8
Nonlinear optical properties and Q-switch performance of silica glasses doped with Cu x Se nanoparticles Svetlana A. Zolotovskaya, Vasily G. Savitski, Pavel V. Prokoshin, and Konstantin V. Yumashev International Laser Centre, Belarusian National Technical University, F. Skaryna Avenue 65, Building 17, 220013 Minsk, Belarus Valerij S. Gurin Physico-Chemical Research Institute, Belarusian State University, 220080 Minsk, Belarus Alexander A. Alexeenko Gomel State Technical University, 246699 Gomel, Belarus Received February 3, 2006; accepted February 27, 2006; posted March 9, 2006 (Doc. ID 67659) Glasses containing copper selenide nanoparticles Cu x Se reveal an intense absorption band peaking at 1 m 1.24 eV. The transient bleaching and intensity-dependent transmission of silica glasses with Cu x Se nanopar- ticles of different stoichiometry are studied with 1.08 m 1.15 eV picosecond pulses. The bleaching relaxation time decreases with a shift in the absorption band maximum to the lower photon energies. The dependence of absorption on the input energy of the pulses is saturationlike at the beginning of the plateau at 40 mJ/cm 2 . Passive Q-switching of the Nd 3+ :KGdWO 4 2 laser at 1.067 m is realized with the Cu x Se-doped glasses for different x. © 2006 Optical Society of America OCIS codes: 140.3540, 140.3580, 160.6060, 320.7130. 1. INTRODUCTION Glasses doped with semiconductor nanoparticles are of considerable interest in the context of low-dimensional physics. 1–3 One of their challenging applications is in op- tical switching devices because of their high nonlinear re- sponse to the participation of quantum confined levels; another is in the excitation and relaxation pathways of small particles. 3–7 The size of nanoparticles, chemical composition, crystalline structure, and surface states de- termine the character of the light-absorption processes. Powerful radiation can produce the excited states of nano- particles with different optical features. Interband excita- tion with the development of many excitonic quantum confined levels has been extensively used for the nonlin- ear optical study of nanoparticles of CdS, CdSe, CdTe, CuCl, 8–10 and Cu 2 S. 11–14 Copper chalcogenides embedded into solgel glasses in contrast with II–VI and I–VII com- pound, are shown by their intense absorption band in the near-IR spectral region, which is well developed in the range of 1–1.5 m. 15–18 The general chemical composition of copper selenide can be properly described as a compound with a variable Cu/Se ratio, Cu x Se, since x can cover the range from 1 through 2 and even cases in which x 1 and x 2 are possible. 19–23 Copper selenides also have various crystal- line structures, and the phases are easily transformed at elevated temperatures. 24–26 Moreover, the multivalence of copper and the availability of interaction with atmo- spheric oxygen cause changes in the surface layer of the particles and at the particle–matrix interface. These changes are hard to detect chemically, but they can strongly affect the optical properties. All this increases both scientific and application interest in the new fea- tures of copper selenide nanoparticles; some of the results have been reported by us recently. 27 The intense near-IR absorption band can be effectively bleached with the laser pulses. It has been shown that nanoparticles with similar bandgaps but in a different position of the near-IR ab- sorption band are characterized by various bleaching re- laxation times and ground-state absorption cross sections. A set of intraband energy levels within the copper se- lenide forbidden gap can be responsible for the bleaching and the relaxation mechanisms. Silica glasses containing oxidized copper selenide nano- particles Cu 2 Se have been explored as saturable absorb- ers to create passive Q-switching and mode-locking of the flashlamp-pumped solid-state lasers emitting in the 1–1.5 m spectral range. 15 The present study is to deter- mine the relationships between the nonlinear optical re- sponse of the solgel silica glasses and the chemical com- position of copper selenide nanoparticles. The transient absorption bleaching and absorption saturation of the Cu x Se-doped glasses of different stoichiometry with an IR-absorption band in the range of 1 m 1.24 eV were explored, and an interpretation of the optical properties observed was suggested. The passive Q-switching opera- tion of a diode-pumped Nd 3+ :KGdWO 4 2 (KGW) laser emitting at 1.067 m with Cu x Se-doped silica glasses as 1268 J. Opt. Soc. Am. B/Vol. 23, No. 7/July 2006 Zolotovskaya et al. 0740-3224/06/071268-8/$15.00 © 2006 Optical Society of America

Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles

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Page 1: Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles

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1268 J. Opt. Soc. Am. B/Vol. 23, No. 7 /July 2006 Zolotovskaya et al.

Nonlinear optical properties and Q-switchperformance of silica glasses

doped with CuxSe nanoparticles

Svetlana A. Zolotovskaya, Vasily G. Savitski, Pavel V. Prokoshin, and Konstantin V. Yumashev

International Laser Centre, Belarusian National Technical University, F. Skaryna Avenue 65, Building 17,220013 Minsk, Belarus

Valerij S. Gurin

Physico-Chemical Research Institute, Belarusian State University, 220080 Minsk, Belarus

Alexander A. Alexeenko

Gomel State Technical University, 246699 Gomel, Belarus

Received February 3, 2006; accepted February 27, 2006; posted March 9, 2006 (Doc. ID 67659)

Glasses containing copper selenide nanoparticles �CuxSe� reveal an intense absorption band peaking at 1 �m�1.24 eV�. The transient bleaching and intensity-dependent transmission of silica glasses with CuxSe nanopar-ticles of different stoichiometry are studied with 1.08 �m �1.15 eV� picosecond pulses. The bleaching relaxationtime decreases with a shift in the absorption band maximum to the lower photon energies. The dependence ofabsorption on the input energy of the pulses is saturationlike at the beginning of the plateau at �40 mJ/cm2.Passive Q-switching of the Nd3+:KGd�WO4�2 laser at 1.067 �m is realized with the CuxSe-doped glasses fordifferent x. © 2006 Optical Society of America

OCIS codes: 140.3540, 140.3580, 160.6060, 320.7130.

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. INTRODUCTIONlasses doped with semiconductor nanoparticles are of

onsiderable interest in the context of low-dimensionalhysics.1–3 One of their challenging applications is in op-ical switching devices because of their high nonlinear re-ponse to the participation of quantum confined levels;nother is in the excitation and relaxation pathways ofmall particles.3–7 The size of nanoparticles, chemicalomposition, crystalline structure, and surface states de-ermine the character of the light-absorption processes.owerful radiation can produce the excited states of nano-articles with different optical features. Interband excita-ion with the development of many excitonic quantumonfined levels has been extensively used for the nonlin-ar optical study of nanoparticles of CdS, CdSe, CdTe,uCl,8–10 and Cu2S.11–14 Copper chalcogenides embedded

nto solgel glasses in contrast with II–VI and I–VII com-ound, are shown by their intense absorption band in theear-IR spectral region, which is well developed in theange of 1–1.5 �m.15–18

The general chemical composition of copper selenidean be properly described as a compound with a variableu/Se ratio, CuxSe, since x can cover the range from 1

hrough 2 and even cases in which x�1 and x�2 areossible.19–23 Copper selenides also have various crystal-ine structures, and the phases are easily transformed atlevated temperatures.24–26 Moreover, the multivalence ofopper and the availability of interaction with atmo-pheric oxygen cause changes in the surface layer of the

0740-3224/06/071268-8/$15.00 © 2

articles and at the particle–matrix interface. Thesehanges are hard to detect chemically, but they cantrongly affect the optical properties. All this increasesoth scientific and application interest in the new fea-ures of copper selenide nanoparticles; some of the resultsave been reported by us recently.27 The intense near-IRbsorption band can be effectively bleached with the laserulses. It has been shown that nanoparticles with similarandgaps but in a different position of the near-IR ab-orption band are characterized by various bleaching re-axation times and ground-state absorption cross sections.

set of intraband energy levels within the copper se-enide forbidden gap can be responsible for the bleachingnd the relaxation mechanisms.Silica glasses containing oxidized copper selenide nano-

articles �Cu2Se� have been explored as saturable absorb-rs to create passive Q-switching and mode-locking of theashlamp-pumped solid-state lasers emitting in the–1.5 �m spectral range.15 The present study is to deter-ine the relationships between the nonlinear optical re-

ponse of the solgel silica glasses and the chemical com-osition of copper selenide nanoparticles. The transientbsorption bleaching and absorption saturation of theuxSe-doped glasses of different stoichiometry with an

R-absorption band in the range of 1 �m �1.24 eV� werexplored, and an interpretation of the optical propertiesbserved was suggested. The passive Q-switching opera-ion of a diode-pumped Nd3+:KGd�WO4�2 (KGW) lasermitting at 1.067 �m with Cu Se-doped silica glasses as

x

006 Optical Society of America

Page 2: Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles

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Zolotovskaya et al. Vol. 23, No. 7 /July 2006 /J. Opt. Soc. Am. B 1269

aturable absorbers has been demonstrated. A compari-on is presented of the Q-switching performance withr:YAG crystal and CuxSe-doped glass in the same pump-

ng conditions and with the same cavity design and nu-erical simulation as the laser Q-switched with two dif-

erent types of passive shutters. A Nd3+:KGW laserrystal has been chosen as a gain medium for the-switching experiments because of its attractive fea-

ures. The KGW host can be doped with a high concentra-ion of Nd3+ ions as a result of the compact laser systemsith low threshold and high efficiency. Nd3+:KGW laser

adiation is polarized. Besides, the high-third-order non-inear susceptibility of the KGW host allows the use ofhis crystal for Raman self-frequency conversion. Use of aassive shutter in systems with intracavity Raman con-ersion permits the reduction of the threshold of simu-ated Raman scattering.28

. MATERIALS FABRICATION ANDHARACTERIZATIONilica glass samples containing CuxSe nanoparticles were

abricated by a sequence of operations typical of the well-nown solgel method based on tetraethylorthosilicateTEOS) hydrolysis and modified to facilitate the forma-ion of nanoparticles for the required composition.17,18,29

he main steps are as follows. A sol of polysilicic acid wasrepared by mixing TEOS, ethyl alcohol, water, and amall amount of HCl that served as a hydrolysis catalyst.solid filler in the form of SiO2 particles with a diameter

f 20–50 nm (aerosil) was vigorously mixed with the sol.he latter was transformed into the gel state as a resultf the neutralization of aqueous ammonia �0.1 mol/ liter�o pH=6. The gels obtained were kept in plastic contain-rs and dried in air. Their annealing was done at00–1000 °C providing a control of the porosity before in-roducing copper salts as doping components. With thistep, porous xerogels were fabricated that consisted ofure amorphous SiO2 (with some amount of residual hy-roxide groups).Copper was introduced into the xerogels by impregna-

ion with an alcoholic solution of Cu�NO3�2 with a concen-ration of 3 mmol/ liter followed by air drying and thermalreatment in a hydrogen flow at 600 °C for 1 h. This steprovided the transformation of copper salts and copperxides into metallic copper. The xerogels with Cu werelaced into quartz ampoules containing a weightedmount of Se calculated to produce a selenium partialressure of approximately 0.2–1 atm at a temperature of200 °C. The ampoules were sealed and heated to200 °C in accordance with the specific temperature in-rease rate. As a result the glass samples containinguxSe in the form of nanoparticles were fabricated. Weave chosen three samples with slightly various opticalroperties. A different Cu/Se ratio corresponding to thiseries (Table 1) was done in two ways: (i) by changing themount of selenium that went into the ampoules in whichhe samples were annealed; (ii) by changing the porosityf the xerogels used for preparing the samples.

The variation in the Cu/Se ratio resulted in variousompositions of copper selenide in the samples (Table 1);ccording to the values of E we can state that samples 1,

g

, and 3 correspond to a decrease in x. At present we can-ot give the exact values of stoichiometry coefficient x be-ause of problems in completely directly determining thehemical composition of the nanoparticles within thelasses because of their considerably low concentration.owever, the composition of copper selenide close tou2Se was confirmed by us in earlier studies when Ruth-rford backscattering and high-resolution transverse elec-ron microscopy were used.17,29 Also, the main phaseu2−�Se (JCPDS 06-0680) (Fig. 1) in the glasses was es-

ablished for the samples with an increased concentrationhat possessed analogous absorption spectra. Thus we as-ume that variations in the absorption band position inhe series of samples being studied are provided by ahange in �; the refinement requires further studies. Theize of the main amount of particles in this series ofamples in the 20–50 nm range, which does not varytrongly with Se/Cu; part of the particles are aggregated,nd we show typical micrographs (Fig. 2).The bleaching relaxation time of the glass samples waseasured by the picosecond pump–probe technique with

Table 1. Summary Results of the Bleaching Decayand Intensity-Dependent Absorption

Measurements of Silica Glasses with CuxSe Nano-particles at 1.08 �m „1.15 eV…

ampleEmax(eV)

Eg

(eV)�

(ps)�GSA

�10−17 cm2��max

�10−17 cm2� �R /�0

1 1.21 1.1 �2000 2.6 2.7 0.372 1.13 1.6 1557±427 2.9 2.9 0.143 1.09 1.8 330±32 4.6 4.9 0.09

ig. 1. X-ray-diffraction pattern of CuxSe-doped glasses. Barsndicate the reference data, Cu2−�Se, JCPDS 06-0680.

Page 3: Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles

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1270 J. Opt. Soc. Am. B/Vol. 23, No. 7 /July 2006 Zolotovskaya et al.

n absorption spectrometer based on the passively mode-ocked laser. The Nd:YAlO3 (YAP) laser pulses with a du-ation of 15 ps and a lasing wavelength of 1.08 �m1.15 eV� were used as the pump and the probe beams.he energy density of the sample was �10 mJ/cm2. Theleaching value was defined as differential absorption,OD� , td�=OD� , td�−OD0��, where OD and OD0 are

he optical densities of a sample with and without excita-ion, respectively.

The absorption saturation measurements were per-ormed with the single-beam method. The absorption co-fficient as a function of input energy fluence was deter-ined from the ratio between the pulse energy with andithout the sample. The input energy was varied by a setf neutral filters. The same passively mode-lockedd:YAP laser at 1.08 �m �1.15 eV� was employed as aump source.

. ABSORPTION BLEACHING PROPERTIEShe linear absorption spectra of the glass samples dopedith CuxSe nanoparticles are shown in Fig. 3. There are

wo principal features for all the samples: (i) a steplikeundamental absorption band (viewed rather broadly onhis scale, at 400–600 nm); (ii) the intense absorptionand peaking in the near-IR spectral range. The bandgapg was estimated by replotting the linear absorption spec-

ra as ��= f��−Eg�2 with the assumption of indirectlyllowed transitions.30 This type of fitting was the bestrom trials of different types of transitions (direct and in-irect, allowed and forbidden). The values of Eg and theositions of the absorption band maximum Emax are inable 1. Within the series of samples one can state that,or a greater bandgap less energy is related to the near-IRbsorption band. The latter is attributed to the electronic

ig. 2. Typical micrograph of the nanoparticles produced in theuxSe-doped glasses.

ransitions from the energy levels (A) within the bandgapsee the inset in Fig. 3), which appear because of the mul-ivalence of copper and can correspond to the partial oxi-ation of copper in the nanoparticles.15

Figure 4 shows the kinetics of bleaching relaxation inhe glass samples being studied. The experimental depen-encies have monoexponential decay and can be ex-ressed as

�OD�td� = �OD�0�exp�− t/��, �1�

here � is the characteristic time of the bleaching relax-tion utilized here as an experimental parameter for theamples. The time rises considerably from sample 3 toample 2 in the 0.3–1.6 ns range (Table 1). The completeelaxation process for sample 1 exceeds the maximumvailable delay time in the pump–probe experiment, andhe bleaching relaxation time is estimated to be �2.7 ns.he repeated experiments with the same samples showractically the same results (for an account of the experi-ental errors, see Fig. 4 and Table 1 for the time param-

ters).The dependencies of the absorption coefficient � nor-alized to the initial absorption �0 at 1.08 �m �1.15 eV�

ig. 3. Absorption spectra of the silica glasses embedded withuxSe nanoparticles. The inset is an energy-level diagram for theuxSe nanoparticles.

ig. 4. Kinetics of the bleaching relaxation of the glasses con-aining CuxSe nanoparticles at 1.08 �m �1.15 eV�: Dots, experi-ental; solid lines, linear fit of the experimental data.

Page 4: Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles

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Zolotovskaya et al. Vol. 23, No. 7 /July 2006 /J. Opt. Soc. Am. B 1271

s a function of the incident energy fluence are shown inig. 5. The absorption bleaching relaxation time of theamples being studied is noticeably longer than the pumpulse width �15 ps�; therefore the experimental data arenalyzed within the framework of the slowly relaxing ab-orber model, which is described by the Frantz–Nodvikodified equation31

dE/dz = − h��ln�1/T0�/L�GSA��1 − exp�− �GSAE/h��� − �RE,

�2�

here T0 is the small-signal transmittance, E is the inputnergy fluence, L is the length of the sample, �GSA is theround-state absorption cross section, and �R is the re-idual losses. The values of �GSA and �R, which corre-pond to the numerical simulation results, are collected inable 1. Thus the ground-state absorption cross sectionsf the CuxSe nanoparticles in the different samples are ofhe same order of magnitude and enter the 2.6–4.610−17 cm2 range. This fact suggests that the absorptionechanisms in the copper selenide nanoparticles of differ-

nt stoichiometry with different Eg are similar. Inasmuchs the absorption band in the IR spectral range was as-igned to the transitions from the intraband levels, A (seehe inset in Fig. 3),15 it is evident that they have the sameature for the three samples. The stoichiometry factor ofuxSe changes the position of this additional level and in-reases slightly the ground-state absorption cross sectionn the sample 1–3 series, which can be associated with theariable overlapping orbitals of the level with the excitedtate.

ig. 5. Intensity-dependent absorption of CuxSe nanoparticlesn silica glasses at 1.08 �m �1.15 eV� for 15 ps pulses from the

ode-locked Nd:YAP laser: Dots, experimental data; solid curves,esults of simulation. The inset shows the intensity-dependentbsorption of the CuxSe nanoparticles at low-energy fluence.

The peak absorption cross sections of the CuxSe nano-articles are evaluated by

�0max/���pump� = �max/���pump�, �3�

here �0max is the absorption coefficient at the maximum

f the band. The values of the peak absorption cross sec-ions �max are insignificantly larger than that determinedrom the absorption saturation measurements since theump wavelength practically corresponds to the absorp-ion band maximum position (see Table 1).

The residual losses �R, which are taken into account inq. (2), include nonsaturable losses related to the excited-tate absorption in CuxSe nanoparticles and imperfec-ions in the glass matrix. The values of the residual lossesormalized to the initial absorption at the pump wave-

ength are presented in Table 1. Sample 3 with maximumg shows minimal residual losses, which have a tendency

o increase to sample 1.Note that the set of spectroscopic data reported in Ref.

7 and mentioned above permits maintaining an increas-ng Se/Cu ratio that leads to a rise in the bandgap value

g, decreasing the characteristic bleaching relaxationime � and increasing the peak absorption cross sectionmax. The correlation between the variations in Eg andhe absorption band maximum position Emax was not ob-erved.

. Q-SWITCH PERFORMANCEhe silica solgel glasses containing CuxSe nanoparticlesf different stoichiometry were employed as saturable ab-orbers for the passive Q-switching of a cw diode-pumpedd:KGW laser at a wavelength of 1.067 �m.The experimental setup is shown in Fig. 6. A cw laser

iode with maximum output power of �0.5 W at08.5 nm was used for longitudinally pumping the Nd-KGW active medium. The optical system for focusing theump beam provided a circular spot with a diameter of0 �m. The laser crystal Nd�3 at. % � :KGW with a thick-ess of 4.5 mm and the small-signal transmittance of.2% at a pumping wavelength of 808.5 nm was antire-ection coated at a lasing wavelength of 1.067 �m on thene face, while the other face had a coating with a high

ig. 6. Schematic of the diode-pumped passively Q-switchedd:KGW laser: OC, output coupler; R, radius of curvature; T,

utput transmittance; LD, laser diode; SA, saturable absorber.

Page 5: Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles

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1272 J. Opt. Soc. Am. B/Vol. 23, No. 7 /July 2006 Zolotovskaya et al.

ransmittance of 808.5 nm and high reflectivity of.067 �m. The output couplers were spherical mirrorsith radii of curvature of 50 mm and transmittances of.5% and 7% at the lasing wavelength. The total cavityength lc was �2 cm. The input–output diagrams for thed:KGW laser in the continuous-wave regime are in Fig.. A maximum output power of 263 mW with a slope effi-iency of 71% with respect to the absorbed pump power

ig. 7. Output power for cw and Q-switched (filled circles, 2.5%utput coupler; open circles, 7% output coupler) operations of aiode-pumped 1.067 �m Nd:KGW laser passively Q-switchedith CuxSe-doped glass. The solid lines are guides.

ig. 8. Dependence of the output Q-switched pulse width (filledircles, 2.5% output coupler; open circles, 7% output coupler) andhe repetition rate (filled squares, 2.5% output coupler; open

ix

as obtained with a 2.5% output coupler. For the 7% out-ut coupler the value of the output power achieved was56 mW with a slope efficiency that slightly increased to4%.The Q-switching experiments were carried out with the

avity configuration described above. The parallel glasslates with a small-signal transmittance T0 of �95% at.07 �m and without antireflection coatings wereounted as close as possible to the active medium. The

utput parameters of the cw diode-pumped Nd:KGW la-er passively Q-switched with CuxSe-doped glasses are inable 2. The best results for passive Q-switching are dem-nstrated by sample 3. In the Q-switched mode the laserroduced as much as 33 and 39.5 mW of total outputower with slope efficiencies of 10% and 16% for 2.5% and% output couplers, respectively (Fig. 7). The Q-switchedulses of 130 and 153 ns FWHM at repetition rates of 400nd 330 kHz were obtained at a maximum pump level forhe 2.5% and 7% output couplers, respectively (Fig. 8).he Q-switch conversion efficiency, which is equal to theatio of the Q-switching output power to the free-runningne under the same pump power, was determined to be2.5% and 15% for the corresponding output couplers.he temporal and energetic jitter of the pulsed operationid not exceed 10%. The variation in the Q-switching re-ime parameters with the group of samples 1–3 is con-ected with the different levels of residual losses of thelass samples. The shortest pulse duration and highesteak power are demonstrated by sample 3, which has theighest modulation depth owing to small residual losses.The results are compared with the output parameters

f the same laser system passively Q-switched with ar:YAG crystal that is considered to be the most efficientassive shutter for diode-pumped solid-state lasers emit-ing at 1 �m. The Cr:YAG crystal plate with an internalransmittance T0 of �95% and without antireflectionoatings was placed near the active medium in the cavityescribed above. Q-switched 40 and 45 ns FWHM pulsest a repetition rate of 50 and 33 kHz are achieved at aaximum pump power for 2.5% and 7% output couplers,

espectively. The average output powers ran at 79 and7 mW with a Q-switch conversion efficiency of 30% forhe corresponding output couplers.

The passive Q-switching operations of the Nd:KGW la-er with a Cr:YAG crystal and CuxSe-doped glass wereimulated numerically by using the rate equations for a-switched four-level gain medium32 and were modified

o take the excited-state absorption in a passive shutter

nto account. The basic rate equations of the model are

Table 2. Output Parameters of the Q-Switch Operation for cw Diode-Pumped Nd:KGW 1.067 �m Laserswith CuxSe-Doped Glasses and Cr:YAG Saturable Absorbers at an Absorbed Pump Power of 395 mW

Output CouplerTransmittance (%)

Sample

2.5 7

1 2 3 Cr:YAG 1 2 3 Cr:YAG

Pulse width (ns) 235 170 130 40 290 180 150 45Output power (mW) 19.5 19.5 33 79 29 34 39.5 77

Pulse repetition rate (MHz) 0.33 0.33 0.4 0.05 0.31 0.3 0.33 0.03Peak power (W) 0.25 0.35 0.63 39.5 0.32 0.61 0.78 51.8

quares, 7% output coupler) of a cw diode-pumped 1.067 �md:KGW laser passively Q-switched with Cu Se-doped glass.

Page 6: Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles

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Zolotovskaya et al. Vol. 23, No. 7 /July 2006 /J. Opt. Soc. Am. B 1273

dn�t�

dt= �2�GMlGMnGM�t� − 2�GSAlSAnGSA�t�

− 2�ESAlSAnESA�t� − 2�RlSA − �ln� 1

R − L�n�t�

tc,

dnGM�t�

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nGM�t�

�GM,

dnGSA�t�

dt= − �GSAnGSA�t�cn�t� +

nESA�t�

�SA,

nESA�t� = −ln�T0�

lSA�GSA− nGSA�t�, �4�

here n is the photon density; nGM is the population in-ersion density in the gain medium; nGSA and nESA arehe ground state and the excited-state population densi-ies in the saturable absorber; �GM is the gain mediumimulated emission cross section; �GSA and �ESA are theround-state and the excited-state absorption cross sec-ions, respectively; lGM and lSA are the gain medium andhe saturable absorber lengths; �R is the residual lossesn the saturable absorber; R is the reflectivity of the out-ut coupler; L is the nonsaturable intracavity round-tripptical loss; tc=2lc /c is the round-trip photon transit timen the cavity; � is the inversion reduction factor; �GM andSA are the gain medium and the saturable absorber up-er level lifetimes; and W is the pumping rate that is inirect proportion to the absorbed pump power. The pro-

Table 3. Spectroscopic Characteristics of Cr:YAGCrystal and CuxSe-Doped Silica Glass at È1 �m

Used for the Numerical Simulation of a PassivelyQ-Switched Nd:KGW Laser

Parameter Cr:YAG Crystala CuxSe-Doped Glassb

�GSA �10−17 cm2� 0.35 4.6�ESA �10−18 cm2� 0.22 0

�R �cm−1� 0 0.8�SA (ns) 3,500 0.4

aRefs. 35 and 36.bThe spectroscopic characteristics of sample 3 �Table 1�.

ig. 9. Results of the numerical simulation of a Nd:KGW laserassively Q-switched with (a) Cr:YAG crystal and (b)uxSe-doped glass: solid curves, photon density in the cavity n;otted curves, the saturable absorber transmittance T, as func-ions of time.

ortionality factor between the absorbed pump power andhe pumping rate was adjusted to fit a cw lasing thresh-ld. Equations (4) were solved numerically in the follow-ng initial conditions: nGSA�0�=−�ln�T0�+�RlSA� /�GSAlSA,GM�0�=0, n�0�=1.The gain medium parameters used for the numerical

imulation are as follows: �GM=4.2 10−19 cm2, �GM100 �s,33 �=1 according to Ref. 34, and nGM=1.91020 cm−3. The thickness of the saturable absorbers is

SA=0.01 and 0.036 cm for the CuxSe-doped glass andr:YAG crystal, respectively. The spectroscopic character-

stics of the saturable absorbers used for the simulationsre in Table 3. The nonsaturable intracavity round-tripptical loss L was chosen to be 0.33 and 0.18 for ther:YAG crystal and the CuxSe-doped glass, respectively.he optical loss parameter includes the round-tripresnel losses from the surfaces without antireflectionoatings and intracavity losses. The numerical simulationas carried out for a 2 cm cavity length with a 2.5% out-ut coupler.The numerically simulated Q-switched laser with

r:YAG crystal demonstrated the good agreement of theeak power ��40 W� with the experimental value�39 W� and the repetition rate ��53 kHz� with the cor-esponding experimental result ��50 kHz�. The pulseidth was slightly below ��20 ns� that observed in thexperiment ��40 ns�. The simulation results in the casef CuxSe-doped glass as a passive shutter were in satis-actory accord with the experimental data (Table 2,ample 3): the peak power ��0.66 W� with the experimen-al value ��0.63 W�, the repetition rate ��0.3 MHz� withhe experimental result ��0.4 MHz�, and the pulse width�57 ns� with the observed value ��130 ns�.

The maximum intracavity energy density of ther:YAG achieved 0.24 J/cm2 with a 2.5% output coupler

hat exceeded a saturation energy density value of.05 J/cm2. The saturation intensity and intracavityower density values for sample 3 were estimated to be 12nd 0.1 MW/cm2, respectively. Thus the glass with CuxSeanoparticles was not completely bleached inside the cav-

ty, which was confirmed by the numerical simulationFig. 9). The variation in the CuxSe-doped glass transmit-ance inside the cavity (Fig. 9) from the initial value is notore than 0.003, which is responsible for the relatively

ong-pulse duration and high repetition rate of the-switching operation.Further increasing the pump power, optimizing the

avity configuration, and improving the optical quality ofhe glasses with CuxSe nanoparticles can lead to a short-ning of the Q-switching pulse width and increasing theeak power. Moreover the spectroscopic dataset (shortleaching relaxation time, large ground-state absorptionross section) allow the assumption that the glasses withuxSe nanoparticles can be used as passive mode lockers

or diode-pumped solid-state lasers operating at �1 �m.

. CONCLUSIONolgel silica glasses doped with copper selenide �CuxSe�anoparticles have been fabricated, and their nonlinearptical properties have been studied. A bleaching effectith the pump–probe technique was observed at 1.08 �m

Page 7: Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles

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1274 J. Opt. Soc. Am. B/Vol. 23, No. 7 /July 2006 Zolotovskaya et al.

1.15 eV� with a fast relaxation in the 0.3–2.7 ns rangeor glasses with CuxSe with different x. An increase in thee/Cu ratio of the nanoparticles led to a decrease in theharacteristic bleaching relaxation time and a rise in theeak absorption cross section of the CuxSe nanoparticles.he phenomena were associated with a change in the po-ition of the intraband energy level responsible for the ap-earance of the intense near-IR absorption band in theanoparticles. The passive Q-switching of the diode-umped Nd:KGW laser was obtained with theuxSe-doped glasses as saturable absorbers attaining aulse width of 130 and 153 ns with peak power of 0.63nd 0.78 W for 2.5% and 7% output couplers, respectively.esults of the numerical simulation of the diode-pumpedd:KGW laser passively Q-switched with CuxSe-doped

lass were in good agreement with the experimentalesults.

CKNOWLEDGMENTShis work was partially supported by Veschestvo-2 andANOTEKH and Electronics government programs (e-ail for S.A. Zolotovskaya, [email protected]).

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