484 OPTICS LETTERS / Vol. 25, No. 7 / April 1, 2000

Thermo-optical effect and saturation of nonlinearabsorption induced by gray tracking in a

532-nm-pumped KTP optical parametric oscillator

Benoıt Boulanger, Jean-Philippe Feve, and Yannick Guillien

Laboratoire de Physique de l’Universite de Bourgogne, Unite Mixte de Recherche 5027, Centre National de la Recherche Scientif ique,B.P. 47 870, 21078 Dijon Cedex, France

Received November 4, 1999

We present experiments that show that gray tracking modifies the parametric gain and the generatedwavelengths of a KTP optical parametric oscillator pumped at 532 nm near degeneracy. These perturbationsoccur over a limited range of pump intensity. We propose a satisfactory model that takes into accountphotochromic damage, the thermo-optical effect, and the combined processes of creation and saturation of atwo-photon absorber at 532 nm. The temperature dependence of Sellmeier equations of KTP is also establishedat 20–200 ±C. 2000 Optical Society of America

OCIS codes: 190.4400, 190.4410, 160.4760, 190.4870, 190.4970.

In a recent paper it was demonstrated that thegray tracking induced in a KTP crystal by a laserbeam at 532 nm reaches an asymptotic level near100 MW�cm2: This intensity corresponds to themaximum concentration of color centers, i.e., Ti31 ions,which can be created in f lux-grown crystals accordingto the initial concentration of defects.1 In the samepaper it was also established that gray trackingvanishes above 170 ±C.

We report here original experiments in which thegain curve and the emitted wavelengths of KTP op-tical parametric oscillators (OPO’s) are measured asa function of the pump intensity at 532 nm up to150 MW�cm2. The experiments were performed atroom temperature and at 195 ±C, which is above thegray-tracking vanishing temperature.

We considered two KTP crystals produced by Crys-tal Laser SA with the same aperture but with differ-ent thicknesses: 5 mm 3 5 mm 3 8 mm and 5 mm 35 mm 3 10 mm flux-grown uncoated crystals, cut atu � 90± from the z axis (binary axis) and at f �23.3± from the x axis. KTP was mounted in a heaterthat allows the temperature to be raised to 200 ±Cwith a stability of 60.1 ±C. The heater was thenplaced into a 20-cm linear cavity with plane mirrorsselected to resonate at both signal and idler near1064 nm as a doubly resonant OPO. The 532-nmpump beam was emitted by a seeded Q-switchedand frequency-doubled Nd:YAG laser with a 10-Hz-repetition rate, TEM00, a single longitudinal mode, anda 6-ns half-width duration at 1�e2. A telescope re-duced the beam radius to 1.2 mm at 1�e2. A half-wave plate with a Glan–Taylor polarizer allowedus to vary the intensity from 0 to 150 MW�cm2.The polarization of the pump and signal beams wasin the xy plane, and that of the idler was alongthe z axis of the KTP for phase matching. Thetotal average power and the wavelengths of the sig-nal and idler beams delivered from the output cou-pler of the OPO were measured as a function of thepump energy at 22 and 195 ±C. At room tempera-

0146-9592/00/070484-03$15.00/0

ture, these measurements were performed after opera-tion at 30 mn to ensure that gray tracking reached thesteady state that corresponded to each value of pumpintensity.

The gain curves of the crystal with length L �10 mm are shown in Figs. 1 and 2 at 22 and 195 ±C,respectively, as a function of peak pump intensity.The peak intensity was estimated from the mea-sured energy multiplied by �2�p�3/2�w0

2t, where w0and t are, respectively, the radius and the half-width duration at 1�e2 of the Gaussian beam. Theoscillation threshold was found near 20 MW�cm2 forthe two temperatures. At 195 ±C the gain increasedover all the intensity range considered. The behav-ior was different at room temperature: The gain ex-hibited a plateau from 60 to 80 MW�cm2; from eitherside of the plateau the gain increased at the samerate as a function of the pump intensity. This ef-fect can be reproduced, and it is of the same kindfor 8-mm-thick KTP. The measured idler and signal

Fig. 1. Measured and calculated average power emittedat both signal and idler wavelengths as a function of the532-nm peak intensity at room temperature.

2000 Optical Society of America

April 1, 2000 / Vol. 25, No. 7 / OPTICS LETTERS 485

Fig. 2. Measured and calculated average power emittedat both signal and idler wavelengths as a function of the532-nm peak intensity at 195 ±C.

wavelengths emitted by the 10-mm KTP OPO areplotted in Fig. 3 as a function of the 532-nm peakintensity for the two temperatures. The monochroma-tor is accurate to within 60.3 nm. The wavelengthsmaintained constant values of li � 1073 nm and ls �1055 nm, respectively, for the measurements at 195 ±Cwithin the accuracy of our measurement. The corre-sponding ref lectivities of the input cavity mirror wereRi � 84.2% and Rs � 97.1%; for the output couplerRi � 71.0% and Rs � 75.1%. At 22 ±C we observedchanges in wavelength of 10.2 nm for the idler and20.6 nm for the signal at 90 100 MW�cm2. The re-f lectivities of the cavity mirrors maintained constantvalues of Ri � 93.0% and Rs � 94.7% for the inputmirror and Ri � 73.0% and Rs � 73.6% for the outputcoupler.

These measurements undoubtedly show that graytracking induces modif ications of the OPO’s proper-ties: Gain and wavelength curves are not disrupted athigh temperature, unlike at 22 ±C, where gray tracksare formed. These perturbations occur in the inten-sity range for which the rate of increase of gray track-ing is high.

It is possible to estimate the variation of the linearabsorption coefficient induced by gray tracking as afunction of the 532-nm peak intensity by fitting thetransmission measurements of the 10-mm KTP crystalcited in Ref. 1 with the following function:

a�I � � anir 1 aaC�I � ,

C�I � � 1 21 1 exp�2�I0�A�2�

1 1 exp��I 2 2 I02��A2��, (1)

where I0 � 68 MW�cm2 and A � 24.65 MW�cm2. Themeasurements were performed on a 10-mm KTP crys-tal, which was also used in the present study. aniris the linear absorption coefficient in the limit of Igoing to zero. The absorption that is induced by the532-nm irradiation is aaC�I �. The normed functionC�I � is proportional to the concentration of Ti31 thatis created by the beam at 532 nm with a peak intensity

I ; aa is the asymptotic value of the photoinduced linearabsorption that corresponds to the maximal concentra-tion of Ti31 that can be formed in the KTP crystal. Forexample, the xy components of anir and aa at 532 nmare equal to 1.85 and 1.75 %�cm, respectively. The I2variation in C�I � indicates that the color centers arecreated by a two-photon process.

We can interpret the change in wavelength of theOPO with the pump intensity shown in Fig. 3 as athermo-optical effect that is due to the increase ofthe linear absorption coefficient described by Eq. (1).Within this hypothesis and to estimate the correspond-ing increase of temperature, we measured the ther-mal detuning of the same OPO pumped at 40 MW�cm2.This intensity induces a weak level of gray tracking, sothe perturbation of the OPO will be essentially due tothe heating of the crystal. Starting from the Sellmeierequations of Ref. 2 established at room temperature,the fit of the experimental data allowed us to establishthe three dispersion equations of KTP as a function oftemperature. They are valid from 22 to 200 ±C withthe following form:

ni2�l, T � � ai 1 bi�T2 2 400�

1bi 1 di�T2 2 400�

l2 2 ci 1 fi�T2 2 400�2 �di 1 ri�T2 2 400��l2. (2)

The wavelength l is expressed in micrometers; thetemperature T , in degrees Celsius. The parametersare given in Table 1, where the coefficients ai, bi, ci,and di are those of Ref. 2. We estimate that the in-crease in temperature that corresponds to the changein the idler and signal wavelengths that is inducedby the gray tracking is 15 ±C, according to Eq. (2) and

Fig. 3. Idler li and signal ls wavelengths emitted at 22and 195 ±C versus 532-nm peak intensity. The dashedlines are guides for the eye.

486 OPTICS LETTERS / Vol. 25, No. 7 / April 1, 2000

Table 1. Parameters of the Temperature-DependentSellmeier Equations for KTP Valid for 20–200 ±Ca

Axis

Coefficient x y z

ai 3.0065 3.0333 3.3134bi 0.03901 0.04154 0.05694ci 0.04251 0.04547 0.05657di 0.01327 0.01408 0.01682bi �31027� 25.3580 22.7261 21.1327di �31027� 2.8330 1.7896 1.6730fi �31027� 7.5693 5.3168 20.1601ri �31027� 23.9820 23.4988 0.52833

aSubscript i refers to axes x, y, and z of the crystallographicalframe, where z corresponds to the binary axis.

Table 1. This result is in good agreement with themeasurements of thermal detuning from 25 to 150 ±Cof an eye-safe KTP OPO pumped at 1064 nm: The sig-nal detuning rate dl�dT was found to be 20.022 and20.03 nm�±C for propagation along [100] and [010], re-spectively.3 The agreement with the thermo-opticalcoefficients of Ref. 4 is also satisfactory. Indeed, fromthese data we calculate an increase of 10 ±C for thesignal wavelength change of 20.6 nm. Even if thethermo-optical model is coherent with other measure-ments, we cannot exclude the contribution of anothermechanism whereby gray tracking would directly in-duce a weak change in the birefringencies.

At room temperature, the generated wavelengthsvary but the OPO remains phase matched and doublyresonant over the pump intensities considered. Thusthe plateau of the gain curve of Fig. 1 is not due toa phase mismatch but is necessarily due to losses byabsorption. We performed a numerical calculation ofthe total generated power of the pulsed OPO based ona simplif ied model in which diffraction and walk-offwere neglected, which is justif ied in our case. Thecalculations were made with an effective coefficientxeff � 2deff � 5.53 pm�V (Ref. 5) and the ref lectivi-ties of the cavity mirrors given above. The onlyfitted parameter was the initial value of the signaland idler electric fields, i.e., the parametric f luores-cence. There was satisfactory agreement betweencalculation and experiment at 195 ±C, as is shownin Fig. 2, where the fitted value of the parametricf luorescence is 4.104 V�m. The agreement was alsosatisfactory for the 8-mm crystal with a parametricf luorescence of 2.104 V�m. At 22 ±C we first calcu-lated the generated power by including the linearabsorption term, 2�a�2�E, in the three coupled-waveequations for which the variable linear absorptioncoefficient a is given by Eq. (1). This model didnot describe the behavior of the gain curve, evenwith high and unusual values of aa at pump, signal,and idler wavelengths. So we conclude that thelosses that produce the plateau are due to nonlinearabsorption. Furthermore, the experimental curveof Fig. 1 indicates that perturbation of the gaincurve occurs only over a narrow range of intensity.This suggests that two mechanisms are involvedthat cause opposite variations as a function of the

intensity. Such behavior can be well explainedby the formation and saturation of a two-photonabsorber at 532 nm. The corresponding nonlinearabsorption coefficient b�I � is then proportional to theconcentration of color centers created, i.e., C�I � givenby Eq. (1), and to an intensity-dependent function ofsaturation, S�I �, that gives

b�I � � bmaxC�I �S�I � , S�I � �1

1 1 �I�Ih�2, (3)

where bmax is the maximal level of two-photon ab-sorption. We obtain the S�I � function in the steadystate by considering that the rate equations of popu-lation densities of a two-level system dN�dt depend on6NI2; note that the rate equations of a linear satu-rable filter depend on 6NI , so S�I � varies as I�Ih inthat case.6 We fitted the experimental gain curve ofFig. 1 by including the contribution of two-photon ab-sorption, i.e., 2�b�2�E3, with b given by Eq. (3), in thedifferential equation relative to the 532-nm pump elec-tric field amplitude only. Satisfactory agreement wasfound with the same effective coefficient and paramet-ric f luorescence as those at 195 ±C and with bmax �0.20 cm�GW and Ih � 35.64 MW�cm2. The agree-ment between calculation and experiment was alsosatisfactory for the 8-mm crystal with parameters simi-lar to those of the 10-mm crystal: I0 � 91 MW�cm2,A � 27.5 MW�cm2, Ih � 30.4 MW�cm2, and a para-metric f luorescence of 3.104 V�m. Our model is fur-ther validated because the value of bmax that wasdeduced from our fit is very close to the published coef-ficients measured by Z scan with a picosecond 532-nmlaser: 0.24 cm�GW, 0.14 cm�GW, and 0.16 cm�GWalong [100], [110], and [010], respectively. These threedirections of propagation are contained in the xy planeof KTP as in our case.7 Note that saturation of thelinear absorption was never observed. Confirmationthat it does not occur would imply that the color centerleading to two-photon absorption, which saturates, isnot the same species as for linear absorption, i.e., Ti31.But we can conclude that the two types of color cen-ter are created by the same mechanism, i.e., the two-photon process described by C�I � in Eqs. (1) and (3).

B. Boulanger’s e-mail address is benoitb@satie.u bourgogne.fr.

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