# Laser Diode

## Introduction

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FRED software has great flexibility when it comes to modeling laser diodes. In this application note, laser source models from simple to detailed will be described. The most basic model is a Gaussian TEM0,0 mode. More advanced models include astigmatism in beam waist displacement and divergence. The laser can also be specified using its M2 factor. Finally, an arbitrary mixed-mode laser can be created. This model coherently combines a chosen distribution of Gaussian TEM modes (Hermite, Laguerre, Laguerre Cosine, and Laguerre Sine).

## Example 1: Gaussian 00 Mode

The “Laser Beam (Gaussian 00 Mode)” source consists of a collimated grid of rays which are apodized to have a Gaussian 00 irradiance profile at the beam waist. This source is sufficient for very low divergence beams. Note that if the Grid Size is chosen to be less than the Beam Size, the beam will be truncated and undergo diffraction as if it were blocked by a circular aperture.

**Figure 1**.

*Simplified Laser Beam (Gaussian 00 mode) specifications.*

## Example 2: Astigmatic Gaussian Beam

The “Astigmatic Gaussian Beam” source provides a more realistic model. Most diode lasers suffer from astigmatism: x- and y-components of the beam waist are displaced along the axis. In index-guided lasers, displacement is typically 2-8 µm. In gain-guided lasers, displacement is typically ≈40 µm. Astigmatism can be modeled by specifying x- and y- divergence angle and separation of foci. This source type also allows ray generation at some distance from the beam waist for greater accuracy.

**Figure 2 **. *Simplified Astigmatic Gaussian Beam specifications.*

**Figure 3****. ***Schematic raytrace of a divergent astigmatic laser source along the: x-z axis (left), y-z axis (center), and perspective view (right). Divergence angles are 5° in the x-direction and 15° in the y-direction. Foci are separated by 0.5 units.*

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## Example 3: Laser Diode Beam

The Laser Diode Beam is a newer and more accurate model of an astigmatic divergent laser source. The laser is specified in terms of x- and y- divergence angles and foci positions. In addition, the exact meaning of divergence angle can be specified in terms of various half- and full-widths. This laser model also performs Gabor Synthesis for more accurate modeling of coherent light propagation.

**Figure 4**.

*Simplified Laser Diode Beam specifications.*

## Example 4: M squared Laser Beam

The “M squared Laser Beam” source type models a laser based on its M2 factor, also known as beam quality or beam propagation factor. The smallest possible value of M2 is 1, and this specifies a Gaussian TEM 00 beam. Larger values of M2 indicate a mix of higher order modes in the beam. To determine the mode composition of an M2 beam created in FRED, right-click the Source category on the tree and select Detailed Analysis.

**Figure 5**.

*Left: Simplified M squared Laser Beam specifications. Right: Distribution of modes in this specific M2 laser source.*

## Mixed Mode, Higher Order Modes

A multimode beam occurs if a laser does not have sufficient spatial filtering (the limiting aperture is larger than the lowest order mode radius). As a result, multiple modes exist in the laser cavity. To model a laser with a specific mode distribution, multiple light sources can be assigned to each TEM mode. The Detailed Optical Source type is required to create a mode, and is set up by first choosing a hexagonal or grid plane of ray positions and then. setting a Gaussian Apodization. The apodization allows specification of x and y semi-width, lateral offset, mode number (m, n), and mode type (Hermite, Laguerre, Laguerre Cosine, Laguerre Sine). Irradiance profiles of several TEM modes are shown in Figure 6. A mixed-mode example is shown in Figure 7.

**Figure 6**.

*Irradiance profile of various Gaussian TEM modes as modeled in FRED.*

**Figure 7**.

*Mixed-mode irradiance profile consisting of [1 : 0.5 : 0.25] power distribution of TEM0,0, TEM2,1, and TEM2,3 modes. The TEM2,1 and TEM2,3 modes are also slightly displaced from the axis.*

[3] “Correcting Astigmatism in Diode Lasers.” Accessed 1/28/16. http://uotechnology.edu.iq/eretc/books/corast.pdf.