# OptiGrating Tutorials

## Grating Device Modeling

Single Grating Formula A grating can be represented by the formula that combines a grating shape function, an average index modulation function, a period chirp function, and an apodization function: where n0 – waveguide refractive index Δn – index modulation amplitude θ -grating tilt angle ƒ[Λ(z)/cosθ, z] – shape function Δn0(z) – average index modulation function Λ(z) –…

## Coupled Mode Equations

Assume the electric field is a linear combination of the ideal modes (with no grating perturbation), such that where ai(+) and ai(-) are the slowly varying amplitudes of ith mode traveling in the +z and –z directions. βi and is the propagation constant and modal field of the ith mode. The above electric field is used…

## Transfer Matrix Method

If the device has more than one grating plus phase shifts, the coupled mode equations can be solved by the Transfer Matrix Method. This method can also be used very effectively in the analysis of almost-periodic gratings. The general idea of TMM is that the grating structure is divided into a number of uniform grating…

## Grating Pulse Response

The Coupled Mode Equations are derived in the context of a monochromatic frequency CW light source for linear propagation. The spectrum of the input pulse can be obtained by taking a Fourier transform of the input time-dependent waveform. The response to the input pulse can be calculated by considering each spectral component separately and adding…

## Fiber Grating Sensor

Temperature and strain change the grating period as well as the grating refractive index. Consequently, the response of the grating device is changed when temperature and strain distributions change. Strain-optic effect of fiber Bragg grating The changes of optical indicatrix caused by strain are: where, ε1 = ε2 = –vε, ε3 = ε, ε4 =…

## Grating Device Characteristics

Reflection Reflection at a given position is defined by the ratio of back-reflected power to input power: The program calculates reflection for both coupled modes, called Reflection 1 and Reflection 2 respectively. For Propagation calculations, the reflection is obtained at every point along the grating device. In the case of multiple gratings, the device begins…

## The Inverse Scattering Problem

The reconstruction method uses a layer peeling algorithm, a complete description is found in reference [1]. This method can be implemented after the problem is approximated by a series of discrete layers, each with a constant coupling coefficient. At the beginning of the problem, all these coupling coefficients are unknown. The method uses an iterative…

## References

You will find below a list of general references relevant to waveguide and fiber gratings and to waveguide optics. Optiwave Corporation does not endorse any of the references, nor do the OptiGrating algorithms follow exactly the publications. The references are listed for your convenience: General books about waveguides and fibers [1] M. J. Adams, “An…

## Project Windows

After you create a new project or open an existing one, you will see the OptiGrating Main Window, as shown below. The Main Window The Main Window of OptiGrating 4.2 is a multi-document interface that allows you to open several grating projects simultaneously. The Menu Bar displays the command and option menus that OptiGrating offers you.…

## Basic Concepts

What is a Main Window The main window of OptiGrating is a multi-document interface which allows you to open several grating projects simultaneously. You can also use a Multiple Window view. It is important to remember that you get different tools, exporting curves, and printing options that are specific for each active window, i.e. the…

### Categories

### OptiGrating Manuals

- OptiGrating Tutorials
- Applications
- Overview
- Technical Background
- Integrated & Fiber Optical Gratings
- Coupled Mode Theory
- Index Profile of Fibers or Slab Waveguides
- Waveguide Modes
- Material and Waveguide Dispersion
- Complex Index Profile
- Photosensitivity Profile of the Fiber and the Slab Waveguide
- Grating Device Modeling
- Coupled Mode Equations
- Transfer Matrix Method
- Grating Pulse Response
- Fiber Grating Sensor
- Grating Device Characteristics
- The Inverse Scattering Problem
- References

- Lesson 1 - Fiber Bragg Grating
- Lesson 2 - Sensors
- Lesson 3 - Material Dispersion
- Lesson 4 - Parameter Scan
- Lesson 5 - Synthesis of a Band Pass Filter
- Lesson 6 - Reconstruction of Unknown Grating
- Lesson 7 - Synthesis of a Grating for Dispersion Compensation
- Lesson 8 - Synthesis of a Filter with User-Defined Spectrum
- Sample Files
- Apodized Fiber Bragg Grating Simulation
- Sampled Grating
- Mode Conversion by Fiber Bragg Grating
- Phase-shifted Bragg Grating Filter Based on Planar Waveguide
- Long-period Fiber Grating for Gain Flattening
- Pulse Reshaping by Uniform Fiber Grating
- Pulse Reshaping by Apodized Fiber Gratings
- In-Fiber Moiré Gratings

- User Guide
- Interface Menus
- Appendices

### PIC circuit optimization using compact models with physical parameters

### Evaluations

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