This is a very good reference:
http://www.opticsinfobase.org/josab/abstract.cfm?uri=josab-29-8-2199
Hi Alexander, Thanks for the reference but please provide me the title and doi of the paper as I'm unable to access the link.
Sure, it's "How does it scale? Comparing quantum and classical nonlinear optical processes in integrated devices". I covers Spontaneous Parametric Down-Conversion both in waveguides and resonators, and both with special filtering and without one, and also covers several other nonlinear optical precesses.
http://dx.doi.org/10.1364/JOSAB.29.002199
Also available here:
https://www.researchgate.net/publication/247160700_How_does_it_scale_Comparing_quantum_and_classical_nonlinear_optical_processes_in_integrated_devices
Article How does it scale? Comparing quantum and classical nonlinear...
SPDC process is similar to the reverse of Second Harmonic Generation (SHG) where two photons of same frequency are combined to become one of double the frequency. In this regard, can we say that the efficiency of SPDC is given by the same expression sinc^2(\deltaK) which is for SHG?
Hi,
A short answer to your question is no, since SHG is far more efficient than SPDC. That is, in the presence of nonlinear medium and if the phase matching conditions are met, it is more probable that two photons will be annihilated and create one higher energy photon than for a single photon to be annihilated, thus creating two lower energy daughter photons. You can see it in many lasers that use frequency doubling crystals, where both the pump (e.g., red) and the second harmonic field (e.g., blue) are visible, where the reverse is not true, i.e., SPDC output is usually not visible to the naked eye.
According to my understanding, it has to do with the fact that SHG can be described as a classical process (See R. W. Boyd's Nonlinear Optics), while SPDC is purely a quantum process, which is stimulated by quantum vacuum fluctuation and has no classical analog. If you look at a more complete expression of SHG efficiency you've quoted, you see that I3~I1*I2*Sinc^2(deltaK*L/2). This means that you need two fields present to create a third one, and if you have only the pump field (lets' say I2 with frequency w2), then you get I3=0, since I1=0 (no photons are present before PDC begins). So basically, since PDC can be only described by quantum mechanics, and since it relies on quantum vacuum fluctuations to stimulate it, it is far less efficient than SHG.
I hope it helps,
Assaf
Hi,
This is a related paper published in 2020 which also related with "How does it scale? Comparing quantum and classical nonlinear optical processes in integrated devices".
"High Quality Entangled Photon Pair Generation in Periodically Poled Thin-Film Lithium Niobate Waveguides"
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.163603
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