Soliton-Effect Optical Pulse Compression in Bulk Media with χ (3) Nonlinearity. 1 Introduction

Transcription

1 Nnlinear Analysis: Mdelling and Cntrl, Vilnius, IMI,, N 5 Lithuanian Assciatin f Nnlinear Analysts, Slitn-Effect Optical Pulse Cmpressin in Bulk Media with χ (3) Nnlinearity Received: 9.7. Accepted: G. Tamšauskas, A. Dubietis and G. Valiulis Department f Quantum Electrnics, Vilnius University Saulėteki al. 9, LT-4 Vilnius Lithuania [gintaras.tamsauskas. gintaras.valiulis]@ff.vu.lt Abstract Self-cmpressin f visible ptical pulse in bulk χ (3) medium has been demnstrated taking the advantage f negative grup-velcity dispersin f tilted pulses. Keywrds: tempral slitns, tilted pulses, self-phase-mdulatin, pulse cmpressin 1 Intrductin Optical pulse cmpressin is well-established technique fr pwerful ultrashrt pulse generatin. The technique is based n the pulse chirping in the nnlinear media and the chirp cmpensatin utilizing dispersin btained by gratings r prisms. Using bulk (free f aperture limitatins) materials, pulse chirping under psitive grup-velcity dispersin (GVD) and cmpressin was demnstrated mre than a decade ag [1]. An alternate apprach is t cmbine self-phase-mdulatin (SPM) and negative GVD utilizing the slitn cmpressin effect. Experimental evidence f slitn-effect pulse cmpressin dates back t early 8`s and was preferably studied in ptical fibers with negative GVD [,3]. A cmbinatin f SPM and negative GVD in bulk materials has been nly cnsidered theretically in the sense f generatin f light bullets [4] and directed t the case f wavelengths f arund 1.5 µm that reach an anmalus dispersin regin fr fused silica and glass. Hwever, the methd is nt widely applied fr the pulse cmpressin because f limited wavelength range (~1.5µm) and absence f well-develped laser surces emitting at this wavelength range. 99

2 Recently, tempral slitn frmatin was achieved in visible [5] and near IR [6] by use f tilted-frnt pulses and expliting χ () and χ (3) nnlinearities f the ptical crystals. Mre extended theretical study [7] pinted that the negative GVD cnditin is readily achievable fr a wide range f wavelengths and ptical materials by apprpriate pulse-frnt tilting. Mrever, it has been shwn that pure χ (3) nnlinearity als cntributes fr the tempral slitn frmatin alng with χ () nnlinearity being the driving ne. Numerical Mdel and Cmputer Simulatin The pulse prpagatin in a dispersive medium with instant χ (3) nnlinearity is gverned by the nnlinear Shredinger equatin that in nedimensinal case can be expressed as 1 k A A A i A + g = in z u t t where u is the pulse grup velcity, A, (1) g = ( d k / dω ) is the GVD ω = ω cefficient, ω is the carrier frequency, k =ω /c is the wave number and (3) n = ( π / n ) χ is the nnlinear refractin index satisfying the equatin n=n +n I with I being the applied intensity. The light pulse is called tilted when it pssesses a tempral delay acrss the transverse crdinate [8]. This means that the pulse frnt (the surface f cnstant intensity at a fixed time) is nt parallel t the phase frnt (the surface f cnstant phase at a fixed time) and hence is nt perpendicular t the directin f prpagatin. Usually the pulse frnt tilt is btained by use f ptical elements that intrduce an angular dispersin, i.e. diffractin gratings r prisms. The GVD cefficient f the medium is then g T 1 tanα = g, k u where subscript T refers t the tilted pulse, and α is the pulse-frnt tilt angle. In Ref. 7 it was shwn that in the large-beam apprximatin the prpagatin f a tilted pulse culd be described by the Eq.1 with mdified dispersin f the medium, accrding t the effective values given in Eq.. Obviusly, the pulse-frnt tilting results in a material dispersin cmpensatin r even in the anmalus dispersin. Fig. 1 illustrates the GVD cefficient f BK7 glass versus the tilt angle α fr 57-nm, τ=165 fs pulses. The tilt angles starting frm ~13 deg result in anmalus dispersin f BK7 glass (negative GVD cefficient). The nnlinear refractive index fr BK7 glass () 1

3 n = m /W was taken frm Ref. 9. If the pulse intensity is high enugh fr SPM t ccur, these GVD> 3 g, 1 fs/m T GVD< Pulse-frnt tilt angle, deg Fig. 1.Grup velcity dispersin cefficient f BK7 glass as functin f the pulse-frnt tilt angle α, calculated fr 165-fs pulses. cnditins are suppsed t cause a slitn-effect pulse cmpressin. The main differences as cmpared t the ptical fiber case are the fllwing: 1) the pulse prpagates freely withut aperture limitatin; ) negative grup velcity dispersin is predetermined by the pulse tilt rather than by the material dispersin; 3) due t angular dispersin the tilted pulses will nt peridically recnstruct the tempral shape while prpagating in the media. Pulse duratin, fs α=8, z=3mm α=35, z=3mm α=35, z=16mm α=8, z=16mm Incident pulse intensity, GW/cm Fig.. Pulse duratin dependence n the incident intensity fr different pulsefrnt tilt angles and media length z. 11

4 The simulatins were perfrmed by numerically slving Eq.1 in the plane wave apprximatin. Results f numerical simulatins are presented in Fig.. Fr lw Intensity, GW/cm z= mm z=11 mm z= mm Time, ps Fig. 3. Transfrmatin f the pulse prfile during the prpagatin thugh BK7 glass. Incident pulse frnt is tilted by 8 deg and I=3 GW/cm. intensity pulses the negative GVD dminates ver the SPM, and the result is pulse dispersive bradening. By increasing the input intensity the SPM drives the pulse t cmpress and at certain input intensity the SPM and negative GVD cmpensate fr each ther resulting in chirp-free shrt (<5 fs) pulse. Further intensity increasing leads t frmatin f higher rder slitns. The typical transfrmatin f pulse tempral prfile is shwn in Fig.3. 3 Experiment The 165-fs pulse at 57 nm were delivered by fiberless CPA Nd:glass laser (TWINKLE, Light Cnversin Ltd.), equipped by the nnlinear SH pulse cmpressr [1]. The utput beam has diameter f 6 mm at FWHM and ttal energy f 3 mj. The input pulse was tilted by 6 mm -1 diffractin grating perating at secnd diffractin rder clse t Littrw cnditin. The grating G1 was imaged by a telescpe T1 nt the input face f 16-mm-lng BK7 slab with beam size reductin factr f The grve spacing f the grating and telescpe magnificatin were chsen t achieve a tilt angle f 35 deg inside the glass slab. The identical set f ptics was used fr canceling the pulse-frnt tilt. The spacing between gratings and imaging ptics was aligned fr zer dispersin; it was justified by cmparing input and utput pulsewidths. In the presence f BK7 slab, the rear part f the setup (i.e. telescpe T and grating G which were used t restre the untilted pulse) was realigned t image the 1

5 exit face f the BK7 slab nt the secnd grating. In that way the net dispersin f whle arrangement was set by the dispersin prduced thrugh the pulsefrnt tilting as derived frm Eq.. The accessible range f intensities with all factrs accunted (grating diffractin efficiency, beam-size reductin by imaging telescpe, etc.) was up t 5 GW/cm. G1 Pl λ/ input f1 f f f1 G T1 T BK7 utput f4 Fig. 4. Experimental setup. G1, G diffractin gratings; f1=f4=5 mm, f=f3=3 mm, λ/ half-wave plate, P plarizer, fr the incident intensity adjustment. With increasing the incident pulse intensity, spectrum bradening and pulse self-cmpressin were bserved. At the pump intensity f ~35 GW/cm the cmpressin yielded a pulse with autcrrelatin width f 135 fs, see Fig. 5. Assuming the autcrrelatin/pulsewidth factr f 1.4, which was btained by numerical mdelling, the duratin f the self-cmpressed pulse was evaluated t be 95 fs. The Furier transfrm f the measured spectrum revealed almst the same value, pinting t absence f the residual chirp. Qualitatively the pulsewidth dependence n the incident intensity fllwed the theretical predictins; hwever, the bserved pulses had smewhat lnger duratin. The duratin f the cmpressed pulse versus the input intensity is depicted in Fig. 6. The quantitative discrepancies between the numerics and the experiment may be explained as fllws. At higher intensities (>4 GW/cm ) spatially dispersed white light cntinuum was bserved. The theretical mdel als des nt take int accunt the effect f stimulated Raman scattering whse impact may be mre cmplex than just lss f intensity [11]. Anther nnlinear prcess that was nt taken int accunt was the tw-phtn absrptin. Fr high intensities (abve 5 GW/cm ) nnlinear lsses cnsumed up t % f the incident pulse energy. These three afrementined prcesses exhibit cmplex nnlinear lss mechanism and affect mstly the tp f the pulse, which leads t the increase f pulse duratin. f4 f3 f3 length adjustment 13

6 1..8 u a.6 y nsit.4 e nt I. τ crr =3 fs (a) (b) u a.6 y n sit.4 e nt I τ crr =135 fs (c) (d) Delay, fs Wavelength, nm Fig. 5. Autcrrelatin traces and spectra f incident (a), (b) and selfcmpressed (c), (d) pulses. The incident pulse spectrum (b) with tw peaks is the characteristic ne fr nnlinear SH pulse cmpressin [9]. Autcrrelatin width, fs Incident intensity, GW/cm Fig. 6. Autcrrelatin width dependence n the incident intensity. Anther shrtcming f the theretical mdel is that it des nt take int accunt the spatial distributin f the beam (plane-wave mdel was used). At finite beam diameter and near Gaussian intensity distributin high intensity 14 experiment simulatin

7 beam must experience sme nset f self-fcusing. This means that the directin at which a particular spectral cmpnent prpagates depends nt slely n its wavelength but als n the curvature f spatial intensity prfile at the spt it riginates frm. In cnclusin, the slitn-effect pulse cmpressin in bulk χ (3) medium has been experimentally demnstrated. Anmalus dispersin fr 57-nm pulses in BK7 glass was achieved by an apprpriate pulse-frnt tilting. Cmpressin f 165-fs Nd:glass secnd-harmnic pulse dwn t 95 fs was bserved. References 1. C. Rlland and P. B. Crkum, Cmpressin f high-pwer ptical pulses, J. Opt. Sc. Am. B 5, (1988).. L. F. Mllenauer, R. H. Stlen, and J. P. Grdn, Experimental bservatin f picsecnd pulse narrwing and slitns in ptical fibers, Phys. Rev. Lett. 45, (198). 3. L. F. Mllenauer, R. H. Stlen, J. P. Grdn, and W. J. Tmlinsn, Extreme picsecnd pulse narrwing by means f slitn effect in singlemde ptical fibers, Opt. Lett. 8, (1983). 4. Y. Silberberg, Cllapse f ptical pulses, Opt. Lett. 15, (199). 5. P. Di Trapani, D. Cairni, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, Observatin f tempral slitns in secnd-harmnic generatin with tilted pulses, Phys. Rev. Lett. 81, (1998). 6. X. Liu, L. J. Qian, and F. W. Wise, Generatin f ptical spatitempral slitns, Phys. Rev. Lett. 8, (1999). 7. G. Valiulis, A. Dubietis, R. Danielius, D. Cairni, A. Viscnti, and P. Di Trapani, Tempral slitns in χ () materials with tilted pulses, J. Opt. Sc. Am. B 16, (1999). 8. O. E. Martinez, Pulse distrtins in tilted pulse schemes fr ultrashrt pulses, Opt. Cmmun. 59, 9-3 (1986). 9. D. N. Nikgsyan, Prperties f ptical and laser-related materials, Wiley, Chichester, p.37 (1997). 1. A. Dubietis, G. Valiulis, R. Danielius, and A. Piskarskas, Nnlinear pulse cmpressin by ptical frequency mixing in crystals with secnd-rder nnlinearity, Pure Appl. Opt.. 7, (1998). 11. K. Ch. Chan and H. F. Liu, Effect f third-rder dispersin n slitn effect pulse cmpressin, Opt. Lett.19, (1994). 15