Second-harmonic generation by Nd3+:YAG/Cr4+:YAG-laser pulses with changing state of polarization

Kir’yanov et al. Vol. 17, No. 10 /October 2000 /J. Opt. Soc. Am. B 1657

Second-harmonic generation by Nd31:YAG/Cr41:YAG-laser pulses

with changing state of polarization

Alexander V. Kir’yanov and Vicente Aboites

Centro de Investigaciones en Optica A.C., Apartado Postal 948, Leon 37000, Guanajuato, Mexico

Igor V. Mel’nikov*

Laboratoire d’Optronique, Ecole Nationale Superieure de Sciences Appliquees et Technologie, 6 rue de Kerampont,B.P. 447, 22305 Lannion Cedex, France and General Physics Institute of the Russian Academy of Sciences,

Moscow 117942, Russian Federation

Received November 15, 1999

We describe the passive Q-switching regime of a neodymium laser that contains a Cr41:YAG saturable ab-sorber inside the cavity. Two configurations of the laser cavity are modeled: the cavity containing a partialpolarizer as an additional unit and the microchip laser cavity in which the functions of an active element andsaturable absorber are combined in a single piece of a Nd31:YAG/Cr41:YAG crystal with reflecting facets. Itis shown that both lasers are able to generate a giant pulse with a changing state of polarization. Both thekinetics of the state of polarization of the pulse and its impact on second-harmonic generation are treated nu-merically. We find that the up-conversion efficiency can be enhanced and that harmonic-pulse compressioncan be obtained by means of the proper orientations of the intracavity polarizing elements, for the first con-figuration, or by choosing the polarization of the longitudinal pump and angular orientation of the doublingcrystal, for the second one. The ability of the doubling crystal to analyze the state of polarization of pulseswith nonlinearly changing polarization is discussed. © 2000 Optical Society of America[S0740-3224(00)00510-5]

OCIS codes: 140.3540, 140.3580, 190.2620, 190.5940.

1. INTRODUCTIONIn recent years, the interest in Q-switched neodymium la-sers has increased, owing to the manufacture of a newsaturable absorber (SA) based on a Cr41:YAG crystal,1–19

which has excellent bleaching and thermo-opticsproperties.2,4 In addition, the Cr41:YAG crystal also of-fers another feature that seems to be quite attractive forpossible implementation in the area of Q-switched solid-state lasers. This is the latent anisotropy of absorptionof the crystal, which arises because of the three possiblelocations of the Cr41 ion in the YAG lattice.5,6 The an-isotropy was observed as being dependent on both thetransmission coefficient and the polarization azimuth ofthe radiation of a neodymium laser on the angular orien-tation of the Cr41:YAG crystal outside the laser cavity.7–9

More recently, the dependence of the output parameters[giant pulse (GP) energy and pulse width] of a Nd31:YAGlaser Q switched by a Cr41:YAG SA on the spatial distri-bution of the Cr41 ions and the possible control of thepulse polarization by a weak seeding signal have beenstudied.10–12 It has also been observed that the state ofpolarization of the output pulse of the laser that uses theCr41:YAG crystal as SA depends nonlinearly on suchorientation.13,14

In addition to the rather straightforward implementa-tion as a Q switch, the Cr41:YAG crystal, as a part of theneodymium laser cavity, can also be applied in frequencydoubling of laser pulses.15–17 One may anticipate new

0740-3224/2000/101657-08$15.00 ©

physics arising, say, in type II second-harmonic genera-tion (SHG) when the laser state of polarization changes intime. To the best of our knowledge, this problem has notbeen addressed so far.

Our aim in this paper is to develop a general theoreti-cal description, one that is as simple as possible, to de-scribe the passive Q-switching of a neodymium laser con-taining a Cr41:YAG SA, with an emphasis on thenonlinear rotation of the polarization azimuth during theGP generation. For application, the SHG of such pulseswith changing state of polarization is analyzed for bothtype I and type II synchronism. Two configurations ofthe laser are considered: (A) A neodymium laser inwhich the cavity comprises such units as an active me-dium (AM), Cr41:YAG SA, and polarization controller(PC) in the form of a partial polarizer and (B) a microchipNd31:YAG/Cr41:YAG laser with a monolithic cavitybounded with crystal facets.

2. GENERAL FORMULATIONConsider first, as a most illustrative example, a neody-mium laser (laser A), whose cavity [Fig. 1(a)] is formed bytwo mirrors (1) and (2) and an AM that is a Nd31:YAGcrystal (3). It also contains a SA in the form of aCr41:YAG crystal (4) and a PC in the form of a glass plate(5). Suppose that the plate forms the angle b with theaxis orthogonal to the longitudinal axis of the cavity (z).

2000 Optical Society of America

1658 J. Opt. Soc. Am. B/Vol. 17, No. 10 /October 2000 Kir’yanov et al.

Assume that this axis is parallel to the [001] axis of theCr41:YAG crystal. The other two axes of the Cr41:YAGSA, [100] and [010], lie in the transverse (x –y) plane ofthe cavity and are oriented with respect to the x axis atthe angles u [100] and u1p/2 [010], correspondingly. Inturn, the orientations of the x and y axes are chosen suchthat there are minimum losses along the x axis (aX),whereas the maximum is reached along the y one (aY).Thus the linear anisotropy of the cavity (aY 2 aX) is dueto the PC specific orientation (angle b), whereas its non-linear anisotropy is due to the latent anisotropy of theCr41:YAG SA (i.e., to be determined by the angle u). As-sume, further, that the output GP has an elliptic polar-ization, and the ellipse azimuth is defined as the angle w.

The state of polarization of the laser can be measuredby use of either an extracavity polarizer, e.g., a Glanprism, or a x (2)-nonlinear crystal.20 This is the reasonthat there is a polarization-sensitive element (6) embed-ded into the configuration. Its rotation is described bythe angle c, which corresponds to the maximum trans-mission of the Glan prism or orientation of the axis of thex (2) crystal.

A sketch for the laser of configuration B (laser B) isgiven in Fig. 1(b). In this case the functions of AM andSA can be provided either by the YAG crystal co-activatedwith both Nd31 and Cr41 ions13 or by an element consist-ing of the two adjacent pieces of Nd31:YAG and Cr41:YAGcrystals.15 The output facets of the crystals are assumedto be coated with reflecting mirrors. No additional PC orany other elements are assumed to be inside the cavity inthe last configuration. The longitudinal pumping of thecomposite monolithic AM/SA element is assumed.

The viable standard rate equations that describe theproperties of the Q-switched regime in accordance withour particular task are

dFa

dt5

Fa

tRH 2saNala 2 2ssls@ns

~1 ! cos2~u 2 w!

1 ns~2 ! sin2~u 2 w!#

2 lnS 1

r D 2 ax cos2 w 2 ay sin2 wJ , (1)

dNa

dt5 2gsaNaFac, (2)

dns~1 !

dt5 2ssns

~1 !FacK cos2~u 2 w! 1ns

0 2 ns~1 !

ts

, (3)

dns~2 !

dt5 2ssns

~2 !FacK sin2~u 2 w! 1ns

0 2 ns~2 !

ts

, (4)

where Fa is the average photon density inside the cavityin the AM; Na is the population inversion in the AM; ns

(1)

and ns(2) are the ground-state populations of the Cr41

groups [100] and [010], respectively; ns0 is the initial non-

disturbed ground-state population of the Cr41 centers; sais the lasing cross section of the AM; ss is the Cr41:YAGresonant absorption cross section; la and ls are thelengths of the AM and Cr4 1 :YAG SA, respectively; K5 Sa /Ss is the ratio of the transverse size of the laserbeam in the AM to that in the SA; r is the reflection coef-ficient of the output mirror (2) [Fig. 1(a)]; g is the AMpopulation inversion reduction factor; tR is the round-triptime for the cavity of the length L (tR5 2L/c, where c is the velocity of light); and ts is the re-laxation time of the Cr41:YAG SA. The set of equations[(1)–(4)] corresponds to laser A indicated above and needsonly some formal changes in Eq. (1) for laser B.

To describe the evolution of the state of polarization ofthe laser [see Fig. 1(a), configuration A], assume that thisis always an eigenstate corresponding to the minimum ofthe total intracavity losses. Following the steps on thepolarizability calculation described elsewhere,14 one canexpress the evolution of w(t) as

w~t ! 51

2arctanH sin~2u!

cos~2u! 2aY 2 aX

2lsss@ns~1 !~t ! 2 ns

~2 !~t !#J ,

(5)

where (aY 2 aX) is the PC partial losses difference, beingdetermined from the Fresnel formulas for a tilted glassplate.

For laser B, the subsystem of Nd31 ions in the compos-ite AM/SA matrix plays the role of a PC: The weak am-plification anisotropy of AM21,22 should be accounted forby the nonsaturated components of the amplification co-efficient (kY 2 kX),23 where the x and y components aredetermined by the longitudinal pumping geometry. Fur-ther calculations for the nonlinear rotation f(t) of the GPpolarization in the AM/SA crystal are based on the proce-dure described above, giving rise to

Fig. 1. (a) Schematic of laser A; (b) schematic of laser B.


w~t ! 51

2arctanH sin~2u!

cos~2u!2kY 2 kX

2lsss@ns~1 !~t !2ns

~2 !~t !#J . (58)

Here u is measured with respect to the maximum of am-plification of Nd31:YAG, given in fact by the pump polar-ization direction.21,22

It can be seen that both formula (5) and formula (58)are equivalent. In terms of underlying physics, thismeans that the linear anisotropy of the laser cavity re-sults from the presence of a PC in the form of a tiltedglass plate or Brewster facets of the intracavity elementsin laser A. It can also stem from the weak local-field an-isotropy of Nd31 ions in the YAG lattice and pump linearpolarization, in laser B.

Equations (1)–(5) and (1)–(58) are solved numerically toobtain the GP intracavity intensity, I 5 hvcFa/2LSa (Sais the lasing mode spot size), and polarization azimuthw(t); these describe the nonlinear dynamics of the state ofpolarization. On doing this, one has to bear in mind thatthe nonlinear rotation of the polarization results from theinterplay between the linear anisotropy that is due to thePC (laser A) or Nd31 ions system in the YAG lattice (laserB) and the self-induced nonlinear one that is due to Cr41

ions in the YAG crystal.We now consider the case in which there is a doubling

crystal as the unit (6) of the scheme studied [Fig. 1(a)].

In this case the sets of Eqs. (1)–(5) and (1)–(58) must beextended so as to describe the GP evolution on traversingthe x (2) crystal with type I,

dAp

dj5 2ApAs sin h, (6)

dAs

dj5 Ap

2 sin h, (7)

dh

dj5 d 2 S 2As 2

Ap2

AsD cos h, (8)

or type II synchronism,

dAp~1 !

dj5 2Ap

~2 !As sin h, (9)

dAp~2 !

dj5 2Ap

~1 !As sin h, (10)

dAs

dj5 Ap

~1 !Ap~2 ! sin h, (11)

Fig. 2. Scenarios for laser A (see Table 1) intracavity intensity I (curves 2) and polarization azimuth f (curves 1). (a) u 5 40°, b5 10; (b) 50; (c) 30°; and (d) u 5 45°, b 5 30°.


dh

dj5 d 2 FAp

~2 !As

Ap~1 !

1Ap

~1 !As

Ap~2 !

2Ap

~1 !Ap~2 !

AsGcos h,

(12)

where Ap , Ap(1) , Ap

(2) , and As are the normalized realamplitudes of the pump and second-harmonic (SH)waves, respectively; h is the relative phase between theharmonic and the pump waves (h 5 hs 2 2hp); d is thenormalized phase mismatch; and the nonlinear couplingis chosen as a normalization parameter j.24 The setof Eqs. (6)–(12) is derived under assumptions of thesteady-state interaction between the fundamental waveand the SH in a transparent quadratic material. Thesilent advantage of these approximations is that they arewell suited for the nanosecond pulses that interestus, since they are much longer than nonlinear crystalscurrently available. It is also worthwhile to note thatunder our approximations the amplitude of the fun-damental wave relates to the intensity of the pulse I, thepolarization azimuth w, and the orientation of the dou-bling crystal c as Ap } AI cos( w 2 c) and Ap

(1)

} AI cos( w 2 c); Ap(2) } AI sin( w 2 c) for type I and

type II synchronism, respectively.

3. RESULTS AND DISCUSSIONThe results of calculations for laser A that are governedby Eqs. (1)–(5) are shown in Fig. 2 for the input param-eters listed in Table 1 and obtained from Refs. 14 and 25,where this type of laser has been studied previously. Itis seen that, depending on mutual orientations of theCr41:YAG SA (angle u) and PC (angle b), different re-gimes can be observed. Specifically, one can run the la-ser in the regimes presented in Figs. 2(a) and 2(b), whenchanges of the polarization azimuth can be either large orsmall but always correspond to the very start of the GPgeneration and therefore are not distinguished experi-mentally. However, as can be seen from Fig. 2(c), the po-larization azimuth can also evolve on a time scale veryclose to that on which the GP does. Note that regimesgiven in Figs. 2(a)–2(c) are observed only if the angularorientation of the Cr41:YAG SA is not equal to u ' 0°,645°, 690° ,... ; otherwise, the GP formation is not ac-companied by any change of the polarization state [Fig.2(d)].

It is extremely important to note that these are all theregimes of operation of the neodymium laser A with theCr41:YAG SA, and any of them can be reached by properchoice of the parameters u, b, L, K, etc. Furthermore, thesame results, not shown here, are obtained for the modelof a microchip Nd31:YAG/Cr41:YAG laser B governed byEqs. (1)–(58); that is, the scenarios listed above also takeplace there.

It follows from our numerical observations that if theGP from either of the two lasers is launched into the dou-bling crystal (6) [see Fig. 1(a)] outside the laser cavity thekinetics of the SHG may be modified. First, consider thecase of laser A, which operates in the regime described byFig. 2(c). In Fig. 3 there are snapshots given for the SHnormalized intensities at the maximum conversion effi-

ciency. The calculations are done for the zero values ofthe SH amplitude at the input (jo 5 0), whereas the in-put relative phase and normalized dephasing do are cho-sen to be equal to 0 and 0.01, respectively. This set ofparameters makes the laser-converter system capable ofgenerating pulses whose shape depends on the nonlinearcrystal orientation given by the angle c, with respect tothe reference axis x. It is readily seen from the compari-son of the traces a–e for type I and a–g for type II syn-chronism, respectively.

To obtain a comprehensive picture of the SHG, we alsofulfilled the simulations that use other values of the non-

Table 1. Input Parameters for Laser A

AM SA Cavity

Nd31:YAG Cr41:YAG

sa 5 6.5 3 10219 cm2 ss 5 5.6 3 10218 cm2 r 5 0.86la 5 5 cm ls 5 0.1 cm L 5 30 cmhy 5 1.85 3 10219 J Tin 5 80%,

Tfin 5 98%Spot sizeSa 5 0.075 cm

g 5 0.6 ts 5 3.0 3 1026 s K 5 1.0

Fig. 3. Numerical data for (a) type I synchronism and (b) type IIsynchronism SHG converters. The data correspond to Fig. 2(c).


linear polarization rotation obtained (see Figs. 2(a) and2(b)]. From these results we can conclude that largervalues of the nonlinear rotation of the polarization direc-tion bring more asymmetry into the SH output pulse.But if the polarization of the laser pulse experiences nononlinear rotation [Fig. 2(d)], there is no asymmetry ofthe SH pulse found in our simulations.

It is of straightforward practical interest to comparethe dependencies of the SH peak intensity and SH pulseduration on the orientation of the doubling crystal for thecases of the presence (or absence) of the nonlinear rota-tion of the GP polarization azimuth. These are plotted inFig. 4 for the cases of type I [Figs. 4(a) and 4(c)] and typeII [Figs. 4(b) and 4(d)] synchronism, respectively, and forthe shape of the pumping GP given in Fig. 2(d) (curve 1)and Fig. 2(c) (curve 2). It is seen that our model predictsconsiderable shortening of the SH pulse duration with re-spect to that of a fundamental (1.06 mm) input pulse (bythe factor of 2) in the case of type II synchronism. Such ashortening is observed for all the orientations of the dou-bling crystal and, in particular, for that which providesthe maximum efficiency of conversion, in contrast to thecase of type I synchronism for which it can be observed ata low efficiency SHG only.

It is also seen from Figs. 4(a) and 4(b) that a doublingcrystal might provide a fairly good tool of analysis of the

state of polarization of a pulsed light (note that this facthas been analyzed in Ref. 20 in the steady-state approxi-mation). For example, one can easily find from curves 1and 2 that the maximum polarization azimuth rotationduring the GP is equal to ;25 deg [compare this valuewith the data for polarization azimuth scenarios in Figs.2(c) and 2(d)], but a novel result is that the direction ofthe rotation manifests itself as an asymmetry of curves 2shown in Figs. 4(c) and 4(d).

Let us now analyze results of numerical calculationsmade for the model of the microchip Nd31:YAG/Cr41:YAGlaser B, which is governed by Eqs. (1)–(58) and (6)–(12).Consider, for instance, the experimental data of Ref. 15 inwhich such a Q-switched microchip laser comprises thetwo adjacent crystals of Nd31:YAG and Cr41:YAG. Thissystem has been theoretically studied elsewhere18; weconcentrate here only on such features that have not beenexplained in the previous work15 and might be a result ofthe nonlinearly changing state of the GP polarization ofthe microchip laser.

The parameters of the laser15 are listed in Table 2.Unfortunately, there is no clear experimental evidence ofwhat is an exact value of the parameter (kY 2 kX). Asdefined above, this parameter accounts for the anisotropyof the weak gain, which is due to the nonequivalent loca-tion of Nd31 ions in a YAG lattice. Here we set this pa-

Fig. 4. (a), (b) Dependencies of SHG peak intensity (in units of pump amplitude); (c), (d) SHG pulse duration on SHG crystal angularposition c. Curves 1 and 2 correspond to the laser dynamics in Fig. 2(d) and Fig. 2(c), respectively. (a), (c) Type I synchronism; (b), (d)Type II synchronism.


rameter equal to such a value of (kY 2 kX) ; 0.055,which gives us the best fit to the experimental data of Ref.15, including the SHG in a KTP crystal.

Figure 5 shows us the shape of the GP from the laser ofRef. 15 and corresponding nonlinear rotation of the polar-ization azimuth calculated by means of the procedure de-

Table 2. Input Parameters for Laser B

AM SA Cavity

Nd31:YAG Cr41:YAG

sa 5 2.5 3 10219 cm2 ss 5 6 3 10218 cm2 r 5 0.94la 5 0.05 cm ls 5 0.025 cm L 5 0.075 cmhy 5 1.85 3 10219 J Tin 5 87%,

Tfin 5 99%Spot sizeSa 5 0.0075 cm

g 5 0.6 ts 5 3.0 3 1026 s K 5 1.0

Fig. 5. One of the scenarios of the GP envelope (curve 1) andpolarization azimuth (curve 2) for laser B. Numerical data foru 5 40°, kY 2 kX 5 0.055.

Fig. 6. Experimental oscillation traces of (a) a fundamental(1.064 mm) GP from a microchip laser; (b) a SH (0.532 mm) pulseafter a KTP doubling crystal. Horizontal scale: 200 ps/div.Data from Ref. 15.

scribed in Section 2. These results are in fairly goodagreement with the experimental ones (see Fig. 6, takenfrom Ref. 15). There are, however, some discrepancies inthe absolute values of the output energy and pulse widthof the GP, observed between the experiment and themodel. That is, the numerical values are less than theexperimental ones by the factor of 1.5. This is probablycaused by such approximation of our model as the rectan-gular cross section of generation, etc. (see Ref. 26).

Figure 7(a) represents results of our numerical calcula-tions done for type II synchronism when the polarizationchange of the GP from the microchip laser obeys the sce-nario given by Fig. 5 [compare curve 3 in Fig. 7(a) withthe corresponding experimental curve in Fig. 6(b)]. Tofacilitate analysis of the data obtained, Fig. 7(b) gives theresults obtained for the same laser but in the case whenthe effect of the nonlinear rotation of polarization is notaccounted for. Comparing these results drives us to theconclusion that the double-peak structure of the SH ob-served in Ref. 15 [Fig. 6(b)] can be attributed to the non-linear change of polarization that occurs during the GPgeneration. In this sense it is notable that the differencein the up-conversion efficiency cannot be explained in any

Fig. 7. Theoretical SH pulses generated by GP propagatingalong a KTP crystal cut for Type II synchronism. (a) SH pulsecorresponding to scenario shown in Fig. 5; (b) the same for inputGP without polarization rotation. Labels 1–4 correspond tosnapshots at increasing normalized distances j measured withrespect to doubling crystal.


other way, since it is observed at equal intensities of thefundamental pulse. Furthermore, significant decrease inthe SH pulse duration at low conversion efficiencies ob-served in Ref. 15 can also be explained within the frame-work of the model accounting for the nonlinear rotationphenomenon.

Before concluding, it seems useful to discuss two sug-gestions that might be important for future developmentof this study.

First, a recent suggestion27 that has been successfullyimplemented28 is an efficient compression method of a SHultrashort pulse by the insertion of a predelay betweenthe two pump pulses that propagate along an ordinaryaxis and extraordinary axis, correspondingly. We believethat the same effect could be reached if the pump pulseshave a nonlinearly rotating polarization. That is, the useof such pulses causes a self-induced delay between thee-pulse and the o-pulse and effectively shortens the SHpulse, as has been found in Refs. 27 and 28. Further-more, this method of compression can also be used in thesubpicosecond time scale when the group-velocity walk-off and dispersion become the important factors.

Second, we have considered here the case of extracavitySHG. In the case of intracavity SHG, we may also expectthe appearance of novel dynamics and, in particular, con-siderable shortening of the fundamental and harmonicpulses.

4. CONCLUSIONSIn this paper we have analyzed the passive Q-switchingmode of a neodymium laser with a Cr41:YAG SA for twoconfigurations of the cavity, with emphasis on the nonlin-ear rotation of the polarization azimuth during a GP gen-eration and its impact on the extracavity SHG. We haveshown how the behavior of the polarization azimuth canbe monitored by such laser parameters as linear and non-linear anisotropy of the cavity, cavity length, focusing ofthe intracavity radiation in AM and SA, etc. We havealso considered the processes of both type I and type IISHG for the GP with nonlinearly changing state of polar-ization. Specifically, we have found that the shape of theharmonic pulse is very sensitive to whether the state ofpolarization of the fundamental pulse experiences suchchanges, which has helped to explain some recent experi-mental results on the SHG of the GP emitted by a micro-chip Nd31:YAG/Cr41:YAG laser. We have predicted thatthe nonlinear rotation of the direction of polarization maycause a two-time shortening of the harmonic pulse incomparison with the case in which no rotation occurs.Finally, we have suggested that an extracavity doublingcrystal may be used to control the state of polarization ofnanosecond and subnanosecond pulses, as its response issensitive to, and can give both an absolute value of, thenonlinear rotation and the direction of this rotation.

ACKNOWLEDGMENTSThis study was supported partly by Consejo Nacional deCiencia y Tecnologia (project 32269-E), Russian Fund forBasic Research (project 98-02-17676), and the National

Ministry for Science, Education and Technology of Francevia the International Centre for Foreign Researchers.The authors thank N. N. Ilichev, M. H. Dunn, D. C.Hanna, A. Miller, W. Sibbett, and G. M. Stephan formany helpful discussions.

A. Kir’yanov can be reached by telephone at 52-47-175823, by fax at 52-47-175000, or by e-mail [email protected] and at [email protected].

*Present address, Centro de Investigaciones en Ing-enierias y Ciencias Aplicadas, Universidad Autonoma delEstado de Morelos, 62210 Cuernavaca, Morelos, Mexico.

REFERENCES1. K. Spariosu, W. Chen, R. Stultz, M. Birnbaum, and A. V.

Shestakov, ‘‘Dual Q switching and laser action at 1.05 and1.44 mm in a Nd31:YAG–Cr41:YAG oscillator at 300 K,’’Opt. Lett. 18, 814–816 (1993).

2. H. J. Eichler, A. Haase, M. R. Kokta, and R. Menzel,‘‘Cr41:YAG as passive Q-switch for a Nd:YALO oscillatorwith an average repetition rate of 2.7 kHz, TEM00 modeand 13 W output,’’ Appl. Phys. B 58, 409–411 (1994).

3. Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y.Kalisky, and M. Strauss, ‘‘Repetitively Q-switching of a CWNd:YAG laser using Cr41:YAG saturable absorbers,’’ IEEEJ. Quantum Electron. 32, 305–310 (1996).

4. A. Sennaroglu, ‘‘Continuous-wave power transmission andthermal lensing of a saturable absorber subject to excited-state absorption,’’ Appl. Opt. 38, 3334–3337 (1999).

5. H. Eilers, K. R. Hoffman, M. Dennis, S. M. Jacobsen, andW. M. Yen, ‘‘Saturation of 1.064 mm absorption inCr,Ca:Y3AL5O12 crystals,’’ Appl. Phys. Lett. 61, 2958–2960 (1992).

6. N. N. Il’ichev, A. V. Kir’yanov, P. P. Pashinin, and S. M.Shpuga, ‘‘Investigation of nonlinear-absorption anisotropyin YAG:Cr41, ’’ JETP 78, 768–776 (1994).

7. N. N. Il’ichev, A. V. Kir’yanov, P. P. Pashinin, and S. M.Shpuga, ‘‘Changes in the profile and state of polarization ofa short light pulse (l 5 1.06 mm) during propagation in aCr41:YAG crystal,’’ Quantum Electron. 24, 771–776 (1994).

8. A. Brignon, ‘‘Anisotropic properties of pulsed four-wavemixing in Cr41:YAG saturable absorbers,’’ J. Opt. Soc. Am.B 13, 2154–2163 (1996).

9. S. Camacho-Lopez, R. P. M. Green, G. J. Crofts, and M. J.Damzen, ‘‘Intensity-induced birefringence in Cr41:YAG,’’ J.Mod. Opt. 44, 209–219 (1997).

10. N. N. Il’ichev, A. V. Kir’yanov, and P. P. Pashinin, ‘‘Model ofpassive Q switching taking account of the anisotropy ofnonlinear absorption in a crystal switch with phototropiccenters,’’ Quantum Electron. 28, 147–151 (1998).

11. I. V. Klimov, I. A. Shcherbakov, and V. B. Tsvetkov, ‘‘Con-trol of the Nd-laser output by Cr-doped Q-switches,’’ LaserPhys. 8, 232–237 (1998).

12. A. V. Kir’yanov, V. Aboites, and N. N. Il’ichev, ‘‘Apolarization-bistable neodymium laser with a Cr41:YAGpassive switch under the weak resonant signal control,’’Opt. Comm. 169, 309–315 (1999).

13. S. Zhou, K. K. Lee, Y. C. Chen, and S. Li, ‘‘Monolithic self-Q-switched Cr,Nd:YAG laser,’’ Opt. Lett. 18, 511–512(1993).

14. N. N. Il’ichev, A. V. Kir’yanov, E. S. Gulyamova, and P. P.Pashinin, ‘‘Polarization of a neodymium laser with a pas-sive switch based on a Cr41:YAG crystal,’’ Quantum Elec-tron. 28, 17–20 (1998).

15. J. J. Zayhowski and C. Dill III, ‘‘Diode-pumped passivelyQ-switched picosecond microchip lasers,’’ Opt. Lett. 19,1427–1429 (1994).

16. A. Agnesi, S. Dell’Acqua, C. Morello, G. Piccinno, G. C.Reali, and Z. Sun, ‘‘Diode-pumped neodymium lasers re-petitively Q-switched by Cr41:YAG solid-state saturable ab-


sorbers,’’ IEEE J. Sel. Top. Quantum Electron. 3, 45–52(1997).

17. A. Agnesi, S. Dell’Acqua, E. Piccinini, G. Really, and G.Piccinno, ‘‘Efficient wavelength conversion with high-powerpassively Q-switched diode-pumped neodymium lasers,’’IEEE J. Quantum Electron. 34, 1480–1484 (1998).

18. P. Peterson, A. Gavrielidis, M. P. Sharma, and T. Erneux,‘‘Dynamics of passively Q-switched microchip lasers,’’ IEEEJ. Quantum Electron. 35, 1247–1256 (1999).

19. M. Brunel, O. Emile, M. Vallet, F. Bretenaker, A. Le Floch,L. Fulbert, J. Marty, B. Ferrand, and E. Molva, ‘‘Experi-mental and theoretical study of monomode vectorial laserspassively Q-switched by Cr41:yttrium aluminum garnet ab-sorbers,’’ Phys. Rev. A 60, 4052–4058 (1999).

20. N. Zheludev, S. Saltiel, and P. Yankov, ‘‘Second-harmonicgenerators as a new class of light polarizers and analyzers,’’Sov. J. Quantum Electron. 17, 948–952 (1987).

21. R. Dalgliesh, A. D. May, and G. Stephan, ‘‘Polariza-tion states of a single-mode (microchip) Nd31:YAG laser—Part I: theory,’’ IEEE J. Quantum Electron. 34, 1485–1492 (1998).

22. R. Dalgliesh, A. D. May, and G. Stephan, ‘‘Polarizationstates of a single-mode (microchip) Nd31:YAG laser—Part

II. comparison of theory and experiment,’’ IEEE J. Quan-tum Electron. 34, 1493–1502 (1998).

23. R. V. Goidin, V. S. Kichuk, V. V. Kravtsov, G. D. Laptev, E.G. Lariontsev, and V. V. Firsov, ‘‘Influence of the pump po-larisation on the characteristics of radiation of a ringNd:YAG chip laser,’’ Quantum Electron. 28, 358–360(1998).

24. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan,Handbook of Nonlinear Optical Crystals (Springer-Verlag,Berlin, 1991).

25. N. N. Il’ichev, A. V. Kir’yanov, E. S. Gulyamova, and P. P.Pashinin, ‘‘Polarization characteristics of a neodymium la-ser passively Q-switched with a Cr41:YAG crystal,’’ Quan-tum Electron. 27, 298–301 (1997).

26. N. N. Il’ichev, E. S. Gulyamova, and P. P. Pashinin, ‘‘Pas-sive Q switching of a neodymium laser by a Cr41:YAG crys-tal switch,’’ Quantum Electron. 27, 972–977 (1997).

27. Y. Wang and R. Dragila, ‘‘Efficient conversion of picosecondlaser pulses into second-harmonic frequency using group-velocity dispersion,’’ Phys. Rev. A 41, 5645–5649 (1990).

28. Y. Wang and B. Luther-Davies, ‘‘Frequency-doubling pulsecompressor for picosecond high-power neodymium laserpulses,’’ Opt. Lett. 17, 1459–1461 (1992).

Documents

Second-harmonic generation by Nd3+:YAG/Cr4+:YAG-laser pulses with changing state of polarization