DESIGN OF LONG PERIOD WAVEGUIDE GRATING DEVICES USING NATURAL OPTIMIZATION ALGORITHMS

Abstract

The invention of LASER revolutionized new research in the area of optics and telecommunication. The LASER is a coherent light source which produces the monochromatic, high intensity and directional optical beam. Initially the optical phenomena were studied with the bulk optical material using LASER. The techniques of the prism and grating coupling have been evolved for the coupling of light into thin films. Subsequent research improved the coupling efficiency of light into thin films. The optical phenomena of bulk materials were investigated with the thin film of dielectric materials. The wavelength of light is small; hence the micron order film can guide the light from one place to other place. The specific devices can be designed by controlling the parameters of a waveguide. The devices based on the thin film may be placed close to one another on the single substrate and thin films can also work as interconnect for the thin film photonics devices. A large number of optical devices can be fabricated on the single chip for optical signal processing. The concept for integrated optical devices evolved similar to the integrated circuits and hence the analogous name, integrated optics (IO) was suggested. Planar waveguide is a simpler and effective thin film photonics structure. The advanced photonics devices are designed using the complex multilayer planar structure. The material like glass was primarily used for the fabrication of thin film devices. Only passive devices can be fabricated using glass material. Dielectric material like lithium niobate (LiNbO3) is superior for the fabrication of active devices. Semiconductor materials like silicon and gallium arsenide (GaAs) are also preferred in the integrated optics. The advantage of using semiconductors in IO is that the source and detectors can be fabricated on the same substrate along with the optical devices. The source and detectors requires some electronics circuit such as laser diode driver for source and amplifiers circuits of detector. These electronics circuits can be easily fabricated on the same integrated chip. The semiconductor technology is sufficiently mature. Hence the advantages of fabrication technologies in the semiconductor devices are much useful in the IO technology. Another class of material is the polymer used in integrated optics. The polymer is a low cost material. The polymers are suitable material for the Abstract ii development of IO sensors. The poor shelf life and large temperature coefficient are the biggest disadvantages of polymers which restrict their use in the optical communication. The accuracy of planar waveguide devices depends on the accuracy of the design parameters of waveguide structure. The analysis of simple three layers symmetric and asymmetric guided structure can be analyzed by solving the transcendental equation numerically. The complex multilayer structure requires the accurate and efficient numerical techniques to solve the structure in conjunction with superior computational power. Various numerical techniques have been proposed to compute the modes of a multilayer planar waveguide with the advancement of the computer. Numerical methods such as the semi-analytical-graphical method, iterative method, reflection pole and vector density method, variational method, APM based methods have been used to solve the planar waveguide. Every numerical method used for the design of planar waveguide device has its advantages and disadvantages; hence the suitable choice of numerical technique is important for the design and analysis process. Cylindrical waveguide has been developed for long distance optical communication called the optical fiber. It is an equivalent to the coaxial cable used as communication medium in microwave communication. Initially, the extensive study of light propagation, signal losses and pulse dispersion in the fiber has been carried out to improve the signal quality. Later, a phenomenon of photosensitivity in the germanium doped fiber was observed by Hill in 1978. In the subsequent years, the photosensitivity has been utilized to develop the fiber Bragg grating (FBG). The fiber grating devices have been extensively used for the telecommunication and sensing technologies. The later version of grating was incarnated as long period grating (LPG). The LPG has the advantages of easy fabrication technology, simple alignment and low cost. Fiber gratings have limitations due to selection of material and geometry. Optical fiber is made of silica and has cylindrical geometry. Tailoring of application specific complicated rejection band spectrum in fiber grating is limited due to material and geometrical constrains. LPG in a four layer planar waveguide was proposed to overcome the limitations of fiber gratings and to increase the degrees of freedom in the design process. The grating is popularly known as the long period waveguide grating (LPWG). In recent years, large number of designs based on the LPWG have been proposed and their fabrication as well as characterization has been demonstrated. LPWG generates the symmetric resonance rejection band; however the application Abstract iii specific spectra are asymmetric. Such rejection band spectra can be obtained using the complex waveguide and grating structures. The complex design of LPWG requires an optimization process to optimize the grating and waveguide parameters for achieving application specific complicated rejection band spectra. The optimization techniques such as Lagrange multiplier optimization, genetic algorithm (GA) and particles swarm optimization (PSO) have been implemented for FBG and LPFG devices. Only limited number of grating parameters have been optimized in fiber gratings. The LPWGs possess large degree of freedom due to multilayer structure and freedom of selecting material. The studied of propagation constants and modal fields of the mode of a complex planar waveguide are also required for generating rejection band spectra besides the optimized grating parameters. The application specific target spectrum can be obtained by suitable combination of the grating and waveguide parameters including the waveguide material. In this thesis we have proposed an efficient mode computation method for multilayer planar waveguide followed by two optimization techniques; GA and adaptive PSO; as the efficient tools for optimizing LPWG parameters. Different types of LPWG in planar waveguide structure have been optimized to obtain the application specific pre-defined target spectra. The thesis presents a robust and reliable method for the computation of propagation constants and modal field distributions in a variety of multilayer planar waveguide structures. A technique to solve generalized dispersion equation of multilayer planar waveguide has been demonstrated to obtain all the expected guided modes. The dispersion equation for the guided structure has been solved using bisection method in conjunction of mode identification technique and domain decomposition for isolating the modes. The complex multilayer structures cannot be solved with the bisection method hence a new method has been proposed. The solution of dispersion equation for the complex structure is based on the derivative free method for computing the roots of an analytical function in complex plane. The derivative free method extracts the roots which are very close to actual zeros of the dispersion function. Roots are further refined using the robust iteration method to achieve the desired accuracy. Application of the proposed method has been verified by solving the modes of a variety of structures including lossless structure, leaky structure, quantum well waveguide, active waveguide, non-linear waveguide, ARROW waveguide, Metal clad waveguide, large-core leaky structure and coupled-core waveguide. The method is efficient and computes all modes of planar waveguide with sufficient accuracy. Abstract iv A four-layer planar waveguide has been used to design LPWG. LPWG has numerous applications in the optical communication and sensing technologies. LPWG has been design by embedding corrugated grating in the film of waveguide. The modes of the waveguide have been computed by the method developed in the present thesis. Global optimization properties of genetic algorithm (GA) have been utilized to design LPWG devices for the application specific spectra. Pre-defined target spectra corresponding to single-band, wide-band and dual-band rejection have been considered. The optimized grating parameters of corrugated grating have been obtained using GA optimization to achieve these target spectra. Three parameters namely the grating length, grating period and corrugation height of LPWG have been optimized using GA optimization. The simulation results show that the method is easy to implement and useful to design the grating for a pre-defined application specific spectra. LPWG has large degree of freedom due to selection of materials and geometry. Hence, the complex structure can be tailored to generate the complex rejection band spectra. Complexity of design introduces the large number of design parameters. GA is an efficient method for optimization and performs well for the small number of optimization parameters. The GA optimization becomes slow as the number of parameters increase in the optimization process. Sometimes the process of optimization is stuck and the optimization process is trapped in the local minima with increased number of parameters. In such a case, an efficient optimization method has been explored. To address this, we have presented the design optimization of LPWG based wavelength filters using adaptive particle swarm optimization (APSO) technique. Convergence analysis of APSO algorithm with single-band, wide-band and dual-band rejection filters has been demonstrated first. These filters have been designed in four layer planar waveguide structure with corrugated grating embedded in the guiding film. After convergence tests of algorithm, the optimization technique has been implemented to design LPWG for more complicated application specific filters. The modified complex waveguide structure has been used to generate such complex rejection band filters. Four-layer waveguide structure has been modified by segmenting the cladding into two parts. Each part has same cladding thickness but differs in refractive index. Optimization of grating length of two sections, grating period, corrugation height, cladding thickness and refractive index difference of two cladding section has been carried out to design wavelength filters for achieving a desired target spectrum. Abstract v Rectangular rejection band filter, filters for flattening the ASE of EDFA and gain of EDWA has been designed successfully using segmented cladding LPWG. Another design we have optimized in this thesis has two concatenated gratings on the same substrate. Two sections of grating have different lengths, periods, corrugation heights but have the same cladding profile. Total seven numbers of LPWG parameters have been optimized to achieve various application specific and asymmetric rejection band spectra. Design procedure of the LPWG to generate the rectangular target spectrum has been demonstrated first with APSO. The technique has been extended to optimize the complicated grating structure to generate the asymmetric target spectra. Finally, the design optimization has been illustrated by various examples including filter for flattening the ASE spectrum of EDFA and gain flattening filter for EDWA. The optimization process for simple LPWG, segmented cladding LPWG structure and LPWG with a pair of two concatenated grating has been successfully demonstrated. Apart from these, we have also carried out the optimization in more complex structure namely five-layer plasmon waveguide. The plasmon waveguide is widely used in biomedical applications and in the biological and chemical warfare agent detection. Grating assisted surface plasmon resonance (SPR) waveguides are used as efficient refractive index sensors. APSO has been used to optimize the waveguide and grating parameters of grating assisted SPR sensors. We have considered two waveguide structures in the design optimization process, and the grating and the waveguide parameters have been optimized to achieve the desired results. Total five parameters of waveguide and gratings have been optimized. The designed sensors show extremely good sensitivity of grating assisted SPR refractive index sensors. Finally, we conclude the work carried out in the thesis and propose the outlook of future work.