OptiLayer Targets: Conventional Targets

For each angle of incidence (AOI) you can specify a separate spreadsheet (first column is a spectral unit, for example, wavelength). On the contrast, in angular mode for each wavelength you specify a separate angular page (first column is AOI).

Additional features are target generator, interpolation of target function (increase the number of grid points), estimation of the required number of spectral points, User-Defined Target (UDT) and special editor for group delay/group delay dispersion (GD/GDD). OptiLayer provides wavelength grids of three different types.

• Target function values
• Target function tolerance values
• Target qualifiers (see the details here)

OptiLayer constructs a merit function automatically in the correspondence with the specified target data:

\[ MF^2=\frac 1K\sum\limits_{i=1}^K \frac 1L\sum\limits_{j=1}^L \left[\frac{S(X; \theta_i;\lambda_j)-\hat{S}(\theta_i;\lambda_j)}{\Delta_{i,j}}\right]^2,\]

where \(S\) is the theoretical spectral characteristic, \(\hat{S}\) is the target spectral characteristic, \(\{\lambda_j\}, j=1,…,L\) is the wavelength grid, \(\{\theta_i\}, i=1,…,K\) is the angular grid, \(\Delta_{i,j}\) are target function tolerance values, \(X\) is the vector of design parameters.

Example: target spreadsheet corresponding to a beamsplitter design: target \(R_s=50\%\), \(R_p=50\%\). Spectral range is from 620 nm to 680 nm, AOI=\(45^0\), 61 spectral points.

• Transmittance/Reflectance/Back Side Reflectance, s-, p- and average polarization;
• Absorptance, s-, p- and average polarization;
• Phase shift on reflection/transmission/back side reflection, s- and p- polarization;
• Differential phase shift on reflection/transmission/back side reflection (difference between phase shifts on s- and p-polarization)
• Group delay/Group Delay Dispersion (GD/GDD) for reflection and transmission, s- and p-polarization

Example (right panel): Rs=Rp=0 in the  range from 510 nm to 520 nm, Rs=Rp=100% in the range from 1000 nm to 1500 nm. Design tolerances equal to 0.1 in the vicinity of the wavelength 500 nm. It means that this spectral range is more important for the design problem. Wavelength grid is linear around the wavelength 500 nm and logarithmic in the spectral region from 1000 nm to 1500 nm.  The number of spectral points is 11 in the first spectral range and it is 128 in the second one.

\[ MF^2=\frac 1{11}\sum\limits_{j=1}^{11}\left(\frac{R_s(X;\lambda_j)}{0.1}\right)^2+\frac 1{11}\sum\limits_{j=1}^{11}\left(\frac{R_p(X;\lambda_j)}{0.1}\right)^2+\frac 1{128}\sum\limits_{i=1}^{128}\left(R_s(X;\lambda_i)-100\%\right)^2+\frac 1{128}\sum\limits_{i=1}^{128}\left(R_p(X;\lambda_i)-100\%\right)^2 \]

Logarithmic grid is more sparse in the longer wavelength range and more dense in the shorter wavelength region.