# How to model angle-cleaved fibers

This article describes how to model coupling efficiency for angle-cleaved receiving fibers in OpticStudio. The angle-cleaved fiber facet and the compensating fiber-mode tilt angle can be introduced using the combination of a Coordinate Break (CB) surface and a Tilted Image surface, one of three primary methods. Properly setting up the tilt angle to represent the angle-cleaved fiber is crucial to getting accurate results for coupling efficiency. This article discusses three different approaches to setting up the system, and users can choose based on their preference or application.

Authored By Hui Chen and Ethan Keeler

Example Zemax Models

## Contents

• Understanding the geometry of the angle-cleaved fiber
• Setting up a system with a normal-cleaved fiber
• Coupling without mode-tilt compensation
• Method 1: Using a CB for mode tilt and a Tilted Image surface for cleave angle
• Method 2: Using a Tilted Image surface combined with a mode-tilt angle in the Fiber Coupling tool
• Method 3: Using a CB for tilt combined with a negative mode-tilt angle in the Fiber Coupling tool
• Note about launching the beam from a cleaved-fiber

## Introduction

When designing laser and fiber systems, it is sometimes necessary to use an angle-cleaved fiber in order to reduce back reflections caused by the fiber facet. For example, a typical fiber-air interface with normal cleave introduces ~4% Fresnel reflection or a 14 dB return loss, meaning that about 14 dB of the incoming light will be reflected right back. If we angle the fiber facet with an 8-degree cleave angle, the amount of back reflection can be significantly suppressed, down to ~60 dB. This is particularly important when dealing with high-power laser systems where large back reflections might cause source damage. This can also be important in highly sensitive systems, such as for endoscopy or those that use interference (e.g., optical coherence tomography).

## Understanding the geometry of the angle-cleaved fiber

Consider an angle-cleaved fiber with 8 degrees of cleave angle. Assume the fiber has a refractive index of 1.47. This can be modeled by assigning a Model Glass of n = 1.47 to the Material cell for the Image surface.

Next, we can consider the geometry of this 8-degree cleaved fiber to understand how to set it up.

Assume the incoming beam marked by the green arrow is along the Z-axis. The goal here, by introducing a proper tilt angle, is to align the receiving fiber so its axis is colinear with the refracted beam, thereby maximizing the coupling efficiency. What this means is that the refraction angle, which is the angle between the refracted beam and the facet normal, should be equal to the angle between the fiber axis and the facet normal, which is the cleave angle. In other words, to align the fiber axis with the refracted beam, the refraction angle needs to be the same as the cleave angle.

For this model, we know the fiber index is nfiber = 1.47, and we will assume the light couples from air (n = 1.0). The fiber cleaved angle is 8 degrees, which then sets theta_refract = 8 deg. Applying Snell’s law at the air-fiber interface, we have:

By plugging in the fiber index and refraction angle, we reach qin = 11.8 deg. This tells us that for the given fiber index and cleave angle, we can uniquely determine the required angle of incidence at which to place the refracted beam along the fiber axis and in turn maximize the coupling efficiency.

## Setting up a system with a normal-cleaved fiber

First, we will set up a simple system that uses a singlet lens to couple light from a source fiber into a receiving fiber. The source and receiving fibers are identical, and both have a NA of 0.1. We will start with a normal-cleaved, single-mode receiving fiber (where the facet is normal to the fiber axis). A starting file can be found here: “\Documents\Zemax\Samples\Sequential\Interconnects\Conic interconnect.zmx.” For this exercise, we will first make the following changes:

1. set the system wavelength to 0.55 um,
2. define the system aperture using Object Space NA = 0.2,
3. and set the Apodization factor G = 4.0.

Due to the symmetry of the source and receiving fibers, as well as the equi-convex lens used in this case, the best coupling efficiency is achieved when the system is symmetric in object and image space. To maintain this symmetry during optimization, we’ll first apply a Pickup solve on the Thickness cell of Surface 2 to pick up its value from the Object thickness. We can then use the Quick Adjust tool to find the Image plane location for the smallest spot size location.

Next, we will set up the single mode fiber coupling analysis. You can find the tool at Analyze…Fiber Coupling…Single Mode Coupling. In the analysis window, under Settings, set it up as shown in the screenshot below.

You can see after adjusting the object distance, the current coupling efficiency is computed to be 99.8%. Under Settings, if you check the Use Polarization option to consider Fresnel reflection losses at the two air-lens interfaces, the coupling efficiency drops to 91.5%. If you wish to consider the reflection loss at the air boundary at the receiving fiber facet, you can assign a Model glass to the Material cell of the Image plane, where n = 1.47. OpticStudio will then consider the ~4% loss at the air-fiber interface, and the coupling efficiency further drops to 88.2%. You can find a sample file with these settings in the Downloads section of this article: “conic_interconnect_normal_angle_fiber_coupling.zar.”

## Coupling without mode-tilt angle compensation

Now, we are ready to introduce the 8-degree cleave angle on the receiving-fiber facet. We will first look at the case where we introduce an 8-degree cleaved facet without any effort to realign the receiving fiber. Therefore, there will be no compensation for the added angled cleave.

In this case, the setup is straightforward. All we need to do is tilt the Image surface by 8 degrees. We do so by setting the Image surface type to Tilted, with Tangent Y = 0.140541 [Y = tan(8)]. You can see in the Layout plot that the Image plane is now tilted, resembling the angled-fiber facet. Please note that for demonstration purposes only, in all of the screenshots below, the Clear Semi-Diameter of the Image was temporarily increased to 1 mm to clearly show the Image surface. As expected, without compensation, this angled fiber facet causes the coupling efficiency to drop significantly, from 88.2% to 56.4% (with the Use Polarization option checked to include Fresnel reflection losses).

When using angle-cleaved fibers, the fiber alignment must be adjusted to compensate for the angled facet. The best coupling efficiency is achieved when the fiber axis is along the refracted beam path. Based on Snell’s law, we know that for a fiber with n = 1.47 and an 8-degree cleave angle, the required incident angle on the receiving fiber facet should be 11.8 degrees. This will provide a refraction angle of 8 degrees, which sends the refracted beam along the receiving fiber axis.

In general, tilts can be obtained using either Coordinate Breaks or Tilted surfaces. However, there is a difference between these two approaches. When using CB surfaces to introduce tilts, OpticStudio does so by tilting the local coordinate system, which not only tilts the Image surface, but also causes a tilt in the receiving fiber mode. By default, the receiving fiber is aligned with the local Z-axis. However, using a Tilted Image surface will only tilt the image surface itself without affecting the local coordinate orientation. This leaves the receiving fiber mode un-tilted.

In the following sections, we will introduce three different approaches to setting this up properly in OpticStudio.

## Method 1: Using CBs for mode tilt and Tilted Image surface for cleave angle

This is the recommended method because it separates the cleave angle and the mode-tilt compensation angle. Moreover, comparing with Method 2 where you set up the mode-tilt angle in the Fiber Coupling analysis window, this approach applies the mode-tilt angle through the CB surface in the Lens Data Editor. This makes it easy to access the tilt parameter and can be exposed as a variable for optimization.

In this method, we will first enter a CB surface in front of the Image surface. Assign Tilt X = 3.8 degrees. This is to introduce a tilt to the local Z-axis, which subsequently tilts the Image plane and the receiving fiber mode by 3.8 degrees. Set the Image plane to the Tilted surface type and set its Tangent Y = 0.140541. This corresponds to an 8-degree tilt from the already 3.8-degree tilted local Y axis. Now the angle between the incoming ray and the Image surface normal is 11.8 degrees— the desired angle of incidence. You can see the coupling efficiency goes back up to 88.2% when checking Use Polarization. This value is very close to what was achieved previously in the normal cleaved-fiber case.

## Method 2: Using Tilted Image surface combined with mode-tilt angle in the Fiber Coupling tool

In this method, the Image surface is again set to the Tilted surface type; however, instead of giving it an 8-degree tilt, we will assign Tangent Y = 0.209005 (approximately an 11.8-degree tilt away from the Y-axis). This sets the angle between the incoming beam and the angled-facet normal at 11.8 degrees, which is our desired angle of incidence.

After refraction, the beam forms an 8-degree angle with the angled-facet normal. One thing to keep in mind is that the Tilted surface type does not impact the local coordinate system. This means the local Z-axis at the Image plane remains parallel to the incoming beam, thereby forming a 3.8-degree angle from the refracted beam. To account for this, in the Fiber Coupling tool, we need to tilt the fiber mode by 3.8 degrees to align it along the refracted beam. This can be done by going to Analyze…Fiber Coupling…Single Mode Coupling. Under the Settings drop down, enter 3.8 degrees in the “Tilt About X (deg)” field. This will tilt the fiber mode 3.8 degrees clockwise from the local Z-axis, which then aligns the fiber mode with the refracted beam inside the fiber. After this mode tilt adjustment, you can see the coupling efficiency now goes back up to 88.2% when checking Use Polarization. This is very close to what we obtained using Method 1, and it is also very close to what was computed in the normal-cleaved fiber case.

## Method 3: Using CBs to introduce tilt combined with a negative mode-tilt angle in the Fiber Coupling tool

In this method, we will not use the Tilted surface type for the Image plane. We will first insert a Coordinate Break surface in front of the Image plane and set Tilt About X to 11.8 degrees. This provides the required 11.8-degree incident angle. Additionally, it tilts the local Z-axis by 11.8 degrees clockwise and tilts the receiving fiber mode by 11.8 degrees so it is along the surface normal. From the earlier calculation, we know that the refraction angle is 8 degrees. This means we need to tilt the fiber mode counterclockwise by 8 degrees to place it along the refracted beam path. Similar to Method 2, this fiber mode-tilt angle can be applied through the Analyze…Fiber Coupling…Single Mode Coupling…Settings menu. We will now set the “Tilt About X (deg)” field to -8 degrees. After this adjustment, you can see the fiber coupling efficiency is again back to 88.2% with the Use Polarization option checked.