In nonlinear crystals, a special nonlinear process occurs. A pump photon is spontaneously converted into two complementary photons with lower energy. In this process both energy and momentum are conserved, i.e. and .
In PPKTP Crystal or APKTP Crystal the momentum mismatch of the process is compensated by the crystal reciprocal vector which is determined by the spatial frequency .
Vacuum energy and momentum fluctuations give rise to the spontaneous creation and annihilation of many random photons.
But the output photons of the SPDC (spontaneous parametric down-conversion nonlinear process) are the ones that conserve momentum and energy.
In type 1 SPDC all the photon pairs which conserve momentum are positioned on a ring shaped structure:
In type 1 SPDC all the photon pairs which conserve momentum are positioned on a ring shaped structure:
See a movie
Changing the temperature or wavelength of the crystal will change the phase matching condition thus radius of the rings will be changed as well as seen in the movie.
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