Bragg gratings are important devices for both optical communications and
sensing. These devices are used to design very narrow band optical filters, which can
be used in wavelength division multiplexing (WDM). It is also perceived that Bragg
gratings will be used to compensate the dispersion in modern fibre optic
telecommunication networks. Semiconductor gratings are usually integrated into
lasers to control the operating wavelength.
City University Photonic Modelling Group is a world leading research group on
the use of rigorous numerical techniques to design and optimise advanced photonic
devices for optical communications. The research group has already achieved results
on hypothetical one-dimensional (1-D) and realistic two-dimensional (2-D)
structures. In this project a combination of three numerical methods has been used,
all of which are rigorous, to simulate realistic three-dimensional (3-D) structures in
semiconductor waveguides. The combination of these three accurate methods, the
finite element method (FEM), the least squares boundary residual (LSBR) method
and the transfer matrix method (TMM) turned out to be superior to the widely used
coupled mode theory (CMT).
The numerical study of different Bragg gratings shows interesting dependencies
of the characteristics of the gratings on the different design parameters. The work
was carried out for different mesh distributions, different numbers of mesh divisions
and different computational parameters. Another focus of the work was on the
stability of the transmission and reflection coefficients obtained from the LSBR
program. Furthermore the effect of inaccuracy occurring during the fabrication
process has been studied.
The results of this work have been compared to results found by other groups and
fellows. We can say that this project is quite new in the field of reflection spectrum
computation of realistic 3-D semiconductor Bragg gratings. Up to now only a few
papers have been published on such 3-D semiconductor gratings.
1 INTRODUCTION
1.1 Introduction
1.2 Optical communication systems
1.3 Aims and objectives
1.3.1 Previous works
1.3.2 Work in this project
1.4 Structure of this thesis
2 THEORY
2.1 Chapter overview
2.2 Maxwell’s equations
2.3 Boundary conditions
2.4 Reflection and refraction
2.5 Dispersion and loss
3 DIFFERENT TYPES OF BRAGG GRATINGS
3.1 Chapter overview
3.2 Principle of operation
3.2.1 Uniform gratings
3.2.2 Chirped gratings
3.2.3 Apodised grating
3.2.4 Phase-shifted gratings
3.2.5 Multiple gratings
3.3 Applications of Bragg gratings
3.3.1 Demultiplexer in WDM systems
3.3.2 Dispersion compensation
3.3.3 Applications in lasers
3.3.4 Applications in sensing technology
3.4 Fabrication of Bragg gratings
3.4.1 Fabrication of fibre Bragg gratings
3.4.2 Fabrication of semiconductor Bragg gratings
4 SIMULATION METHODS
4.1 Chapter overview
4.1.1 Introduction
4.1.2 Theory of the FEM
4.2 Least squares boundary residual (LSBR) method
4.2.1 Introduction
4.2.2 Theory
4.3 Transfer matrix method (TMM)
4.3.1 Introduction
4.3.2 Theory for uniform gratings
4.3.3 Theory for apodised gratings
4.4 Overlap integral (OI)
4.5 Coupled mode theory (CMT)
4.5.1 Introduction
4.5.2 Theory
5 SIMULATION RESULTS
5.1 Chapter overview
5.2 Examined structures
5.3 Results obtained from FEM
5.4 Analysis of the discontinuity junction using LSBR
5.5 Simulation of a complete grating using TMM
5.5.1 Introduction
5.5.2 Input data
5.5.3 Uniform gratings
5.6 Results obtained from the CMT
5.7 Simulation of fabrication inaccuracy
5.8 Apodised gratings
5.8.1 Different apodisation profiles
5.8.2 Simulation results
5.9 Chirped gratings
5.10 Phase-shifted gratings
5.11 Multiple gratings
6 CONCLUSION
6.1 Discussion of the results
6.2 Conclusion
6.3 Further work
Research Objectives and Themes
The primary research objective of this thesis is the accurate characterisation of three-dimensional (3-D) semiconductor Bragg gratings. The work addresses the challenges associated with dispersion and loss in modern optical communication systems by employing a rigorous combination of numerical simulation techniques, specifically the finite element method (FEM), the least squares boundary residual (LSBR) method, and the transfer matrix method (TMM), to evaluate their superiority over existing coupled mode theory approaches.
- Numerical characterisation of 3-D semiconductor Bragg grating structures.
- Evaluation and comparison of FEM, LSBR, TMM, and CMT simulation methods.
- Investigation of the impact of structural design parameters and fabrication inaccuracies on reflection spectra.
- Study of various grating configurations, including uniform, apodised, chirped, phase-shifted, and multiple gratings.
Excerpt from the Book
3.2.1 Uniform gratings
A fibre Bragg grating is a simple and extremely low cost wavelength selective filter. It is constructed by periodically varying the refractive index of the core along the fibre length. In contrast to that in a semiconductor grating the effective index perturbations are obtained by removing material from the guiding layer. The effective index varies with the changed size of the cross section (Fig. 3-1). Due to this property light waves of a special frequency are reflected and the filter characteristic is a band-stop. The centre wavelength of the reflection band is λB = 2navΛ, where Λ is the grating period and nav the average refractive index [7].
As light moves along the fibre and encounters refractive index changes, a small part of it is reflected at each discontinuity. The periodic nature of the index variations causes the forward- and backward-propagating waves to couple at wavelengths close to the Bragg wavelength. This forms the filter characteristic, which is a band-stop notch filter. The remaining frequencies can pass the grating without being influenced.
Summary of Chapters
1 INTRODUCTION: This chapter provides an overview of optical communication systems, defines the research aims for characterizing 3-D semiconductor Bragg gratings, and outlines the thesis structure.
2 THEORY: This chapter covers fundamental theories of light propagation, including Maxwell's equations, boundary conditions, and the physical principles of reflection, refraction, dispersion, and loss.
3 DIFFERENT TYPES OF BRAGG GRATINGS: This chapter details various Bragg grating types—uniform, chirped, apodised, phase-shifted, and multiple gratings—along with their operational principles and fabrication methods.
4 SIMULATION METHODS: This chapter describes the mathematical and numerical frameworks employed, specifically FEM, LSBR, TMM, CMT, and the overlap integral method.
5 SIMULATION RESULTS: This chapter presents the comprehensive numerical findings for the simulated semiconductor structures, including stability analysis, fabrication inaccuracy effects, and spectral comparisons.
6 CONCLUSION: This chapter summarizes the project results, discusses the validity of the applied simulation methods, and suggests directions for future research.
Keywords
Bragg gratings, semiconductor waveguides, optical communications, finite element method, FEM, least squares boundary residual, LSBR, transfer matrix method, TMM, coupled mode theory, CMT, dispersion compensation, wavelength division multiplexing, WDM, photonic devices.
Frequently Asked Questions
What is the primary focus of this research?
The research focuses on the accurate numerical characterisation of three-dimensional (3-D) semiconductor Bragg gratings for use in optical communication and sensing applications.
What are the core thematic areas covered in this thesis?
The core areas include the theoretical framework of light propagation, different configurations of Bragg gratings, specific numerical simulation methodologies, and the impact of fabrication errors on grating performance.
What is the central research goal?
The goal is to simulate realistic 3-D semiconductor grating structures using a combination of rigorous numerical methods (FEM, LSBR, TMM) to provide more accurate results than traditional coupled mode theory (CMT).
Which scientific methods are utilized?
The study employs the Finite Element Method (FEM) for modal solutions, the Least Squares Boundary Residual (LSBR) method for discontinuity junctions, and the Transfer Matrix Method (TMM) to calculate overall reflection spectra.
What topics are discussed in the main body of the work?
The main body treats the theory of Maxwell's equations, various grating architectures, detailed simulation results for different structure parameters, and the analysis of fabrication inaccuracies.
Which keywords define this study?
Key terms include Bragg gratings, semiconductor waveguides, optical communications, FEM, LSBR, TMM, CMT, dispersion, and WDM.
Why are semiconductor Bragg gratings significant?
They are essential for implementing narrow-band optical filters, controlling operating wavelengths in integrated lasers, and compensating for signal dispersion in high-speed networks.
What were the specific findings regarding CMT?
The study found that the standard Coupled Mode Theory (CMT) significantly underestimates reflection coefficients for 3-D semiconductor gratings when compared to the proposed TMM/LSBR approach, though it captures bandwidth characteristics well.
How does fabrication inaccuracy affect the grating performance?
The simulations demonstrate that while minor fabrication errors (below 1%) have negligible impact, significant inaccuracies (around 10%) lead to shifted peaks and compromised grating periodicity.
- Citation du texte
- Dr.-Ing. Stephan Pachnicke (Auteur), 2001, Bragg gratings in semiconductor waveguides, Munich, GRIN Verlag, https://www.grin.com/document/50382
