The Design of an On-Chip Silicon Photonic Diode

The Design of an On-Chip Silicon Photonic Diode

ABSTRACT

This work presents numerical calculation of electromagnetic waves in unidirectional on-chip silicon optical diodes. An original optical diode, designed by Wang et. al. [Opt. Express. 19, 26948-26955 (2011)], is based on breaking of spatial inversion symmetry and the directional band gap difference of two 2D photonic crystals comprising a hetero-junction structure. The dimensions of our structure are however different from those of Wang et. al. The electromagnetic waves in the diode obey the Maxwell’s equations which were solved with appropriate boundary conditions using the finite difference time domain as implemented in the MEEP software. MEEP is an acronym for M.I.T. Electromagnetic Equation Propagation. Our solutions show the existence of a distinct unidirectional isolation effect in the designed hetero-junction slab. The band structures for the lowest frequency mode of the transverse electric fields in the bulk of each of the 2D crystals comprising the hetero-junctions were also determined by solving the wave equation in frequency space. The MPB (M.I.T Photonic Bands) software was used. The band structures reveal directional band gaps which are responsible for the optical isolation property of the composite hetero-junction.

TABLE OF CONTENTS

LIST OF FIGURES ………………………………………………………………………………………………………………………………. VI
CHAPTER 1 …………………………………………………………………………………………………………………………………………. 1
1.1 INTRODUCTION …………………………………………………………………………………………………………………………….. 1
1.2 OVERVIEW OF THE THESIS …………………………………………………………………………………………………………… 4
CHAPTER 2 …………………………………………………………………………………………………………………………………………. 5
2.1 BANDGAP ………………………………………………………………………………………………………………………………………. 5
2.2 THE SIZE OF THE BAND GAP ……………………………………………………………………………………………………………… 9
2.3 SIGNAL CONTRAST (S) ……………………………………………………………………………………………………………………. 11
2.4 MAXWELL’S EQUATIONS …………………………………………………………………………………………………………………. 12
2.5 MEEP …………………………………………………………………………………………………………………………………………. 12
2.6 MPB …………………………………………………………………………………………………………………………………………… 13
2.7 UNITS …………………………………………………………………………………………………………………………………………. 13
2.8 BOUNDARY CONDITIONS …………………………………………………………………………………………………………………. 13
Chapter 3 …………………………………………………………………………………………………………………………………………. 15
3.1 Maxwell’s Equations in two dimensions……………………………………………………………………………………………. 16
3.2 Calculation of the Transmission Coefficient ………………………………………………………………………………………. 19
3.3 Calculation of the photonic band structure …………………………………………………………………………………………. 20
Chapter 4 …………………………………………………………………………………………………………………………………………. 23
4.1 Results and Discussions …………………………………………………………………………………………………………………. 23
4.2 Conclusion …………………………………………………………………………………………………………………………………. 32
4.3 Recommendation …………………………………………………………………………………………………………………………………………..32
Appendix …………………………………………………………………………………………………………………………………………………………..33
Appendix A ……………………………………………………………………………………………………………………………………………………….33
Reference ………………………………………………………………………………………………………………………………………………………….53
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CHAPTER ONE

1.1 Introduction

Just like an electrical diode which allows current to flow in one direction only, a photonic diode allows light to propagate in one direction but blocks counter propagating photons. Why photonic diode? We are living in the information age where there is incessant clamor for faster information processing, more efficient telecommunication, miniaturization of electrical appliances for easy mobility, and availability of quantum computer for scientific purposes. These “basic” needs highlighted above can only be met in the realm of photonics. That is, there is a need to migrate from the use of electrical circuits, which formed the backbone of our information age, in our designs to opto-electrical circuit, the future of our quantum computers. In other words, imagine a world where electrons, which are the active carrier of signal in this age, are replaced with photons. Certainly there would be accelerated growth in information processing, telecommunication, etc. For the new generation of circuits to be functional, there is a need to begin the design of the corresponding electrical circuit components for photonic circuits. One of these components is a diode; in the new case, it is the photonic diode. The successful implementation of this component would serves as a platform for the design of upcoming integrated circuits. Over the years, various schemes have been proposed to construct compact and highly efficient all-optical diodes. Some of the schemes that have been proposed cannot be implemented on a silicon chip because either they require magneto-optical materials or strong magnetic field. We are all aware of the consequence of using magnetic field in systems like computers. Definitely it would affect the storage “organs”. In addition some of these schemes depend on non-linear media, thus they require high electric field, meaning they are not compatible with complementary metal-oxide-semiconductor (CMOS). Over the years, all-optical diodes have captured much attention for their potential application in integrated photonic circuits, all optical signal processing, and telecommunications in the future.

Various schemes have been proposed to construct compact and highly efficient all-optical diodes [2-9]. Scalora et. al. suggested using one-dimensional nonlinear photonic crystals with a spatial graduation in the linear refractive index to realize unidirectional propagation of signals in 1994 [1].

Feise et al. demonstrated the bi-stable diode action in an asymmetric multilayer structure consisting of left-handed materials [3]. Philip et al. studied numerically and verified experimentally the passive alloptical diode behavior utilizing asymmetric nonlinear absorption [4]. Configurations of a photonic crystal (PC) waveguide with embedded nonlinear PC defects and with asymmetric defect pair are found to display nonreciprocal effects as well [5–8]. However, the achieved transmittance contrasts of all-optical diodes in the schemes mentioned above are all lower than 100. In order to improve the transmission contrast, very recently, Xue et. al. suggested using one-dimensional PC-metal hetero-structures to achieve highly efficient all-optical diode action [10], and Hu et. al. proposed a strategy for obtaining ultrahigh-contrast all-optical diodes based on tunable surface Plasmon polaritons [11].

However, the transmission contrast of the former one is only about 124, still not high enough. For the latter one, although the transmission contrast ratio can be as high as 2166, the forward transmittance is only 0.06, which is too low to be used in the practical applications. Recently, Cai et. al. studied the transmission property of two directly coupled nonlinear defects and proposed that it can function as an all-optical bi-stable switch or diode with high transmission contrast if we deliberately and properly misalign the resonant frequencies of the two defects [12]. The application of this kind of configuration in optical switching has already been demonstrated [13]. Cai et. al. designed photonic crystal structures composed of three or four nonlinear defects, and showed that all-optical diodes can be realized for this configuration and the transmission contrast can be further increased by selecting the resonant frequencies of the constitutional defects properly [14]. Li et. al. reported a method for making unidirectional on-chip optical diode based on directional band gap difference of two 2D photonic crystals, and confirmed the existence of the isolation effect [16].

Obtaining on-chip optical signal is a primary problem in the integrated photonics. The clamor to overcome this problem is increasingly becoming urgent, specifically with the emergence of silicon nano-scale photonics.

Until now, there have been no techniques that account for complete on-chip signal isolation using materials or processes that are compatible with silicon CMOS processes. Optical isolation can also be achieved using dynamic photonic structures. Wang et. .al. proposed all-optical diode based on a moving photonic crystal generated in a three level electromagnetically induced medium [18]. Zongfu and Shanhui showed that nonreciprocal isolation with linear and broadband can be achieved by spatial-temporal refractive index modulation [19]. This work demonstrates that on-chip isolation can be achieved with static photonic structures in standard linear and non-magnetic material systems that are widely used for integrated optoelectronics applications. We used the photonic structure designed by Chen et .al in the paper “On-chip optical diode based on Silicon photonic crystal” [16]. However the dimensions of our structure are different. Our work entails numerical simulation; calculation of transmittance and plotting of band structure of the proposed linear and non-magnetic photonics structures that support nonreciprocal optical isolation. The proposed structure is:

On-chip optical isolators based on the directional band gap difference of two dimensional square-lattice photonic crystals comprising a hetero-junction structure and the breaking of the spatial inversion symmetry. In this structure, effort would be made to simulate the field patterns, calculate the forward and backward transitivity of the isolator and obtain the band structure.

1.2 OVERVIEW OF THE THESIS

1) Chapter two reviews basic concepts of non-reciprocal optical devices used throughout the thesis: band gap, signal contrast, the Maxwell’s equations as they apply to dielectric crystal materials, and an introduction to the MEEP software used in the solution of Maxwell’s equations. That is, it contains the basic equations governing electromagnetic wave interaction with dielectric functional materials.

2) Chapter three demonstrates the solution of Maxwell’s equations as it applies to lossless dielectric structures via a discretization approach and by the use of a (plane wave) basis set.

3) In Chapter four, the results obtained from simulations and calculations are presented and discussed. A conclusion is also given in this chapter.