M Hosseini Farzad
Articles written in Pramana – Journal of Physics
Volume 69 Issue 3 September 2007 pp 395-409 Research Articles
Optical parametric amplification beyond the slowly varying amplitude approximation
The coupled-wave equations describing optical parametric amplification (OPA) are usually solved in the slowly varying amplitude (SVA) approximation regime, in which the second-order derivatives of the signal and idler amplitudes are ignored and in fact the electromagnetic effects due to exit face of the medium is not involved. Here, an analytical plane-wave solution of these coupled-wave equations in a non-absorbing medium is presented. The solutions are derived beyond the SVA approximation up to order of $\kappa = k$ (coupling constant over the wave number). The intensity distributions of the signal and the idler waves show a periodic behavior about their corresponding distributions of SVA-adapted solution. This behavior can be explained by the interference of the forward propagating signal (idler) wave and the corresponding backward one resulted from the reflection by the end face of the medium. Furthermore, this interference pattern in the medium can in turn serve as a periodic source for the next generations of the signal and idler waves. Therefore, the superposition of the waves, generated from different points of this periodic source, at the exit face of the medium shows an oscillatory behavior of the transmitted signal (idler) wave in terms of normalized coupling constant, $\kappa L$. This study also shows that this effect is more considerable for high intensity pump beam, high relative refractive index and short length of the nonlinear medium.
Volume 78 Issue 4 April 2012 pp 595-612 Research Articles
Light squeezing in optical parametric ampliﬁcation beyond the slowly-varying amplitude approximation
Optical parametric ampliﬁcation (OPA) described usually by the coupled-wave equations with the ﬁrst-order derivatives of the signal and idler waves, is solved under the slowly-varying amplitude approximation (SVA). In this article, by keeping the second-order derivatives in the coupled-wave equations, we obtained an analytical solution for the output signal and idler waves up to the ﬁrst order of $(\kappa/k)^1$; the ratio of coupling constant to the wave number. Furthermore, here the signal and the idler waves are distinguished only by their polarizations with the same frequency. Light squeezing is observed in normally ordered variances of the two quadrature operators of the output combined mode when plotted against $\kappa L$, where 𝜅 is the coupling constant and 𝐿 the interaction length. The variances have different signs for a range of values of $\kappa L$ and their variations are in opposite directions. We also show that this property is strongly dependent on the relative refractive index of the medium (𝑛). It is worth mentioning that the relative index dependency is not an explicit feature in squeezing of OPA under SVA approximation. Furthermore, the squeezing vanishes when $n \to 1$ and $\kappa /k \to 0$.
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