# US 7,609,917 B2 · Method and apparatus for controlling waveguide birefringence by selection of a waveguide core width for a top cladding

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- Number: US 7,609,917 B2
- Document ID: US7609917B2
- Status: Granted
- Kind: B2
- Application number: 12/079,930
- Filed: 2008-03-28
- Published: 2008-10-02
- Granted: 2009-10-27
- Earliest claimed: 2005-10-11
- Assignees: Lightwave Microsystems Corporation
- Inventors: Farnaz Parhami; Liang Zhao; Fan Zhong
- Web page: https://patentgrep.com/patent/US7609917B2

## CPC

- G02B 6/12023: {characterised by means for reducing the polarisation dependence, e.g. reduced birefringence}
- G02B 6/126: using polarisation effects {(G02B6/1226 takes precedence)}
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS

## Abstract

A method and apparatus for controlling waveguide birefringence by selection of a waveguide core width for a tuned top clad is described herein. In one example, a dopant concentration within a top cladding material is between 3-6% (wt.). Given a tuned top cladding composition, a width of the waveguide core is pre-selected such that birefringence is minimized, i.e., a zero, or near zero. The desirable width of the waveguide core is determined by calculating the distribution of stress in the top cladding over a change in temperature. From this distribution of stress, a relationship between the polarization dependent wavelength and variable widths of the waveguide in the arrayed waveguide grating are determined. This relationship determines a zero value, or near zero value, of polarization dependent wavelength for a given range of waveguide widths. Accordingly, the width of the waveguide may be selected such that the polarization dependent wavelength is minimized.

## Claims

### Claim 1

A method of controlling birefringence in an arrayed waveguide grating comprising:
determining a stress distribution in a top cladding layer and in at least one waveguide in the arrayed waveguide grating over a change in manufacturing temperature, the top cladding layer having a dopant in the range of 3-6% by weight;
determining a relationship between polarization dependent wavelength and a width of the waveguide from the stress distribution; and
selecting the width of the waveguide such that the polarization dependent wavelength is a predetermined value.

### Claim 2 (depends on 1)

The method of claim 1 wherein the predetermined value is a minimized polarization dependent wavelength.

### Claim 3 (depends on 1)

The method of claim 1 further comprising determining an elastic modulus of each of the top cladding layer and the waveguide prior to determining the stress distribution.

### Claim 4 (depends on 3)

The method of claim 3 further comprising determining a coefficient of thermal expansion in each of the top cladding layer and the waveguide.

### Claim 5 (depends on 1)

The method of claim 1 wherein determining the relationship between polarization dependent wavelength and the waveguide width from the stress distribution further comprises mapping the stress distribution into an index distribution.

### Claim 6 (depends on 5)

The method of claim 5 further comprising determining an effective index of each of the waveguide and the top cladding.

### Claim 7 (depends on 1)

The method of claim 1 wherein determining the relationship between polarization dependent wavelength and the waveguide width from the stress distribution further comprises determining a distribution of refractive index in the top cladding from the stress distribution.

### Claim 8 (depends on 2)

The method of claim 2 wherein the minimized polarization dependent wavelength is zero.

### Claim 9 (depends on 1)

The method of claim 1 wherein the top cladding layer is disposed over the waveguide.

### Claim 10 (depends on 9)

The method of claim 9 wherein the top cladding layer is disposed over a substrate.

### Claim 11 (depends on 10)

The method of claim 10 wherein the substrate comprises silicon.

### Claim 12 (depends on 10)

The method of claim 10 wherein the substrate has a thickness of about 625 μm.

### Claim 13 (depends on 10)

The method of claim 10 wherein the substrate is disposed over a first layer of SiO2.

### Claim 14 (depends on 13)

The method of claim 13 wherein a second layer of SiO2 is disposed over the substrate.

### Claim 15 (depends on 1)

The method of claim 1 wherein the waveguide further comprises at least one dopant.

### Claim 16 (depends on 15)

The method of claim 15 wherein the at least one dopant is selected from the group consisting of Germanium and Phosphorus.

### Claim 17 (depends on 1)

The method of claim 1 wherein the waveguide comprises at least one material selected from the group consisting of polyacrylates, polymethacrylates, polysilicone, polyimide, epoxy, polyurethane, polyolefin, polycarbonate, polyamides, polyesters, acrylate-methacrylate copolymers, acrylic-silicone copolymers, epoxy-urethane copolymers, and amide-imide copolymers.

### Claim 18 (depends on 1)

The method of claim 1 wherein the dopant comprises Boron.

### Claim 19 (depends on 1)

The method of claim 1 wherein the change in manufacturing temperature is about 900° C.

### Claim 20 (depends on 1)

An arrayed waveguide grating manufactured according to the method of claim 1.