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# Lesson 16: Graded Index Fiber Modes

## Introduction

Optical fiber is an important component of any device used for making fiber directional couplers and for launching and receiving light from an integrated optical waveguide In a device where a small length of fiber is used, the only characteristics needed to simulate for a fiber are the effective mode indices and mode field profiles.…

## Graded Index – Core Fiber

Graded Index Core fibers with α – refractive index profile in the core are often desired for several applications in telecommunications, such as shifting zero dispersion wavelength to 1.55 microns.We will demonstrate the design for a triangular core fiber ( α = 1 ). We will also compare the results of the 3D Mode Solver with the Finite Difference Method…

## Fiber Parameters and Refractive Index Profile of Triangular Core Fiber

Core radius: 3.00μm Refractive index of core: 1.48 Refractive index of cladding: 1.444 Wavelength: 1.55μm Figure 1: Refractive index profile of a triangular core fiber The procedures are: •     Creating the material •     Defining user variables •     Defining user functions •     Defining the User defined profile •     Defining the layout settings •     Creating the linear…

## User Function Profile

The Triangular core fiber can be defined as: To implement the above equation in User Function Profile, we will first explain the User Variables and User Functions (see Table 12). Table 12: User Variables and User Functions Therefore, Triangular Core Fiber equation can be defined as follows: with the limits as follows:

## Developing the User Defined Profile

In order to define the profile, perform the following procedures. Creating the material Step Action 1 From the File menu, select New.The Initial Properties dialog box appears. 2 Click Profiles and Materials.The Profile Designer opens. 3 In the Materials folder, right-click the Dielectric folder and select New.The Dielectric dialog box appears. 4 Create the following…

## Defining User Functions

To define the user functions identified within Table 12 and in Equation 1 and Equation 2, perform the following procedure. Step Action 1 In the Profile Designer, select Tools > Edit Variables and Functions. The Variables and Functions dialog box appears. 2 On the User Function tab, type the following: Function specification: Delta(n_core,n_cl)Expression: (n_core*n_core-n_cl*n_cl)/ 2/…

## Defining the User Defined Profile

Step Action 1 In the Profile Designer, right-click the Profiles folder, and select User Function Profile > New. The User Function Profile dialog box appears. 2 Type/select the following: Profile name: GradedFibre Function specification: fgr(x,y) Function body: n_core*sqrt(1-2*Delta(n_core,n_cl)*(pow((r(x,y)/radius),1))) 3 Select Use limits and type the following: Use limits: x*x+(y-y0)*(y-y0)<radius*radius 4 Make the following associations on the…

## Defining the Layout Settings

Step Action 1 In the Layout Designer, select Edit > Wafer Properties. 2 Type/select the following: Wafer Dimensions tab Length (μm): 100 Width (μm): 30 2D Wafer Properties tab Material: cladding 3D Wafer Properties tab Cladding Material: cladding Thickness: 0.1 Substrate Material: cladding Thickness: 30 3 Click OK to apply the layout settings.

## Creating the Linear Waveguide Fiber

To create the linear waveguide fiber, perform the following procedure. Step Action 1 In the layout, draw a linear waveguide. 2 To open the properties dialog box for the waveguide, double-click on the waveguide. The Linear Waveguide Properties dialog box appears. 3 In the Linear Waveguide Properties dialog box, type/enter the following: Start offset: Horizontal:…

## Setting Simulation Parameters

To set the simulation parameters, perform the following procedure. Step Action 1 In the Simulation Parameters dialog box, click the 3D Isotropic tab. 2 Type/select the following: Number of points in mesh Number of points/ μ m X: 10 Y: 10 View cut X Mesh Pt: 151 Y Mesh Pt: 151 3 Click OK.