JWB952005 Quantum Electronics and Laser Science Conference (QELS)

Superluminal light propagation through a diode-pumpedNd:YVO4 crystal

Roman A. Panov, Anton A. Novikov, Andrey P. Zinoviev, Oleg L. AntipovInstitute ofApplied Physics of the Russian Academy ofScience,

46 Uljanov St., Nizhny Novgorod 603950,, RussiaTel.: + 7(8312)384547; Fax: +7(8312)363792;

e-mail: anti ov@appl.sci-nnov.ru

Abstract: The group velocity of optical pulse in an amplifier in the presence of populationoscillations was studied both theoretically and experimentally. The superluminal propagation ofharmonically modulated light was measured in a diode-pumped Nd:YVO4 crystal.©2005 Optical Society of AmericaOCIS codes: (190.5530) Pulse propagation and solitons, (140.3280) Laser amplifier

1. Introduction

Propagation velocity of light signals through different media has been studied for almost a century. Recently, it hasbeen understood that the group velocity of a light could be slower or even faster then the velocity of light in vacuum[1-4]. The great interest to this phenomenon is inspired by both the need in a deeper understanding of physical lawsand promising applications such as controllable optical lines, optical processing and date storage and others.Previous investigations have shown that an optical solitary pulse can propagate in an amplifier faster than in

vacuum [1]. Most of recent studies on slow and fast light were performed by use of the electromagnetic inducedtransparence technique at low temperatures [2], or resonant absorbing media [3,4].In this report, we present the results of our theoretical and experimental investigations of superluminal propagation

of long optical signals in an inverted laser crystal at room temperature. The quantum effect of coherent populationoscillations in a diode-pumped Nd:YVO4 laser crystal was used to achieve superluminal propagation of a longamplitude-modulated optical signal.

2. Theoretical prediction

The propagation of an amplitude-modulated optical wave E=(Eo+Elexp(iQt)+E1exp(-itlt))exp(iot-ikz) (at theresonant frequency co of an amplifying transition) through a four-level active medium (with population of the upperlevel of the laser transition N= No+N1exp(iQt)+N_1exp(-iQt)) can be described (for small modulation depthIEot2>>IEt1(2) by the following set of equations

°E = aN EO = YN0Ern + cN,r,Eo exp(-imQt), (1)dz dz

t +No0+ °NoE +V (2)dT T, IsT,

dN N _( (EN E 0E0EM)+Nm.[I )exp(imQ.t),dT' l, isT ISTjwhere m = +1, a = oo(l+i13), (T is the cross-section of the resonant transition, ,B is the ratio of the imaginary and realparts of the resonant susceptibility, T1 is the life-time of the upper level of the laser transition, Is is the saturationintensity of the resonant transition, and Vp is the pump velocity. The steady-state solution of the set of equations (1)-(3) gives an optical wave amplitude at the amplifier output (z = 1) in the following form

E(I,it) = IE(>O - 2438 FIO cOs(n t) + (I + iP )z( costQ t +2' QT IS f + E )2E ) N (Qz') t)-'{Y)=Eoo i l cos(Qi t) + (I+ i3)E10 cs t+ 2o' Qi TlIoIs+f (z2)2+(QljT) dz(4

xexp- 2QOf E°(a1T (d 71Eo( ex iN0(zt)d,-zexp(ift-No(zz'I J EZ' ) )2 '((iL+uJI )2..0 ('I +f0z' +( I1) )J 0

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where Eoo = Eo(z=0), Elo = Ei(z=O) = ER1(z=O), No(z)=VW/(l+IEo(z)j2IS).Expression (4) shows that the propagation velocity of the modulation patterns in the amplifiers is defined (under

conditions of a small imaginary part of susceptibility B<<1 and a small gain oNokl<1) by the following expression

Vg c[no -20Q ( +I )((I +o 2 + (QT,I,)2)'(where c is the velocity of ligth in vacuum, no is the linear refractive index of the wave, and Io is the intesity of theoptical wave.Expression (5) shows that the velocity of the modulation pattern can be higher than the ligth velocity in meduim

and even higher than in vacuum.

3. Experimental investigations

In the experiment we used a diode-pumped master oscillator based on a Nd:YVO4 crystal (Fig. 1). The laser beampassed through an electro-optical modulator (a Pockels cell with polarizers) and a laser amplifier (based on a side-pumped Nd:YVO4 slab with the Nd-ion concentration of 0.4 at. %). The modulator provided harmonic modulationof the laser beam (the modulation frequency was varied from several Hz to several tens of kHz, the depth of themodulation was about 10%.). The optical signal was measured before and after the Nd:YVO4 amplifier.

1~~~1Fig. 1. Schematic of the experiment: 1 - master oscillator (Nd:YV04 laser), 2 - electro-optical modulator, 3 - beam splitters, 4 - cylindrical

lenses, 5 - laser amplifier (Nd:YV04 crystal), 6 - diode pump, 7 - spherical lenses, 8 - photodetectors,9 - absorbers, 10- double-beam oscilloscope.

The comparison of the signal before and after laser amplifier showed a phase shift of the modulation pattern (Fig. 2).The harmonic signal after the amplifier was advanced in comparison with the signal before the amplifier. At thepump power amounting to 20 W, the maximal advance was about 2ts. The advance was found to depend on themodulation frequency (Fig. 3). The maximal advance corresponded to a modulation of about 10 kHz.

The experimental result can be explained by a faster propagation of the modulated signal in the laseramplifier in comparison with its propagation in air. The value of displacement depended on the modulationfrequency. This result is in good accordance with theoretical predictions.

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2.5 -

2E

~,1.5

29 0.5

0

0 5 10 15 20Frequency of modulation, kHz

Fig. 2. The modulation pattern before and Fig. 3. The measured advance of the modulation pattern (after andafter the Nd:YVO4 amplifier. before the laser amplifier) in ls as a function of modulation

frequency.

Thus, the theoretical and experimental investigations showed superluminal propagation of the modulated opticalsignal in the laser amplifier. This effect may be used for controllable delay/advance optical lines or opticalcomputations.

References[1] A.N. Oraevsky, Usp. Phys. Nauk 12 1311-1321 (1998) (Rus.).[2] A. Kasapi, et all. Phys. Rev. Lett 74, 2447 (1995).[3] Matthew S. Bigelow, Nick N. Lepeshkin, Robert W. Boyd Science 301,200-203 (2003)[4] Matthew S. Bigelow, Nick N. Lepeshkin, Robert W. Boyd Phys, Phys. Rev. Lett. 90, 1139031-1139034 (2003).

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