DR. MOHAMAD HALIM BIN ABD. WAHID

INVESTIGATION OF BRAGG GRATING REPORT

KHAIRUL RIDZUAN B. ABD. MALEK 131180682

LOURINE ANAK MANO 131180864

TRUE ONG 131182754

WAN ‘ALYA AMALINA BT. WAN ALI 131182785

NOR FARIHANA BT. MUHAMAD BADRI 131181698

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TABLE OF CONTENTS

NO. CONTENTS PAGE

1 Abstract (English) 2

2 Abstrak (Malay) 3

3 Chapter One : Introduction / Theory 4-7

4 Chapter Two: Methodolody 8

5 Chapter Three : Results 9-12

6 Chapter Four : Discussion 13

7 Chapter Five: Conclusion 14

8 References 15

9 Appendix 16-17

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ABSTRACT

From this project, we intend to know about a fiber Bragg grating (FBG). FBG is a

type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects

particular wavelengths of light and transmits all others. We used OptiFDTD software to

create grating layout and simulation of Bragg grating. This software provides comprehensive

post-simulation analysis tools, such as transmittance spectrum analysis, mode overlap

calculation, input overlap calculation, far field calculation, pointing vector analysis, polarized

power calculation and so on. These analysis tools were mainly used in the analyzer. Some

users may want to perform the sweep simulation and want feedback the results to the layout

designer so that the layout can be optimized, or some users may want to get the power

transmission/reflection spectrum results without the manipulation of opening the analyzer.

We can know the Bragg properties by changing the wavelength and the tilted angle of the

incident wave.

From this project, we hope to know and learn to use OptiFDTD software to create a

simulation of gratings created with VB Script. We also learn how to generate the grating

layout using VB scripting and to simulate the grating layout and post-processing analysis.

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ABSTRAK

Penghasilan projek ini adalah untuk mempelajari tentang jeriji fiber Bragg (FBG)

dengan lebih terpeinci. FBG ialah sejenis pemantul agihan Bragg yang dicipta di dalam

segmen pendek fiber optik bertujuan untuk memantulkan saiz gelombang cahaya tertentu

dan membiarkan gelombang cahaya yang selebihnya untuk tembus. Kami menggunakan

perisian OptiFDTD untuk mencipta bentangan jeriji dan mensimulasi jeriji Bragg. Perisian ini

menyediakan alat analisis terpeinci selepas simulasi, seperti analisis spektrum pemindahan,

mod pengiraan pertindihan, pengiraan pertindihan input, pengiraan bidang ini, menunjuk

analisis vektor, pengiraan kuasa polarisasi dan sebagainya. Alat-alat analisis telah digunakan

terutamanya dalam penganalisis. Sesetengah pengguna mungkin mahu untuk

melaksanakan simulasi sapu dan mahu maklum balas keputusan kepada pereka susun atur

supaya susun atur yang boleh dioptimumkan, atau sesetengah pengguna mungkin mahu

mendapatkan keputusan penghantaran kuasa / spektrum renungan tanpa manipulasi membuka

penganalisis. Kita dapat mengetahui sifat-sifat Bragg dengan mengubah panjang gelombang

dan menukar sudut condong gelombang kejadian itu.

Daripada projek ini, kami berharap dapat tahu dan belajar bagaimana untuk

menggunakan perisian OptiFDTD untuk membuat simulasi jeriji dicipta dengan VB Script.

Kami juga belajar bagaimana untuk menjana bentangan jeriji menggunakan VB skrip dan

untuk mensimulasikan bentangan jeriji dan analisis selepas pemprosesan.

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INTRODUCTION

An optical Bragg grating is a transparent device with a periodic variation of the

refractive index, so that a large reflectivity may be reached in some wavelength range. Before

entering the theory of fiber Bragg grating, it needs to review the Bragg's law. Bragg

diffraction occurs for an electromagnetic radiation whose wavelength is the same order of

magnitude of the atomic spacing, when incident upon a crystalline material. In this case the

radiation is scattered in a specular fashion by the atoms of the material and experiences

constructive interference in accordance to Bragg's law. For a crystalline solid with lattice

planes separated by a distance d, the waves are scattered and interfere constructively if the

path length of each wave is equal to an integer multiple of the wavelength. Bragg's law

describes the condition for constructive interference from several crystallographic planes of

the crystalline lattice separated by a distance d:

2d sinθ = nλ (1)

where θ is the incident angle, n is an integer and λ is the wavelength. A diffraction pattern is

obtained by measuring the intensity of the scattered radiation as a function of the angle θ.

Whenever the scattered waves satisfy the Bragg condition it is observed a strong intensity in

the diffraction pattern, known as Bragg peak. Nowadays, the majority of Bragg gratings

produced are based in optical fiber and often referred to as fibre Bragg grating (FBG). Other

applications of Bragg grating are X-ray diffractometer (XRD), laser resonator,

photorefractive grating and laser diodes such as distributed feedback lasers (DFB lasers) or

distributed Bragg reflector lasers (DBR lasers).

Fibre Bragg grating represents an important element in the emerging fields of optical

communications and optical sensing. It is widely used in optical sensing because their

resonant (reflected) wavelength is highly sensitive to environmental parameters such as

temperature and strain. Despite its vast usefulness, the device is comparatively simple. The

fiber Bragg grating is a periodic variation of the refractive index along the propagation

direction in the fiber core. It can be manufactured by exposing the optical fiber core to

intense short wavelength ultraviolet (UV) radiation along the length of grating. This induces

the refractive index change along the core of the fiber. Typically a dielectric cylinder of index

n1, usually referred as core, is surrounded by a concentric dielectric cylinder of index n2,

which is referred to cladding area. The two refractive indices obey the relation n1 > n2. If

medium 1 index is larger than medium 2 indexes, and the incident angle is large enough, then

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total internal reflection occurs. In such an arrangement, since the field decays exponentially

inside region of index n2, practically no field exists outside of region n2. This is the basis for

how an optical waveguide works. In its simplest form a fiber Bragg grating consists of a

periodic modulation of the refractive index in a core of a single mode optical fibre, where the

phase fronts are perpendicular to the fibre’s longitudinal axis and with grating planes having

a constant period. Because of its intrinsic simple physical nature, the theory behind Bragg

grating is equally simple. Light, guided along the core of an optical fiber, is scattered by each

grating plane. If the Bragg condition is satisfied, the contributions of reflected light from each

grating plane add constructively in the backward direction to form a back reflected peak with

center wavelength defined by the grating period. A considerable amount of theoretical work

has been reported with various approaches giving reasonable results in predicting the

reflectivity as a function of wavelength.

Figure 1: The spectral response of a FBG

The figure above shows how the light is being reflected and transmitted by a FBG.

When an incident light with many wavelengths is launched into a FBG, at a particular

wavelength, all reflected signals are in phase with the grating period and add constructively

and a back reflected signal centred about the Bragg wavelength is observed. Reflected

contributions from light at others wavelength does not add constructively and cancelled out.

As a result, these wavelengths are transmitted through the grating since they are not in phase

with the grating period. Moreover, this structure selectively reflects a very narrow range of

wavelengths while transmitting others. Only those wavelengths that satisfy the Bragg

condition are affected and strongly reflected. The reflectivity of the input signal reaches a

peak at the Bragg wavelength. The explanation is that at the end of the fibre about 4% of the

light was reflected by Fresnel reflection which, in its way backwards, interfered with the

ongoing light producing an interference pattern. This pattern contained peaks and valleys of a

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stationary wave which imprinted permanently the pattern into the core of the fibre as an index

of refraction modulation. Initially, the reflected light intensity is low, but after some time, it

grows in intensity until almost all the light launched into the fibre is back-reflected. The

growth in back-reflected light was explained in terms of a new effect called

―photosensitivity‖, whereby the index of refraction in the core of the fibre is increased by

exposure to intense laser radiation. Photosensitivity caused such gratings usefulness to be

limited because they could only be reflected at wavelengths close to the writing light. They

also took a long time to produce and the strength of the gratings varied along the length of the

fibre.

After the inscription of the grating into the fiber’s core, due to the periodic

modulation of the index of refraction, light guided along the core of the fibre will be weakly

reflected by each grating plane by Fresnel effect. The reflected light from each grating plane

will join together with the other reflections in the backward direction. This addition may be

constructive or destructive, depending whether the wavelength of the incoming light meets

the Bragg condition.

Bragg's law states the following condition:

λB = 2neff Λ (2)

where λB is called the Bragg wavelength, neff is the effective refractive index and Λ is the

grating period of the index perturbation. The Bragg wavelength (λB) of an FBG can thus be

altered by changing the parameters neff and Λ. The Bragg wavelength is also affected by

additional factors such as the grating length. The diagram below shows a typical Bragg

reflection peak.

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Figure 2: A typical reflectivity vs wavelength curve

In this mini project, we are going to use photonic simulation software which is called

OptiFDTD (Finite-Difference Time-Domain simulator) to generate the grating layout and

also shows the power transmittance and reflection using VB script. In addition, we need to

improve or enhance 10 sets of value that shows significant difference between them.

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METHODOLOGY

The tasks given for our group was Lesson 15 and Lesson 16. For both lessons we

completed by using Optiwave Software. The objectives that were needed to achieved from

Lesson 15 are to use VB scripting to generate the grating (or periodic) layout and to produce

grating layout simulation and post-processing analysis. To achieve the objective, these steps

have to be followed. First, open the Waveguide Layout Designer. Next, create a new

project. Create a dielectric material with refractive index, n=1.5 with name

ChannelPro_n=1.5, and ChannelPro_n=3.14. Then, also create a profile with material

ChannelPro_n=1.5and ChannelPro_n=3.14. In the OPtiFDTD_Designer window, draw two

linear waveguides. Then, define an horizontal input plane. Overwrite the current script. Next,

delete all the objects in the layout window. Run the VB script code. VB scripting provides a

way to generate the periodic layout. VB script can also design other objects that can be drawn

in the layout such as input plane, Observation Objects. After setting up the simulation

parameters, perform the simulation. Last but not least, perform far field analysis for the

diffraction wave.

As for Lesson 16 – Calculating Power Transmittance and Reflection using VB Script,

the purposes of the lesson are to calculate power at the specified Wavelength. This function

should be used with 2D GMCW simulations. It can be used with 2D CW simulations as well.

However, in this case it makes sense only when nonlinear materials have been used to

construct project components, and one can expect some harmonic frequencies to be

generated, calculates power spectrum for the specified number of wavelength sampling

points. This function can be used only with 2D GMCW simulations. When used with other

type of simulations, the function will return zero as the power value, to retrieve a value of

previously calculated power at the specified sampling point. The function will return zero if

called before the CalcPowerSpectrum() has been executed, to calculates power spectrum

normalized to the power signal of the specified Input Plane, for the specified number of

wavelength sampling points. This function can be used only with 2D GMCW simulations.

When used with other type of simulations, the function will return zero as the power value

and to retrieve a value of previously calculated power at the specified sampling point. The

function will return zero if called before the CalcNormalizedPowerSpectrum() has been

executed.

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RESULTS (LESSON 15)

Table 1: Diffraction wave for different wavelength and tilted angle

Wavelength (um) Tilted angle

(deg)

Diffraction angle (deg) Diffraction angle intensity

0.2 45 -45.25

-25.25

-8.75

7.50

24.25

2446.73

369.11

875.20

271.72

520.69

0.63 (original) 45 -36.25

-18.5

-2

31.5

11542.67

10905.68

11860.41

1318.60

1.5 45 -7.5

8.5

23888.52

2685.04

0.63 0 -34

-16.25

0

16.25

34

3463.59

15584.61

19450.33

15589.37

3463.53

0.63 80 -25.5

-8.75

23.75

1387.17

1298.90

178.54

0.63 160 -7.25

8.5

25.5

18861.11

10516.46

24723.27

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Wavelength=0.2um, Angle=45o Wavelength=0.63um, Angle=45

o

Wavelength=1.5um, Angle=45o Wavelength=0.63um, Angle=0

o

Wavelength=0.63um, Angle=80o Wavelength=0.63um,Angle=160

o

Figure 1.1: Far Field Pattern

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RESULTS (LESSON 16)

Table 2: Power reflectance and transmittance for different number of grating

Number of

grating

Refractive

index (n)

Bragg wavelength

(um)

Power Reflectance at

Bragg wavelength

(W/m)

Power Transmittance

at Bragg wavelength

(W/m)

1 3.14 1.490 -1.02e-10 2.74e-8

20 3.14 1.490 -3.02e-9 2.44e-8

36 (original) 3.14 1.490 -8.43e-9 2.06e-8

51 3.14 1.490 -1.12e-8 1.87e-8

100 3.14 1.490 -1.12e-8 1.87e-8

Figure 2.1 Reflection spectrums for different number of grating

Figure 2.2 Transmission spectrums for different number of grating

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Table 3: Bragg wavelength, power reflectance and transmittance for different refractive index

Number of

grating

Refractive

index (n)

Bragg wavelength

(um)

Power Reflectance at

Bragg wavelength

(W/m)

Power Transmittance

at Bragg wavelength

(W/m)

36 1.50 1.414 -1.66e-9 1.01e-7

36 3.14 1.490 -8.43e-9 2.06e-8

36 3.20 1.519 -8.97e-9 2.11e-8

36 3.30 1.566 -9.37e-9 2.05e-8

36 3.80 1.573 -5.96e-9 1.83e-8

36 5.90 1.550 -1.92e-9 5.80e-11

Table 4: Bragg wavelength, power reflectance and transmittance for different wafer

properties

Wafer refractive

index (n)

Bragg wavelength

(um)

Power Reflectance at

Bragg wavelength

(W/m)

Power Transmittance

at Bragg wavelength

(W/m)

1.0 (Air) 1.490 -8.43e-9 2.06e-8

2.0 1.511 -5.93e-9 2.66e-8

3.14 - - -

Table 5: Bragg wavelength, power reflectance and transmittance for different wafer

dimension

Length (um) Width (um) Bragg wavelength

(um)

Power Reflectance

at Bragg

wavelength (W/m)

Power

Transmittance at

Bragg wavelength

(W/m)

13 3 1.490 -8.43e-9 2.06e-8

13 6 1.504 -8.40e-9 2.16e-8

13 13 1.490 -8.47e-9 2.07e-8

13 16 1.504 -8.42e-9 2.17e-8

20 3 1.490 -8.43e-9 2.06e-8

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DISCUSSION

Based on the results in Table 1, the diffraction angle and intensity varied as we

changed the wavelength and tilted angle of the incident wave. The diffraction angle intensity

is significantly increased with the increasing of wavelength. The incident wave was diffracted

and interfere constructively which formed the peak of intensity that showed in figure 1.1.

Constructive interference occurs when the path difference is an integral number of

wavelengths. The peaks can be the order of diffraction angles. We observed every peak

formed at certain angles means that the incident wave is diffracted at these angles. Therefore,

the diffraction is depends on the wavelength.

In Table 2, when we fixed the refractive index and varied the number of grating, the

results showed that the reflected power increases. The negative sign for power denotes

reflection. The number of grating increases means that the length of grating has been

increases also. The number of grating affected the reflected power because the incident light

is reflected at each planes of grating. So the entire reflected light waves are combined into

one large reflection at a particular wavelength. The wavelength at which this reflection occurs

is called the Bragg wavelength. Due to the original refractive index of material which is

n=3.14, the reflected wavelength is at 1.49um. In addition, when the reflected power

increases, the transmitted power decreases. This is because a light wave travelled in the fiber

will be reflected or transmitted through the planes of grating. Based on the figure 2.1, it is

significantly increase in the reflectivity of side lobes. The bandwidth also becomes narrower

when the grating length increases. Theoretically the reflected power will increase until it

achieves the maximum value when the length of grating increases, but when we modified the

structure over 51 gratings, the result did not show any changes of this parameter. So, we

conjecture that this software has it limitation.

Besides that, the results showed the Bragg wavelength changed when the refractive

index changed without changing the number of grating in Table 3. Based on the result, the

Bragg wavelength is shifted towards longer wavelength when the refractive index increases.

The reflected power also increased when the refractive index increased until n=3.30 but the

power dropped when further increased the index. According to the Bragg condition of

Equation (2), refractive index can affect the Bragg wavelength. The light waves are reflected

by each of the grating plane due to the periodic variation of index of refraction. Thus,

different refractive index will select different wavelengths.

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CONCLUSION

Finally, our investigation about Bragg grating comes to the end .We had spent our

time to make sure we achieved the objectives for this investigation. Through our research,

starting from the first day we got the task until today, all of our objectives have been able to

accomplish nicely.

In this, many things that related to Bragg grating was dismantled one by one. Based

on our first objective, we may learn and get extra knowledge about what it is mean by Bragg

grating. During this period, we already know the basic things that relate to this topic. As

contained in the introduction, we can define the Bragg grating based on the Bragg’s Law.

Besides that we also can determine the basic structure of the Bragg grating and also different

type of grating that had been apply in many optical instruments.

From the research, we also know about the application of the Bragg grating in

nowadays technologies. Fiber Bragg Grating (FBG) is the most famous optical fiber that

applies the Bragg grating theory. Based on the information we obtained from some reference,

FBG also can be divided into several types based on the grating structure: uniform FBG,

chirped FBG, tilted FBG and superstructure.

Our next objective is to generate the grating (or periodic) layout using VB scripting

and to simulate the grating layout and post-processing analysis. By following the step in

Lesson 15 and Lesson 16, it make our knowledge about Bragg grating become clear. We

understand the theory and the differences in transmittance and reflection when we change

some parameter, (result and discussion). From the lesson 15, we use the VB scripting to

generate the periodic layout and also design some other objects that can be draw in the

layout. For example, in our layout we draw the input plane and two observation planes

(transmission and reflection). And then the far field analysis for the diffraction wave can be

performed. To accomplish our last objective, we follow Lesson 16. We succeed in simulate

the grating layout. As a conclusion, our objectives had been successfully accomplished within

the given time.

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REFERENCES

1) Marcelo M. Werneck, Regina C. S. B. Allil, Bessie A. Ribeiro and Fábio V. B. de Nazaré

(2013), "A Guide to Fiber Bragg Grating Sensors", in Current Trends in Short-and Long-

Period Fiber Gratings, DOI: 10.5772/54682.

2) Hill, K & Meltz, G 1997, 'Fiber Bragg Grating Technology Fundamentals and Overview',

Journal of Lightwave Technology, vol. 15, no. 8, pp. 1263-76.

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APPENDIX

Lesson 15 - Simulations of Gratings Created

with VB Script

Grating layouts in most cases are the periodic structure. There are two ways in OptiFDTD to

realized the periodic layout: PBG editor and VB scripting, PBG layout and corresponding

simulations are discussed in Lesson 3, Lesson 11 - 14. This lesson will focus the following

features:

• Using VB scripting to generate the grating (or periodic) layout.

• Grating layout simulation and post-processing analysis

Note: It is assumed that you are familiar with Lesson 1—Getting started and with material

and profile definition.

Introduce the layout

We are going to simulate a 2D grating layout that is shown in the Figure 1.

Figure 1 Layout

Note: Note: The corresponding project file can also be found in the Sample file

folder, Sample37_2D_VB_Script_Grating.FDT

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Lesson 16 – Calculating Power Transmittance

and Reflection using VB Script

OptiFDTD provides comprehensive post-simulation analysis tools. Such as transmittance

spectrum analysis, mode overlap calculation, input overlap calculation, far field calculation,

Poynting vector analysis, polarized power calculation and so on. These analysis tools were

mainly used in the analyzer. Some users may want to perform the sweep simulation and want

feedback the results to the layout designer so that the layout can be optimized, or some users

may want to get the power transmission/reflection spectrum results without the manipulation

of opening the analyzer. Now these works are possible by using the VB script for the 2D

layout.

Access to the simulation result data of Observation Objects is a critical feature needed for

optimization of the designed devices. Exposure of the available data through the VB Script

interface allows for implementation of the basic optimization algorithms within the script and

provides the means to access third party solutions supporting COM Automation

OptiFDTD provides the following VB script function based the Observation Line Power

post-simulation analysis.