Thông tin tóm tắt về những đóng góp mới của luận án tiến sĩ: Nghiên cứu, thiết kế cấu trúc tinh thể quang tử 1D và 2D ứng dụng cho linh kiện lưỡng trạng thái ổn định.

Nguyen (2018), Induced high- order resonance linewidth shrinking with multiple coupled resonators in silicon-organic hybrid slotted two-dimensional photonic crystals for reduc[r]

MINISTRY OF EDUCATION

AND TRAINING

VIETNAM ACADEMY

OF SCIENCE AND TECHNOLOGY

GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY



HOANG THU TRANG

DESIGN AND INVESTIGATION OF 1D, 2D PHOTONIC

CRYSTALS FOR BISTABLE DEVICES

9

The thesis was completed at Key Laboratory for Electronic Materials and Devices, Institute of Materials Science, Vietnam Academy of Science and Technology

Supervisors:

1 Assocc Prof Dr Ngo Quang Minh

2 Prof Dr Arnan Mitchell

The thesis could be found at:

- National Library of Vietnam

- Library of Graduate University of Science and Technology

- Library of Institute of Science Materials

INTRODUCTION

1 The urgency of the thesis

Micro- and nano-structured photonic and optoelectronic devices have been the great interests for their outstanding applications and features in integrated micro-optoelectronic circuits with high processing speed Their unique properties have been expected to realize the new generation of opto-electronic components with high efficiency, low cost, and low energy consumption [1-5] There are two main approaches to improve the efficiency, functionality and reduce the cost of photonic and opto-electronic devices: (i) firstly of using new structures for the core elements that build up the devices; (ii) the other approach is the use of advanced materials with many special features Within the framework of my Ph.D thesis in materials science, speciality in optical materials, opto-electronics and photonics,

I will study in depth and present the use of new structures for photonic materials and devices which have not been available in nature, for

applications in telecommunication and optical processing

Photonics was appeared in the 80s of the XIX century [6] and developed very actively in the XX century, especially since the discovery of a new material with artificial structures such as photonic

crystals (PhCs), plasmonics and metameterials (MMs) [7-9] The PhC

structure is the periodicity of elements with different dielectric constants The periodic of the refractive indices of the dielectric materials enables the PhC structure can manupulate the light without loss The light/electromagnetic waves transmitted inside the PhC structure interact with the periodic of the dielectric elements and create the photonic bandgap (PBG) Light/electromagnetic waves with

frequencies (or wavelengths) in the PBG region cannot pass through the PhC structure Besides, we can easily capture, control, and direct lights in the identical media as desired Light/electromagnetic wave propagation can be made in the PBG region by creating the cavities or waveguides in the PhC structure The cavity and the waveguide are the key elements that build up the integrated optical and opto-electronic components such as switches and optical processing that the thesis will mention

PhC structures have been studied and developed widely around the world, particular the research group of Professor J.D Joannopoulos at Massachusetts Institute of Technology (USA) [10,11] The group's key research members come from different departments such as Physics, Materials Science, Electronics and Computer Engineering, Mathematics Every year, many excellent publications are published

in high impact journals such as Science, Nature, Physical Review Letters Many computational softwares have been known widely such as MIT Photonic-Bands (MPB), MIT Electromagnetic Equation Propagation (MEEP) [10,11]

In Vietnam, the research on photonic and opto-electronic devices using PhC structure is a new topic that has been attracting much attention from researchers at institutes and universities: research group

at Institute of Materials Science and Institute of Physics which belong

to Vietnam Academy of Science and Technology (VAST), Hanoi University of Science and Technology [14] At the Institute of Materials Science, the research teams of Assoc Prof Pham Van Hoi and Assoc Prof Pham Thu Nga have successfully fabricated 1D and 3D PhC structures [15-17], based on porous silicon and silica, used for the liquid sensors In addition, my research group at Institute of

Materials Science developed the computation, simulation of some micro and nano-photonic devices using 1D and 2D PhC structures, such as the micro-resonantors, surface plasmon resonance structures toward for optical communication, switching, and optical processing Some achived results were published in the high impact journals [18-21] Two methods have been used to calculate and simulate the 1D and 2D PhC stuctures: (i) Finite-difference time-domain method (FDTD) and (ii) Plane wave expansion method (PWE) These are modern methods with high accuracy that allow solving the specific problems using Maxwell's equations in time and frequency domains These were embedded in two highly reliable, free open-source softwares, which called MEEP and MPB, developed by Massachusetts Institute of Technology (USA) MEEP and MPB were installed in high-performance parallel computing systems of our Lab The results

of calculation and simulation confirm the correction and accuracy of the theoretical model Based on the good results obtained in recent years including theory, computation, and simulation [18-26], I present

the research content of the dissertation entitled: “Design and

Investigation of 1D, 2D photonic crystals for bistable devices”

2 The main theme of the dissertation

The dissertation targets the basic research on the physical models and new structures; calculating and simulating the bistable devices using 1D, 2D PhC structures The effects of the PhC configuration and structural parameters on the optical characteristics and working performance of bistable devices will be investigated The contents of the dissertation:

+ Overview of PhC structures and bistable devices

+ Propose new photonic structures, theoretically calculate their characteristic parameters and compare with the simulation results + Study and simulation for optimizing the structural parameters of 1D, 2D PhC structures for optical bistable devices which have high quality factor, low optical intensity and time for switching

+ Propose and design some integrated photonic structures which have high performance and special characteristic for bistable devices

3 The main research contents of the thesis

+ Design and analysis the optical properties of 1D and 2D PhC structures

+ Optimization of the structural parameters and resonant spectra of the grating structures to increase the quality factor and reduce the optical intensity for switching

+ Investigation of the bistability characteristics of the optimal grating structures

+ Design and simulation the narrow high-order resonance linewidth shrinking with multiple coupled resonators in SOH slotted 2D PhCs for reduced optical switching power in bistable devices

Differences and new ones in the research content of the thesis:

+ Currently in Vietnam, there are very few subjects and thesis mention the PhC structures for application in optical comunication due

to the lack of fabrication equipment This dissertation is considered as the first in computation and simulation of optical bistable devices

using 1D and 2D PhC structures in Vietnam

+ This dissertation uses the modern and highly accurate calculation and simulation methods to verify the achieved theoretical results, so the dissertation contributes to increase the professional research

This dissertation includes five chapters:

Chapter 1 Overview

Chapter 2 Calculation and simulation methods

Chapter 3 Optimization of quality factor and resonant spectra of grating structures

Chapter 4 Optical bistability in slab waveguide gratings

Chapter 5 Optical bistability based on interaction between sloted cavities and waveguides in two-dimensional photonic crystals

CHAPTER 1: OVERVIEW 1.1 Photonic crystal structures

The first concept of PhCs was proposed by Yablonovitch and John

in 1987 [7] PhCs are the periodic structures of the dielectric elements

in space Due to the periodic of the refractive indices, the PhC structures produce the PBGs Depending on the geometry of the structure, PhCs can be divided into three categories, namely one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) structures The examples are shown in Figure 1.1

Figure 1.1 1D, 2D, and 3D PhC structures (a) 1D PhC, (b) 2D PhC, (c) 3D PhC [27]

1.2 Optical bistable devices

Two features are required for presenting the bistable behavior: nonlinearity and feedback Both features are available in nonlinear optics An optical system is shown in Figure 1.33, this system exhibits

the bistable behavior:

For small inputs (Ivào < 1) or large

inputs (Ivào > 2), each input value

has a single response (output) In

the intermediate range, 1 < Ivào <

2

 , each input value corresponds

to two stable output values.

CHAPTER 2 CALCULATION AND SIMULATION METHODS 2.1 Coupled mode theory (CMT)

Using a simple LC circuit, I have given the dependence of the

voltage amplitude on time This is the method used to calculate the transmission and reflection spectra of the structures

2.2 Plane wave expansion method (PWE)

In order to exploit the extraodinary properties of PhCs, the calculation method is required to accurately determine the PBG One

of the most common methods is the plane wave expansion (PWE) This method allows for solving wave vector equations for electromagnetic fields, calculating the eigen frequency of the PhCs In addition, it is also used to calculate energy diagram as well as PBG

2.3 Finite-difference time-domain method (FDTD)

The FDTD method is one of the time domain simulation methods based on the mesh generation Maxwell's equations in differential form are discrete by using the approximation method for differential

of the time and space The finite differential equations will be solved

by software according to the leapfrog algorithm This method aims to provide the mathematic facilities for calculating and simulating the

Figure 1.33 Ouput versus input of the bistable device

The dashed line represents an unstable state [85]

device characteristics using PhC structures such as: transmission spectra, energy diagrams, and the characteristics of stability

CHAPTER 3 OPTIMIZATION OF QUALITY FACTOR AND RESONANT SPECTRA OF GRATING STRUCTURES 3.3 Optimization of structural parameters and resonant spectra

In this chapter, I will introduce some methods to optimizing the

Q-factors and resonant spectra of grating structures

3.3.1 Slab waveguide grating structure combining with metallic film

Based on the study of waveguide grating structure, so that in order

to increase the Q-factor, the grating depth must be reduced, but due to

the limitation of manufacturing technology, the grating depth is not too thin of less than 10 nm Therefore, I have optimized the grating

structure by adding a silver (Ag) layer of thickness d (> 50 nm)

between the slab waveguide grating and the glass substrate This thin layer supports a strongly asymmetric resonant profile in the nonlinear slab waveguide grating and reflects the light waves in any direction due to its high reflectivity These reflected waves will then be coupled into guided-mode resonances in the grating [23]

Figure 3.14 (a) Metallic assisted guided-mode resonance structure with normally incident light (b) Transmission and reflection spectra for several Ag layer thicknessed d

This results obtained with metallic assisted guided-mode resonance

(MaGMR) structure provide the enhancement Q-factor coefficients

greater than 1, therefor this structure has a higher Q-factor than grating waveguide structure Combining with metallic film, the Q-factor has

been enhanced

3.3.2 Coupled grating waveguide structures

The second optimal method,

coupling two slab waveguide

gratings to obtain a higher

Q-factor and change the shape of

the resonant spectrum Here, the

Q-factor is controlled based on

the distance between the two

slab waveguide gratings The

schematic of two coupled

gratings facing each other with a

gap-distance of d and horizontal shifted-alignment of s is shown in

Fig 3.18 Each slab waveguide grating supports the Fano resoance, where key structural parameters are defined as the guiding layer made

of chalcogenide glass (As2S3, n = 2.38) with a thickness (t) of 220 nm

on a thick glass substrate (n=1.5) The grating slit aperture (w) is

formed by a rectangular corrugation in As2S3 guided layer with the depth and periodicity of 220 nm and 860 nm, respectively A normally

incident plane wave with transvere electric (TE) polarization is ussed

Figure 3.18 Sketch of coupled slab waveguide gratings The gap-distance d and horizontal shifted- alignments s are tuned for exciting Fano resonances

Figure 3.19 shows the

reflection spectra for various the

distances d With this

gap-distance 50 nm ≤d ≤ 300 nm, the

resonant wavelengths shifts

towards the short wavelenth

The Q-factor increases as the

gap-distance d increases due to the

long distance of Fabry-Perrot

resonantor formed between two

slab waveguide gratings

3.3.3 Multilayer dielectric grating structure

Figure 3.21 Multilayer nonlinear dielectric grating structure The structure consists of N-pair

of bilayer As 2 S 3 /SiO 2 gratings

The structure consits of identically layers of As2S3 and SiO2 with

thickness of t = N*(d H + d L ), where N are the repetitive identical

bilayers of As2S3 and SiO2, and d H và d L are the thickness of As2S3 and SiO2 layers, respectively In our design, the optical thicknesses of

As2S3 and SiO2 layers are chosen to satisfy the quarter-wavelength

condition, that mean n H *d H = n L *d L = λ/4, where n H and n L are the refractive indices of As2S3 and SiO2, respectively In calculations, the

center wavelength λ center = 1550 nm, d H = 162,8 nm và d L = 267,2 nm

are used Figure 3.22 shows the transmission spectra with N = 3 pairs

Figure 3.19 Reflection spectra of the coupled slab

waveguide gratings depicted in Fig 3.18

of As2S3/SiO2 layers for several grating widths w from 30 nm to 150

nm There exits two Fano resonances within the interested wavelength regims, which are associated with the guided-mode resonances in the long and short resonant spectra from 1460 nm to 1610 nm and from

1340 nm to 1480 nm As it is shown, the increase of grating width w makes the resonance shifts to the short wavelength and the Q-factor

decreases In addition, the spectral resonances show that the side band degrees of Fano lineshapes do not change, it even shows that the linewidths and peaks of resonances change when the grating widths change

Figure 3.22 Transmission spectra of this structure depicted in Fig 3.18 with N = 3

We investigated and found that the Fano lineshapes were

reproducible and readily controlled via the number of layers N and the grating width w, demonstrating the robustness of the suggested structure With the given grating width w of 70 nm, the resonant peaks and Q-factors of the long and short resonances for several number of layers N were evaluated using Fano lineshapes and plotted in Figure 3.23 When the number of layers N increase, redshifts in resonance, higher Q-factor, and lower sidebands are obtained

Figure 3.23 Resonant peaks and Q-factors of the structure as depicted in Fig 3.21 for several

number of layers N

CHAPTER 4 OPTICAL BISTABILITY IN SLAB

WAVEGUIDE GRATINGS

After optimizing the Q-factor and resonance spectra of the slab

waveguide grating structure as presented in Chapter 3, in this chapter

I will examine the bistability characteristics of optimal structures

4.1 Optical bistability in slab waveguide grating structure combined with metallic film

The third-order nonlinear coefficient at a working wavelength of

As2S3 is n 2 = 3,12x10-18 m2/W (χ (3) = 1,34x10-10) In order to see the optical bistability in MaGMR, we excite the devives with an incident

CW source having a suitable working wavelength (frequency) on the surface of the structure In general, the relation between the working frequency and the resonant frequency requires that [66]:

  0   3 (4.1)

where, τ is a photon life time, to observe bistability For our case of an

inverse Lorentzian shape, we choose a working wavelength at 80%

reflection, which corresponds to a frequency detuning of (ω 0 - ω)τ=2

for the Lorentzian shape

In this work, we keep the slab and Ag thickness at 380 nm and 100

nm, respectively The grating depth δ (< 120 nm) is found close to an

optimal value Table 4.1 shows the trends for the resonant wavelength,

the quality factor Q, and the Q-factor enhancement when the grating depth δ changes As the grating depth increases, the resonant

wavelength of MaGMR shifts to shorter wavelengths It seems that the

deeper the grating depth, the more leaky the waveguide mode The

Q-factor enhancement increases as the grating depth increases For

example, a Q-factor enhancement of 5.56 occurs for a grating depth δ

of 120 nm

Table 4.1 Linear and nonlinear characteristics of MaGMR gratings with a Ag thickness d =

100 nm for several grating depths

Resonant wavelength (nm) 1574,75 1560,61 1524,51 1516,81 1494,55

Reduced switching intensity 0,42 2,57 10,7 24,5 45,0

4.2 Optical bistability in coupled grating waveguide structures

calculated bistable behaviors of

the perfect alignment coupled

slab wavelength gratings for the

gap-distance d of 50 nm, 100 nm,

170 nm, and 300 nm Bistable

behaviors are clearly observed

In each bistable curve, the

switching can be estimated as

the input intensity for which the reflection increases abruptly in the dotted solid curve The estimated switching intensities are 1427,1 MW/cm2; 104,1 MW/cm2; 16,2 MW/cm2; và 2,2 MW/cm2;

Figure 4.5 Bistability curves of the coupled gratings for various gap-distances d of 50 nm,

100 nm, 170 nm, and 300 nm, respectively