Bmix_h.txt

Bmix calculates the properties of biaxial crystals for propagation in any direction including out of the principal planes (in contrast to Qmix where propagation in a principal plane is assumed).  The calculations are based on the d-tensor and Sellmeier listed in Qmix. Phase matching curves are computed along with the associated effective nonlinearity, walkoff, and acceptance angles.  The purple circle on the phase matching plot indicates the location of the optic axes in the x-z plane. Parallel propagation directions (k vectors) of the three interacting waves red1, red2, and blue are assumed.

All angles are in the optical frame difined by nx<ny<nz. Phase matching angles theta and phi are customarily measured from the z axis toward the x-y plane for theta and from the x-z plane toward the y-z plane for phi.  This is the case for Bmix if the Rotation Axis Z is selected as the rotation axis.  Unfortunately, with this convention, plots of the index matching loci are often double valued.  To avoid this, select the X or Y Rotation Axis. When X is selected, theta is measured from the x axis and phi is measured y-toward-z.  When Y is selected, theta is measured from the y axis and phi is measured z-toward-x. The information is the same no matter which axis is chosen, but the display is easier to interpret if the plots are single valued.

The walkoff angles are specified for the two eigenpolarizations, lo and hi.  Walkoff of each is in the direction of the eigenpolarization of the optical E field so lo and hi walkoff directions are orthogonal. The total walkoff is (lo^2 + hi^2)^.5. Walkoffs are not specified for the three separate wavelengths because they are approximately independent of wavelength.  Ref: F. Brehat and B. Wyncke J. Phys. B: At. Mol. Opt. Phys. vol 22 p 1891 (1989).

The values of deff listed are wavelength scaled (usually from those for 1064 nm SHG) using Miller's rule.  They also include the correction due to birefringent walkoff.

The group velocities are specified for the two eigenpolarizations, lo and hi.

The eigenpolarization directions for the lo and hi refractive indices are not specified here but could easily be added on request. They can also be found from the delta output angle in Ref. Ind.

The range of phi is -180 to 180 degrees for deff plots rather than 0 - 90 degrees as it is for the other plots because deff can be asymmetric in phi whereas the linear optical properties such as phase matching loci, acceptance angle, and walkoff are symmetric.

The results from Bmix are saved in ascii file BMIX.DAT in the format displayed by the view function.

The surface plotted by the 'Phasematched d_eff on d surface' button is |d_eff (theta,phi)|, where theta and phi define the propagation direction for the three parallel beams. Theta and phi are specified relative to the chosen 'Rotation Axis' (x,y, or z). For z axis, theta is measured from the z-axis and phi is measured from the xz plane toward the yz plane. For x axis, theta is measured from the x-axis and phi is measured from the xy plane toward the xz plane. For y axis, theta is measured from y axis and phi is measured from zy plane toward xy plane. The d surface is different for Type 1 (hi hi-lo) and Types 2 (hi lo-lo) or 3 (lo hi-lo), which are similar. The surfaces vary with wavelength but slowly. We do not indicate the sign on d-effective because it gets too confusing. Only the absolute value of d-effective is plotted. The d surface often has sharp spikes or dips that appear near the optic axes which lie in the xz plane. For example, the d surface for Type 1 mixing in KTP has pronounced spikes 17 degrees from the z axis in the xz plane. The symmetry of the d surface reflects the symmetry of the crystal.

The magenta line that is imposed upon the d surface is the loci of the phasematched points for the specified wavelengths and mixing type. Only 1 of 2 mirror image phasematching curves (the one with theta<90 degrees). The phasematch loci computed with different 'Rotation Axis' contain the same information although the curves may have different discontinuities depending on the chosen axis.

The surface can be rotated, expanded and panned through the buttons on Matlab's figure toolbar, and the phasematch values can be traced out by using Matlab's interactive Data Cursor to select the magenta line and using the arrow keys. You can compare the values along the phasematched line with the values plotted through the 'Deff' button.

If the d surface is plotted when the Bmix 'Print' button is pressed the d surface will be printed. Otherwise the 'Print' button will print a figure containing the phasematching, d-effective, temperature range, group velocity and walkoff curves.

Last used input set is saved in mix.mat so if you would like to save those settings for later recall, copy mix.mat to another file name to store. Copy the file back to mix.mat to restore.

Acceptance angles and acceptance bandwidths can be calculated from the walkoff and group velocity data.  See Qmix help for details.

Examples 25, 30. See file Examples with exercises and descriptions.pdf in mlSNLO folder, or on our website at as-photonics.com/examples

Detailed discussions of crystal nonlinear optics and SNLO examples are presented in the book "Crystal nonlinear optics: with SNLO examples," advertised on the SNLO download page or at as-photonics.com/book