Initial Conditions: Wavelength or Frequency

As indicated in the sections Optical Dispersion Models and Thermo-Optic Dispersion Models, the refractive index of real materials is often a function of the vacuum wavelength or frequency of the propagating rays.

In the Geometrical Optics interface, you can make the released rays monochromatic or polychromatic. If the released rays are polychromatic, you can either specify their frequency ν (SI unit: Hz) or their vacuum wavelength λ0 (SI unit: m). If the medium is not a vacuum, the actual wavelength of the rays in the medium λ is automatically computed by dividing the vacuum wavelength by the absolute refractive index.

To trace polychromatic light, in the settings for the Geometrical Optics interface, locate the section. From the list, select either or ; the default is .

Then, when releasing rays into the model (for example, with a Release or Release from Grid node), you can enter a value or expression for the wavelength or frequency directly, or sample multiple values from a distribution, by selecting an option from the list in the or section.


	In ray release features, different options that control the number of released rays or the number of values in a distribution are multiplicative, not additive. For example, if you use the Release node and set the Number of rays per release equal to 100, then release a Normal distribution of frequency values and set the Number of values to 1000, the total number of released rays will be 100,000.

Normal Distribution

The wavelength or frequency is sampled from the distribution function

where μ is the mean and σ is the standard deviation.

Lognormal Distribution

The wavelength or frequency is sampled from the distribution function

where M is the median and GSD is the geometric standard deviation, which are related to the arithmetic mean μ and the standard deviation σ by the relations

Uniform

The vacuum wavelength or frequency has a uniform probability within an interval bounded by the specified maximum and minimum values, and zero probability outside this interval.

Blackbody


	This subsection refers to the Blackbody option in the Initial Ray Frequency or Vacuum Wavelength section of most general-purpose ray release features such as Release and Release from Grid. These settings only affect the distribution of the spectral variable and do not affect, for example, the initial ray intensity or power. The dedicated Blackbody Radiation node also controls the ray direction distribution and the total emitted power; for more information, see Blackbody Radiation Theory.

The option samples the vacuum wavelength and frequency of released rays as if they were released from a blackbody radiation source at a specified temperature; that is, the probability distribution of wavelength or frequency follows Planck’s law.

To be able to speak of both wavelength and frequency at the same time, first define the dimensionless variable x (not to be confused with the spatial x-coordinate)

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h = 6.62607015 × 10-34 J·s is Planck’s constant,

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c = 299,792,458 m/s is the speed of light in a vacuum,

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kB = 1.380649 × 10-23 J/K is the Boltzmann constant,

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T (SI unit: K) is the surface temperature,

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ν (SI unit: Hz) is the ray frequency, and

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λ0 (SI unit: m) is the vacuum wavelength.

Then the dimensionless form of Planck’s law states that the normalized probability distribution of this variable is

It might be useful to exclude outliers corresponding to extremely large or small values of the wavelength or frequency when sampling from this distribution function. You can choose to specify maximum and minimum values of the wavelength or frequency, which are first converted to upper and lower limits on x; or you may choose to and then specify a fraction slightly less than 1, so that the lower and upper tails of the distribution are automatically excluded.