header for SPIE use
How to select nonlinear crystals and model their performance using SNLO
software
A. V. Smith
Sandia National Laboratories, MS 1423, Albuquerque, NM 87185
ABSTRACT
SNLO is public domain software developed at Sandia Nat. Labs. It is intended to assist in the selection of the best nonlinear crystal for a particular application, and in predicting its performance. This paper briefly describes its functions and how to use them. Keywords: optical parametric mixing, optical parametric oscillator, nonlinear crystals, nonlinear optics software
1. INTRODUCTION
The advent of powerful desktop computers has made it possible to automate calculations of the linear and
nonlinear properties of crystals, and to perform detailed simulations of nonlinear mixing processes in
crystals. The purpose of SNLO is to make these calculations available to the public in a free, user-
friendly, windows-based package, with the hope that this will advance the state of the art in applications
such as optical parametric oscillators/amplifiers (OPO/OPA), optical parametric generation (OPG),
frequency doublers, etc. There are three types of functions included in the SNLO menu, shown to the
gb2626一2006right. The first set help in computing the crystal properties such as phase-matching angles, effective
nonlinear coefficients, group velocity, and birefringence. They include functions Ref. Ind., Qmix, Bmix,
QPM, Opoangles, and GVM. The second set, functions PW-mix-LP, PW-mix-SP, PW-mix-BB, 2D-
mix-LP, 2D-mix-SP, PW-OPO-LP, PW-OPO-SP, PW-OPO-BB, and 2D-OPO-LP, model the春暖花开 亚洲
performance of nonlinear crystals in various applications, and the third set, Focus, Cavity, and Help, are
helper functions for designing stable cavities, computing gaussian focus parameters, and displaying help
text for each of the functions. The capabilities of select functions are presented below.
2. CRYSTAL PROPERTY CALCULATIONS
2.1 Selecting angle-tuned crystals
The function QMIX is the best starting place for
selecting a nonlinear crystal for your application.
When you select a crystal from the list of 40+
crystals, the viewing area will display its properties,
including the transmission range (as a plot if the
information is available), references for Sellmeier
data, nonlinear coefficients, damage thresholds, etc.
Enter the wavelengths for your mixing process and push the ‘Run’
button to compute information specific to all possible phase-matched
processes for the selected crystal at the specified wavelengths. The
figure to the left shows one example. Note that for biaxial crystals only
the principal planes are allowed in QMIX. If you are curious about a
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biaxial crystal’s properties outside the principal planes, you can explore
them using BMIX. Further information on crystal properties is available
in the papers listed in the bibliography ‘Crystals.pdf’ included with
SNLO. It references over 600 papers relating to nonlinear optical
crystals.
2.2 Selecting quasiphase-matched crystals
The function QPM helps you find the right quasiphase matched poling period for any of the popular quasiphase matchable crystals. It also computes temperature and pump wavelength tuning properties for the crystal. You can chose the polarizations for your processes as well, although the zzz polarization is usually the one of practical interest.
2.3 Selecting angle-tuned OPO crystals
As shown below, the function Opoangles displays a plot of the signal/idler wavelength versus crystal
angle for a given pump wavelength. It also computes the nonlinear coefficient and the parametric gain versus angle. Comparing gain over the wavelength range of interest between different crystals and phase matching types gives a good indication of relative OPO performance. Note that this function permits noncollinear phase matching. Clicking on the ‘pump tilt’ edit box displays a diagram of the noncollinear angles. The signal is assumed to remain aligned to the cavity of an OPO, the pump is tilted by a fixed angle relative to the signal while the crystal and idler tilt by variable amounts to achieve phase match.复合氨基酸
2.4 Computing a crystal’s linear optical properties
The function Ref. Ind. can be used to compute refractive indices, group velocities, group velocity dispersions, and birefringent walk off for a given propagation angle, temperature, and wavelength. This is useful if you want to make your own calculations of phase matching, group velocity matching, etc.
2.4 Computing group velocity in angle-tuned crystals
The function GVM computes the phase matching angles and group velocities for noncollinear phase matching. The slant parameter specifies the angle between the pump (bluest) wave’s pulse envelope and its k-vector. All the pulse envelopes are assumed to have the same orientation so if they are all group velocity matched there is no temporal (longitudinal) walk off, but there is spatial (lateral) walk off. For a set of wavelengths and polarizations, the relative group velocities can be varied by changing the value of the slant. In many cases it is possible to achieve perfect group velocity matching in this way. This has obvious application in fs mixing, but it can also be used in mixing broadband light with temporal structure on a fs or ps scale.
3. NONLINEAR MIXING MODELS
3.1 Modeling single-pass mixing
The functions with ‘mix’ in their title handle single-pass mixing, as opposed to mixing in an optical cavity. The functions with the ‘PW’ prefix model plane-wave mixing, those with the ‘2D’ prefix include Gaussian spatial profiles with diffraction and birefringent walk off. The plane-wave models run much faster than the ‘2D’ models, so they can be used to arrive at an approximate set of conditions that can then be fine tuned with the diffractive models.
The functions with suffix ‘LP’ ignore group velocity effects and are appropriate for monochromatic ns and longer pulses, or for monochromatic cw beams. Functions with suffix ‘SP’ incorporate group velocity effects and are useful for ps and fs pulses. The suffix ‘BB’ indicates that the pulses are long but broadband so there is temporal structure on a time scale short enough to require inclusion of group velocity effects.
The figure below shows an example of the function 2D-mix-LP. Using the input parameters shown on the input form to the right, it computes near- and far-field spatial fluence profiles as well as spatial profiles and phase profiles as a function of time. Other computed parameters include spectra, power, and beam parameters focus, tilt, and M2.亲核反应
Usually mixing of low power beams involves focused light, often with
a confocal length set comparable to the crystal length. The helper
function Focus, shown at the right, is included to help calculate the
wavefront curvature at the entrance face of the crystal for such
focusing beams. Its output values are automatically updated whenever
one of the input parameters is changed.
The function PW-mix-BB can be used to model optical parametric generation (OPG) as a high-gain case of single-pass mixing in the plane-wave approximation. You must specify the correct signal and idler energies, bandwidths, and mode spacings to simulate start-up quantum noise. The mode spacing should be the inverse of the signal/idler pulse length. For example, if you have a 1 ps pump pulse, you could use 5 ps signal and idler pulses (to allow for temporal walk off) and a signal/idler mode spacing of 100 GHz. The bandwidth should be set to several times the OPO acceptance bandwidth, and the pulse energy of the signal and idler should be set so there is one photon per mode, ie energy hν×bandwidth÷(mode spacing). Because the gain is very high for OPG, the number of z integration steps must be quite large. I suggest you start with 100 steps and double it until the results converge. Each run will use different start up noise, so convergence does not mean identical results here. A good test is to look at both the irradiance and spectral plots and make sure they are both similar to the previous run with fewer integration steps. The figures above show an example of an OPG calculation. The parameters are specified in the input form on the left and the output time profile is shown below.
The functions PW-mix-SP and 2D-mix-SP model
single pass mixing for pulses short enough that group velocity effects are important. The figure below show an example for the plane-wave case. The signal and idler pulses are given an input energy and the pump pulse is generated in the crystal. The signal and idler pulses separate in time due to group velocity differences and reshape due to group velocity dispersion. The slower pump pulse emerges with a time delay. The “movie” button displays the pulses as they would appear inside the crystal propagating at different velocities and changing strength through nonlinear mixing. In this function as well as most of the other functions, you can specify the energy in any of the pulses, there is no assumption of sum-frequency mixing or optical parametric gain. Mixing will proceed just as in a real crystal. If there are three nonzero inputs, the direction of energy transfer will depend on the relative phase of the three beams.
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