bbo crystal second harmonic generation
The spectral and temporal characteristics and optical-conversion efficiency of ∼150−fs∼150-fs laser pulses at 400 nm generated by second-harmonic generation (SHG) of a regeneratively amplified mode-locked Ti:sapphire laser were investigated both theoretically and experimentally. The theoretical investigation was done by taking into account cubic nonlinearity, pulse walk-off, group-velocity dispersion, Kerr nonlinearity, quadratic broadening, frequency chirping of the fundamental pulse, and higher-order nonlinear mixing such as backconversion and optical parametric processing. The experimental studies of the effects of LiSAF, LiSGaF and LiCAF laser crystals and pumping intensity on the pulse duration, the spectrum, and the optical-conversion efficiency of the SHG were carried out in BBO crystals and LBO crystals of various thicknesses and compared with the theory. It was found that in a non-transform-limited pulse, the most significant contribution to the temporal and spectral distortion of the ∼150−fs∼150-fs SHG pulses is mainly due to the chirping of the fundamental beam and self-phase modulation at high pumping intensity and no-doped LiSAF, LiSGaF and LiCAF crystals length. The optimum crystal length and pumping intensity for obtaining a high optical-conversion efficiency and a pure spectrum in SHG are also calculated and experimentally investigated. It was found that a transform-limited fundamental pulse is essential to obtain a high conversion efficiency and to preserve the temporal profile of the second-harmonic pulse. It is also found that for a non-transform-limited ∼150−fs∼150-fs pulse, a 0.5–0.6-mm stock/large size/IBS coated LBO nonlinear crystal and a modest pumping intensity of ∼40 GW/cm2∼40 GW/cm2 are the most suitable for SHG.
Why does this make entangled photons? Well, in quantum physics a photon that has diagonal polarization can just as well be said to be both vertically and horizontally polarized, in the same sense that Schroedinger’s Cat is said to be both alive and dead before you look at it (that is, it is a superposition of horizontally and vertically polarized). So if a photon that is both horizontally and vertically polarized is downconverted, it becomes two photons that are either both horizontally polarized or both vertically polarized- but neither has a definite polarization until it is measured, and each is guaranteed to have the same polarization as the other. And that’s precisely what it means to be entangled.
Regarding the experiment that you suggest, remember how I defined entanglement: the polarization of each photon looks individually random, and it is only why you compare photons from the same pair that you see anything interesting. So any experiment that measures each stream of photons individually won’t see anything interesting. The interesting experiments have a form like this: you change something about one of the photons, and then measure its entangled partner. There are a lot of fun but similar ideas
*Pedantic note: I’m simplifying some of the geometry slightly here. In the setup I’m familiar with downconverted light was perpendicular to the nonlinear optic axis, and the downconverted light was itself perpendicular to the pump photons.