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MODELING AND ANALYSIS OF

OPTICAL FIBERS AND FIBER DEVICES

by

JACINTHA KOMPELLA

Thesis submitted in fulfilment of the requirements for

the degree of

DOCTOR OF PHILOSOPHY

Department of Physics

INDIAN INSTITUTE OF TECHNOLOGY, DELHI

NEW DELHI-110016, INDIA August, 1989

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CERTIFICATE

This is to certify that this thesis entitled MODELING AND ANALYSIS OF OPTICAL FIBERS AND FIBERS DEVICES, being submitted by Jacintha Kompella, to the Indian Institute of Technology, Delhi, is a record of bonafide research work carried out by her. She has worked under our guidance and supervision and has fulfilled the requirements, which to our knowledge, have reached the requisite standard for the submission of this thesis. The results contained in this thesis have not been submitted in part or full to any other University or Institute for the award of any degree or diploma.

(A.K.GHATAK) (ANURA SHARHA)

Professor of Physics Assistant Professor

Department of Physics

Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016

INDIA

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AS s T RA C r- r

The increasing applications of optical fibers and fiber devices in optical communication, optical signal processing and optical sensing have provided an impetus for the design and development of a wide variety of fiber profiles. It is imperative then, to understand in depth, the propagation characteristics of optical fibers. Hence, there has been considerable research interest to develop models that can analyse fibers with a variety of profiles. Efforts are on to study fiber devices, which do not maintain the cylindrical symmetry of the original fiber. We have developed a few models that are suitable for obtaining relevant characteristics of fibers and devices based on them.

The first model is based on the Equivalent Step Index (ESI) approximation which has been proposed on the knowledge that, the modal field distribution of a single mode fiber is, to a large extent, 'insensitive to the details of its index profile. We have shown that a proper choice of fiber characteristics is necessary to obtain an appropriate ESI model. On the basis of this, a new ESI model has been developed. In the new model, there are three adjustable parameters, which are determined by matching the bendloss data and Petermann II spotsize data at one convenient wavelength in the range of 1300-1600 nm. We have carried out numerical simulation studies for fibers with parabolic and triangular index profiles having zero total dispersion at

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1300 or 1550 nm. The results show that our model is both very stable, with respect to the wavelength of matching, in the range 1300-1600 nm, and very accurate for predicting fiber characteristics over this range of wavelength. The maximum errors of prediction are less than 5-6%.

Directional couplers and coupler half blocks with an overlay are in-line fiber optic devices that form an integral part of fiber links. We have developed a model for single mode fibers suitable for analysing such fiber devices. The model is based on obtaining an equivalent step index planar guiding structure for the fiber used in making the device. The resulting equivalent planar device structure can be studied analytically. This model simplifies the analysis of polished fiber directional couplers, with a buffer layer, and coupler half blocks, with dielectric and metallic superstates. We have illustrated the use of this model with some numerical examples.

Considerable research efforts have been made to reduce a 2-I) index profile to an equivalent 1-D profile.

The model described above is an example of one such effort.

However the above model is based on two assumptions (i) the field of the fiber is separable in the cartesian coordinates x and y (ii) the fields in the x and y directions are assumed to be a two parameter cosine exponential function.

While the first assumption is necessary and is dictated by the aim of separating the two dimensions so that a 1-D

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equivalent waveguide can be obtained, the second assumption is open to other choices of the form of the field. We have developed a method for obtaining equivalent planar structures for circular and elliptical core fibers, without an apriori assumption for the form of the trial field. It is an iterative method based on the variational principle which

leads to an optimum equivalent graded planar structure.

Finally we have developed a method of analysis for

multimode graded index media. Such media have found wide applications in the field of optical imaging, optical sensing and local area networks. The rays in multimode waveguides exhibit radiation losses when they encounter

bonds. Hence a knowledge of the exact ray paths and exact positions of ray caustics is necessary to calculate the power attenuation. We have developed a Lagrangian formulation for studying the ray paths in cylindrically symmetric media. We have illustrated its use for bent slabs as well as fibers with separable profiles.

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ACKNOW L. E DGEMEN

TS

Be-Z,ng a member (24 the Opt-icat Waveguide Group unden the b and expert guZdance o4 Pno4. A. K. Ghatah ha4 been a newandtng expentence. I am extnemeZy gaate4u.e. 4on 1144 4.nop-inatZon, guidance and chanm whLah kept me on my toe5 aZZ through the wonh. I cannot adeguateey expne44 my gnatttude to 04. Anunag Sharma. h4.-5 -oupeAv-4..-6Zon o4 th-44 work and who w-4:.th pat.c.ence and cane ha-4, been a 6ntend and gu.4,de to me. It ha..6 been my good. 4ontune to have wonted cZo4ety wt-th both Dn. Enate-oht Shanma and Dn. Ramanand Tewaa.4,. 014-4cu.64.4-on4 wtth them have gneatty heeped to .4-mpnove the qua-64-ty o4 wont.. I am aLoo thank42e to I.C. Goyae, Dn. B.P. Pat., Dn. K. Thyaganajan, DA. Arun Kaman. Dn. 8.D. Gupta, Dn. Adtt Kaman, Dn. M.R. Shenoy and 04. R.K. Va4.-Ahney 04 the4,n 4eadtne-5-4 to a44-4.4t.

T woutd take tht4 oppontum.i.ty to thank my eateague-e, Venghe.6e Pautoze, V-1.15hnu Ray.i.ndaa S4nha, Ume4h

Supra-i.ya D-Oga , awagata Bannendee, Saeed P42evaa, Saeed

Gh444,42,4- Va-inda Khunana, P.C.Subnaman-Lam Pu4hpa 84ndat,

Anju Tone, a, Suhhdev Roy, Hemant .S.Zngh, Ia4pneet S-Lngh and Aday Partizan, who n no 4mat.e way made my 4-taw with, the group

veay memonabte and an enjoyabte one ,

I woad to acknomeedge the 4 h e.e.eo h4/0 gntzrz ted by The f o o4 Sc.-tent-4.44c and rndu4tntat, Re4eanch (Ind.4,a).

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FtnaZey,

To my biwtheit my a44ecti.on and -Cove.

La,5t and moot o4 aZZ, to my hu4band Vacha,spath4, Pete., who-oe. Zoe, undeitAtand,4,n9 and encowtagement have meant a Lot

to me. HJ ab4ence towa4d4 the end o1 my wo.1.12, to,Lov4..ded the nece44arty tmpett4.4 4on. the 44-mat% da4h to the 4Znt4h4.ny .etne I

(JacZntha KomPeLea)

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CONTENTS

CHAPTER PAGE

1. INTRODUCTION 1

2. EQUIVALENT STEP INDEX MODEL (ESI): A CRITICAL STUDY OF THE EXISTING METHODS AND A NEW MODEL WITH

IMPROVED PERFORMANCE 17

2.1 Introduction 17

2.2 The ESI Methods 21

2.3 Bend Loss and the ESI Model 29 2.4 The Number and Choice of ESI Parameters 33 2.5 Choice of Fiber Characteristics to

Determine BSI Parameters. 35 2.6 Extraction of ESI Parameters from Bend

Loss and Spot Size at One Wavelength. 36 2.7 Performance of the New ESI Model:

Simulation Studies. 37

2.8 Summary. 52

A MODEL FOR SINGLE MODE FIBERS TO ANALYSE FIBER

DIRECTIONAL COUPLERS AND COUPLER HALF BLOCKS. 54

3.1 Introduction. 54

3.2 Existing Methods. 57

3.3.1 Basis of Equivalence of Slab with Fiber. 62 3.3.2 Equivalent Slab Structure. 68 3.3.3 Empirical Formulae to Obtain the

Equivalent Slab. 69

3.4 A Simple Directional Coupler. 71 3.5 Directional Coupler with a Buffer Layer. 73 3.6 Polished Coupler Half Blocks. 79

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3.6.1 Dielectric External Medium. 81 3.6.2 Metallic External Medium 85

3.6.3 Numerical Examples 85

3,7 Summary 87

4. A METHOD TO OBTAIN AN OPTIMUM EQUIVALENT 1-D INDEX

PROFILES FOR CIRCULAR AND ELLIPTICAL CORE FIBERS 90

4.1 Introduction 90

4.2 Principle of the Method. 92 4.3 Implementation Procedure. 97 4.4 Performance of the Method. 99

4.5 Summary. 103

A LAGRANGIAN FORMULATION TO TRACE RAY PATHS IN

BENT WAVEGUIDES 106

5.1 Introduction 106

5.2 The Optical Lagrangian in Cylindrical

Co-ordinates. 107

5.3 Ray Paths in Cylindrically Symmetric

(2-Independent) Refractive Index Profiles. 109 5.4 Ray Invariants and Equations for Profiles of

the Form nl'(r,z) = ne(r) + ne(x). 110 5.5 Ray Paths in a Bent Slab Waveguide. 113 5.6 Ray Paths in a Bent Fiber. 121 5.7 Power Attenuation in a Bent Waveguide. 122

5.8 Summary. 125

REFERENCES 128

BIO-DATA 145

References

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