How to simulate exit pupil expander (EPE) with diffractive optics for augmented reality (AR) system in OpticStudio: part 2

In this article, an example is demonstrated to set up an exit pupil expander (EPE) using the RCWA tool for an augmented reality (AR) system in OpticStudio. The planning of gratings in k-space (optical momentum) is first explained, and the details of setting up each grating is discussed.

Authored By Michael Cheng

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Introduction

This article is part 2 of 3 articles, which builds the exit pupil expander system with a waveguide and 3 gratings. Links to other parts are listed below for reader’s convenience.

How to simulate exit pupil expander (EPE) with diffractive optics for augmented reality (AR) system in OpticStudio: part 1

How to simulate exit pupil expander (EPE) with diffractive optics for augmented reality (AR) system in OpticStudio: part 3

How to simulate exit pupil expander (EPE) with diffractive optics for augmented reality (AR) system in OpticStudio: part 4

Waveguide and first (in-coupling) grating

The first step is to set up the waveguide and first grating as shown in Figure 1. Users can open the attached “step1_waveguide_and_first_grating.zar” to check the system at this stage.


Figure 1 Waveguide and first grating

Key points to know when checking this file:

1.    The waveguide is built with a Rectangular Volume (Object 1). 

2.    The grating of the waveguide is built with a Diffraction Grating object (Object 2). In the Object Property settings, the Diffraction Grating is set with the diffractive DLL “srg_trapezoid_RCWA.dll”, as shown in Figure 2. This will act as a binary grating which has a shape shown in Figure 3. The DLL calculates diffraction efficiency with the RCWA method for surface-relief gratings. See Simulating diffraction efficiency of surface-relief grating using the RCWA method for more information about this DLL.


Figure 2 RCWA DLL is used for simulating the gratings in this system.


Figure 3 The grating shape used for RCWA.

3.    The Diffraction Grating is made of the same material as the Rectangular Volume. Additionally, the Diffraction Grating is placed completely inside the waveguide, as shown in Figure 4. Face 1 of the Diffraction Grating overlaps the Rectangular Volume’s Face 1. Note the grating structure is assumed to be on the Face 1 on the Diffraction Grating, not the whole volume of the object. The diffractive surface is considered as having virtually no thickness in the ray-tracing model. The real micro-structure is only considered in the RCWA core which calculates efficiency and polarization for diffracted rays.


Figure 4 The object Diffraction Grating is defined inside of the Rectangular Volume and its Face 1 overlaps to Face 1 of the Rectangular Volume.

4.    The Diffraction Grating object must be defined after the Rectangular Volume in the Non-Sequential Component Editor. By doing this, the properties of the Diffraction Grating take higher priority. This is a result of the nesting rule. See Improving non-sequential ray tracing speeds with nested and Boolean objects for more information.

5.    The parameter “Only these orders” of the RCWA DLL is set to 8, which means only order T-1 (Order -1 in transmission) will be traced. This is a trick to make the system simulation faster. When a ray hits the grating, it should split into several diffraction orders. However, in this system, only the T-1 order is required. More details about this parameter can be found in Simulating diffraction efficiency of surface-relief grating using the RCWA method.

6.    The Face 0 (Side Face) of the Rectangular Volume is set to Absorbing, which makes rays absorbed at the edge of the waveguide, as shown in Figure 5. This also makes the simulation more efficient.

7.    The Source Ellipse launches a collimated beam which is normally incident on the first grating. This is a testing beam representing light from the central field of the image source in light engine. There should be a light engine that converts the image source (ex. DMD, LCoS, LCD, …) to be afocal before entering the first grating.


Figure 5 Face 0 (Side Face) of the Rectangular Volume is set to Absorbing.

Second (turning) grating

In the second step, a turning grating is added. This grating expands the incident beam in one direction and turns its propagation direction by 90 degrees. The system file at this step is saved as “step2_turning grating.zar”. 


Figure 6 A turning grating added to the system.

Key points to know when checking this file:

1.    The grating is built with a Boolean Native (Object 6) with two parent objects. The Diffraction Grating object (Object 5) provides the diffraction effect while the Extruded object (Object 4) provides the required shape. This is how users can make a grating with any desired shape.

2.    The Extruded object reads a UDA file located in “\Documents\Zemax\Objects\Apertures” and extrudes the 2D aperture to form a 3D volume. The UDA file is defined as shown in Figure 7.


Figure 7 UDA defined in the system.

3.    The parameter “Rotate Grating” for the diffraction DLL in Object 5 is set to 45 degrees. This means the grating lines are aligned to be from the top left to bottom right, and the grating is periodic going from the bottom left to the top right.

4.    There are two ways a ray can be diffracted in the turning grating as shown in Figure 8. Note the Start Order and Stop Order parameters of the DLL in Object 5 is set to -1 and +1, so the diffraction order -2 and +2 or higher order are ignored.

5.    In “System Explorer > Non-Sequential”, the 3 parameters Maximum Intersections Per Ray, Maximum Segments Per Ray, and Minimum Relative Ray Intensity are modified to a larger number so that the ray tracing will not stop in the turning grating. Without these modifications, rays may reach the minimum energy limit when tracing the split rays and wrongly stop.


Figure 8 There are two main ways that a ray can be diffracted inside of the second (turning) grating.

Third (out-coupling) grating and detector

The final step is to add the third grating and a detector to detect the out-coupled light. When rays hit the third grating, they split. Part of energy goes to diffraction order +1 and leaves the waveguide. Another part of the energy keep going in the same direction, which is the zero order. The system file at this step is saved as “step3_out-coupling grating.zar”.


Figure 9 Exit pupil expander with 3 gratings.

Key points to know when checking this file:

1.    User Defined Object (Object 7) with “DiffractionGrating.DLL” is used instead of the Diffraction Grating object, because a rectangular-shaped grating is desired. It is also possible to write a user-defined object for more complicated and flexible shapes.

2.    The detector (Object 8) is supposed to be used for checking the energy distribution at the exit pupil (eye box). One of the important goals in designing this kind of system is to make sure the energy is uniformly distributed in pupil space. Note the detector is 15 mm away from the waveguide. The distance can be considered as the eye relief of the system.

3.    This Source Ellipse represents light from the central field in this system. To simulate light from other fields, the Source Ellipse need to be modified as below. The file with the following modifications is saved as “step3_out-coupling grating_2.zar”

•    Z Position = 0
•    Object Property > Source > Pre-Propagation = -10
•    Change Tilt About X and Tilt About Y for your desired angle. For example, light from an X angle of 10 degrees has an energy distribution as shown in Figure 11.


Figure 10 Energy distribution at the extended pupil location from the central field.


Figure 11 Energy distribution at the extended pupil location from a field angle of 10 degrees in the X direction.

Previous Article: How to simulate exit pupil expander (EPE) with diffractive optics for augmented reality (AR) system in OpticStudio: part 1

Next Article: How to simulate exit pupil expander (EPE) with diffractive optics for augmented reality (AR) system in OpticStudio: part 3

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