Coupling efficiency into multi-mode fiber can be calculated using the geometric image analysis feature.

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. If the fiber is multi-mode in the sense that two or three modes are supported, physical optics must be used. 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.
 

The geometric image analysis can generate the irradiance at any surface, from an extended source with specific size and shape at the object surface. In addition, it can filter out rays that have larger incident angle than a definable threshold, at the evaluating surface. Using the attached sample file, we will demonstrate how to use the geometric image analysis feature to calculate multi-mode fiber coupling efficiency.

Open the included sample file from the last page of this article. This file models coupling to a multi mode fiber with 0.1mm 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 0.1mm radius circular aperture on the images 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 Geometrical Image Analysis window under Analysis > Image Analysis > Geometric Image Analysis and open its settings window.

The NA of the receiving fiber is specified in the NA box. Since the we are assuming on-axis point source located at infinity, Field Size (size of the extended source) parameter 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 10000 to speed up the calculation.

Click OK.

The coupling efficiency, of only about 2%, is reported in 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 saved setting in the .CFG file. To store the desired geometric image analysis settings in the .CFG file, we need to click the Save button the settings window.

The IMAE operand will now report the correct coupling efficiency by using the saved settings. 

The value will be slightly different then what is reported in the geometric image analysis window, since the IMAE operand uses different random set of rays.

Since the thickness of surface #3 is already set as variable, all we need to do is to optimize the system by clicking on Tools...Optimization...Optimization and choosing the Othogonal Descent optimizer:

Look in the merit function editor, or update the geometric image analysis window and note that the new coupling efficiency is about 54%.

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.

Check the “use polarization” option in the geometric image analysis settings.

Click OK.

The new coupling efficiency is about 47%.

This article has demonstrated how to compute multi-mode fiber coupling efficiency using the Geometric Image Analysis feature. The Fresnel loss and glass bulk absorption can also be accounted for by enabling the polarization option in the settings.