326 OPTICS LETTERS / Vol. 25, No. 5 / March 1, 2000

Pixellike parametric generator based on controlledspatial-soliton formation

Stefano Minardi, Samantha Sapone, Walter Chinaglia, and Paolo Di Trapani

Department of Chemical, Physical and Mathematical Sciences, University of Insubria, Via Lucini 3, 22100 Como, Italy

Audrius Berzanskis*

University of Applied Sciences, Tatzendpromenade 1b, 07745 Jena, Germany

Received September 7, 1999

We report the observation of a stable matrix of diffraction-limited solitary beams in a monolithic, single-pass,parametric amplif ier pumped by a spatially modulated beam. 2000 Optical Society of America

OCIS codes: 190.4970, 190.5530.

The process of spatial-soliton generation in quadraticnonlinear media1,2 represents a very promising ap-proach for the development of simple, compact, andhigh-spatial-quality3 sources of tunable, intense, ultra-short pulses. The simplest setup for spatial-solitongeneration, consisting of a single-pass, single-crystal,quantum-noise optical parametric amplif ier (OPA), al-lows one to achieve simultaneously �50% energy con-version, energy stability better than that of the pump,and a truly diffraction-limited output beam.4 Notethat this performance is hardly achievable in a conven-tional and more-complex multipass OPA,5 since the gainsaturation that is used to increase efficiency and im-prove stability unavoidably affects beam quality. Thedrawback of working in the soliton regime comes fromthe small size of the solitary beam (typical diameter,10 20 m FWHM), which practically limits the maxi-mum achievable pulse energy to 1 2 mJ�ps.

In this Letter we show how to overcome thislimitation. By employing an amplitude-modulatedpump, we are able to produce a fairly large and well-ordered matrix of solitary beams. In a similar way,amplitude-modulated filters were used to implementhigh spatial coherence in the case of a large-beam pho-torefractive resonator.6 Recently, the generation ofcavity–soliton matrices was investigated theoreticallyfor the case of semiconductor microcavities.7 Our re-sults are, as far as we know, the first from a cavitylessscheme.

Our experiment consists of three parts: (1) char-acterization of the pixellike OPA source in terms ofnear-f ield and far-field intensity profiles to provethat the solitary regime was reached for the case ofquantum-noise amplification, (2) the same character-ization seeded OPA, and (3) investigation of limitationsowing to pixel–pixel interaction.

The setup used for the first part of our experiment isbased on a 15-mm temperature-tuned lithium triboratecrystal, operated in noncritical phase matching (i.e.,without walk-off) and pumped by a 1.5-ps, 527-nmpulse from an amplified, frequency-doubled Nd:glasslaser. We set the crystal temperature to 107 ±C toobtain generation at 1.8 mm (idler) and 0.75 mm(signal), ensuring minimum group-velocity mismatchamong the interacting pulses. Figure 1(a) shows thepump intensity profile at the input face of the nonlinear

0146-9592/00/050326-03$15.00/0

crystal. The matrix is composed of a set of Gaussian-like beams of 35-mm FWHM diameter, with a 110-mmlattice step and contrast V � 0.97 [defined as theMichelson visibility ratio,8 V � �Imax 2 Imin���Imax 1

Imin�]. This shape is obtained from a quasi-f lat-toppedbeam profile by means of a gridlike photo slide placedin the pump-beam path. A two-lens telescope imagesthe grid onto the crystal input face with suitabledemagnif ication. An aperture in the first lens’s focalplane is used to smooth the pump profile and to achievethe required spot size.

Figure 1(b) shows the pump-beam intensity profileat the output of the crystal in the case of linear propa-gation (i.e., when the low-intensity pump is taken).Increasing the pump intensity enables us to achievethe solitonlike regime for each single beam formingthe matrix, as is evident from the high-intensityoutput pump and signal profiles shown in Figs. 1(c)and 1(d), respectively. These profiles, whose pixelelements are Gaussian-like beams of 20-mm FWHMdiameter, show mutual trapping and diffraction-free

Fig. 1. Experimental observation of a soliton matrix:(a) input-pump profile, achievement of the solitary regimefronting (b) the low-intensity output-pump profile with(c) the high-intensity profile; (c) output-pump and (d) in-tensity profiles. Note the mutual trapping in (c) and(d). Photograph width, 550 mm.

2000 Optical Society of America

March 1, 2000 / Vol. 25, No. 5 / OPTICS LETTERS 327

propagation; the crystal length is twice the Rayleighrange of the 35-mm input beams. This result isobtained with �70-GW�cm2 peak input intensity andleads to a total �signal 1 idler� conversion efficiency of60%. Measurements of the FWHM divergence of theoutput single-pixel beams confirm the achievement ofthe diffraction limit for both the pump and the signalbeams, which is also a typical signature of the solitonregime. The weak background in the output-pumpprofile (�10% of the peak intensity) probably is dueto a small portion of the pump pulse that is notcoupled to the signal–idler fields because of a weakgroup-velocity mismatch. As a final confirmationthat we obtained output in the soliton regime, we men-tion that we also obtained virtually identical outputprofiles with a 30-mm lithium triborate crystal for thesame lattice step. These results are fully consistentwith our previous reports for the case of single-solitongeneration.4,9

To get a better insight into the dynamics of thesoliton-matrix formation we numerically simulate the2 1 1-dimensional three-wave coupled equations fromRef. 1 for the same conditions as those in the ex-periment described above. For the initial conditionswe use a 100%-modulated pump beam and delta-correlated (in x and y) noise for the signal. The re-sults are shown in Fig. 2 for both the pump (top) andthe signal (bottom). The first 8 to 10 mm of propaga-tion are characterized by linear diffraction of the pump.As for the signal, spatial mode locking4 (not visible inthe adopted linear scale) allows the formation of a ma-trix of independent, diffraction-limited beams underexponential parametric amplification before gain satu-ration occurs. The last 5–7 mm of propagation showgain saturation and mutual trapping: At 15 mm weobtain a beam diameter of 20 mm (FWHM) for boththe signal and the pump waves, in excellent agree-ment with the experiment. The numerical resultsshow that the phases of the pixel solitons are ran-domly distributed. Simulation over a 30-mm lengthshows that the solitons keep propagating with an oscil-lating diameter and without signif icant soliton–solitoninteraction.

The randomness of the pixel soliton phases can beremoved by employment of a seed beam. This resultis demonstrated by the second part of our experiment.Here we use a plane-wave quasi-monochromatic seedat 0.8 mm, with an intensity 105 times weaker thanthat of the pump. The injection seed was provided bya conventional parametric generator pumped by a por-tion of the same laser pulse. It is quite diff icult tech-nically to measure the phases of the beams directly,and thus we restrict ourselves to registration of thefar field of the output signal beam without [Fig. 3(a)]and with [Fig. 3(b)] seeding. Obviously, the injectionseeding causes a drastic increase in the spatial coher-ence of the spectra, which is a signature of enhancedorder in the near field. Numerical simulation alsoconfirms that the phases of the pixel solitons are lockedin the case of seeding. It must be noted that no differ-ence is observed in the near-field profiles.

The adopted input-pump profile [see Fig. 3(a)] defi-nitely ensures that each pixel evolves as a single

independent element of light (for the given propagationlength), leading to a one-to-one correspondence be-tween the output solitons and the input-pump beams.This correspondence is a quite-relevant issue for ap-plications since, as we will show, it prevents the oc-currence of distortion in the generated output matrix.The actual pixel-to-pixel independence is also con-firmed by the results in Fig. 4 showing how it is pos-sible for one to excite only some selected solitons in thematrix by suitably obscuring the corresponding pumpbeams. This configuration, however, is not optimizedin terms of the maximum achievable lattice packing

Fig. 2. Numerical results on the evolution inside the crys-tal of top, the pump and bottom, the signal one-dimensionalintensity profiles. The input pump parameters are thesame as in the experimental case.

Fig. 3. Far-field signal profiles (a) without and (b) withinjection seeding. Photograph aperture, �20 mrad.

328 OPTICS LETTERS / Vol. 25, No. 5 / March 1, 2000

Fig. 4. Excitation of selected pixels (without injectionseeding). (a) Input pump, (b) output signal. The inputpeak intensity and the lattice spacing are the same as inFig. 1.

Fig. 5. Output-pump near-field profiles: (a) small latticestep �65 mm�, (b) low contrast �V � 0.3�. The spatial scaleis the same as in Fig. 1.

and energy-conversion eff iciency. The last part of theexperiment is therefore designed to shed light on thelimiting operating conditions that are due to the effectsof the pixel–pixel interaction.

Our measurements reveal that 80 mm is the mini-mum lattice step that ensures the generation of stable,well-ordered soliton matrices such as those shown inFigs. 1(c) and 1(d) for the given input peak intensity,contrast, single-beam diameter, and crystal length).For smaller steps the output patterns do not recreatethe geometrical structure of the input-pump beam[Fig. 5(a)]. Numerical simulations clarify that thishappens because of the diffractive broadening andinterference of neighboring pixel beams, which giverise to the formation of new peaks in the pump profilebefore the onset of the soliton propagation regime.Concerning the overall energy-conversion efficiency(from the laser pulse to the signal), the main lossarises from the high-contrast slide, whose integraltransmission is only 8%. Both measurements andsimulations show that the minimum contrast requiredfor high-quality outputs such as those in Figs. 1(c) and1(d) is V � 0.7 (integral transmission, 20%). For thisvalue all the energy contained in the fairly large inputbackground is still converted into solitary beams. Inthis case, both the output-pump and the signal beamsexhibit peak intensities that are twice as large as inthe V � 0.97 case (for the same input peak intensity).For lower contrast values we observe disorderedmultisoliton patterns such as that shown in Fig. 5(b)(pump profile) for the case of V � 0.3. It is interestingto note that numerical results indicate very different

behavior for the injection-seeded OPA, whose hightranslation symmetry allows one to reduce the inputcontrast to V � 0.1 while keeping a well-formed, regu-lar output matrix. Finally, the 110-mm lattice-stepsoliton-matrix structure is stable up to a pump in-tensity of three to four times the threshold valuefor its formation ��50 GW�cm2�. Higer intensitieslead to distorted lattices owing to soliton–solitoninteraction.10 – 12

In conclusion, we have demonstrated and tested anovel pixellike OPA source that provides both highoutput power and the unique features of the solitaryregime. We believe that this highly coherent and po-tentially tunable source of ultrashort pulses could finduseful applications for image processing in nonlinearoptics and time-resolved spectroscopy as well as foroptical parallel data processing in telecommunicationnetworks.

This work was partially supported by the Ministerodell’ Universita, Ricerca Scientifica e Tecnologicaproject 970222268683-001, UNESCO Venice Office,Regional Office for Science & Technology for Europe,under contract 875.670.9, and by the Conferenzadei Rettori delle Universita Italiane-Vigoni pro-gram. P. Di Trapani’s e-mail address is ditrapan@fis.unico.it.

*Permanent address, Laser Research Center, VilniusUniversity, Sauletekio 9, Building 3, 2040 Vilnius,Lithuania.

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