Published on 31 October 2008

This article explains how fluorescence can be modeled in the non-sequential mode of ZEMAX using the Bulk Scattering Wavelength Shift capability.

The term fluorescence describes the process by which light is absorbed within an object and then re-emitted at a different (usually longer) wavelength. The light may also be (and usually is) re-emitted at a different angle. This process can be modeled in the non-sequential mode of ZEMAX using bulk scattering.

An example file has been setup to illustrate modeling of a fluorescent object in the non-sequential mode of ZEMAX. This file (Fluorescence Example.ZMX) is provided as a part of the ZEMAX installation, and may be found in the directory \ZEMAX\Samples\Non-sequential\Scattering\. In this simple system, a Source Ellipse is used to launch a collimated beam of rays towards a volumetric object in which bulk scattering may occur. Each ray has a wavelength of 0.450 mm, as defined by wavelength #1 in the system:

Wavelength definitions in the simple example file

Each ray may bulk scatter a maximum of once in the volume, as specified by the Bulk Scatter option in the Sources tab of the properties dialog box for the Source Ellipse:

How to limit each ray to only one bulk scattering event in a volume

The Sobol sampling method has also been chosen for launching rays from this source. The Sobol algorithm is more efficient at generating ray distributions with "optimally random" statistics, as compared to the random ray generation algorithm. More details on Sobol sampling may be found in the chapter of the ZEMAX manual entitled "Non-Sequential Components", as well as in the article entitled "Understanding Sobol Sampling".

Within the volume, bulk scattering occurs according to the Angle Scattering distribution, with a mean free path of 0.5 mm and a maximum angle for scattering of 10 degrees:

Parameters used to define fluorescence via bulk scattering

Under this tab, there is an option to modify the wavelength of any rays that undergo bulk scattering using the “Wavelength Shift” dialog box. The syntax to use for data entry into this box is “in, out, prob”, where “in” is the input wavelength number, “out” is the output wavelength number, and “prob” is the relative probability that the wavelength will be modified during a bulk scattering event. In this simple example, rays that start out with wavelength #1 will be shifted to wavelength #2 with a 100% probability, i.e. all of the input rays (with a wavelength of 0.450 mm) that undergo bulk scattering will also undergo a wavelength shift (to 0.650 mm). In general, inputs to the “Wavelength Shift” box are not restricted to a single wavelength transition, and not all rays which undergo bulk scattering are required to undergo a wavelength shift. You can read more about the variety of options available with the “Wavelength Shift” tool in the chapter of the ZEMAX manual entitled “Non-Sequential Components”. Using this tool, wavelength transitions which occur during fluorescence may be modeled in ZEMAX as a part of bulk scattering.

To test that the “Wavelength Shift” tool is working correctly, another rectangular volume object is included in the file, which has on its front face the BEAMSPLIT table coating:

Application of the beam-splitter coating on the front face of the rectangular volume object

This coating is defined in the default COATING.DAT file that is provided as a part of the ZEMAX installation:

TABLE BEAMSPLIT
ANGL 0.0
WAVE 0.45 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
WAVE 0.65 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0

You may read more about table coatings in the chapter of the ZEMAX manual entitled “Polarization Analysis”, as well as in the article entitled “How To Model a Dichroic Beam Splitter”.

According to the BEAMSPLIT table coating, all rays with a wavelength of 0.450 mm will be reflected, and all rays with a wavelength of 0.650 mm will be transmitted. This result can be confirmed in the Layout plot, when coloring rays in the plot by wavelength number:

Layout settings illustrating how to select rays by wavelength

As we can see in the Layout plot, all of the input rays which do not undergo bulk scattering are reflected from the front face of the rectangular volume object, while all of the rays which do undergo bulk scattering are transmitted:

Results in the Layout plot when rays are colored by wavelength

A filter string is also available to select those rays which undergo a wavelength shift during bulk scattering. The filter string is X_WAVESHIFT(i,j), where i represents the input wavelength number and j the output wavelength number. In our system, we may apply this filter string to the Layout plot:

Filter string used to isolate rays that undergo a wavelength shift during bulk scattering

to isolate those rays that only undergo a wavelength shift during bulk scattering:

Results in layout plot with use of filter string

You may read more about the use of filter strings in the chapter of the ZEMAX manual entitled “Non-Sequential Components”, as well as in the article entitled “How To Perform Stray Light Analysis”.