Studies on Some Aspects of Light Beam Propagation Through ...

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6 Optical Solitons : An Introduction It is the natural property of a beam of light to diverge when propagating through a medium. A collimated beam of light with a diameter d will spread with an angle Aid owing to diffraction. Such divergence is compensated and the beam propagates with out any change in its shape when propagating through a suitable nonlinear media. The intense beam of light modifies the optical properties of the medium through which it propagates such that it is focused inside the medium. This effect is known as self-focusing. Such effects are known as self-action effects in which a beam of light modifies its own propagation by means of the nonlinear response of the medium. If the effect is such that there is an exact balance between self-focusing and diffraction so that the beam of light propagates with a constant diameter, this is known as the selftrapping of light. There is a possibility of another effect which can occur. If the power of the beam is such that it is much greater than a critical power, then the beam can breakup into many components each having a power approximately equal to the critical power. This critical power in case of a Kerr type nonlinear media is obtained to be lO Per = 71"(0.61)2 A6. BnOn2 (1.12) The beam can self-trap only if the power of the beam is exactly equal to the critical power. The schematic illustration of the self-focusing effect and the self trapping effect is shown in Fig. 1.2. In one transverse dimension, diffraction can be formally considered as representing the anomalous dispersion in case of temporal solitons. We can define a characteristic length known as the diffraction length for the propagation of the soliton. This is the distance at which the beam broadens appreciably in space if the propagation is linear and is given by 1 2 71" 2 LdiJJ = 2kowo = -:\wo, (1.13) where Wo is the radius of the beam. The idea of controlling light with light by taking advantages of nonlinear optical effects, has become a topic of interest to many researchers and scientists. The fundamental benefit is in the possibility of avoiding any opto-electronic conversion process, and hence increasing the device speed and efficiency. It is in this scenario that these self-guided beams called "spatial soli tons" find importance. The areas of application include all optical switching devices,l1 optical computing, all optical polarization
Spatia l solitons Figure 1.2: Schematic diagram of self-focusing (top) and self-trapping (bottom) effects occurring in a Kerr media. modulators,12 logic gates 13 etc. The prospect of forming aH-optical switches and logic gates presents promise for generations of novel optical interconnects for computing and communications. From a mathematical point of view, continuous wave beam propagation in planar waveguides is identical to the phenomenon of pulse propagation in fibers because of the spatiotemporal analogy14 and is described by the NLS equation of the form .{)u 1 {)2u 2 ,- + -- + lul u = 0 {)z 2 {)x 2 ' - 7 (1.14)
Page 1 and 2: STUDIES ON SOME ASPECTS OF LIGHT BE
Page 3 and 4: DECLARATION I hereby declare that t
Page 5 and 6: viii CONTENTS 4 Modulational Instab
Page 7 and 8: x Preface a cubic-quintic medium wi
Page 9 and 10: Publications related to the work pr
Page 11 and 12: ACKNOWLEDGEMENTS r would like to ta
Page 13: The beginning is the most important
Page 16 and 17: 4 Optical Solitons : An Introductio
Page 20 and 21: 8 Optical Solitons : An Introductio
Page 23 and 24: Variationa l m ethod 11 o X (Ilffi)
Page 29: Historical developments and current
Page 33 and 34: Outline of the thesis of steady-sta
Page 37 and 38: REFERENCES [37] [38] [39] M. O. Cas
Page 40 and 41: 28 Solitons in Bulk Cubic-Quintic M
Page 43 and 44: Model equation and analysis lifted
Page 48: 36 Solitons in Bulk Cubic-Quintic M
Page 51: Spatio-temporal solitons stabilized
Page 62: 50 Solitons in Photorefractive Poly
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56 Solitons in Photorefractive Poly
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Conclusions Figure 3.11: Soliton pr
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70 REFERENCES [24] A. Mohamadou and
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Modulational Instability in Photore
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Two wave mixing geometry 77 mutual
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Two wave mixing geometry 79 Let the
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88 REFERENCES but results only by v
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5.1 Introd uction T IllS Self-writt
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Photosensitivity 93 Figure 5.1: Ini
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Theoretical Model 95 acteristics su
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100 Potential Self-written waveguid
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104 Self-written wavcguidc in a met
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106 REFERENCES [12] J.-W. Kang, J.-
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Dynamics of a light induced self-wr
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Model equation and analysis using a
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Analytic solution 115 0.6 0.4 a 0.8
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120 REFERENCES uides. The coupler w
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What we call the beginning is often
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125 into the photopolyrnerizable ma
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absorption coefficient, 40 anomalou
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