Beam splitters are popular optical devices which can be used to divide incident optical energy into reflected and transmitted beam paths. The three general types of beam splitters are:

• Cube beam splitters
• Plate beam splitters
• Pellicle beam splitters

Beam splitters divide energy into the reflecting and transmitting paths based on various factors including:

• Angle of incidence
• Polarization state
• Wavelength

Each of these types of beam splitters can be modeled in a variety of ways in ZEMAX in both sequential and non-sequential mode. The Knowledge Base article “How to Model a Beam Splitter in Sequential ZEMAX” demonstrates how to model a generic cube beam splitter in sequential mode.

This article demonstrates how to model a dichroic (i.e. wavelength-dependent) plate beam splitter in non-sequential mode.

Dichroic coatings are easily modeled in ZEMAX using table coatings. This article assumes that you are already familiar with the basics of modeling ideal coatings in ZEMAX. If you are not, take a look at the Knowledge Base article “How To Model A Partially Reflective and Partially Scattering Surface” before proceeding.

There are a variety of dichroic beam splitters available from various vendors. The dichroic beam splitter that we will be modeling is based on one that can be purchased from CVI Laser, LLC. The dichroic beam splitters available for purchase from CVI can be assigned any one of a number of dichroic coatings that are available.

The beam splitter that we will be modeling is a Short Wave Pass (SWP). This particular type of beam splitter is characterized by high transmission (i.e. low reflectivity) at short wavelengths along with low transmission (i.e. high reflectivity) at longer wavelengths. Here is a transmission vs. wavelength curve for a typical SWP dichroic coating:

Full details on CVI Laser’s SWP dichroic beam splitters can be found on this webpage:

            http://www.cvilaser.com/Catalog/Pages/Template2.aspx?pcid=87&filter=0

Dichroic coatings are characterized by a pass band (wavelength region of high transmission/low reflectivity), a stop band (wavelength region of low transmission/high reflectivity) and a transition region (the wavelength region between these two bands):

For more information on how dichroic beam splitters work, please see the following document:

            http://www.cvilaser.com/Common/PDFs/Dichroic_Beamsplitters_Discussion.pdf

For the purposes of modeling simplicity, we are going to model a somewhat idealistic version of a typical SWP dichroic beam splitter from CVI. Our modeling assumptions will include:

• We do not have access to the full coating prescription data
• The dichroic coating with be polarization insensitive
• The transmission in the pass band will be 100%
• The reflection in the stop band will be 100%
• We will not do any modeling of the transition region

It is important to note that these idealistic assumptions are certainly not required in ZEMAX. As you will see, ZEMAX’ coating modeling capabilities allow for very realistic coating modeling. We are making the above assumptions simply to simplify the work that we will have to do in this case.

The SWP dichroic beam splitter that we will model will have the following properties:

• Substrate:  N-BK7
• Clear Aperture:  1”
• Thickness:  0.25”
• Dichroic coating on front surface of substrate
• Pass wavelength:  0.400 mm
• Stop wavelength:  0.525 mm
• The rear and edge surfaces of the substrate will be coated with an ideal 1% reflection/99% transmission anti-reflection (AR) coating

So that you can focus on the specific modeling capabilities introduced by this article, please download the attached non-sequential ZEMAX file on the last page of this article:

FILE:  “Dichroic_BS_Start.ZMX”

This starting point includes a Source Ellipse, a Standard Lens (to model the plate beam splitter) and two Detector Rectangles (one to characterize the pass band and one to characterize the stop band):

To model the dichroic coating, we will use a table coating in ZEMAX. Of the different coating formats available in ZEMAX, table coatings are among the most flexible. Table coatings allow the transmission, reflection and absorption properties of a coating to be wavelength, polarization and angle of incidence dependent. Phase rotations can also be modeled by table coatings. All of this can be done without knowing the specific material properties of the coating being modeled. This is useful because many coating vendors are unwilling to provide specific coating prescriptions. They are usually more willing, however, to provide coating performance information (i.e. relative transmission/reflection data at various wavelengths/angles of incidence).

The table coating format in ZEMAX is compatible with the output from The Essential Macleod thin film software (www.thinfilmcenter.com).

For table coatings, data is normally specified at multiple angles of incidence. At each angle of incidence specified, the polarization dependent reflection and transmission for several wavelengths is specified. The syntax for table coatings is as follows:

where:

Rs = Reflection coefficient for S polarization

Rp = Reflection coefficient for P polarization

Ts = Transmission coefficient for S polarization

Tp = Transmission coefficient for P polarization

The remaining parameters are the phase rotation angles. These are optional and, in our case, can be left off. If the angles are omitted, no phase change will be introduced by the coating.

Since the reflection and transmission coefficients can be defined separately for S and P polarization states, table coatings can be used to model polarizing beam splitters in ZEMAX.

Given the geometry of our system, we are only interested in one angle of incidence (45 degrees) and two wavelengths (0.400 and 0.525 mm). As stated previously, we are going to assume that our dichroic coating is polarization insensitive (for simplicity). As such, the amount of reflection will be the same for S and P polarization orientations (as will the amount of transmission). Since the 0.400 mm wavelength is in the pass band, the transmission at this wavelength should be 100% and the reflection should be 0%. Likewise, since the 0.525 mm wavelength is in the stop band, the transmission at this wavelength should be 0% and the reflection should be 100%. As such, the resulting table coating is:

TABLE SWP

ANGL 45

WAVE 0.400 0.0 .0.0 1.0 1.0

WAVE 0.525 1.0 1.0 0.0 0.0

Using a text editor (such as Notepad or EditPlus2), enter in this table coating.

We will also need to setup our ideal AR coating. Recall that the AR coating we are going to model in this case is one which reflects 1% and transmits 99%. Since we are not modeling any absorption, wavelength or angle of incidence dependence for this coating, we can use the simple I.transmission ideal coating format:

COAT I.99

Add this coating to your file as well.

Once you have defined the two coatings, save your coating file using an appropriate filename (such as DICHROIC.DAT) in the appropriate directory. Remember that the coating file must end in the extension .DAT and must be stored in the same directory as your other coating files (the default is {zemaxroot}/Coatings/).

With the necessary coatings defined, we can now apply the coatings to our plate beam splitter.

First, open the menu option, “System » General” and then choose the “Files” tab. Select the coating file that you just saved in the “Coating File” drop-down box:

To apply the coatings, open the Object Properties dialog for object 2 and then select the “Coat/Scatter” tab. The Coat/Scatter tab will initially show the coating and scattering settings for face group 0, the side faces of the plate beam splitter. For these faces, we want to apply our I.99 ideal AR coating:

Do the same for face group 2, the back face of the plate:

Lastly, apply our dichroic coating, SWP, to face group 1, the front face of the beam splitter:

With the appropriate coatings applied, we can now analyze the performance of our dichroic beam splitter. The primary effect of this type of beam splitter is the separation of light based on wavelength. To see this in our layouts, set the “Color Rays By” setting in both the 3D Layout and Shaded Model Layout to “Waves”:

The differing colors of rays drawn in the layouts now will indicate rays of different wavelengths. The coloring of the rays on the layouts clearly demonstrates that our dichroic beam splitter is working correctly. The blue rays (representing wavelength 1 at 0.400 mm) transmit through the beam splitter since they are in the pass band. The green rays (representing wavelength 2 at 0.525 mm) reflect off of the beam splitter since they are in the stop band.

Run an analysis trace in the Ray Trace/Detector Control dialog using the following settings:

Looking at the resulting display in the Detector Viewers, it is clear that our initial 1 Watt of energy is being divided nearly equally among the two beam paths:

We have used the dichroic table coating that we created successfully at two wavelengths, 0.400 mm and 0.525 mm. What about the performance of this coating at other wavelengths?

Open the Wavelength Data dialog and add wavelengths to extend our sampling spectrum as shown:

Open the menu option, “Analysis » Coatings » Transmission vs. Wavelength”. Change the settings of this analysis to show the coating performance of our dichroic coating at an angle of incidence of 45 degrees:

Here is the resulting plot:

As you can see, ZEMAX is modeling the transition region in a linear fashion while, in reality, the transition region adjusts from high transmission to low transmission in a very non-linear fashion. In this case, the transition region is modeled linearly due to the limited amount of data that we used to define the SWP table coating. For table coatings, the transmission and reflection for wavelength values between wavelengths defined in the table (i.e. wavelengths between 0.400 mm and 0.525 mm) are determined via linear interpolation. In other words, as the wavelength increases from 0.400 mm, the transmission drops in a linear fashion until it reaches 0 at 0.525 mm. If we wanted to model the transition region more accurately, we would just have to add the transmission and reflection coefficients for additional wavelengths between 0.400 mm and 0.525 mm in our table coating definition.

Notice that for wavelengths outside of the range of wavelengths defined in the table coating (i.e. wavelengths shorter than 0.400 mm as well as wavelengths longer than 0.525 mm), the transmission remains constant in these regions. For wavelengths that fall outside of the range of wavelengths defined in the table coating, no extrapolation is done. ZEMAX will simply use the transmission and reflection coefficients for the nearest defined wavelength. Thus, we would have to add the transmission and reflection coefficients for the additional wavelengths to expand the wavelength band of our table coating accurately.

For the dichroic beam splitter that we have been modeling, the angle of incidence of all rays incidence on the dichroic coating is 45 degrees given the orientation of our plate beam splitter as well as the fact that our source is collimated. How would sources that are not collimated (i.e. with rays that have angles of incidence on the beam splitter other than 45 degrees) be handled?

Open the menu option, “Analysis » Coatings » Transmission vs. Angle”. Change the settings to show the performance of our dichroic coating:

Here is the resulting transmission vs. angle curve:

Notice that the coating performance is the same across all angles of incidence. While, in reality, this is highly unlikely, it is the case with our SWP coating because we only defined one angle of incidence in our table. The rules defined above for wavelength data apply in the same fashion for angle of incidence data. So, to more accurately model the angle of incidence dependence of our dichroic coating, we would have to add the transmission and reflection coefficients for additional angles of incidence.

Similarly, all of the plots generated by ZEMAX suggest that the performance for S and P polarization states is the same. In reality, the amount of transmission and reflection for a dichroic coating is not just dependent upon wavelength and angle of incidence, but also polarization state. When defining our SWP table coating, we chose not to define different transmission and reflection coefficients for the S and P polarization states though we certainly could have.

Imagine that we wanted to more accurately model our SWP dichroic coating at 45 degrees of incidence. By adding more data to our table coating, we could model:

• The transition region
• The polarization dependence of the coating
• The actual amount of transmission and reflection (rather than assuming that they are either 100% or 0%)

If this is our SWP coating performance at an angle of incidence of 45 degrees:

Here is a more detailed version of the corresponding table coating:

TABLE SWP_REALISTIC

ANGL 45

WAVE 0.350 0.06 0.00 0.94 1.00

WAVE 0.355 0.02 0.00 0.98 1.00

WAVE 0.360 0.01 0.00 0.99 1.00

WAVE 0.365 0.06 0.00 0.94 1.00

WAVE 0.370 0.04 0.00 0.96 1.00

WAVE 0.375 0.00 0.00 1.00 1.00

WAVE 0.380 0.03 0.00 0.97 1.00

WAVE 0.385 0.07 0.00 0.93 1.00

WAVE 0.390 0.04 0.00 0.96 1.00

WAVE 0.395 0.00 0.00 1.00 1.00

WAVE 0.400 0.03 0.00 0.97 1.00

WAVE 0.405 0.07 0.00 0.93 1.00

WAVE 0.410 0.05 0.00 0.95 1.00

WAVE 0.415 0.00 0.02 1.00 0.98

WAVE 0.420 0.03 0.03 0.97 0.97

WAVE 0.425 0.07 0.02 0.93 0.98

WAVE 0.430 0.06 0.00 0.94 1.00

WAVE 0.435 0.05 0.02 0.95 0.98

WAVE 0.440 0.07 0.04 0.93 0.96

WAVE 0.445 0.08 0.06 0.92 0.94

WAVE 0.450 0.07 0.05 0.93 0.95

WAVE 0.455 0.15 0.00 0.85 1.00

WAVE 0.460 0.25 0.02 0.75 0.98

WAVE 0.465 0.21 0.13 0.79 0.87

WAVE 0.470 0.08 0.20 0.92 0.80

WAVE 0.475 0.70 0.16 0.30 0.84

WAVE 0.480 0.90 0.06 0.10 0.94

WAVE 0.485 0.98 0.13 0.02 0.87

WAVE 0.490 0.98 0.53 0.02 0.47

WAVE 0.495 0.99 0.84 0.01 0.16

WAVE 0.500 0.99 0.90 0.01 0.10

WAVE 0.505 1.00 0.94 0.00 0.06

WAVE 0.510 1.00 0.96 0.00 0.04

WAVE 0.515 1.00 0.97 0.00 0.03

WAVE 0.520 1.00 0.97 0.00 0.03

WAVE 0.525 1.00 0.97 0.00 0.03

WAVE 0.530 1.00 0.97 0.00 0.03

WAVE 0.535 1.00 0.97 0.00 0.03

WAVE 0.540 1.00 0.97 0.00 0.03

WAVE 0.545 1.00 0.965 0.00 0.035

WAVE 0.550 1.00 0.96 0.00 0.04

On the left below is the more detailed version of the SWP coating. On the right is our original idealized SWP coating:

Obviously, the coating detail has improved greatly. The coating could be further improved by adding even more data points if desired.

This article has demonstrated how table coatings can be used to model dichroic beam splitter coatings. Using the ray splitting capabilities of non-sequential mode, the wavelength separation that results from dichroic coatings can easily be modeled. Keep in mind that table coatings, while very useful and flexible, are only as accurate as the data used to create them. The more wavelength and angle of incidence data provided, the greater the accuracy these coatings will have. Table coatings allow for different transmission and reflection coefficients to be specified for the S and P polarization states. This provides for accurate coating modeling when coatings are used but the coating prescription data is not available.