Journal of Luminescence 87}89 (2000) 930}932

Subpicosecond four-wave-mixing spectroscopy in ferroelasticcrystal NdGaO

3S. Nakanishi!,*, M. Ishii", N. Kosaka", H. Itoh!

!Department of Advanced Materials Science, Faculty of Engineering, Kagawa University, Saiwai-cho 1-1, Takamatsu city,Kagawa 760-8526, Japan

"Faculty of Education, Kagawa University, Takamatsu City, Kagawa 760-8526, Japan

Abstract

We report the results of four-wave-mixing (FWM) spectroscopy in ferroelastic crystal NdGaO3

on subpicosecond timescale. It is observed that the Stark-split absorption lines at 585 nm in NdGaO

3show subpicosecond dephasing and

FWM signal of a symmetric time pro"le at low temperature when excited by incoherent laser light. The behavior of theabsorption lines is considered to result from the ferroelastic nature of NdGaO

3. A femtosecond dephasing at room

temperature is also reported. ( 2000 Elsevier Science B.V. All rights reserved.

Keywords: Four-wave mixing; Subpicosecond dephasing; NdGaO3

Four-wave-mixing (FWM) spectroscopy is one of themost versatile techniques in the ultrafast spectroscopy onpicosecond and femtosecond time scales. It has beenapplied to the investigations of various materials to eluci-date the ultrafast response and its physical origin [1]. Inthis paper, we present the results of subpicosecond FWMspectroscopy in a ferroelastic crystal NdGaO

3. By excit-

ing with incoherent laser light, the four Stark-split ab-sorption lines at 585 nm in NdGaO

3are observed to

reveal a subpicosecond dephasing and an almost sym-metric FWM signal even at 10 K. These "ndings indicatethe homogeneous broadening of the absorption lines at10 K in NdGaO

3crystal, which probably results from

the fast phase #uctuation due to the ferroelastic nature[2]. We analyze the observed FWM signal by the numer-ical simulation based on the perturbation theory to ob-tain the dephasing time for the absorption lines. Thesimulation can also reproduce the modulation of FWMsignal. We consider that the homogeneous broadening ofabsorption lines is very novel in solid materials. In addi-tion, we brie#y present the femtosecond dephasing of thelines observed at 300 K.

*Corresponding author. Fax: #81-87-832-1417.E-mail address: nakanishi@eng.kagawa-u.ac.jp (S. Nakanishi)

The experimental apparatus for FWM spectroscopyconsisted of an incoherent dye laser and two-beam exci-tation geometry [3]. The output pulse of 8 ns durationfrom the laser was split into two beams and both beamswere focused onto the NdGaO

3crystal in a cryostat. One

beam was time delayed with respect to the other bydisplacing a corner-cube re#ector. The bandwidth oflaser light was approximately 1.4 and 6.9 nm for thenarrowband and broadband excitations, respectively.The attainable time resolution in our FWM spectro-scopy is determined solely by the bandwidth of the laserthat was 0.46 and 0.14 ps for the narrowband and broad-band excitations, respectively [4,5]. The incoherent laserpulses excited an absorption band at 585 nm of NdGaO

3at 10 K, as shown in Fig. 1 where the narrowband laserspectra are also displayed by the dotted lines. The ab-sorption band consists of several Stark-split lines and theabsorption lines we studied are labeled as A, B, C and D.The time-integrated FWM signal in the direction of2k

2}k

1was measured as a function of the delay time

q between the two beams, where ki

denotes the wavevector of the laser beam at the sample position.

Fig. 2 shows the FWM signals of NdGaO3

obtained at10 K for the narrowband excitation with changing theexcitation wavelengths around 585 nm. The solid linesdepict the time pro"les of the FWM signal and the dotted

0022-2313/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 4 7 7 - 9

Fig. 1. Absorption spectrum of NdGaO3

around 585 nm at 10K. The dotted lines denote the spectrum of laser pulse used toobtain the FWM signal.

Fig. 2. FWM signal at 10 K obtained for the narrow-band excitation at (a) 589.8 nm, (b) 588.5 nm and (c)585.5 nm. The dotted line represents the autocorrelation of thelaser pulse.

line represents the autocorrelation trace of the laser pulsecorresponding to the time resolution in our experiment.The excitation wavelengths for the FWM signals (a), (b),and (c) were 589.8, 588.5, and 585.5 nm, respectively. Itcan be observed that all FWM signals decay very fasteven at 10 K, indicating the subpicosecond dephasing ofthe absorption lines. This "nding is signi"cantly in con-trast to the long dephasing time measured for the absorp-tion band at 580 nm of Nd3` ions doped in a glass andcrystal [6,7]. The subpicosecond dephasing at 10 K wascon"rmed by measuring the FWM signal with muchhigher time resolution in our previous study [8]. Inaddition, it appears that the FWM signals (a) and (b)show an almost symmetric time pro"le with respect to q,while the FWM signal (c) evidently reveals an asymmet-ric time pro"le. It is also noted that the modulation

frequency of the FWM signal (c) di!ers from those of (a)and (b).

Taking into account the excitation bandwidth used,the FWM signal in Fig. 2 is considered to include thepredominant contributions from two adjacent absorp-tion lines B and C for (a) and (b), C and D for (c). As weuse the incoherent laser pulse, the symmetric time pro"lemeans the homogeneous broadening of the absorptionlines [4]. Therefore, we conclude lines B and C arehomogeneously broadened, whereas line D seems to havethe inhomogeneous broadening as seen in signal (c). Themodulation of FWM signal is considered to occur asa consequence of the interference between two adjacentlines B and C for signals (a) and (b), C and D for thesignal (c).

In order to derive the exact dephasing times from thedata in Fig. 2 for the absorption lines, we employed thenumerical simulation based on the perturbation theory.Following Ref. [9], when the sample is excited by twoincoherent laser pulses, the intensity I(q) of the FWMsignal in the direction of 2k

2}k

1from the homogeneously

broadened lines is expressed as

I(q)JCP=

~=

S0(u)F(u)cos(uq) duD

2

#CP=

~=

S0(u)F(u)sin(uq) duD

2, (1)

where S0(u) and F(u) stand for the power spectrum of

laser pulse and total absorption spectrum of homogene-ously broadened lines at angular frequency u, respective-ly. In the numerical simulation, we assumed that F(u) isa sum of four homogeneously broadened lines A, B,C and D, i.e. F(u)"+D

i/Agi/M(u!u

i)2#1/¹2

2iN, where

Lorentzian line shape is used with the center frequencyu

i, dephasing time ¹

2iand absorption intensity g

i. Since

the measured values and laser spectrum in Fig. 1 wereused for u

i, g

iand S

0(u), the dephasing time ¹

2iwas the

only "tting parameter in our numerical simulation. It isnoted that the present simulation gives the symmetricFWM signal as seen in Eq. (1).

Fig. 3 summarizes the results of numerical simulationsfor the observed FWM signals in Fig. 2. Also, shown bythe dotted lines are the calculated autocorrelation tracesof laser pulse expected from the laser spectrum S

0(u).

One can see the good agreement in the decay and modu-lation pro"le between the observed and simulated FWMsignals for (a) and (b). From these simulations weobtain the dephasing times ¹

2B"¹

2C"0.90$0.10 ps.

Simulation (c) was calculated by using ¹2B

"¹2C

"

¹2D

"0.90 ps. The simulation disagrees in the decaypro"le with the observed signal (c) in Fig. 2, which showsan asymmetric decay with respect to q. The discre-pancy arises probably because of the inhomogeneousbroadening of line D that is not taken into considerationin the simulation. Nevertheless, simulation (c) evidently

S. Nakanishi et al. / Journal of Luminescence 87}89 (2000) 930}932 931

Fig. 3. Numerical simulation for the observed signal in Fig. 2. Inthe calculation we used ¹

2B"¹

2C"¹

2D"0.90 ps. The dot-

ted line represents the autocorrelation of the laser pulse cal-culated from the measured spectrum S

0(u).

Fig. 4. FWM signal at 300 K obtained for the broadbandexcitation at 608.6 nm. The dotted line represents the autocorre-lation of the laser pulse.

indicates the subpicosecond dephasing of line D and thatthe modulation of FWM signal (c) results from the inter-ference between lines C and D.

Finally, we present the femtosecond dephasing ob-served for the lines at 300 K, as depicted in Fig. 4. In thiscase, the sample was excited at 608.6 nm with a band-width of 6.9 nm, because the absorption lines were redshifted by about 20 nm. Compared to the autocorrelationof the laser pulse shown by a dotted line, it is evident thatthe absorption lines still have a de"nite femtoseconddephasing at 300 K. From a similar numerical simulationwe obtain the dephasing time of approximately 0.22 psfor the lines at 300 K.

In conclusion, we have observed the subpicosecondand femtosecond FWM signals at 10 and 300 K for theabsorption lines at 585 and 605 nm in NdGaO

3crystal.

We have found the novel features of the lines, i.e. theextraordinarily fast dephasing at 10 K and the homo-geneous broadening. We consider that these featuresresult from the ferroelastic nature of NdGaO

3, where the

atomic positions are wondering among the several poten-tial minima. It is also our important result that thechange of dephasing time from 0.9 ps at 10 K to 0.22 ps at300 K infers the weak dependence of dephasing on tem-perature in NdGaO

3. Further detailed study on the

temperature dependence of dephasing would provide uswith valuable information about the e!ect of phonons ondephasing in the ferroelastic crystal NdGaO

3.

References

[1] S. Mukamel, Principles of Nonlinear Optical Spectroscopy,Oxford University Press, Oxford, 1995.

[2] E.K.H. Salje, Phase Transitions in Ferroelastic and Co-elastic Crystals, Cambridge University, Cambridge, 1990.

[3] S. Nakanishi et al., J. Chem. Phys. 100 (1994) 3442.[4] N. Morita, T. Yajima, Phys. Rev. A 30 (1984) 2525.[5] S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys.

Rev. A 29 (1984) 2286.[6] R.M. Shelby, Opt. Lett. 8 (1984) 88.[7] K.W. Ver Keith, A.Y. Karasik, R.J. Reeves, T.T. Basiev,

R.C. Powell, Phys. Rev. B 51 (1995) 6085.[8] S. Nakanishi, H. Itoh, Phys. Rev. B 59 (1999) 5990.[9] X. Mi, H. Zhou, R. Zhang, P. Ye, J. Opt. Soc. Am. B 6 (1989)

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