Caustic Light in Nonlinear Photonic Media

Supervisor’s Foreword
Peer-Reviewed PublicationsA. Zannotti, F. Diebel, M. Boguslawski, C. Denz, Optical catastrophes of the swallowtail and butterfly beams, New J. Phys., 19, 053004 (2017).A. Zannotti, M. Rüschenbaum, C. Denz, Pearcey solitons in curved nonlinear photonic caustic lattices, J. Opt., 19, 094001 (2017).A. Zannotti, F. Diebel, C. Denz, Dynamics of the optical swallowtail catastrophe, Optica, 4, 1157 (2017).A. Zannotti, J. M. Vasiljević, D. V. Timotijević, D. M. Jović Savić, C. Denz, Visualizing the energy flow of tailored light, Adv. Opt. Mat., 6, 1701355 (2018).A. Zannotti, C. Denz, M. A. Alonso, M. R. Dennis, Shaping caustics into propagation-invariant light, submitted to Nature Communications (2020). Publications Independent of this ThesisA. Zannotti, F. Diebel, M. Boguslawski, C. Denz, Chiral light in helically twisted photonic lattices, Adv. Opt. Mat., 5, 1600629 (2017).J. M. Vasiljević, A. Zannotti, D. V. Timotijević, C. Denz, D. M. Jović Savić, Creating aperiodic photonic structures by synthesized Mathieu-Gauss beams, Phys. Rev. A, 96, 023840 (2017).J. M. Vasiljević, A. Zannotti, D. V. Timotijević, C. Denz, D. M. Jović Savić, Elliptical vortex necklaces in Mathieu lattices, Phys. Rev. A, 97, 033848 (2018).A. Zannotti, J. M. Vasiljević, D. V. Timotijević, D. M. Jović Savić, C. Denz, Morphing discrete diffraction in nonlinear Mathieu lattices, Opt. Lett., 44, 1592 (2019).A. Zannotti, J. M. Vasiljević, D. V. Timotijević, D. M. Jović Savić, C. Denz, Expanding Discrete Optics with Mathieu Beams, Optics & Photonics News, December, 52 (2019).J. M. Vasiljević, A. Zannotti, D. V. Timotijević, C. Denz, D. M. Jović Savić, Light propagation in aperiodic photonic lattices created by synthesized Mathieu-Gauss beams, submitted to Appl. Phys. Lett. (2020). Conference ProceedingsA. Zannotti, F. Diebel, M. Boguslawski, C. Denz, Discrete vortex propagation in three-dimensional twisted waveguide arrays, Nonlinear Optics, Kauai, Hawaii, USA, NM3B.7 (2015).A. Zannotti, F. Diebel, M. Boguslawski, C. Denz, Caustic diffraction catastrophes: Optical swallowtail and butterfly beams, Nonlinear Photonics, Sydney, Australia, NW2A.2 (2016).A. Zannotti, F. Diebel, M. Rüschenbaum, C. Denz, Controlling light in Airy and higher-order caustic photonic structures, Photorefractive Photonics, Qingdao, China, J. Phys.: Conf. Ser. 867, 012022 (2017).C. Mamsch, A. Zannotti, C. Denz, Embedding umbilic catastrophes in artificially designed caustic beams, CLEO Europe, Munich, Germany, EF_4_5 (2017).A. Zannotti, C. Mamsch, M. Rüschenbaum, C. Denz, Realizing curved nonlinear photonic caustic lattices by tailored optical catastrophes, Nonlinear Optics, Waikoloa, Hawaii, USA, NF2A.5 (2017).A. Zannotti, C. Mamsch, M. Rüschenbaum, C. Denz, Caustic-based nonlinear photonic lattices, Nonlinear Photonics, Zurich, Switzerland, NpTh3I.1 (2018).A. Zannotti, C. Mamsch, M. Rüschenbaum, C. Denz, Nonlinear light propagation in hexagonal morphing umbilic caustic lattices, Nonlinear Photonics, Zurich, Switzerland, NpTh3I.4 (2018).A. Zannotti, C. Mamsch, M. Rüschenbaum, C. Denz, Caustic light-based fabrication of advanced photonic structures, SPIE Optics + Photonics, San Diego, California, USA, Proc. SPIE 10720, Nanophotonic Materials XV, 1072002 (2018).A. Zannotti, D. Ehrmanntraut, C. Denz, Rogue waves by caustic networks in random media, Photorefractive Photonics and beyond, Gérardmer, France, (2019).A. Zannotti, D. Ehrmanntraut, C. Denz, Enhanced optical rogue waves by scattering caustic networks in tailored disorder, Nonlinear Optics, Waikoloa, Hawaii, USA, (2019).
	Publications Independent of this Thesis
	Conference Proceedings
Acknowledgement
Contents
1 Introduction and Motivation
	References
2 Waves, Caustics, and Catastrophes
	2.1 Waves in Structured Nonlinear Photonic Media
	2.2 Caustics are Catastrophes in Light
		2.2.1 Caustics as Singularities of Gradient Maps
		2.2.2 Diffraction Catastrophe Integrals
		2.2.3 The Topologies of Catastrophes
	References
3 Realization and Exploration  of Structured Light and Photonic Structures
	3.1 Spatially Structured Light
		3.1.1 Creating Scalar Structured Light Fields with Phase-Only Spatial Light Modulators
		3.1.2 Digital Holographic Phase Metrology
	3.2 Photorefractive Nonlinearity in SBN
		3.2.1 Linear Electro-optic Effect
		3.2.2 Band Transport Model and Anisotropic Approximation
	3.3 Refractive Index Modulations in Photorefractive SBN Crystals
		3.3.1 Optical Induction of Refractive Index Modulations
		3.3.2 Analysis of Optically Induced Photonic Structures
	References
4 Elementary Optical Catastrophes and Caustic-Based Photonic Structures
	4.1 Evaluation of the Oscillatory Integrals of Diffraction Catastrophes
	4.2 Optical Catastrophes in Light
		4.2.1 Airy and Pearcey Beams
		4.2.2 Optical Swallowtail and Butterfly Catastrophes
		4.2.3 Hyperbolic and Elliptic Umbilic Beams
	4.3 Caustic Light-Based Fabrication of Photonic Structures
		4.3.1 Waveguiding in Caustic Photonic Lattices
		4.3.2 Formation of a Pearcey Soliton
		4.3.3 Elliptic-Umbilic-Based Morphing Lattices
	References
5 Propagation-Invariant Caustics
	5.1 Caustics in Propagation-Invariant Light
		5.1.1 The Bessel Beam Caustic
	5.2 Visualising the Energy Flow of Tailored Light
	5.3 Shaping Caustics into Propagation-Invariant Light
		5.3.1 Inverse Caustic Design I: Differential Equation
		5.3.2 The Bessel-Lattice Beam
		5.3.3 Self-healing and Momentum Transfer in Tailored Caustics
		5.3.4 Inverse Caustic Design II: Bessel Pencil
	References
6 Caustic Networks and Rogue Waves
	6.1 Formation of Caustic Networks
		6.1.1 Caustic Networks from Gaussian Random Fields
		6.1.2 Analysing the Evolution of Caustic Networks
	6.2 Enhanced Random Focusing in Nonlinear Anisotropic Media
		6.2.1 Focusing by Modulation Instabilities
		6.2.2 Enhanced Focusing of Caustic Networks
	6.3 Random Scattering of Caustic Networks
		6.3.1 Extreme Events by Scattering at Random Potentials
		6.3.2 Rogue Wave Formation in Weakly Scattered Caustic Networks
	References
7 Conclusion and Outlook
	References
Appendix A Fourier Transform, Dirac Delta Function, Convolution, and Correlation
A.1  Fourier Transform
A.2  Dirac Delta Distribution
A.3  Convolution and Correlation
Appendix B Solving the Nonlinear Schrödinger Equation Numerically
Appendix C Numerical Calculation of Optically Induced Refractive Index Modulations in Biased SBN Crystals
Appendix D Angular Spectrum Method and Fresnel Propagation
D.1  Angular Spectrum Method
D.2  Fresnel Propagation
Appendix E Complex Gaussian Integral and Tschirnhaus Transformation
E.1  Complex Gaussian Integral
E.2  Tschirnhaus Transformation
	References
Appendix  Curriculum Vitae | Alessandro Zannotti