Photoluminescence is the phenomenon where photons are absorbed in a medium and part of the absorbed energy is reemitted as photons. Broadly speaking, there are two categories of photoluminescent emission, fluorescence and phosphorescence. Each of these can be modeled in OpticStudio using the photoluminescence bulk scattering model available in Non-Sequential mode.

Authored By Shawn Gay

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Introduction

Photoluminescence is the phenomenon where photons are absorbed in a medium and part of the absorbed energy is reemitted as photons. Broadly speaking, there are two categories of photoluminescent emission, fluorescence and phosphorescence. We will show how to model these in OpticStudio using the photoluminescence bulk scattering model available in Non-Sequential Mode.

NOTE: The phosphors and fluorescence model was updated in OpticStudio 17. For information on model parameters and usage, please refer to the article entitled "Modeling photoluminescence in OpticStudio: A photoluminescent solar concentrator".

OpticStudio's photoluminescence model

The photoluminescence model in OpticStudio is phenomenological. The software does not model the details of what happens to a photon, rather, rays are probabilistically absorbed, downconverted, and scattered based on a set of user provided spectra. For a single ray entering a photoluminescent material, the algorithm can be summarized as follows:

1. Based on the path length of the rays associated with the incident photons probabilistically determine if the ray is:
   • Absorbed (dependent on the wavelength of the photons and the material absorption spectrum)
   • or Mie scattered by the host material
2. If the ray is absorbed, probabilistically determine whether a photoluminescent transition is excited using the material excitation spectrum.
3. If an excitation event occurs, probabilistically calculate the downconverted photon wavelength using the material emission spectrum and scatter the downconverted photon uniformly into the 4π sphere of directions. If no excitation event occurs, the photon is scattered using Mie scattering as determined by the mean diameter of scattering particles.

Thus, three spectra must be specified to fully determine the photoluminescence model:

1. Absorption spectrum
2. Emission spectrum
3. Quantum Yield spectrum

Setting it up in Non-Sequential mode

Any Non-Sequential volume object can be modeled as photoluminescent in OpticStudio. To add photoluminescent scattering, navigate to the Volume Physics section of the object’s Non-Sequential editor settings as shown below. There are two Photoluminescence models: Basic and Standard. Standard is recommended in all cases and the Basic model is only supported for backwards compatibility.

Figure 1: Photoluminescence Model Settings in OpticStudio

You will need to select spectrum files for the absorption and emission spectra and the quantum yield spectrum. Additionally, you will need to specify a few parameters to set up the Mie scattering and photoluminescent mean free path.
One important thing to note is that the rays traced in the simulation can be allowed to undergo multiple absorption/emission/scattering events. To select between single-scattering or multiple-scattering, on each source navigate to the Sources section of the objects Non-Sequential Component Editor settings and in the Raytrace group box, select either “Once” or “Many” for the bulk scatter behavior.

A second thing to keep in mind is that the Photoluminescence model in OpticStudio requires all sources in the system to use System Wavelengths for the source color. If even one source has a source color other than System Wavelengths, photoluminescent scattering will be turned off for all materials.

Figure 2: Source Settings Affecting the Photoluminescence Model

And that’s all it takes to simulate a photoluminescent material in Non-Sequential mode. Of course, the results of the simulation are critically dependent on the material properties, so it is reasonable to expect that you might need measured data for the spectra used as input.

Viewing and editing spectrum files

In the Libraries ribbon, there is a button group called “Phosphors and Fluorescence”. You can use the actions available through these buttons to view and edit input spectrum files for use in the Photoluminescence model.

Figure 3: Ribbon Bar Buttons for Viewing/Editing Photoluminescence Spectra

If you select View Spectrum File, you will see an analysis window like the following:

Figure 4: Example Absorption Spectrum Displayed in the Spectrum Viewer

In the settings for this analysis, you can select the spectrum type, the specific data file and, for emission spectra, the excitation wavelength.

Figure 5: Settings Available in the Spectrum Viewer

File formats

Absorption Spectrum

The absorption spectrum represents the probability that a photon of a certain wavelength is absorbed by a molecule. This spectrum is used to calculate a factor applied to the intensity of the ray. If the factor is zero, then the ray is not down-converted but is scattered. The absorption spectrum defined in a .zas text file stored in {Zemax}\Objects\Photoluminescence Files. This file contains pairs of double precision floating point wavelength and probability values that define the absorption spectrum. The file header specifies the number of data pairs in the file and a wavelength unit flag (0 for microns and 1 for nanometers). Absorption spectra must contain at least five wavelengths.

   !comment
   #_of_points wavelength_unit_flag
   wavelength probability

If the wavelength of a ray falls outside the absorption spectrum range, then it will not be absorbed and will just Mie scatter.

Emission Spectrum

The emission spectrum is the intensity spectrum of the photoluminescent emission. This spectrum is used to calculate a probability spectrum for emission of certain wavelength of light. From this probability spectrum any down-converted rays are probabilistically assigned a new wavelength. The ZES files stored in {Zemax}\Objects\Photoluminescence Files contain a grid of values that define several emission spectra for different incident wavelengths:

   !comment
   #_emission_wavelengths #_incident_wavelengths wavelength_unit_flag
   incident_wavelength_1 ... incident_wavelength_n
   emission_wavelength_1 relative_power ... relative_power
   emission_wavelength_2 relative_power ... relative_power

If five or fewer incident wavelengths are defined then then intermediate values will be linearly interpolated. If more than five incident wavelengths are defined, then a cubic spline interpolation will be used.

Quantum Yield Spectrum

The quantum yield spectrum is the efficiency of the down-conversion process but does not take into account the down-conversion effect on the ray intensity. This is included internally to OpticStudio by multiplying the down-converted ray intensity by the ratio of the incident and emitted wavelengths, known as the Stokes shift:

Emitted intensity = Incident intensity * A * Q * (Incident wavelength/Emitted wavelength)

where A is the absorption coefficient and Q is the quantum efficiency. The ZQE files stored in {Zemax}\Objects\Photoluminescence Files contain pairs of values that define several emission spectra for different incident wavelengths:

   !comment
   #_of_points wavelength_unit_flag
   wavelength yield

Assumptions and conventions

There are a few assumptions and conventions to keep in mind:

• Emission spectra must contain at least five emission wavelengths.
• A ray will only be shifted to a longer wavelength than its original value. Up conversion to shorter wavelengths is not possible.
• If a ray is absorbed, but its wavelength is outside the range of the excitation spectrum its flux will be set to zero and it will be terminated.
• For quantum yield spectra, if only one yield value is listed in the ZQE file then it is used for all wavelengths.
• Only sources that use system wavelengths are compatible with the photoluminescence model. Selecting a source that does not use system wavelengths will prevent the photoluminescence model from being applied for all sources in the system.

Example file

A simple hypothetical example is provided using the three sample spectra provided in OpticStudio. The Non-Sequential system has three objects, a ray source, a rectangular volume with the photoluminescent model applied, and a color detector.

Figure 6: Sample 1 Absorption Spectrum

Figure 7: Sample 3 Quantum Yield Spectrum

Figure 8: Sample 1 Emission Spectrum

Running a ray trace with 1E6 analysis rays yields the following Flux vs Wavelength result:

Figure 9: Flux vs Wavelength Resulting from 1E6 Rays

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