Multilayer on Polymer Waveguide

for Advanced Integrated Photonics

Ezekiel Obadia Kuhoga

MSc Thesis

June 2018

Department of Physics and Mathematics

University of Eastern Finland

Ezekiel Obadia Kuhoga Master student, 39 pages

University of Eastern Finland

Master’s Degree Programme in Photonics

Supervisor Prof. Matthieu Roussey

Abstract

Recently Bloch surface waves (BSWs) based devices have been attracting a lot of

interests, and especially for sensing application. BSW devices are purely dielectric-

based platforms exhibiting lower losses and therefore longer propagation length com-

pared to their equivalent using metallic film for sustaining surface plasmon polari-

tons (SPP). In this work we demonstrate the possibility to excite, confine and guide

BSWs in a slot waveguide combined with the two photonic crystals (PhCs). This

configuration will make a great deal contribution to the on-chip integrated sen-

sors development. Its applications extend in many aspects such chemical sensing,

biosensing, enhanced raman scattering, and enhanced fluorescence detection.

Keywords: Bloch surface waves; Photonic crystals; Polymer waveguides; Guided

waves; Integrated optic devices; Sensors; Optical waveguides; Refractive index; Ef-

fective index; Photonic band gap.

Preface

For long time I have had a desire to work with optical waveguides following their

daily life applications. To be in the institute of photonics at the university of Eastern

Finland is a great opportunity happened to me. I am grateful as well for being a

part of the for part of the integrated optics group where where I have been able to

learn about presentation, and other necessary skills.

Well, first of all I thank God the Almighty for it is by His grace and mercy that I

have managed to be where I am now. With all the people I have met, all the places

I have been, have made me who I am now, and I do know it is by His doing, and so

glory to Him.

Moreover, there are people who have been so helpful to me, and i would love

to acknowledge their presence in my life. I extend my heart of appreciation to the

supervisor of my thesis work, Prof. Matthieu Roussey for his guidance, supervision

and patience towards me, his trust and mostly his selfless spirit. All of this make my

learning process possible, easy and enjoyable. I also thank Prof Seppo Honkanen for

his consultation and words of encouragement which push me forward. I acknowlegde

the support from Dr. Martti Makinen in this work for he had given his own time

to help me understand the matlab codes which also played a very important role in

this work. I would also love to thank M.S. Lewis Asilevi and M.S. Segolene Peliset

for their support in perfoming the simulation works.

My heartfelt appreciation also goes to my mother Enid Kuhoga. She has trusted

me and she has been willing and supported me always even when it seemed least

convenient. In addition to that, I also would love to acknowledge my other family

members i.e. my father Obadia Kuhoga, and a brother Ibrahim Kuhoga for being

ready to support me in the time of my need. Surely, without the support from my

family, I wouldnt have been here. On top of that, I would love to appreciate my

girlfriend, Linda Yuda for her support from the beginning up to the moment.

My regards to M.S. Boniphace Kanyathare for his support during his presence at

the university. In addition to that I appreciate M.S. Leonard Shayo and Ms. Elemina

John for they were the bridge that connected me to the university of Eastern Finland.

Nevertheless, I deeply would love to thank the whole UEF staff panel in the

photonics department; I believe the learning especially related to physics/photonics

is not always easy, but the bridge developed between the staff and the students

iii

makes the learning process very accomodative.

Lastly, I would love to acknowledge all of my fellow students in the photonics

class 2016-2018 for the friendship, togetherness and support that we all had for each

other. I would also love to appreciate all those who contributed to this work on one

way or the other but I have forgotten to show my acknowledgement to you, just

know that your contribution to my work is highly appreciated.

Joensuu, the 5th of May 2018 Ezekiel Obadia Kuhoga

iv

Contents

1 Introduction 1

2 Theory on optical waveguides 4

2.1 Dielectric slab waveguides . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Maxwell’s equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Wave propagation in slab waveguides . . . . . . . . . . . . . . . . . . 7

2.5 Slot waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Theory on Bloch surface waves 14

3.1 Bloch surface waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 BSWs propagation in 1-DPhCs . . . . . . . . . . . . . . . . . . . . . 16

3.3 Photonic band-gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 BSWs characterization and application . . . . . . . . . . . . . . . . . 20

4 Simulations on BSWs 23

4.1 Proposed design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Simulations based on TMM . . . . . . . . . . . . . . . . . . . . . . . 24

4.3 FDTD simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3.1 Influence of the slot width . . . . . . . . . . . . . . . . . . . . 27

4.3.2 Influence of the angle of incidence . . . . . . . . . . . . . . . . 29

4.4 Discussion and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.4.1 Dielectric material selection . . . . . . . . . . . . . . . . . . . 30

v

4.4.2 PBG and BSWs . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.4.3 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Conclusions and future outlook 32

References 34

vi

Chapter I

Introduction

For many years there has been a strong interest on photonic sensors in both research

and industrial applications, such as biomedics, security, environment exploration,

and many other fields. This follows their advantages compared to conventional sen-

sors such as high selectivity and sensitivity, no electrical and electromagnetic inter-

ferences, temperature stability, compactness, more affordability, and flexibility [1].

However, with respect to the advancement of photonic integrated circuits (PICs),

there has been a rise in interests to have more sensitive and compact optical sen-

sors [2]. Passaro et al. in [3] have mentioned some of recently advanced integrated

photonic sensors for instance, waveguide based devices such as ring resonators, sur-

face plasmon resonance sensors, Sagnac effect based sensors, Fano resonance based

sensors, Mach-Zehnder interferometers sensors, and sensors based on photonic crys-

tals (PhCs).

PhCs are photonic composite materials with a periodically varying dielectric con-

stants in one, two or three dimensions [4]. However in this work we focus mainly on

1-DPhC. 1D-PhCs are stacks made of two alternating layers of dielectric materials

with different refractive indices [5]. A PhC can exhibit a photonic band gap (PBG)

in its spectrum, for which wavelengths no light is allowed to propagate through the

structure [6–9]. PhCs, in this work, are transparent to light in the visible range

for angles less than critical angles. For angles larger than the critical angle the

total internal reflection (TIR) is experienced. TIR is a condition where almost all

of the incident light from the high index medium towards low index medium is re-

flected at the interface back to high index medium. However, electric field can still

penetrate the interface carrying the energy in form of an evanescent wave for nano

1

scale distance before bringing them back to the incident medium [10]. This can be

demonstrated by adding a third high index medium next to low index medium in

nanometer scale distance from the first medium. This offers the frustrating effects

referred to as the frustrated TIR where the energy is trapped and prevented from

going back into the medium one [10–12]. During TIR the Bloch wave vector K

becomes complex within the PBG, and the imaginary part gives rise to evanescent

waves which are now referred to as Bloch surface waves (BSWs) [6]. BSWs can be

excited at the surface of a PhC using different angles of the incident light through

Kretschmann’s configuration [13]. Kretschmann’s configuration uses a prism to cou-

ple light and thus excite the surface waves on the surface of a truncated PhC [13,14].

BSWs propagates at the interface between PhC and low index medium [15,16]. One

way of which BSWs can be analyzed is by observing angular dependence of the

reflected light. BSWs are characterized by a resonance dip at a particular angle of

incidence and wavelength within the PBG of the structure. BSWs have found their

application in many fields such as in biosensing [15, 17–20], enhanced fluorescence

detection [21–23], gas sensing, and enhanced Raman scattering [17].

BSWs are compared to surface plasmon polaritons SPP in many ways including

their excitation, operations, sensitivity, and application [23–26]. The advantages of

BSWs compared to SPPs is their lower propagation losses [27]. This is mainly due

to dielectrics having less absorption compared to metals in SPP thus having sharper

resonance dips and stronger local fields with longer propagation length [21, 22, 28].

Another advantage with BSWs is that it is possible to excite a BSW at a specific

wavelength by adjusting multilayer parameters, i.e., layers’ thicknesses, number of

periods, and the angle of incidence of the illumination [29]. On top of that, TM and

TE polarized BSWs can be excited at the same time, while SPPs are only compatible

with TM polarization [30]. Moreover, BSW-based sensors have a potentially higher

sensitivity [31,32]. Currently most of BSWs based sensors are based on the angular

and spectral intensity reflection measurement [29].

A slot waveguide is a recently developed waveguide composed of two high refrac-

tive index rails separated by a thin low index gap, typically less than 100 nm [33–35].

From the boundary conditions as discussed by Yariv, A and Yeh, P in [6], we can

see that, the tangential component of electric field is continuous at the boundary

surface. In addition to that, the normal component of electric field is discontinuous

across the interface [6]. Slot waveguide configuration uses electric field discontinuity

2

at the interfaces to confine and enhance the optical field intensity within the low

index slot [33–36]. Confinement factor within the slot makes this configuration very

useful for optical sensing.

In this work we demonstrate how to excite BSWs at a wavelength of 488nm

and confine the surface waves within a slot-waveguide. This involves designing and

combining together two identical PhCs in close proximity to each other such that

they form a slot in between. The size of the slot is 50 nm which is smaller than the

decay length of the BSWs and it leads to the enhancement of the confined waves.

The illumination beams are guided through a polymer waveguide towards the PhCs’

surfaces and are made incident on both sets of PhCs with an angle of incidence of

around 55◦ for BSWs excitations. The excited BSWs from both PhCs are therefore

being superimposed and confined within the formed slot. The designed PhCs are

composed of a high refractive index layer Titanium oxide TiO2 and a low refractive

index layer Al2O3 with thicknesses 62 nm and 94 nm respectively, and TiO2 as a top

additional layer of 30 nm thickness. The BSWs excitation and confinement within

the slot is demonstrated using transfer matrix method (TMM) and finite difference

time domain (FDTD) method using matlab and optiwave softwares respectively.

TiO2 and Al2O3 are transparent in the visible range, chemically, thermally, and

physically stable [37–39]. Using polymer, allows a relaxed and cost-efficient fabrica-

tion [36,40].

In this work on chapter two we explain briefly the basic theory related to optical

waveguides. Chapter three gives a brief theory related to photonic band gap and

BSWs. In chapter four we demonstrate simulations done using both TMM and

FDTD methods, discussed, analyzed, and justified the results obtained. Lastly,

chapter five provides the conclusion and the future outlook of this work.

3

Chapter II

Theory on optical waveguides

In this chapter, the basic theory on optical waveguides in given in brief. This is

expected to provide a basic understanding on how optical waveguides operate.

2.1 Dielectric slab waveguides

Optical waveguides are structures used in guiding light waves as the light propagates

from one point to another. Dielectric slab waveguides are the simplest optical waveg-

uides in structure and geometry [41]. The structure of slab waveguide includes a

core which is a high refractive index region, a substrate, and a surrounding medium

having lower refractive index compared with the core [42]. Figure (2.1) shows a sim-

ple structure of a slab waveguide. The principle of operation of the slab waveguide

is based on a total internal reflection (TIR) phenomenon whereby the propagating

waves are being confined and propagate within the core [42]. In slab waveguides,

TIR is experienced when the light from the core hits the core-cover or core-substrate

interface at an angle of incidence larger than the critical angle. This Phenomenon

causes the light to be reflected back to the core. Equation showing how to achieve

the condition for total internal reflection in slab waveguide is expressed as [42],

ncore sin(π/2− φ) ≥ nclad, (2.1)

where ncore is the refractive index of the core, nclad is the refractive index of the

cladding and φ is the refracted angle at the air-core interface. The expressed phe-

nomena leads to the definition of the acceptance angle of incident light at the air-core

4

Figure 2.1: Schematic diagram showing the geometry of a symmetric slab

waveguide. The guiding layer is a slab with a refractive index n2, surrounded

by low index media of refractive index n1 [6].

interface so known as the numerical aperture (NA) of an interface. NA is the max-

imum acceptable angle of an incident light at the air-core interface for getting the

total internal reflection. NA is defined on the equation below [42]

NA = θmax = ncore

√2∆, (2.2)

where ∆ is the refractive index contrast of a waveguide presented as [42],

∆ =ncore − nclad

ncore

(2.3)

However, due to phase shifting of reflected light rays at the core-cladding interface

within the waveguide, not all light rays incident within the acceptable angle are able

to propagate in the waveguide. For light rays to propagate successfully they need to

satisfy the phase-matching condition for optical paths. Phase-matching condition is

expressed as [42],

tan(kncorea sinφ− mπ

2

)=

√2∆

sin2 φ− 1 (2.4)

5

where φ is the angle between the ray and the z-axis, a is the core radius, and

m = 0,+1,+2, .... The field allowed to propagate at m = 0 is referred to as the

fundamental mode, while other modes propagating at m ≥ 1 are being referred to

as higher-order modes [42]. The propagation constants along z and x axes are given

as [42],

β = kncore cosφ, (2.5)

κ = kncore sinφ. (2.6)

2.2 Maxwell’s equations

Propagation of electromagnetic waves in a medium obeys Maxwell’s equations which

are [6],

∇×E = −∂B

∂t, (2.7)

∇×H =∂D

∂t+ J , (2.8)

∇ ·D = ρ, (2.9)

∇ ·B = 0, (2.10)

where E and H are electric and magnetic fields, D and B are electric displace-

ment and magnetic field vectors and J and ρ represent electric current and charge

density respectively. Moreover, Maxwell’s equations are being constituted by the

constitutive equations for electric displacement and magnetic induction vector [6]

D = εE, (2.11)

B = µH , (2.12)

where ε is makes the relative permittivity of the medium and µ makes relative

permiability of the particular medium.

2.3 Boundary conditions

When a light is propagating across one or more interfaces between dielectric media

the physical properties associated with permittivity ε and permiability µ change

6

abruptly [6]. However, despite the change in the physical properties there ex-

ists a continuity relationship at the interfaces for some of the components of the

fields. These continuity relations are derived from Maxwell’s equations and ex-

pressed through equations known as boundary conditions [6]. Equations 2.13 to

2.16 express the boundary conditions for both electric and magnetic fields. From

these conditions we can see that the tangential component of the electric field is

always continuous across the interface while the normal component of electric field

is discontinuous across the interface [6]. As we are dealing the dielectric material,

therefore the charge and current densities becomes zero for this case. The following

equations represents boundary conditions [6],

B2n = B1n, (2.13)

D2n = D1n, (2.14)

E2t = E1t, (2.15)

H2t = H1t, (2.16)

The normal component of B and the tangential component of E are continuous

across the interface. The normal component of D and the tangential component

of H are not. If there are no charges at the interface then the normal component

of D is continuous, if there are no current, then the tangential component of H is

continuous.

2.4 Wave propagation in slab waveguides

Consider a monochromatic wave propagating along z-direction in a symmetric slab

waveguide as shown in figure 2.1. Its propagation can be analyzed using Maxwell’s

equations [6],

∇×H = iωε0n2E, (2.17)

∇×E = −iωµH , (2.18)

where n represents the refractive index profile of the structure, ω is the angular fre-

quency of fields. ε0 and µ represent vacuum permittivity and absolute permeability

7

of the particular medium. Solutions to wave equations (2.17) and (2.18) represents

the wave equations for electric and magnetic fields respectively [6],

E(x, t) = Em(x) exp[i(ωt− βz)], (2.19)

H(x, t) = Hm(x) exp[i(ωt− βz)], (2.20)

where β is the propagation constant, E(x) and H(x) are the wavefunctions of the

modes guided in a waveguide and m representing the mode number. From equations

(2.17) and (2.18), TE-mode electric field is expressed as [6],

(∂2

∂x2+

∂2

∂y2

)E(x, y) + [k2

0n2(r)− β2]E(x, y) = 0, (2.21)

where k0 represents the wavenumber in vacuum, β is the propagation constant. The

condition for β of a guided mode in a waveguide is such that,

β >n1ω

c, (2.22)

β <n2ω

c, (2.23)

where n1 and n2 are the refractive indices for surrounding media and the core re-

spectively as defined by the refractive index profile in equation 2.24 [6]. All the

modes confined in the core satisfy the propagation condition as given in the above

equations [6],

n(x) =

{n2, if |x| < d/2,

n1, if otherwise.(2.24)

Propagating modes in the slab waveguide can be categorized generally into two

modes which are transverse-electric (TE) modes and transverse magnetic (TM)

modes. TE-modes have electric field amplitude oscillating perpendicular to the

plane of propagation, and TM-modes have electric field propagating tangential to

the plane of incidence [6]. TE-mode field amplitude is expressed as [6],

Ey(x, y, z) = Em(x) exp[i(ωt− βz)], (2.25)

8

where Em(x) represents the wavefunction of a mode as a function of distance from

the centre of the waveguide [6],

Em(x) =

⎧⎪⎨⎪⎩A sinhx+B coshx, if |x| < 1

2d

C exp(−qx), if x > 12d

D exp(qx), if x < −12d.

(2.26)

A, B, C and D are constants and h and q parameters represents propagation constant

relation where [6];

h =

[(n2ω

c

)2

− β2

] 12

, (2.27)

q =

[β2 −

(n2ω

c

)2] 1

2

. (2.28)

2.5 Slot waveguide

Slot waveguide is formed when the low index slot is situated between high index

dielectric slabs [35](see figure 2.2). As a result of TIR within high index slab(s),

electromagnetic waves penetrate the high-low index interface into the slot in form

of evanescent waves [43]. The propagating fields in the slot can be categorized into

transverse electric (TE) and transverse magnetic (TM) fields where in TE field the

component of electric field oscillates perpendicular to the plane of propagation and in

TM field the the component of magnetic field oscillates perpendicular to the plane of

propagation. The continuity behaviour of the fields due to the boundary conditions

results into high confinement of optical intensity for TE fields [33,35,36,44,45].

The size of the slot is always made smaller than the decay length of an evanescent

tail. This always helps to enhance the field intensity in the slot [35]. Figure 2.3 shows

a field intensity profile of a slot waveguide. We can see that due to factors such as

discontinuity of the TE-mode electric field, and nanometer scale slot, the intensity in

the slot region is highly enhanced. Equation 2.29 shows the analytical solution of the

transverse electric field profile of the fundamental TM eigenmode of the slab-based

slot waveguide [43],

9

Ex(x) = A

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩1n2Scosh(γSx), |x| < a

1n2Hcosh(γSa) cos[κH(|x| − a)] + γS

n2SκH

sinh[κ(|x| − a)], a < |x| < b

1n2C

{cosh(γSa) cos[κH(b− a)] +

n2HγS

n2SκH

sinh(γSa)

× sin[κH(b− a)]}exp[−γC(|x| − b)], |x| > b

(2.29)

where κH is the transverse wavenumber in the high index medium, γC is the field

decay coefficient in the cladding, γS is the field decay coefficient in the slot, a and

b are the distances of low-to-high and high-to-low interfaces respectively from the

centre of the slot as shown in figure 2.2b), and constant A is given by the following

equation [43].

A = A0

√k0n2

H − κ2H

k0, (2.30)

Where A0 is a constant and k0 = 2π/λ0.

(a) (b)

Substrate

High refractive index rails

slot

Figure 2.2: Diagram showing (a) the basic structure and (b) the geometry

of an optical slot-based waveguide [43].

With slot-waveguides, the sensing application is always done by placing the an-

alyte as a cover or as medium within the slot. The presence of the analyte would

result in the change of effective index of the whole structure or the slot depending

where it is placed. Change in effective index would in turn affect the position of

characteristic resonance and the magnitude of the confined optical intensity. Solving

10

x-axis(wafer width)

slot region

high index regions

Norm

alized inte

nsity

Figure 2.3: Intensity distribution on the cross-section of a slot waveguide(x-axis).

equation 2.29, leads to a relationship between amplitude on the interface in the low

index side and amplitude in the high index region. The relationship is such that

the amplitude at the interface in the low index side, is n2H/n

2S times as much as the

amplitude in the high index medium [43]. High confinement and enhancement of

the optical intensity within the slot, thus leads to strong light analyte interaction.

This effect paves a way to high sensitivity sensors and biosensors.

The magnitude of field confinement in the slot is dependent on the refractive

index contrast between high and low index media across an interface. From the

boundary conditions we have seen that we have seen that that at the interface

rail/slot, the field amplitude in the slot is n2H/n

2S times as much as the field amplitude

in the high index region. High confinement and enhancement of the optical fields

in the slot results into a very strong light-analyte interaction hence enhancing the

sensitivity of sensor [43, 45]. Figure 2.4 shows the relationship between the power

confinement factor and the refractive index in the slot region while keeping the index

of the slabs constants.

Homogeneous sensing is defined as changing of the effective index of the guid-

ing medium with respect to the change in the refractive index of the cover [46,

47]. Through this optical sensitivity of the waveguide it becomes possible to mea-

sure/sense the concentration of fluid/liquid/gaseous solution material placed as cover

11

Figure 2.4: Dependence of power confinement factor in the slot region pro-

vided the refractive index of the rails is constant [33].

to the slot waveguide. Homogenous sensitivity is mentioned in [46] to be propor-

tional to the optical field confinement factor in the cover. Homogeneous sensitivity

is generally expressed in equation 2.31 [46].

Sh =dneff

dnc

(2.31)

where neff is the effective index of the propagating mode.

Confinement factors in the slot and the cover are given as [46],

ΓS =

∫∫S|E(x, y)|2dxdy∫∫

∞ |E(x, y)|2dxdy,(2.32)

ΓC =

∫∫C|E(x, y)|2dxdy∫∫

∞ |E(x, y)|2dxdy, (2.33)

whereE(x, y), S and C indicates the electric field, slot and cover regions respectively.

Effective index of the slot can be calculated from the decay rate of the field at

the cladding from the center of the slot waveguide taking the assumption that the

field is exponentially decaying with respect to the radial distance towards the centre

of the waveguide [35].

neff ≈ (n2C +

γ2

k20

)12 , (2.34)

12

where neff is the effective index, nC is the cladding index, k0 is the wavenumber in

the vacuum and γ is the decay rate of the field.

Slot waveguide can also do surface sensing where the particles or molecules of a

particular medium to be measured are passed through the slot or cover medium

of the waveguide. In this case the effective index of the mode will be affected by

the change in thickness of the added layer.Hence the waveguide sensitivity can be

generally expressed as [46];

Ss =dneff

dρ, (2.35)

where ρ is represents the molecular layer thickness.

13

Chapter III

Theory on Bloch surface waves

This chapter explains the basic theory on Bloch surface waves (BSWs), photonic

bandgaps (PBGs) and their associated features and behaviours. By the end of

this chapter the reader should be able understand what are BSWs and how they

are excited, the conditions for excitation and propagation, their characteristics and

their possible application.

3.1 Bloch surface waves

Boch surface waves (BSWs) are electromagnetic waves generated at the interface

between a truncated PhC, i.e., a non-infinite multilayer and a low index medium

as a result of frustrated TIR. Dielectric multilayer structures, also referred to as

photonic crystals (PhCs), are formed by periodically alternating two dielectric media

of different refractive indices. PhCs can be arranged periodically in either 1-D, 2-

D or 3-D as shown in figure 3.1. A PhC possesses a region within a wavelength

range known as a photonic band gap (PBG) [48]. A PBG is a region where no light

waves are allowed to propagate through the structure. This causes almost all the

light which is incident on the surface of the multilayer to reflect back, see figure

3.5(b). However because of TIR, small part of light passing through a multilayer

is reflected back but cannot enter back because of the PBG. This squeezed wave

between the two media is the BSW. BSWs are excited within the PBG of a multilayer

structure [49, 50]. Width and location of a PBG can be controlled by parameters

such as layers’ thicknesses, number of periods, and refractive indices. On top of

the multilayer structure often lays a top layer which can also be used to control the

location, wavelength, and profile of the BSW mode [50].

14

Figure 3.1: Diagram showing 1-D, 2-D and 3-D PhCs [5].

BSWs are excited in Kretschmann’s configuration where a prism is used to couple

light to the multilayer structure as shown in figure 3.2. If light is incident on a

interface as it propagates from high index medium to low index at an angle of

incidence larger than the critical angle, total internal reflection will occur. However,

not all the light is reflected back as some of the energies always penetrate an interface

as evanescent waves. For the case of multilayer structures, these leaky waves are

trapped on the surface of the multilayer therefore leading to what is known as Bloch

surface waves (BSWs). Hence BSWs are waves sustained on a surface of a multilayer

structure and they are decaying exponentially in the direction perpendicular to the

surface. This is shown and explained later in Figure 3.6(b), for instance.

Incident light

Reflected light

Multilayer structureTop layer

Prism

BSWs

Figure 3.2: Diagram showing BSWs excitation using Kretschmann’s config-

uration. Λ represents one period of the PhC.

15

3.2 BSWs propagation in 1-DPhCs

Figure 3.3: Periodic layered structure with refractive indices n1 and n2 and

thicknesses a and b respectively [6].

Propagation of waves in a dielectric multilayer structure is demonstrated using

a simple diagram as shown in Figure 3.3. The structure is composed of alternating

layers of refractive indices n1 and n2 with thicknesses a and b respectively. The

medium is assumed to be homogeneous along the y-axis and the optic waves gener-

ated in the structure are assumed to propagate along the z-axis [6]. In these periodic

structures, material properties like dielectric and permeability constants are periodic

functions of position, and are shown as [6]

ε(z) = ε(z + Λ), (3.1)

µ(z) = µ(z + Λ), (3.2)

where Λ = a + b represents one period of the multilayer with a and b being thick-

nesses for high and low index layers respectively. Propagation of light waves in the

homogeneous dielectric media can also be explained by Maxwell’s equations given

J = 0 and σ = 0 [51]. For instance incase of dielectric multilayers, equations 2.17

and 2.18 give rise to what is known as Bloch theorem. In this theory, the trans-

lational symmetry of the periodic medium is used to define the normal modes of

propagation expressed as [6],

E = EK(z) exp−iK.z , (3.3)

H = HK(z) exp−iK.z , (3.4)

16

where by the amplitudes EK(z) and HK(z) are periodic functions with respect to

period Λ and K represents the Bloch wavevector [6]

EK(z) = EK(z + Λ), (3.5)

HK(z) = HK(z + Λ). (3.6)

The solution for the wave equation in the medium shown in figure 3.3, can be

given as [6],

E(x,y, z) = E(z) exp i(ωt− kyy), (3.7)

where

E(z) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩an exp−ik1z(z − nΛ)

+bn exp+ik1z(z − nΛ, nΛ− a < z < nΛ

cn exp−ik2z(z − nΛ + a)

+dn exp+ik1z(z − nΛ + a), (n− 1)Λ < z < nΛ− a,

(3.8)

where an, bn, cn and dn are constants, n represents nth layer, and

k1z =

√(n1ω

c

)− k2

y, (3.9)

k2z =

√(n2ω

c

)− k2

y, (3.10)

Taking into consideration the continuity conditions on the electric and magnetic

fields inside the multilayer structure, and with the help of equation 3.8, the fields

relationship between one layer and the other layer of the same refractive index can

be expressed by the use of translation matrix given as [6],[an−1

bn−1

]=

[A B

C D

][an

bn

], (3.11)

17

where the elements of matrix for TE modes are

A = exp i(k1za)

[cos(k2zb) +

i

2

(k2z

k1z

+k1z

k2z

)sin(k2zb)

], (3.12)

B = exp−i(k1za)

[i

2

(k2z

k1z

− k1z

k2z

)sin(k2zb)

], (3.13)

C = exp i(k1za)

[− i

2

(k2z

k1z

− k1z

k2z

)sin(k2zb)

], (3.14)

D = exp−i(k1za)

[cos(k2zb)−

i

2

(k2z

k1z

− k1z

k2z

)sin(k2zb)

], (3.15)

and the elements for TM modes are,

A = exp i(k1za)

[cos(k2zb) +

i

2

(n22k1z

n21k2z

+n21k2z

n22k1z

)sin(k2zb)

], (3.16)

B = exp−i(k1za)

[i

2

(n22k1z

n21k2z

− n21k2z

n22k1z

)sin(k2zb)

], (3.17)

C = exp i(k1za)

[− i

2

(n22k1z

n21k2z

− n21k2z

n22k1z

)sin(k2zb)

], (3.18)

D = exp−i(k1za)

[cos(k2zb)−

i

2

(n22k1z

n21k2z

− n21k2z

n22k1z

)sin(k2zb)

]. (3.19)

Taking into account equation (3.3), and equation 3.5, propagating wave can be

expressed in terms of the column vectors as shown in equation3.20. The field is now

assumed to propagate normal to the interfaces along the z-axis within a multilayer

structure with a period Λ.[an

bn

]= exp−i(KΛ)

[an−1

bn−1

]. (3.20)

Now, taking into account the translation matrix as expressed in equation 3.11, the

periodic condition can be re-expressed as in equation 3.21 making the phase factor

exp i(KΛ) the eigenvalue of the translation matrix [6],[A B

C D

][an

bn

]= exp i(KΛ)

[an

bn

]. (3.21)

The phase factor, exp i(KΛ) can be expressed as cos(KΛ) = 12(A +D) and is used

to provide the dispersion relation existing between the frequency ω, propagation

18

wavenumber along the y-axis, ky and the Bloch wavenumber K as shown in equation

[6],

K(ω,ky) =1

Λcos−1[

1

2(A+D)]. (3.22)

From the expression given in equation 3.22 it is clear that the real values of K(ω,ky)

will be obtained for values of 12(A + D) ranging between −1 and 1. This region

corresponds to the allowable region for the Bloch waves to propagate. However,

outside of that range, the values forK(ω,ky) will be complex with an imaginary part

representing the Bloch wave as an evanescent wave. The regions where the values

of K are complex are referred to as photonic bandgap of the multilayer structure

as shown in figure 3.4. The Bloch wave vector at the edges of the bandgap is

determined by the values where |12(A+D)| = 1 [6,7]. The dark zones in the diagram

represents the regions where the value of Bloch wavenumber K is real, hence the

Bloch waves can propagate in the medium, and the lighter regions before the dashed

line represents the photonics bandgaps. The dashed line is ky = (ω/c) sin θB and it

marks the area where the bandgaps vanish at the brewster angle as the incident and

the reflected waves are uncoupled. When a light wave is incident on a multilayer

(a) (b)

Figure 3.4: Photonic band structure for (a)TE and (b)TM waves. The dark

regions corresponds to areas where values of K are real, hence allowable pho-

tonic bands. The black dashed line in (b) marks the region where the bandgaps

for TM modes vanishes at the brewster angle and is represented by the prop-

agation wavevector ky = (ω/c)n2 sin θB [6].

structure, a normal wave will propagate for the regions where the Bloch wavenumber

19

is real, meaning there are allowed bands. For the case where the light frequency

corresponds to the photonic bandgap, an evanescent wave is generated which decays

exponentially as it propagates in the structure and is referred to as a Block surface

wave. In this region of photonic bandgap, the multilayer structure acts as a good

reflector of an incident wave corresponding to that particular frequency range. Yariv

and Yeh in [6], has related this phenomenon to the diffraction of X-rays by the crystal

lattice planes and hence is referred to as a Bragg reflector.

3.3 Photonic band-gap

Taking into account the dispersion relation ω = ω(K) existing in multilayers, for

the case where angle of incidence is less than the critical angle, Bloch wavevector

K becomes a real vector. The situation leads to a normal propagation of waves

as in homogeneous medium where the amplitudes will still be periodic functions of

position and there would be no losses. When the angle of incidence is larger than

the critical angle, K becomes a complex vector. In this case the waves do not

propagate in the infinite periodic structure. The spectral regions where we have a

complex Bloch wavevector are referred to as photonic bandgaps (PBG). However, as

explained above the BSWs are excited within the PBG of a mutlilayer structure [6].

The propagating BSWs modes in the multilayer structure are highly confined near

the edges following the fact that modes in the centre of the band gap experience

strong attenuation comparing to those near the edges [50]

Propagation constant β of the BSW in the bandgap increases with respect to

the increase in thickness of the top most layer as shown in figure 3.5(a). The green

continuous line in figure 3.5(b) shows the angular reflectance of a reflected light.

Propagation constant of the BSW in the bandgap is expressed as [6],

β =

(2π

λ

)n sin θ, (3.23)

where λ, n and θ are the wavelength of the incident light, the refractive index of the

prism and the incident angle respectively.

3.4 BSWs characterization and application

Usually BSWs are characterized by a resonance dip in the angular reflectance as

shown in figure 3.6(a). In comparison with SPPs, BSWs are created from and

20

Figure 3.5: Diagram showing (a) the relation between dispersion line in the

band gap and the thickness of the top layer vs additional layer (b) plot of

absorption and reflection spectrum of the structure with the additional layer

of 60 nm with respect to effective index [50].

propagates on pure dielectric material. Therefore they possess lower absorption

losses and this results into a narrower resonance dip and longer propagation length.

This property offers more sensitivity to the device. Moreover, the presence of a PBG

offers high wavelength selectivity to the BSWs based optical device by filtering out

all of unwanted wavelengths.

Despite BSWs being excited and propagating on dielectric lossless material, yet

they experience some losses. One main factor for the losses is the field leakage into

the prism. On top of that, there is also a leakage of the field into the multilayer.

However the decay coefficient for leakage into the multilayer can be minimized ex-

ponentially with respect to increased number in multilayers [50].

Following their method of excitation, and their characterization, BSWs based

devices are potential for use as sensors and biosensors.

21

Figure 3.6: Diagram showing (a) the characteristic dip in the angular-

reflectance spectrum, and (b)a field distribution as the light is coupled to

the PhC and hence leading to excitement of the surface wave [13].

22

Chapter IV

Simulations on BSWs

This chapter presents the configuration for BSWs excitation and confinement. In

addition, it demonstrates the simulations perfomed using transfer matrix method

(TMM) and finite difference time domain (FDTD) through Matlab and Optiwave

softwares respectively.

4.1 Proposed design

The proposed structure includes two similar 1DPhCs, which are placed close to each

other to make a slot in between, and polymer layers which guide the incident light

beams towards the multilayer surfaces and the reflected beam away from the surface.

This structure is to be fabricated on top of a silicon dioxide (SiO2) substrate. The

excitation of the two BSWs is done by illuminating a beam of light on the surface

of a multilayer with an angle of incidence larger than the critical angle at polymer-

multilayer interface. The wavelength of interest in this work is 488 nm. Therefore

parameters of the whole structure will be adjusted to excite and enhance BSWs at

this wavelength.

The multilayer structure is composed of titanium dioxide (TiO2) and aluminium

oxide (Al2O3) layers with refractive indices 2.4823 and 1.6071 respectively at λ =

488 nm. The multilayer is a stack of five periods of alternating layers TiO2 and Al2O3

with thicknesses 62 nm and 94 nm respectively, and TiO2 as a top terminating layer

with a thickness of 30 nm. In a first approximation the input waveguides are replaced

by side slab layers, intended to be fabricated in polymer, of refractive index n = 1.57.

The slot embedded between multilayer stacks is filled with air medium and has a

size of 50 nm.

23

(a) (b)

Incident light beam

Reflected light waves

Substrate

Polymer waveguide

Multilayer structures

slot

BSWs

sideslab

Λ

Incident light Reflected light

50 nm

Confined BSWs

slot

Multilayer

Structure

Polymer waveguide

9.18 μm

toplayers

slot

sideslab

Figure 4.1: Proposed structure showing (a) BSWs-based photonic integrated

structure and (b) the top view of the structure. Λ = a + b is one period of

the multilayer, where a = 62 nm and b = 94 nm are thicknesses of the TiO2

and Al2O3 layers respectively. The structure has five periods and a top layer

of TiO2 with the thickness of 30 nm.

4.2 Simulations based on TMM

Simulations were performed using TMM and FDTD methods. In TMM we were

able to demonstrate the presence of PBG, as well as, the presence and the location

of the excited BSWs.

The calculations are performed in simulations using the effective indices of the

materials. For this, we take into account the SiO2 wafer, and the cover which is air

with refractive index 1,the calculated effective indices for TM0-modes are as follows:

Polymer waveguide has effective index of 1.453, TiO2 layer has effective index of

2.225 and Al3O3 has an effective index of 1.465. We consider for all materials an

imaginary part of the refractive index of 0.001.

Figure 4.2 shows the spectral-angular reflectance in the wavelength range 300 nm

- 800 nm and incident angles 0◦ - 90◦. Using effective indices in the calculation, the

polymer-multilayer interface exhibits a critical angle of 43.6 degrees. Figure 4.2(a)

indicates the presence and location of a PBG of the multilayer structure. The PBG

spans between λ = 470 nm and 650 nm. Figure 4.2(b) is the reflectance after the

critical angle only, showing with a better contrast the BSW inside the PBG.

The BSWs are indicated by the the characteristic dips as shown on figure 4.3

both on the spectral and angular reflectances. For the case of spectral reflectance,

24

(a) (b)

Figure 4.2: Angular and spectral dependence of the reflection through the

structure: a) over a broad range and b) in the interesting zone.

the angle of incidence used for calculation is 54.5◦ and the wavelength range of

interest is from 300 nm to 450 nm. BSWs is located at wavelength 488 nm. For the

case of angular reflectance the range of angles used in the calculation are from 40◦

to 80◦. BSWs is seen to be excited at an angle 54.5◦.

It is to be noted that the geometrical parameters, i.e., the period, the thicknesses

of the layers, and the terminating layer, have been optimized thoroughly in order to

obtain a BSW at the desired wavelength.

(a) (b)

Figure 4.3: Diagrams showing (a) the spectral reflectance at an angle 54.5◦

with the characteristic dip located at 488 nm and (b) the angular reflectance

at the wavelength of 488 nm with the dip located at 54.5◦.

25

4.3 FDTD simulations

Finite difference time domain is a computational electromagnetic simulation tool

which solves time dependent Maxwell’s equations using explicit leapfrom time-

stepping scheme [52, 53]. The parameters defined above, i.e., thicknesses, effective

indices for TiO2, Al2O3, and polymer layers, number of periods for the multilayer

stack and, the size of the air slot embedded between multilayer stacks were used in

FDTD simulation.

Figure 4.4(a) shows the excited BSWs from the multilayer structure after the

illuminating beam is incident on a multilayer surface at an angle of incidence 55

degrees. Figure 4.4(b) shows the normalized intensity distribution on along the

x-axis at the position along z highlighted by a white dashed line.

(a) (b)

air

polymer

multilayerstack

BSWs

reflected lightincident light

BSWs

air polymer

multilayer stack

Figure 4.4: Single multilayer: (a) Amplitude distribution of Ex-field in the

plane of the structure. (b) Field intensity profile along x-axis at the position

along z-axis indicated by a dashed line.

Figure 4.5 shows the field amplitude in (a) and intensity distribution in (b) when

the two multilayer structures are put close to each other to form the slot in between.

The BSWs are confined and enhanced in the slot. One can remark that for the single

BSW, the maximum is 1, while for the double stack, the maximum is close to 3.

This proves the effect of the slot waveguide, without which the maximum intensity

would have been only twice the intensity of a single BSW structure.

The simulations was also performed on a slightly different design where 500 nm

wide polymer strips acted as input to guide the incoming light to the multilayers.

26

(a) (b)

BSWs

Multilayerstacks

(slot region)

polymer

polymer

BSWs

polymer

multilayer stacks

polymer

Figure 4.5: two multilayer stacks forming a 50 nm slot in between: (a)

Amplitude distribution of Ex-field in the plane of the structure. (b) Field

intensity profile along x-axis at the position along z-axis indicated by a dashed

line.

For instance figure 4.6 shows the field amplitude and intensity distribution when the

angle of incidence was 75◦.

(a) (b)

polymer layers

BSWs

Multilayer stacks

BSWsmultilayer stacks

polymer polymer

Figure 4.6: two multilayer stacks with a 500 nm wide polymer layer acting

as the input waveguide: (a) Amplitude distribution of Ex-field in the plane of

the structure. (b) Field intensity profile along x-axis at the position on the

z-axis indicated by a dashed line.

4.3.1 Influence of the slot width

The slot width ws represents the spacing between the two faces of the multilayers

bounding the slot. For this study we consider an infinite polymer layer with a slit

in the middle and the multilayer inside the slit. Two Gaussian waves illuminate the

27

multilayers from the positive and negative regions at angles θ and −θ corresponding

to BSWs excitation angle. In this case the slot width is adjusted from 0 nm to

200 nm. For BSWs study, the transverse electric field is more interesting. Figure

4.7 shows the results of the calculations performed by 2D-FDTD with a spatial

mesh size of 10 nm. Note that for the polymer layer we consider the effective index

approximation (light is guided in this layer), while for the materials constituting the

multilayer, i.e., TiO2 and Al2O3, the refractive index is taken into account as well

as an absorption of 10−4.

0

0.5

-0.5

1

-1

1.5

-1.5

2

-2

2.5

-2.5

x[µ

m]

0 20 40 60 80 100 120 140 160 180 200

ws [nm]

0

0.4

0.8

1.2

1.6

2

Inte

nsi

ty[a

.u.]

|E|

x

2

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Am

pli

tude

in t

he

slot

[a.u

.]

ws [nm]

Max

imum

enhan

cem

ent

a) b)

Multilayer

} Polymer

Increasingslot width

Figure 4.7: Influence of the slot width. (a) Field intensity as a function of

the slot width for 0 nm<ws<200 nm. (b) Maxima in the centre of the slot.

Figure 4.7(a) represents the electric field intensity as a function of the slot width

and the direction x (perpendicular to the slot). In this study θ = 64◦. One can first

remark fringes on both polymer sides corresponding to the interference between the

incident light and the reflection on the multilayer. The periodicity of these fringes

does not vary with ws because the multilayer, and therefore its reflection coefficient,

and the incident angle θ do not vary.

An obvious increase of the field intensity inside the slot is clearly visible when

ws increases. This enhancement can be quantified on figure 4.7 where the maxima

in the center of the slot as a function of ws are plotted. The maximum is obtained

when ws = 90 nm.

Three regions can be clearly identified: 1) ws = 0 nm corresponds to a thick

multilayer for which the reflection is relatively high, i.e., higher than a multilayer

with fewer amount of layers. No BSW are visible because the system is symmetric

and no total internal reflection can occur. 2) 0 nm < ws < 90 nm, is the region

28

where the BSW overlap is predominant and one can see that the intensity in the

slot increases, and the contrast of the fringes reduces. 3) For ws > 90 nm, one can

see a slow decrease of the field inside the slot corresponding to two separate BSWs.

One can also note, for region 2, that the intensity inside the multilayer increases,

which is a signature of the transmission of the amplitude through the different layers,

and thus of the frustrated TIR leading to the BSW. This region can therefore be

attributed to the BSW excitation region with slot enhancement.

4.3.2 Influence of the angle of incidence

For a slot width ws = 50 nm, we have performed FDTD calculations for incident

angle 60◦ < θ < 80◦. Results are presented in Fig. 4.8. In this representation of

the results, the fields have been normalized so they can be compared. The total

input field intensity remains the same in all the calculation. A part is reflected by

the multilayer and a part is partially transmitted through the multilayer to benefit

(or not, depending on θ) to the BSW. All fields are normalized by the amount

of intensity inside the polymer layer. From Fig. 4.8b), in particular, one can see

a maximum around θ = 78◦. This represent a significant variation compared to

the results obtained with the TMM. This can be explained by the more realistic

structure simulated here, but also by the relatively large spatial mesh, which does

not allow a good enough definition of the multilayer. And as we have seen earlier,

the BSW resonance depends drastically on all the geometrical parameters.

0

0.5

-0.5

1

-1

1.5

-1.5

2

-2

2.5

-2.5

x[µ

m]

60 62 64 66 68 70 72 74 76 78 80

q [nm]

0

0.2

0.4

0.6

0.8

1

Norm

aliz

ed i

nte

nsi

ty [

a.u.]

Am

pli

tude

in t

he

slot

[a.u

.]

a) b)

Multilayer

} Polymer

60 62 64 66 68 70 72 74 76 78 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Max

imum

enhan

cem

ent

q [nm]

Figure 4.8: Influence of the angle of incidence. (a) Field intensity as a

function of the angle of incidence for 60◦ < θ < 80◦. (b) Maxima in the centre

of the slot.

29

4.4 Discussion and Analysis

In this section we present the discussion in general about the proposed design. More-

over it discusses on the results obtained from the simulations in chapter two.

4.4.1 Dielectric material selection

The objective for this proposed design is to be able to excite BSWs at wavelength

488nm which corresponds to the excitation wavelength for dyes. We have chosen

layers of TiO2 and Al2O3 for making a PhC because they are transparent in the

visible range. On top of that these materials are chemically, physically and thermally

stable. Moreover, polymer waveguide is also transparent in the visible spectrum.

Also, it allows the fast and inexpensive inexpensive fabrication.

4.4.2 PBG and BSWs

At normal incidence of the illumination beam towards the surface of a multilayer

structure in the given spectrum, PBG is seen to extend the wavelengths 470 nm-650

nm. This means that all the light waves with wavelengths belonging to the PBG,

will be reflected back and all light outside of that range will be fully transmitted.

PBG seems to be shifting to lower wavelengths with respect to increase in the angles

of incidence from normal as shown in figure 4.2(a). BSWs seem to be excited from

an angle of incidence 43◦ to around 75◦; see figure 4.2(b). However, BSW excited

for each different angle correspond to a different wavelength. This gives the ability

to select any wavelength of interest just by adjusting the angle of incidence of the

illumination beam. The parameters of the proposed design i.e. number of periods,

thicknesses of dielectric layers and indices have a direct effect on the location and

width of the PBG in the angular-spectral reflectance [51]. Not only that, the pa-

rameters also have effect on the magnitude and location of BSWs excited within the

PBG.

In this case, the wavelength of interest was 488nm, and so the proposed param-

eters make the PBG to be situated in wavelength range 470nm-650nm. BSWs at

wavelength 488nm are generated when the incident light beam needs hits the surface

of a multilayer at an incident angle of around 54.5 degrees. In figure 4.3a) BSWs are

indicated by a characteristic dip at at 488nm. In figure 4.3b) BSWs are indicated

by a characteristic dip on angle 54.5◦.

30

In FDTD simulations, this angle is slightly different because of reasons inherent

to the calculation method itself. Mainly, the mesh used in the code does not allow

all the layer thicknesses and the refractive indices are slightly different. Moreover, it

is to be noted that TMM is a very simplified method, showing as a result the ideal

case.

4.4.3 Sensitivity

Overall effective index and thickness of the PhC is 1.782 and 0.81 µm respectively.

Now, analytically from equation 2.29 we know that the field amplitude at the inter-

face in the slot region should be as n2H/n

2S times higher than that in the high index

medium. Therefore we get to see that the ratio of the optical intensity in the slot

with respect to intensity in the high index medium (total effective index), is 10.11:1

as the slot is filled with air medium with index 1. Hence the enhancement is 10.11

times as much as in the high index dielectric walls of the multilayer.

Angular reflectance of the structure by TMM as shown in figure 4.3 gives us the

normalized intensity transmittance of about 0.35/µm2 at an angle of incidence 54.5

degrees. From figure 4.5 we can see that the amplitude goes as high as 1.69/µm

which give rise to around 2.86/µm2 intensity.

From the FDTD simulation, sum of the field intensity along x-axis is around

103.5123/µm2 , and sum of intensity within the slot at the same point is 13.9948/µm2.

With respect to equation 2.32 we get the slot confinement factor of about 0.1352.

This value marks the maximum value for this configuration since the cover is as-

sumed to be air with a refractive index of 1. Once a cover medium is introduced

the confinement factor will decrease thus creating a sensing effect. Hence confine-

ment factor establishes a direct relationship to sensitivity of the optical slot-based

waveguide sensor.

31

Chapter V

Conclusions and future outlook

In this work simulations on photonic band gap (PBG) and Block surface waves

(BSWs) has been demonstrated. The proposed design configuration involves polmwer

waveguides which guides the light waves of the illuminating beam towards and away

from the multilayer surface. It also have a two sets of dielectric multilayer structures,

which all together make a nanometer size slot between them. This configuration is

designed to operate in the visible light wavelength range 300nm-800nm.

This thesis work focuses on combining two main ideas which are excitation of

BSWs at wavelength 488nm; and confinement and enhancement of the excited BSWs

in the slot. This will thus results into a BSWs-based polymer slot-waveguide pho-

tonic structure. Advantages experienced from the multilayer includes high wave-

length selectivity. This is contributed first by the presence of PBG where all wave-

lengths within the gap are rejected. Second, BSWs of a particular wavelength can

be excited with a different angle of incidence of the illumination beam. Hence it is

possible and easy to select the wavelength of an excited BSWs by simply adjusting

the angle of incidence of illuminating beam. In this work the PBG is available in the

wavelength range 470nm-650nm through the window 300nm-800nm for the case of

normal incidences. However as you increase the angle of incidence, the PBG shifts

to lower wavelengths. BSWs are excited within PBG for angles of incidence larger

than the critical angle which is around 43.5 degrees.

For the case of slot waveguide, the proposed configuration uses the discontinuity

conditions to confine and enhance the optical intensity in the embedded slot. High

confinement and enhancement of the optical intensity in the slot improves the sen-

sitivity of the device. Enhancement in the slot is also affected by the relationship

32

between the index in the high index medium to low index medium. The relationship

is such that field amplitude at the interface in the slot region is n2H/n

2S times as much

as the field amplitude in the high index medium. The BSWs on the surface have an

evanescent tail which decays exponentially as they propagate away from the surface.

Having a slot size which is much less than the decay length of the evanescent tail,

will results in the enhancement of the optical intensity of the fields. The size of the

slot used in the proposed design is 50nm and is filled with air which has an index

of 1. Taking into account both cases, the optical intensity in the slot has reached a

level of 2.86µm2.

On top of that, in comparison to SPPs, this proposed design will advantages

such as possessing both TE and TM-modes BSWs, lower absorption losses which

results to longer propagation lengths and sharper resonance dips. All this together

improves the sensitivity of the device.

At the moment fabrication was not possible as the electron beam which is to be

used for fabrication, was faulty. However in the near future we wish and are looking

forward to fabrication of the proposed device. Moreover, we recommend more study

of the spectral properties of the BSWs. Success in this would assist a big deal to

miniaturization of the proposed device.

Last but not least, fabrication and success of a proposed design will play a great

role to on-chip fabrication of photonic devices. Photonic device with this feature

could be applicable to sensing and biosensing.

33

References

[1] D. Ahuja and D. Parande, “Optical sensors and their applications,” Journal of

Scientific Research and Reviews 1, 060–068 (2012).

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