This article demonstrates the use of the Geometric Image Analysis feature to compute multi-mode fiber coupling efficiency. We also use the IMAE operand to optimize the system for multi-mode fiber coupling efficiency. This method only works for multi-mode fibers that contain a large number of modes. A sample file is attached.

**Authored By Nam-Hyong Kim, Updated by Kristen Norton**

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## Introduction

OpticStudio may be used to model the coupling of single or multi-mode fibers. In order to use geometrical rays to model multi-mode fiber coupling, the fiber core diameter has to be at least 10 times larger than the wavelength, such that many transverse modes can be supported. In this article, 'multi-mode' is taken to mean that there are so many modes supported that the fiber can be treated as a light-pipe.

Using the attached sample file, we will demonstrate how to use the Geometric Image Analysis feature to calculate multi-mode fiber coupling efficiency. The same result can also be targeted in the Merit Function using the IMAE operand; optimization in this way is also shown.

Calculating coupling efficiency with Geometric Image Analysis

To begin, download and open the sample file listed at the beginning of this article. This file models coupling to a multi-mode fiber with 0.1 mm core radius and NA of 0.2. For now, we will ignore the Fresnel (reflection) losses from air-glass interfaces, including the fiber.

The size of the fiber core is modeled by specifying 0.1 mm radius circular aperture on the Image Surface. Since in this file the aperture type is Floating, the size of the circular aperture is controlled by the Semi-Diameter of the Image Surface.

Open the Geometric Image Analysis window under **Analyze...Extended Scene Analysis...Geometric Image Analysis**. Geometric Image Analysis can generate the irradiance at any surface, from an extended source with a specific size and shape at the object surface. In addition, it can filter out rays that have larger incident angles than a definable threshold at the evaluating surface.

There should already be a Geometric Image Analysis window in the provided sample file. The settings are shown below.

The NA of the receiving fiber is specified in the NA box. Since we are assuming on-axis point source located at infinity, the Field Size (size of the extended source) is zero and the shape of the source, controlled by the File option, does not matter. The Image Size option determines the area of interest at the evaluation plane; you can also think of it as the size of the detector. We will limit the number of rays to 10,000 to speed up the calculation.

The IMAE operand

The coupling efficiency is just over 2% and is reported in the text of the Geometric Image Analysis window.

We will optimize the image surface position (receiving fiber position) to maximize the coupling. The IMAE operand in the Merit Function Editor reports the coupling efficiency at the image surface. Since there are more settings in the Geometric Image Analysis than the number of available columns in the Merit Function Editor, the IMAE operand uses the last saved settings from the analysis window. These settings are saved in a CFG (configuration) file, which can be generated or updated (overwritten) by clicking the Save button in the Geometric Image Analysis settings.

The IMAE operand will now report the correct coupling efficiency by using the saved settings. The value will be slightly different than what is reported in the Geometric Image Analysis window since the IMAE operand uses a different random set of rays.

Because the Thickness of surface #3 is already set as variable, all we need to do is to optimize the system by clicking on the **Optimize Ribbon...Optimize!**

Select the **Damped Least Squares** algorithm, and then click **Start**:

The Merit Function should drop very quickly. Once the optimizer is complete, click **Exit**. Update the Merit Function Editor, and you’ll notice that the coupling efficiency has increased to about 54%. We can also see this in the Geometric Image Analysis window:

Accounting for Fresnel Losses

Let's assume that the core is made of N-BK7. If we want to account for the Fresnel losses from all air-to-glass interfaces, including at the fiber core, we need to enable the polarization option in the Geometric Image Analysis settings. The polarization calculation will also account for bulk absorption of the bi-convex lens.

Specify N-BK7 glass at the Image surface as fiber core glass material and check on **Use Polarization** in the Geometric Image Analysis settings.

In order to see the correct efficiency in the Merit Function Editor, make sure you save the analysis settings. The new coupling efficiency has dropped to just over 47%.

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