The Simple efficiency table for diffraction gratings allows the user to define the relative power in each diffraction order as a function of wavelength. Efficiency values are calculated during the raytrace by linearly interpolating across the table for the appropriate wavelength value. If the wavelength being traced lies outside the bounds of the values specified in the table, the nearest endpoint value is used. Specifying a single wavelength in the table will force all wavelengths to use the specified efficiency values. Note that there is no designation of angle, polarization, reflection or transmission dependence on efficiency with this model (see the Full Efficiency Table specification).
The Simple efficiency table specification can be accessed from the Grating tab of a surface dialog. The section on the right hand side of the dialog corresponds to the diffraction efficiency specification for the grating. In the drop-list box, select "Simple efficiency table (function of wavelength only)".
Although diffractive components are designed to operate in a particular diffraction order, diffractive components rarely diffract light into just a single order. In real hardware, the incident energy is partitioned into the intended order and a range of nearby unintended orders. To the stray light analyst, knowledge of the diffraction efficiencies in the various orders is therefore a matter of significance. Unfortunately, the analyst very often has no knowledge of the magnitudes of the diffraction efficiencies in any order for a variety of reasons; the vendor does not provide this data, the part has not been fabricated, there is a large variability in the surface structure leading to a large variation in the diffraction efficiencies, etc.
Rigorous diffraction theory involving numerical solutions to Maxwell’s equations is required to determine the efficiency with which light is redistributed among the various diffraction orders. However, this is a non-trivial calculation involving an exact description of the surface structure and a knowledge of the electrical, optical and bulk properties of the substrate and film(s). This type of numerical solver is not available within FRED itself, though it is implemented in a number of commercial software packages such as GSolver (www.gsolver.com).
For many applications, scalar diffraction theory can offer a more expedient calculation of the diffraction efficiencies than rigorous Maxwell's solvers at the expense of accuracy. Implicit in the scalar calculations is the assumption that the local period of the diffractive structure is much larger than the wavelength of the incident light (with extended scalar diffraction theory, the ratio of the wavelength of incident light to the local period can be as high as 0.5).
Reference: Swanson, G., “Binary Optics Technology: Theoretical Limits on the Diffraction Efficiency of Multilevel Diffractive Optical Elements”, MIT Technical Report 914 (1991)).
Scalar Diffraction Efficiency Calculator When the simple efficiency table option is selected, a scalar diffraction efficiency calculator can be used to populate the efficiency table with approximate values based on scalar diffraction theory for blazed gratings, kinoforms, binary optics, and sinusoidal gratings. The diffraction efficiency calculator dialog can be opened by right mouse clicking in the simple diffraction efficiency table spreadsheet and selecting "Set Diffraction Efficiency" from the list menu.
Note that this tool populates the existing table with efficiency values. All wavelength and orders desired to be included in the efficiency calculations should be added to the table prior to running the scalar diffraction efficiency calculator tool.
Diffraction efficiency for an Ideal Blazed grating For the Ideal Blazed grating type, the efficiency for all wavelengths at the reference order is set to 1 and the efficiency at all other orders is set to 0. This behavior is similar to the default behavior found in most optical design programs.
Diffraction efficiency and phase for a Binary Optic In a binary optic, the linear ramp phase function is approximately by P equally incremented constant phase steps. The diffraction efficiency at a specific order m and wavelength l is given by:
where m0 is the reference diffractive order, and a is given by (l0/l)*(d/dmax) where l0 is the reference wavelength, d is the blaze depth, and dmax is the optimum blaze depth.
The phase function is shown in the following diagram:
Diffraction efficiency and phase for a Kinoform In a kinoform, the phase function is a simple linear ramp. The diffraction efficiency at a specific order m and wavelength l is given by:
where m0 is the reference diffractive order, and a is given by (l0/l)*(d/dmax) where l0 is the reference wavelength, d is the blaze depth, and dmax is the optimum blaze depth.
The phase function for the Kinoform is the following:
Diffraction efficiency and phase for a sinusoidal grating In a sinusoidal grating, the phase function is a sine wave. The diffraction efficiency at a specific order |m| and wavelength l is given by:
where d is the blaze depth, and Dn is the absolute value of the refractive index difference across the interface. Note that the diffraction efficiency of a sinusoidal grating is substantially less than those of other grating types.
The phase function for the Sinusoidal Grating is shown in the following diagram:
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