about

This page is related to the design of an optical system for the second harmonic (SH) generation in a PPLN crystal. It calculates the paraxial parameters of an optical system enabling to focus a collimated beam at the fundamental (F) wavelength in the middle of a PPLN crystal and to collimate the generated SH beam. The input parameters are the waist radius (W_Fin) and wavelength (λ) of the incident F beam, the waist radius of the F beam to be focused in the middle of the PPLN (W_Fppln), the PPLN material (here LibNO3 with 5% MgO), length (length_ppln), thickness (thickh_ppln) and temperature (temp_ppln) as well as the waist radius of the collimated SH beam (W_SHout).

First, the engine calculates the focal length (f₁) of the adequate thin lens (L₁) focusing the incident F beam in the middle of the PPLN, its distance to the PPLN entrance (dist_{L1_ppln}) and from the incident F beam waist (dist_{WFin_L1}) located in its front focal plane. It calculates as well the focal length (f₂) of the adequate lens collimating the SH beam generated in the PPLN and its distance from the PPLN exit (dist_{ppln_L2}) as well as its distance to the waist of the output collimated SH beam (dist_{L2_WSHout}) located in its back focal plane. Finally it calculates the waist radius of the SH beam in the PPLN (W_SHppln).

Then, it searches real lenses with focal lengths the closest from the previously calculated ones. Real configurations with aspherical and plano convex lenses are proposed for each F and SH beams.

It is possible to load any of the configuration in the "Advanced Calculations" tool for analysis and for eventual optimization. Loads related to the F beam propagation and to the SH beam propagation are processed separately by clicking respectively on the related LOAD_F_X or LOAD_SH_X button.

A configuration corresponding to the F beam propagation includes the focusing lens L1 and the PPLN. The waist of the incident beam is in the front focal plane of the focusing lens at the F wavelength and the PPLN is positionned so that the focused F beam waist (and therefore the generated SH waist) is located in the middle of the PPLN.

A configuration corresponding to the SH beam propagation includes the PPLN and the collimating lens L2. The waist of the generated SH beam is located in the middle of the PPLN and the collimating lens is positionned so that the waist of the collimated beam is in the back focal plane of the lens.

For both F and SH systems, the adequate wavelength (F or SH wavelength), waist radius of the incident beam ( collimated incident F beam or generated SH beam in the PPLN) are loaded as well and can be edited respectively in the "input/wavelengths" and "input/light source" pages.

The list of links to the "Handy Calculations" executed for solving this user case is displayed at the bottom of the page. they are listed in the order of execution. ,