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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Cross phase modulation in photonic crystals

Karolina Słowik, Andrzej Raczyński, Jarosław Zaremba, S. Zielińska-Kaniasty, M. Artoni, Giuseppe Carlo La Rocca

Published May 5, 2011• 0 citations
Publisher

Abstract

In the present paper we consider a simultaneous propagation of two weak pulses (the 'probe' and 'trigger') in the tripod configuration atomic medium, irradiated by a strong quasi-standing control field. The latter leads to a periodic modulation of the refractive index of the medium which now becomes a photonic crystal. While propagating in such a medium both probe and trigger are split into transmitted and reflected components the nonlinear phase shifts of which are of particular interest. We calculate the nonlinear periodic susceptibilities and make numerous simulations of the propagation of the stationary pulses in different conditions. We calculate the phases of the outgoing fields and find the optimal values of parameters characterizing the system, i.e. when the nonlinear phase shifts of both transmitted and reflected probe and trigger components are large. We show a convenient way of controlling the process by shifting the frequency of the incoming probe. We plot the transmission and reflection spectra for different values of parameters of the system, which could be used as a flexible beam splitter, for which the phases and intensities of outgoing beams can be independently changed.

DOI
10.1117/12.886760

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BENTHAM SCIENCE PUBLISHERS eBooks•Jan 1, 2009•0 citations
In the present paper we consider a simultaneous propagation of two weak pulses (the 'probe' and 'trigger') in the tripod configuration atomic medium, irradiated by a strong quasi-standing control field. The latter leads to a periodic modulation of the refractive index of the medium which now becomes a photonic crystal. While propagating in such a medium both probe and trigger are split into transmitted and reflected components the nonlinear phase shifts of which are of particular interest. We calculate the nonlinear periodic susceptibilities and make numerous simulations of the propagation of the stationary pulses in different conditions. We calculate the phases of the outgoing fields and find the optimal values of parameters characterizing the system, i.e. when the nonlinear phase shifts of both transmitted and reflected probe and trigger components are large. We show a convenient way of controlling the process by shifting the frequency of the incoming probe. We plot the transmission and reflection spectra for different values of parameters of the system, which could be used as a flexible beam splitter, for which the phases and intensities of outgoing beams can be independently changed.
The cross-Kerr effect is studied for two weak beams, probe and trigger, propagating in an atomic medium in a tripod configuration, dressed by a strong standing wave coupling beam in a regime of electromagnetically induced transparency. The nonlinear phase shifts for both transmitted and reflected probe beams induced by the trigger's presence are found to depend on the probe detuning, the control beam's intensity, the relaxation rates and, in particular, on the redistribution of the population among the atomic levels. Such a quantitative analysis indicates that the transmitted and reflected probe beam components and their respective phase shifts can be easily controlled and optimized.
The cross-Kerr effect is studied for two pulses propagating in an atomic medium in a tripod configuration, dressed by a strong standing wave coupling beam. Nonlinear phase shifts for both transmitted and reflected beams are calculated taking into account the redistribution of the population among the atomic levels which allows one to study the phase shifts in a wide range of pulse detunings. The influence of other parameters, e.g., the intensity of the control field and the relaxation rates, on the cross-Kerr effect is also examined in detail.
Cross-Kerr nonlinearities are analyzed for two light beams propagating in an atomic medium in the tripod configuration, dressed by a strong standing-wave laser field that induces periodic optical properties. The reflection and transmission spectra as well as the phases of both the reflected and transmitted components of the two beams are analyzed theoretically with nonlinearities up to third order being taken into account. Ranges of parameters are sought in which the cross-Kerr effect can be used as the basis of the phase gate.
We study the transmission spectra of a one-dimensional photonic crystal with a defect containing a four-level atomic medium that exhibits a greatly enhanced third-order susceptibility while having a vanishing linear susceptibility dependent on the electromagnetically induced transparency. Two ways of controlling the transmission of a photonic crystal are discussed: via absorption, i.e., nonlinear (two-photon) absorption of the probe field enhanced by constructive quantum interference, and via dispersion, which comes down to shifting the resonance frequency of the defect mode for the probe field by varying the refractive index based on the giant Kerr nonlinearity (cross-phase modulation). We demonstrate that such systems enable nonlinear all-optical switching at ultralow intensities of the coupling and switching laser fields.
A possible switching mechanism has been investigated for nonlinear photonic crystals doped with an ensemble of non-interacting three-level nanoparticles. In this scheme, an intense pump laser field is used to change the refractive index of the nonlinear photonic crystal while a weaker probe field monitors an absorption transition in the nanoparticles. In the absence of the strong laser field the system transmits the probe field when the resonance energy of the nanoparticles lies near the edge of the photonic band gap due to strong coupling between the photonic crystal and the nanoparticles. However, upon application of an intense pump laser field the system becomes absorbing due to a band edge frequency shift that arises due to a nonlinear Kerr effect which changes the refractive index of the crystal. It is anticipated that the optical switching mechanism described in this work can be used to make new types of photonic devices.
In this chapter, we give a brief review of our recent research works on photonic bandgaps induced by standing-wave (SW) coupling fields in the regime of electromagnetically induced transparency (EIT). EIT refers to the absorption suppression or elimination of a weak probe going through an atomic ensemble at the presence of a strong coupling, which is a result of laser induced destructive quantum interference. On the other hand, a light signal cannot freely propagate in the media with periodic refractive indices (the so-called photonic crystals) if its carrier frequencies fall inside the photonic bandgaps. Utilizing a SW coupling to attain the periodically modulated refractive index with little absorption, one can establish an induced photonic bandgap with its width and position dynamically tunable. The potential media may be either cold atomic ensembles or solid materials exhibiting defect states, such as Pr3+: Y2SiO5 and diamond containing N-V color centers. We first consider the steady optical responses of the atomic and solid media with dynamically induced bandgaps to a time- independent probe by focusing on the dispersion curves of Bloch wave vectors and the spectra of reflection and transmission. Then, we examine the propagation dynamics of a probe pulse through a cold atomic sample in two different situations where a dynamically induced bandgap exists or not. We find that the SW coupling field can be easily modulated to mold the traveling-light flow and to control the stationary-light generation with quite high flexibility, and thus may have applications in the fields of classical and quantum information processing of optical signals. In performing theoretical simulations, we also demonstrated several different but almost equivalent mathematical methods, i.e. the two-mode approximation method, the transfer-matrix method, and the Maxwell-Liouville equation method, to deal with the problems of SW-EIT. Comparison of these methods is quite helpful to understand the underlying physics of the formation of dynamically induced photonic bandgaps.