Thesis (M. Phil.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 59-64). Also available in print.

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Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures are engineered to control the dispersion and local field enhancements of the electromagnetic field. Ultra-short pulse propagation in a polarization-maintaining microstructured fibre (with 1 um core diameter and 1.1 m length) is investigated experimentally and theoretically. For an 80 MHz train of 130 fs pulses with average propagating powers in the fibre up to 13.8 mW, the output spectra consist of multiple discrete solitons that shift continuously to lower energies as they propagate in the lowest transverse mode of the fibre. The number of solitons and the amount that they shift both increase with the launched power. All of the data is quantitatively consistent with solutions of the nonlinear Schrodinger equation, but only when the Raman nonlinearity is treated without approximation, and self-steepening is included. The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in 3D photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated using 3D finite-difference time-domain (FDTD) simulations. Squeezing up to ~20% below the shot noise level is predicted for reasonable optical excitation levels. To preserve the squeezed nature of the light generated in the microcavity, a unidirectional coupling geometry from the microcavity to a ridge waveguide in a slab photonic crystal structure is studied. The structure was successfully fabricated in a silicon membrane, and experimental measurements of the efficiency for the signal coupled out of the structure are in good agreement with the result of FDTD simulations. The coupling efficiency of the cavity mode to the output channel is ~60%. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The area of quantum information promises to deliver a range of new technologies in the fields of quantum computing and quantum communication. Devices based on semiconductor quantum dots hold great potential for the practical realisation of many of the components required in the proposed schemes. This thesis describes the development of several quantum dot devices. By integrating a quantum dot into a p-i-n diode, it was possible to control the dominant emission lines in its photoluminescence spectrum and to maximise the degree of polarisation correlation between the two photons emitted in the biexciton decay. With the same device under a magnetic field, a digital memory was demonstrated. The polarisation information of a single photon was stored as the spin of an electron inside the quantum dot, and was deterministically recovered some time later by the application of an electrical trigger. A fabrication process was developed in order to produce high quality two dimensional slab photonic crystals operating with a photonic band gap at ~ 900 nm. By placing a quantum dot into an appropriately designed H1 photonic crystal cavity, strong coupling was achieved between the dot and the monopole mode of the cavity. The vacuum Rabi splitting was found to be constant for all linear polarisations due to the unpolarised nature of the far-field of the mode. Finally, a new kind of cavity based on photonic crystal waveguides was developed. A Purcell enhancement of the in-plane spontaneous emission from a quantum dot coupled to a unidirectional photonic crystal waveguide was demonstrated.

archives@tulane.edu / 1 / Madhu Sudan Gaire

Photonic crystals are media with periodically varying optical properties. Photonic crystals enable exquisite control of light propagation in integrated optical circuits and also emulate advanced physical concepts. However, common photonic crystals directly pattern the optical medium and thus are unfit for in-operando on/off controls. In this dissertation, we introduced, fabricated, and studied the properties of graphene polaritonic crystals. Our polaritonic crystal system consists of a pristine sheet of graphene in a back-gated platform with nano-structured gate insulators. We employed scattering-type scanning near-field optical microscopy (s-SNOM) to study the novel properties of polaritons propagating in the polaritonic crystal. We demonstrated the formation of a polaritonic bandgap, variations of the polaritonic local density of states, and the emergence of polaritonic domain wall states. We also revealed the programmable control of the polariton propagation direction and reconstructed the polaritonic bandstructure from real-space polariton images. The exploration of topological polaritonic phenomena in the polaritonic crystal relies on the selective excitation of topologically non-trivial modes using a chiral polariton launcher. We searched for the design of an efficient chiral polariton launcher. Throughout the journey, we visualized the polaritonic vortex mode of hBN phonon-polaritons. We discovered that the optical spin angular momentum of hBN phonon-polaritons resembles nano-scale meron spin textures. The meron spin texture possesses a half-integer topological charge determined by the handedness of the incident beam. The polaritonic crystal platform studied in this dissertation sheds light on the exploration of topologically non-trivial polaritonic states, such as valley plasmons and topological edge states. In addition, our electrostatically-tunable polaritonic crystals are derived from standard metal oxide semiconductor field-effect transistor technology and pave a way for practical on-chip light manipulation.

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Pages (41,133,161,209) were omitted from the thesis as they were completely blank pages. / <p> In this thesis, we propose efficient approaches for design optimization of passive and active photonic devices. These approaches are based on utilizing gradient based optimization algorithms for efficient optimization of photonic devices. Some of the proposed approaches obtain the required gradient (sensitivity) information efficiently using adjoint variable method (AVM) applied directly to the exploited numerical techniques. Other approaches are based on formulating the design problem as an optimization problem using convex programming. These approaches utilize the gradient-based interior point method (IPM) for solving the design.</p> <p> The AVM aims at efficiently obtaining the sensitivity information using the numerical technique. This technique requires a solution of an additional simulation of the adjoint system. The information obtained from the original and the adjoint simulation is sufficient to obtain the response and the sensitivity of the response with respect to all the design parameters. The AVM technique differs for different numerical method. </p> <p> The obtained sensitivity using the AVM approach is not only useful for exploiting gradient based optimization for design optimization, but also for yield and tolerance analyses of the newly proposed designs. </p> <p> We proposed a second order accurate approach to obtain the sensitivity information using finite difference time domain (FDTD) technique. This approach utilizes the AVM to efficiently obtain the sensitivity information. This approach is exploited for efficiently obtaining the sensitivity of the power reflectivity and coupling coefficient of various devices. This approach has been also utilized for obtaining the sensitivity of the dispersion characteristics of different guided wave structures.</p> <p> We also introduce a novel approach for sensitivity analysis of photonic devices using the beam propagation method (BPM). This approach is simple and easy to implement. It exploits the existing factorization of the system matrices for efficient calculation of the sensitivity of the required objective function. This approach is also utilized for sensitivity analysis of the vectorial modal properties of different guided wave structures. This approach is also exploited for sensitivity analysis of various surface plasmon devices. </p> <p> This AVM approach is also exploited to propose a novel design of an optical switch with wide working wavelength band and compact size. The switch is based on the self imaging theory in multimode waveguide with a refractive index has approximate parabolic profile. The design problem is formulated as two stage optimization procedure. The optimization algorithm exploits the efficiently obtained sensitivity information from a BPM simulation. The final design has interesting characteristics.</p> <p> An efficient approach is also proposed to obtain the sensitivity of the energy levels and wavefunctions of different quantum structures obtained using time dependent and time independent Schrodinger equation. This approach is exploited for design optimization of different quantum well lasers.</p> <p> We also propose a convex formulation for the design problem of multilayer optical coatings. This formulation allows for efficient design of structures with large number of layers in fractions of a second without an initial design.</p> / Thesis / Doctor of Philosophy (PhD)

In this work, we investigate several aspects of photonic crystal waveguides through modeling and simulation. We introduce a one-dimensional model for two-dimensional photonic crystal fibers (PCFs), analyze tapered PCFs, analyze planar photonic crystal waveguides and one-dimensional PCFs with infinite periodic cladding, and investigate transmission properties of a novel type of fiber, referred to as Fresnel fiber. A simple, fast, and efficient one-dimensional model is proposed. It is shown that the model is capable of predicting the normalized propagation constant, group-velocity dispersion, effective area, and leakage loss for PCFs of hexagonal lattice structure with a reasonable degree of accuracy when compared to published results that are based on numerical techniques. Using the proposed model, we investigate tapered PCFs by approximating the tapered section as a series of uniform sections along the axial direction. We show that the total field inside the tapered section of the PCF can be evaluated as a superposition of local normal modes that are coupled among each other. Several factors affecting the adiabaticity of tapered PCFs, such as taper length, taper shape, and number of air hole rings are investigated. Adiabaticity of tapered PCFs is also examined. A new type of fiber structure, referred to as Fresnel fiber, is introduced. This fiber can be designed to have attractive transmission properties. We present carefully designed Fresnel fiber structures that provide shifted or flattened dispersion characteristics, large negative dispersion, or large or small effective area, making them very attractive for applications in fiber-optic communication systems. To examine the true photonic crystal modes, for which the guidance mechanism is not based on total internal reflection, photonic crystal planar waveguides with infinite periodic cladding are studied. Attention will be focused on analytical solutions to the ideal one-dimensional planar photonic crystal waveguides that consist of infinite number of cladding layers based on an impedance approach. We show that these solutions allow one to distinguish clearly between light guidance due to total internal reflection and light guidance due to the photonic crystal effect. The analysis of one-dimensional PCFs with infinite periodic cladding is carried out in conjunction with an equivalent T-circuits method to model the rings that are close to the core of the fiber. Then, at sufficiently large distance from the core, the rest of the cladding rings are approximated by planar layers. This approach can successfully estimate the propagation constants and fields for true photonic crystal modes in both solid-core and hollow-core PCFs with a high accuracy. <i>Original file (released May 10, 2007) replaced Oct. 3, 2012 GMc per DePauw]</i> / Ph. D.