### Introduction

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.

### 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.

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Figure 2

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.*

### 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.

### Example 4: M squared Laser Beam

The “M squared Laser Beam” source type models a laser based on its M^{2} factor, also known as beam quality or beam propagation factor. The smallest possible value of M^{2} is 1, and this specifies a Gaussian TEM 00 beam. Larger values of M^{2} indicate a mix of higher order modes in the beam. To determine the mode composition of an M^{2} beam created in FRED, right-click the Source category on the tree and select Detailed Analysis.

### 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.

[1] Paschotta, R. “M2 Factor.” Accessed 1/28/16. <https://www.rp-photonics.com/m2_factor.html>.

[2] Ready, J. F. Industrial applications of lasers. Academic press, 1997.

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