal was collected by a300 lm active area InGaAs 1 GHz bandwidth PIN photo-diode, which was connected to a Tektronix 2792 radio-fre-quency spectrum analyzer. The remaining signal wasoptically monitored for modal structure, using a confocalFabry–Perot interferometer.

3. Laser and self-heterodyne performances

As shown in Fig. 2 both the ceramic and crystalline con-figurations had a pump power threshold of approximately225 mW and over the entire pumping range had identicaloutput powers. At an inversion ratio (r) of approximately1.15, each configuration oscillated with equal intensityorthogonally polarized states of a single longitudinal modeand continued to oscillate in this regime until a second lon-gitudinal mode arose at approximately 15 mW of total out-put power (r � 1.5). Typically the second longitudinalmode oscillated on one stronger polarization and in someinstances contributed to a second beat signal, especiallywhen the frequency separation of the fundamental polari-

Fig. 2. Laser output power as a function of incident pump power forcrystalline (dashed, open circles) and ceramic (solid, open squares)configurations. Inset shows the typical photodiode intensities of the twoorthogonally polarized modes as a function of total output power for theinversion ratio (r) range of 1–2 at low drive voltages (�500 V) to thelithium niobate.

A. McKay et al. / Optics Communications 272 (2007) 425–430 427

zation modes was close to half one free spectral range. Theinset in Fig. 2 shows the dc photodiode signal as a functionof the ceramic laser output power for one polarization, andthen, by rotating the HWP in Fig. 1 by 45� the other polar-ization. This agreement between polarization intensitieswas typical in both the ceramic and crystalline configura-tions. The remaining experiments in this section were con-ducted with a pump inversion ratio between 1.2 and 1.5.

To measure the self-heterodyning performance of thelaser, we varied the drive voltage to the lithium niobatecrystal and thus varied the relative frequency differencebetween the two optical modes. The optical output wasthen converted to an electrical signal using a high band-width photodiode and analyzed on a broad sweep settingof the spectrum analyzer. By periodically adjusting theangle of the intra-cavity etalon and monitoring the opticalmode structure on a Fabry–Perot interferometer (whilstmaximizing the beat-note signal on the fast photodiodeby fine-tuning the HWP angle) over the entire range ofdrive voltages, both laser configurations were held to a sin-gle longitudinal mode and both orthogonally polarized

Fig. 3. Comparison of key RF parameters between two similar ceramicand crystalline configurations of a single dual frequency solid-state laser.(a) Beat frequency tuning exceeding half a free spectral range, k/4-voltageand half free spectral range shown as dashed lines. (b) Peak RF power ofthe ceramic and crystalline lasers shown over the linear range of the photo-detector at discrete center beat frequencies as shown in (a). Dashed lineshows half a free spectral range of the cold cavity. The instrumental noisefloor in these measurements was approximately �85 dBm.

modes were maintained with approximately equalintensities.

The beat frequency was obtained at discrete lithium nio-bate voltages and plotted as shown in Fig. 3a. The corre-sponding beat powers are plotted in Fig. 3b. AlthoughLamb’s analysis [9] has been used successfully [11,10] todescribe the behavior of these lasers employing a phase-sensitive coupled rate equations approach, the experimen-tal beat-frequency tuning in both configurations agree wellwith the simple cold-cavity approximation given by Eq. (1).There is a slight deviation of the center beat frequency inFig. 3a for the ceramic configuration at low frequencies,probably because the stress axes of the gain material, thedominating source of birefringence at low drive voltages,are misaligned with respect to the birefringence axes ofthe lithium niobate.

Longitudinal mode hopping is also shown in Fig. 3a forthe crystalline configuration near quarter-wave voltagetuning. The mode hopping is the result of one polarizationstate increasing or decreasing its longitudinal mode index[8]. Our ceramic configuration, however, showed unex-pected behavior in regards to longitudinal mode hopping.In a number of repeated experiments, the laser with theceramic material did not show evidence of mode hoppingnear its half-free spectral range. At much higher voltageshowever, near half-wave-voltage, the laser did show evi-dence of mode hopping and in this case the resulting beatfrequency followed that of the crystalline configuration.Kawai et al. [18] considered the ceramic active materialas consisting of randomly distributed single-crystal grainssurrounded by scattering grain boundaries. One effect ofthese randomly-oriented crystallites is stronger couplingbetween the intensities of the orthogonally polarizedmodes, which is described in Section 4. We attribute thereduced mode hopping to this stronger coupling withinthe gain medium of the ceramic laser compared to the crys-talline counterpart.

Furthermore, considering the angular spatial hole-burn-ing argument of Bouwmans et al. [8] each orthogonallypolarized intensity induces a population grating for ionsalong its own polarization and another weak grating(depending of the strength of coupling) in the orthogonalpopulation. The spatial population gratings serve torestrict the laser modes hopping to the next longitudinalmode index.

Additionally we can use the same argument to accountfor the logarithmic reduction in beat power with beat fre-quency shown in Fig. 3b. The ‘‘weak’’ orthogonally polar-ized spatial population inversion grating due to thecoupling phenomenon is out of phase with the normal pop-ulation inversion–intensity interactions. So small frequencydifferences between the two modes have little effect apartfrom contributing constructively to the depth (accordingto the amount of coupling) of the population gratings ineither population inversion. Increasing the frequency spac-ing between the orthogonal modes blurs the visibility of thepopulation gratings due to the decreasing spatial overlap

428 A. McKay et al. / Optics Communications 272 (2007) 425–430

along the optical path of the coupled components with theorthogonal states. This affects the slow amplitude modula-tion of the intensities of the orthogonal modes, and alsodecreases the amount of coupling [1].

Fig. 3b compares the peak beat power of the ceramicand crystalline configurations, the former showing a stron-ger beat note (6 dB increase) across all frequencies. Forboth the ceramic and crystalline configurations, the dccomponent of the photocurrent with no drive voltage tothe lithium niobate was identical. The scatter in Fig. 3b isattributed to noise (including electronic noise and mechan-ical instabilities of the laser) and the measurement resolu-tion and digitization of our RF analyzer over the largescan bandwidths used in these experiments.

4. Intra-cavity mode coupling

To investigate and compare the nonlinear couplingbetween the polarization modes on the laser material weimplemented a polarization sensitive feedback technique.This technique was first applied by Alouini et al. [6] formode coupling dynamics in doped-glass microchip lasers.We use, as shown in Fig. 4, a combination of a HWPand a polarizing cube (PBS 1) to select one of the twopolarization eigen-states. A piezoelectric-driven high reflec-tor (PZT-HR) at 1064 nm, driven with a triangle-wavesignal, modulated the loss of that polarization state byre-injecting that polarization into the cavity. The mirrorwas driven so that the loss modulation was in the rangeof 660–690 Hz, away from electronic and mechanical noisefrequencies and many orders smaller than relaxation oscil-lation frequencies. Optical density filters were added toreduce the re-injected intensity to �1 part in 105. A non-polarizing beam-splitter cube (NPBS) was inserted betweenthe HWP and PBS 1 so that the out-going wave from thelaser was split and passed through another PBS (PBS 2,which was aligned similarly to PBS 1). Two large area pho-todiodes collected the individual polarization states. Clear

PZT HR mirror

Neutral densityfilters ~ 1.5 OD

PBS 1

PBS 2

NPBS

HWPPinhole

PD 1

PD 2

Fabry-Perotinterferometer

Detector 1Detector 2

Dual frequency laser(see Fig. 1)

Modulation direction

Time

Inte

nsi

ty (

arb

.)

Fig. 4. Polarization-sensitive feedback arrangement used to slowly mod-ulate the gain of one polarization state.

out-of-phase intensity modulations were seen and an exam-ple is shown in the insert of Fig. 4.

Following from Lacot and Stoeckel’s paper [10] onmodelling the nonlinear mode coupling dynamics inmulti-mode microchip lasers, the phenomenological rateequations for the normalized population inversion (Nx,y)and normalized intensities (Ix,y) are

dNx;y

dt¼ N 0gx;y � N x;y � ðbx;ygx;yIx;y þ hxy;yxgy;xIy;xÞNx;y ; ð2Þ

dIx;y

dt¼ cNx;yIx;y � cIx;y � cflNx;y ; ð3Þ

where N0 is the steady-state value of normalized popula-tion inversion in the absence of stimulated emission whichdepends on the pumping level. gx,y represents the gain ex-pressed as a ratio with respect to the strongest mode; this,in our case, can be set to unity for both modes. c is the ratioof the population-inversion lifetime to the cavity lifetimes,and fl is the effect of spontaneous emission. bx,y and hxy,yx

are the self-saturation and cross-saturation terms for x andy polarization modes. Using this notation, Lamb [9] de-fined a mode coupling constant C as the ratio of cross-sat-uration (in this case, gain available to orthogonalpolarization states) to the self-saturation (here, effectivelythe spatial hole-burning of same polarization states),

C ¼ hxyhyx

bxby: ð4Þ

When the loss modulation is much smaller than therelaxation oscillations (in amplitude and frequency) wecan consider the laser to be in a stationary state andthe modulation is a simple perturbation of this case. Asshown in Fig. 5a, the polarization mode coupling canbe directly determined by the change in modulated inten-sities and the application of a simple relationshipC = (�DIy/DIx)2.

For the crystalline and ceramic laser arrangements asoutlined earlier in the paper, we evaluated the polariza-tion mode coupling constant. In both cases, the laserwas operated with a frequency difference between thetwo orthogonal modes of approximately 200 MHz.Although no effort was made to lock this frequency, thelaser was mechanically and thermally stable and driftedless than 50 kHz over the period of the experiment. A sta-ble region of operation was found by varying the inver-sion ratio until the experimentally determined couplingconstant remained constant (see Fig. 5b). In this regionboth the beat frequency and the beat amplitude were alsovery stable. The coupling constant for crystallineNd:YAG was measured to be 0.16 ± 0.05 and is in closeagreement with a coupling measurement made with a spa-tially separated technique reported in [12]. The ceramicNd:YAG laser had a significantly higher coupling con-stant of 0.72 ± 0.05.

The increased coupling between the eigen-polarizationsin the gain medium is related to the increased beat strength

Fig. 5. (a) Typical experimental results for the ceramic and crystallineconfigurations showing the intensity of one polarization mode as afunction of the other mode (plotted as detector current). Data pointsshown are the voltage–time traces over five modulation periods, and fromthe gradient of the fitted data squared, the polarization mode couplingconstant can be directly determined. (b) Lamb’s coupling constant C as afunction of the inversion ratio r. A stable dual frequency region exists forr J 1.15 until a second longitudinal mode starts to oscillate near r � 1.5.

A. McKay et al. / Optics Communications 272 (2007) 425–430 429

in the ceramic configuration. Coupling, in general, comesfrom the competition for the same excited Nd ions by thetwo modes and depends heavily on the gain saturationand gain spatial hole-burning effects. In crystalline YAG,the orientations of the six possible active sites (three setsof orthogonally directed sites [20,21]) allow cross satura-tion between the two polarizations, depending on crystalcut and crystal angle with respect to the laser axes. How-ever, in ceramic YAG, the optical modes pass throughmany randomly distributed and randomly oriented crystal-lites. The optical modes therefore experience more than the6 possible active site orientations of a single YAG crystal,especially at the grain boundaries. To consider the effect ofthermally induced birefringence, ceramic has been mod-elled as a series of phase plates with arbitrary eigen-polar-izations and phase delays [22] that effectively introduce aweak ellipticity to the two orthogonally polarizationmodes. Although this depolarization effect is weak at theintensities that we are discussing in this paper comparedto the effect of the randomly oriented crystallites, the over-all effect is to provide stronger cross-saturation and cou-pling in the ceramic gain medium.

In the single mode case, the spatial hole-burning can betreated as a population grating with a period of half the las-

ing wavelength (K = k/2). In the presence of two weaklycoupled (0 6 C < 1) orthogonal modes an amplitude mod-ulation of the population gratings occurs. The populationor gain grating, because of this amplitude modulation,gains a spatial frequency component of the other mode.Modulation depth is related to the cross-saturation term,or in effect, the coupling constant. Thus, the period ofthe modulation envelope is the frequency differencebetween the two modes. The resulting effect is a narrowingof the self-heterodyne beat signal. In traditional two laserheterodyne systems the beat width is governed by the rela-tive frequency stability of the two lasers. In this case withboth polarization modes containing like frequency compo-nents and with increased mode coupling, a narrowing ofthe beat signal results, while total power remains constant.

5. Conclusions

In conclusion we have observed two-frequency orthogo-nally polarized operation of a Nd-doped ceramic YAGlaser. A 6 dB beat-signal enhancement (i.e., a four-foldincrease on a linear power scale) is seen in ceramicNd:YAG as compared with crystalline Nd:YAG. Similarly,the ratio of the ceramic to crystalline polarization modecoupling constants shows experimentally, also, an approx-imate four times increase. Furthermore longitudinal modehopping is somewhat restricted in this ceramic material andthe continuously-tuned frequency difference between thetwo orthogonal modes exceeds 1.5 GHz, much greater thanhalf the longitudinal mode spacing in the cavity used. Weattribute these phenomena to an increased polarizationmode coupling constant in the ceramic Nd:YAG material.Here, the random crystallite structure of the ceramic mate-rial, especially along the optical axis, leads to more effi-ciently coupled polarized states.

Acknowledgements

The authors would like to acknowledge fruitful discus-sions with Jong-Dae Park of the Pai Chai University, Kor-ea, and the funding and support of the Defence Science andTechnology Organization (DSTO), the Australian Re-search Council and Macquarie University.

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