This page provides more information on the Overlap Analysis part of the Eigensolver analysis window.
An overlap is calculated between one of the entries in the mode list and an entry in the deck. The image plots in the screenshot above show the near field data for the currently selected mode in the mode list (on the left) and in the deck (on the right). The mode plot options are the same as those discussed in the Modal analysis section.
The OVERLAP ANALYSIS tab is comprised of the following parts:
- Option tabs - This allows the user to choose between Overlap calculations or to create/modify a Gaussian Beam as described below.
- Option settings - This is where the user specifies the parameters for each option.
- Modal area - A quantitative measure for the effective mode area. For a 2D z-normal Eigenmode Solver simulation region, It is defined as:
$$ \text{modal area } =\frac { (\int |H|^2 dxdy )^2}{\int |H|^4 dxdy} $$
(The modal areas for other orientations of the Eigenmode Solver are similarly defined.)
For more information about the overlap analysis calculation, please see Overlap analysis.
Overlap
Choosing the "Overlap" tab results in the following screen shot. Some of the parameters can be set through the List of commands. For more info, please visit Overlap analysis - FDE.
The parameters and buttons shown include:
- CALCULATE: pressing this button will calculate the overlap and the power coupling of the currently selected mode with the currently selected D-CARD. The D-CARD profile is offset in x, y and z by the amounts indicated in X SHIFT, Y SHIFT and Z SHIFT.
- OVERLAP: the result of the overlap. The overlap calculation gives the fractional power coupling from the D-CARD profile (E2,H2) into the mode (E1,H1). The overlap does not take into account reflections due to a mismatch in effective indices between the D-CARD profile and the mode. The overlap is given by the following formula.
$$\text{overlap} = Re\left[ \frac{(\int \overrightarrow{E_{1}}\times\overrightarrow{H_{2}^{*}}\cdot d\overrightarrow{S})(\int \overrightarrow{E_{2}}\times\overrightarrow{H_{1}^{*}}\cdot d\overrightarrow{S})}{\int \overrightarrow{E_{1}}\times\overrightarrow{H_{1}^{*}}\cdot d\overrightarrow{S}}\right] \frac{1}{Re(\int \overrightarrow{E_{2}}\times\overrightarrow{H_{2}^{*}}\cdot d\overrightarrow{S})} $$
For details, see Snyder and Love "Optical Waveguide Theory", Chapman & Hall, London, England, 1983.
- POWER COUPLING: the power coupling gives the total input coupling, taking into account both the mode overlap and the mismatch in effective indices between modes. In simple cases, this reduces to the product of the OVERLAP and the Fresnel transmission.
- SHIFT BEAM CENTER: clicking this allows you to offset the D-CARD profile by X SHIFT, Y SHIFT and Z SHIFT.
- RECENTER: You can use this pulldown button to re-center the X SHIFT, Y SHIFT and Z SHIFT to (0,0,0), or such that the center of the D-CARD profile coincides with the center of the currently selected mode. It is a good idea to do the latter before trying to optimize the position of the X SHIFT, Y SHIFT and Z SHIFT.
- X SHIFT: the actual shift amount in the x direction.
- Y SHIFT: the actual shift amount in the y direction.
- Z SHIFT: the actual shift amount in the z direction.
- OPTIMIZE POSITION: this button will try to calculate the optimum values for X SHIFT, Y SHIFT and Z SHIFT to maximize the overlap between the currently selected D-CARD profile and the currently selected mode.
Beam
The Beam tab allows you to modify the default Gaussian beam for overlap calculations, as well as create Gaussian beams in the deck which will be accessible from the scripting environment. There are two types of Gaussian beams, and the user can choose between the scalar approximation for the electric field or the fully vectorial beam profile option:
For the Gaussian Beam Source, please see the Gaussian source
Fully vectorial beam
- NA: This is nsin(α) where n is the refractive index of the medium in which the source is found and α is the half angle as shown in the figure below. Please note that the index will not be correctly defined in dispersive media and lenses should only be used in non-dispersive media. The refractive index for the source is determined at X, Y (and Z).
- Distance from focus: The distance d from focus as shown in the figure below. A negative distance indicates a converging beam and a positive distance indicates a diverging beam.
- Fill lens: Checking this box indicates that the lens is illuminated with a plane wave which is clipped at the lens edge. If FILL LENS is checked, then it is possible to set the diameter of the thin lens (LENS DIAMETER) and the beam diameter prior to striking the lens (BEAM DIAMETER), as shown in the figure below. A beam diameter much larger than the lens diameter is equivalent to a filled lens.
- Number of plane waves: This is the number of plane waves used to construct the beam. The beam profile is more accurate as this number increases but the calculation takes longer.
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Note : References for the thin lens source The field profiles generated by the thin lens source are described in the following references. For uniform illumination (filled lens), the field distribution is precisely the same as in the papers. For non-uniform illumination at very high NA (numerical aperture), there are some subtle differences. This is due to a slightly different interpretation of whether the incident beam is a Gaussian in real space or in k-space. This difference is rarely of any practical importance because other factors such as the non-ideal lens properties become important at these very high NA systems
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Scalar approximation
- Define Gaussian beam by : This menu is used to choose to define the scalar beam by the WAIST SIZE AND POSITION or the BEAM SIZE AND DIVERGENCE ANGLE.
If WAIST SIZE AND POSITION is chosen, the options are:
- Waist radius: 1/e field (1/e2 power) radius of the beam for a Gaussian beam, or a half-width half-maximum (HWHM) for the Cauchy/Lorentzian beam.
- Distance from waist: The distance, d, as shown in the figure below. A positive distance corresponds to a diverging beam, and a negative sign corresponds to a converging beam.
If BEAM SIZE AND DIVERGENCE ANGLE is chosen, the options are:
- Beam radius: 1/e field (1/e2 power) radius of the beam for a Gaussian beam, or a half-width half-maximum (HWHM) for the Cauchy/Lorentzian beam.
- Divergence angle: Angle of the radiation spread as measured in the far field, as shown in the figure below. A positive angle corresponds to a diverging beam and a negative angle corresponds to a converging beam.
For both types of beams:
- The polarization angle is defined with respect to the horizontal-axis for normal incidence fields. When the incidence is off-axis, the polarization angle should be 0 for p-polarized light and 90 for s-polarized light.
- The refractive index is the refractive index of the homogenous material in which the Gaussian beam is found.
- The angle theta is the angle between the normal-axis and the direction of propagation.
- The angle phi is the angle between the direction of propagation projected onto the Eigenmode Solver plane and the horizontal-axis.
- Create Beam: this button will add a new Gaussian beam to the deck based on the above specifications.