OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 18 — Sep. 8, 2003
  • pp: 2206–2210
« Show journal navigation

Complex soliton-like pattern generation in Potassium Niobate due to noisy, high intensity, input beams

Ladislav Jankovic, Sergey Polyakov, George Stegeman, Silvia Carrasco, Lluis Torner, Christian Bosshard, and Peter Gunter  »View Author Affiliations


Optics Express, Vol. 11, Issue 18, pp. 2206-2210 (2003)
http://dx.doi.org/10.1364/OE.11.002206


View Full Text Article

Acrobat PDF (503 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We report the generation of complex soliton-like patterns in non-critically-phase-matched potassium niobate which occur in random spatial patterns from shot-to-shot. Up to five spots have been generated at input intensities of 10’s GW/cm2, many times the single soliton threshold. The mechanism which leads to the symmetry breaking required for the complex patterns is interpreted to be random noise imprinted on the input light.

© 2003 Optical Society of America

1. Introduction

A key property of many optical solitons, that is intrinsically linked to their stability, is their existence as the lowest-energy state of a dynamical system, and hence their ability to emerge from arbitrary initial conditions [1

1. N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman-Hall, London, 1997).

,2

2. Yu.S. Kivshar and G. Agrawal, Optical Solitons, (Academic, New York, 2003).

]. Quadratic solitons exhibit this property since they can be generated by inputting only a fundamental beam and the harmonic required for a stationary soliton can be generated on propagation into the medium [3

3. W. E. Torruellas, Z. Wang, D J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995). [CrossRef] [PubMed]

,4

4. W. Torruellas, Y. Kivshar, and G.I. Stegeman, “Quadratic Solitons”, in “Spatial Solitons”, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127–168.

]. However, because these excitation conditions might be very far from the stationary soliton solutions, the solitons evolve non-adiabatically and large amounts of radiation might be emitted [5

5. S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002). [CrossRef]

]. It has recently been shown that this emitted radiation can lead to the formation of additional solitons, either by their coalescence in certain regions of space or by the fast break-up of the input beams [6

6. M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. Carrasco, and L. Torner, “Second Harmonic Generation Tuning Curves In Quasi-Phase-Matched KTP With Narrow, High Intensity Beams,” J. Appl. Phys. 93, 8852 (2003). [CrossRef]

10

10. S. Polyakov, L. Jankovic, H. Kim, G. Stegeman, S. Carrasco, L. Torner, and M. Katz, “Properties of Quadratic Multi-Soliton Generation Near Phase-Match in Periodically Poled Potassium Titanyl Phosphate,” Opt. Express 11, 1328 (2003). [CrossRef] [PubMed]

]. These additional solitons have been predicted to align themselves either along directions dictated by the anisotropy in the diffraction in the crystals, [8

8. S. Polyakov, R. Malendevich, L. Jankovic, G. Stegeman, Ch. Bosshard, and P. Gunter, “Effects of Anisotropic Diffraction on Quadratic Multi Soliton Excitation in Non-critically Phase-matched Crystals,” Opt. Lett. 27, 1049 (2002). [CrossRef]

] and more typically by dominant elliptical asymmetries in the incident beam [9

9. S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, and M. Katz, “Observation of multiple soliton generation mediated by amplification of asymmetries,” Phys. Rev. E 67, 046616 (2003). [CrossRef]

]. To date the experiments on multi-soliton generation have all reported multi-soliton generation to occur along lines in space [6

6. M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. Carrasco, and L. Torner, “Second Harmonic Generation Tuning Curves In Quasi-Phase-Matched KTP With Narrow, High Intensity Beams,” J. Appl. Phys. 93, 8852 (2003). [CrossRef]

10

10. S. Polyakov, L. Jankovic, H. Kim, G. Stegeman, S. Carrasco, L. Torner, and M. Katz, “Properties of Quadratic Multi-Soliton Generation Near Phase-Match in Periodically Poled Potassium Titanyl Phosphate,” Opt. Express 11, 1328 (2003). [CrossRef] [PubMed]

]. However, it was also predicted that in the case of ideal continuous-wave illumination, quasi-random 2D patterns of the generated solitons should be possible due to the amplification of the spatial noise on the input beam. Furthermore, at high input intensities, the presence of temporal noise can also drastically impact the light evolution, as revealed recently in the time-resolved experimental investigation of the properties of quadratic solitons reported by Minardi and co-workers [11

11. S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

]. In this paper we observe the generation of patterns of soliton-like spots in the energy-integrated output images whose spatial distribution changes on a shot-to-shot basis in non-critically-phase-matched (NCPM) potassium niobate (KNbO3).

2. Results and discussion

The current experiments on soliton-like pattern generation were performed in a 1 cm long KNbO3 crystal with propagation along the “b”-axis [6

6. M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. Carrasco, and L. Torner, “Second Harmonic Generation Tuning Curves In Quasi-Phase-Matched KTP With Narrow, High Intensity Beams,” J. Appl. Phys. 93, 8852 (2003). [CrossRef]

]. For fundamental light polarized along the “a”-axis, the second harmonic is generated via birefringence NCPM polarized along the “c”-axis with an effective nonlinearity of -12pm/V at room temperature at an incident wavelength of 983.5nm [12

12. I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, and B. Zysset, “Refractive indices of orthorhombic KNbO3. II Phase-matching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B 9, 507 (1992). [CrossRef]

]. Collinear multi-soliton generation has been reported previously in this sample geometry [6

6. M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. Carrasco, and L. Torner, “Second Harmonic Generation Tuning Curves In Quasi-Phase-Matched KTP With Narrow, High Intensity Beams,” J. Appl. Phys. 93, 8852 (2003). [CrossRef]

]. An EKSPLA OPG/OPA (optical parametric generator/optical parametric amplifier), pumped by the harmonic of a Nd:YAG laser was used to generate tunable radiation in the 980nm wavelength range with typical shot-to-shot variation in pulse energies of ±7%, rms. The pulses were approximately 22ps in duration with a bandwidth of ≈0.5 nm, with a repetition rate of 10Hz. The output beam was spatially filtered to give a M2≈1.05, where the laser beam quality factor M2 is defined in terms of w(z) the beam waist at beam propagation position z after the minimum beam waist w0 and λ the laser source wavelength with w(z)=w01+[M2λz(πw0)]2 . The energies and spatial distributions of all of the relevant beams were measured and cameras were used to image the input and output intensity distributions. Figure 1 shows a typical measured, color coded, two dimensional intensity distribution of the input beam for a single pulse. The presence of significant spatial noise is clear.

Fig. 1. A typical, experimental intensity distribution of the input beam in 2 and 3D.
Fig. 2. (Movies 128KB, 288KB and 423KB) Three collages of output beam patterns obtained for peak input fundamental beam intensities of 8 GW/cm2, 15 GW/cm2 and 30 GW/cm2. Successive frames correspond to successive laser pulses at the same peak input intensity.

The evolution obtained for the different patterns observed are shown in Fig. 2 for three different intensities, namely 5, 15 and 30 GW/cm2. In each case there is a collage of output patterns corresponding to successive laser pulses of nominally the same total energy and pulse width. In fact, as a result of random temporal and spatial noise on the pulses, the successive patterns vary widely from one another. In Fig. 2(a) (5 GW/cm2 peak intensity input), the predominant pattern consists of two localized beams aligned approximately horizontally. Note that the single soliton threshold for these conditions (i..e, a beam waist ~18µm, with M2≈1.0) is about 2.7 GW/cm2, [7

7. R. Malendevich, L. Jankovic, S. Polyakov, R. Fuerst, G. I. Stegeman, Ch. Bosshard, and P. Gunter, “Two-Dimensional Type I Quadratic Spatial Solitons in KNbO3 Near Non-Critical Phase-Matching,” Opt. Lett. 27, 631 (2002). [CrossRef]

] thus the input peak intensity in Fig. 2(a) is subcritical for two solitons to be formed at these sample lengths. Therefore, the soliton nature of the two spots visible in the plot is questionable. Still, the generation of two well-defined light spots is clearly visible. For fundamental beam inputs of ≈15 GW/cm2 peak intensity, i.e., 5 times the single soliton threshold (Fig. 2(b)), the output patterns are more complex, exhibiting 2–3 localized spots, frequently non-collinear along a single line. At even higher input intensities, of order 7–10 times the single soliton threshold peak intensity (Fig. 2(c)), the successive output patterns vary widely from shot-to-shot. Up to 5 non-collinear light spots are observed.

In Fig. 3 is shown a variety of interesting patterns observed experimentally, and the conditions under which they were obtained. Notice that in all of the acquired images some of the light spots exhibit irregular shapes and that the different spots carry widely different energies. The former observation is partially attributed to the off-axis overlap produced by the collage of several laser pulses shown in each plot and the latter to the asymmetric input beam break-up. Also, we stress that with increasing input intensity, the differences between the successive output light spots patterns increased, an indication that the observations are driven by the spatio-temporal dynamics mediated by both, the spatial noise imprinted on the beams and the temporal noise imprinted in the light pulses.

Fig. 3. Selection of four output patterns obtained under different conditions.

On the other hand, potassium niobate exhibits a variety of linear and nonlinear properties besides the usual diffraction and purely quadratic nonlinearities, whose combination can also impact the precise outcome of the experiments. First of all, potassium niobate is a biaxial crystal which exhibits anisotropic diffraction, with diffraction ratios, D11/D12=0.966, and D21/D22=1.176, for the fundamental and harmonic beams respectively where D11, D12, D21 and D22 stand for the diffraction of a fundamental wave (FW, first index is 1) and second harmonic (SH, first index is 2) along the y (second index is 1) and z (second index is 2) axes respectively (see [8

8. S. Polyakov, R. Malendevich, L. Jankovic, G. Stegeman, Ch. Bosshard, and P. Gunter, “Effects of Anisotropic Diffraction on Quadratic Multi Soliton Excitation in Non-critically Phase-matched Crystals,” Opt. Lett. 27, 1049 (2002). [CrossRef]

] for full details). Second, two-photon absorption (TPA) is large at the harmonic wavelength (TPA coefficient α2≈4×10-11 m/W) at the intensity range used here [13

13. A. D. Ludlow, H. M. Nelson, and S. D. Bergeson, “Two-photon absorption in potassium niobate,” J. Opt. Soc. Am. B 18, 1813 (2001). [CrossRef]

]. Cubic, third-order nonlinearities are small at this wavelength (i.e., n2≈6×10-6 cm2/GW) [14

14. Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect,” Phys. Rev. Lett. 74, 2816 (1995). [CrossRef] [PubMed]

]. Note, in particular, that the strong TPA reduces the beam intensities very significantly inside the sample, thus weakening or even destroying the soliton-like nature of the output light spots.

It is thus important to stress that elucidation of the detailed origin of the observed multiple-spot light patterns is a complex problem to which several physical effects can contribute and requires extensive, detailed simulations, to be performed in the future. For example, not only are quadratic nonlinearities important, but at high intensities higher-order effects must be also taken into account, especially two photon absorption.

3. Conclusion

In summary, the symmetry of the spatial distribution of the multiple light spots generated for input intensities a few times the single soliton threshold no longer holds at intensities an order of magnitude larger than the single soliton threshold in the presence of noise on the spatial profile and in the temporal pulse envelope. The beam and pulse break-up induced at such conditions dominates the soliton generation process and leads to the generation of non-colinear patterns of multiple light spots. Finally, two-photon- absorption of the harmonic light is an important feature in soliton generation in KNbO3 at high peak powers.

Acknowledgments

This research in the U.S. was supported by an Army Research Office MURI on Solitonic Gateless Computing and in Spain by the Generalitat de Catalunya and by the Spanish Government through grant TIC2000-1010.

References and links

1.

N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman-Hall, London, 1997).

2.

Yu.S. Kivshar and G. Agrawal, Optical Solitons, (Academic, New York, 2003).

3.

W. E. Torruellas, Z. Wang, D J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995). [CrossRef] [PubMed]

4.

W. Torruellas, Y. Kivshar, and G.I. Stegeman, “Quadratic Solitons”, in “Spatial Solitons”, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127–168.

5.

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002). [CrossRef]

6.

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. Carrasco, and L. Torner, “Second Harmonic Generation Tuning Curves In Quasi-Phase-Matched KTP With Narrow, High Intensity Beams,” J. Appl. Phys. 93, 8852 (2003). [CrossRef]

7.

R. Malendevich, L. Jankovic, S. Polyakov, R. Fuerst, G. I. Stegeman, Ch. Bosshard, and P. Gunter, “Two-Dimensional Type I Quadratic Spatial Solitons in KNbO3 Near Non-Critical Phase-Matching,” Opt. Lett. 27, 631 (2002). [CrossRef]

8.

S. Polyakov, R. Malendevich, L. Jankovic, G. Stegeman, Ch. Bosshard, and P. Gunter, “Effects of Anisotropic Diffraction on Quadratic Multi Soliton Excitation in Non-critically Phase-matched Crystals,” Opt. Lett. 27, 1049 (2002). [CrossRef]

9.

S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, and M. Katz, “Observation of multiple soliton generation mediated by amplification of asymmetries,” Phys. Rev. E 67, 046616 (2003). [CrossRef]

10.

S. Polyakov, L. Jankovic, H. Kim, G. Stegeman, S. Carrasco, L. Torner, and M. Katz, “Properties of Quadratic Multi-Soliton Generation Near Phase-Match in Periodically Poled Potassium Titanyl Phosphate,” Opt. Express 11, 1328 (2003). [CrossRef] [PubMed]

11.

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

12.

I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, and B. Zysset, “Refractive indices of orthorhombic KNbO3. II Phase-matching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B 9, 507 (1992). [CrossRef]

13.

A. D. Ludlow, H. M. Nelson, and S. D. Bergeson, “Two-photon absorption in potassium niobate,” J. Opt. Soc. Am. B 18, 1813 (2001). [CrossRef]

14.

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect,” Phys. Rev. Lett. 74, 2816 (1995). [CrossRef] [PubMed]

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Research Papers

History
Original Manuscript: July 24, 2003
Revised Manuscript: August 23, 2003
Published: September 8, 2003

Citation
Ladislav Jankovic, Sergey Polyakov, George Stegeman, Silvia Carrasco, Lluis Torner, Christian Bosshard, and Peter Gunter, "Complex soliton-like pattern generation in Potassium Niobate due to noisy, high intensity, input beams," Opt. Express 11, 2206-2210 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-18-2206


Sort:  Journal  |  Reset  

References

  1. N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman-Hall, London, 1997).
  2. Yu.S. Kivshar and G. Agrawal, Optical Solitons, (Academic, New York, 2003).
  3. W. E. Torruellas, Z. Wang, D J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner and C. R. Menyuk, �??Observation of two-dimensional spatial solitary waves in a quadratic medium,�?? Phys. Rev. Lett. 74, 5036 (1995). [CrossRef] [PubMed]
  4. W. Torruellas, Y. Kivshar and G.I. Stegeman, �??Quadratic Solitons�??, in �??Spatial Solitons�??, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127-168.
  5. S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, �??Quadratic solitons: Existence versus excitation,�?? IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002). [CrossRef]
  6. M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. Carrasco, and L. Torner, �??Second Harmonic Generation Tuning Curves In Quasi-Phase-Matched KTP With Narrow, High Intensity Beams,�?? J. Appl. Phys. 93, 8852 (2003). [CrossRef]
  7. R. Malendevich, L. Jankovic, S. Polyakov, R. Fuerst, G. I. Stegeman, Ch. Bosshard and P. Gunter, �??Two- Dimensional Type I Quadratic Spatial Solitons in KNbO3 Near Non-Critical Phase-Matching,�?? Opt. Lett. 27, 631 (2002). [CrossRef]
  8. S. Polyakov, R. Malendevich, L. Jankovic, G. Stegeman, Ch. Bosshard and P. Gunter, �??Effects of Anisotropic Diffraction on Quadratic Multi Soliton Excitation in Non-critically Phase-matched Crystals,�?? Opt. Lett. 27, 1049 (2002). [CrossRef]
  9. S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, and M. Katz, �??Observation of multiple soliton generation mediated by amplification of asymmetries,�?? Phys. Rev. E 67, 046616 (2003). [CrossRef]
  10. S. Polyakov, L. Jankovic, H. Kim, G. Stegeman, S. Carrasco, L. Torner and M. Katz, �??Properties of Quadratic Multi-Soliton Generation Near Phase-Match in Periodically Poled Potassium Titanyl Phosphate,�?? Opt. Express 11, 1328 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1328">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1328</a>. [CrossRef] [PubMed]
  11. S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, �??Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,�?? arXiv: physics/0304030 (2003), <a href="http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf">http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf</a>.
  12. I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, and B. Zysset, �??Refractive indices of orthorhombic KNbO3. II Phase-matching configurations for nonlinear-optical interactions,�?? J. Opt. Soc. Am. B 9, 507 (1992). [CrossRef]
  13. A. D. Ludlow, H. M. Nelson and S. D. Bergeson, �??Two-photon absorption in potassium niobate,�?? J. Opt. Soc. Am. B 18, 1813 (2001). [CrossRef]
  14. Ch. Bosshard, R. Spreiter, M. Zgonik and P. Gunter, �??Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect,�?? Phys. Rev. Lett. 74, 2816 (1995). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 

Supplementary Material


» Media 1: GIF (129 KB)     
» Media 2: GIF (288 KB)     
» Media 3: GIF (423 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited