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Advances in Lasers and Electro Optics Part 3

Tham khảo tài liệu 'advances in lasers and electro optics part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Semiconductor Ridge Microcavities Generating Counterpropagating Entangled Photons 87 stands for hermitian conjugate term. The integration is performed over the interaction volume which in our case is the illuminated portion of the waveguide. The suitability of a photon pair source for a given quantum optics application largely depends on the joint spectral intensity JSI of the generated photons S as a defined as the probability that the signal idler photon frequency is as a . In the following we make explicit the link between the JSI and the characteristics of the pump beam in order to clarify the physical parameters that can be used to tailor the two-photon state. A classical pump field on the air side of the air semiconductor interface is given by Ep z t J daE a A z a sln6 a 5 where we have neglected the pump variation along the y axis. In this expression the spatial profile A z can be engineered through linear optics E a is the spectral distribution characterized by a center frequency ap and a bandwidth op 6 a is the angle of incidence of the a component of the field which can be engineered through a dispersive element such as a quartz wedge or a diffraction grating. Following the derivation of Grice et al. 2001 and assuming incident signal and idler fields in the vacuum states the first-order perturbation solution of the Schrodinger equation using Equation 4 gives the generated two photon state 1 J J dasdaif as ai â as ai ai va 6 Here â and ai are the photon creation operators for the signal and idler beams and the probability amplitude f as ai is given by f a a i E a a ộ os a i 7 with the phase-matching function b a a dzv p z A z ei k a-a z 8 Y as ai yzx f z z z e V Ák as a k as ai sin6 as ai -Ps as IP a being the z component of the wave vector mismatch and Pspa the effective propagation constant of the signal and idler photon respectively. As the JSI is related to the two-photon probability amplitude by the simple relation S as ai 1f as ai it is clear that .