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Kerr non-linearity induced light trapping in negative index medium

Dimishree Neog, Abhijeet Das, Subrata Hazarika

Published Jul 3, 2024• 0 citations
Publisher

Abstract

Kerr non-linearity can induce epsilon-near-zero (ENZ) material characteristics in negative index material when incident pulse intensity I=Ith , the threshold intensity. Such Kerr induced ENZ regime in NIM, where group velocity approaches zero and phase velocity diverges, is ideal for strong exciton -photon interaction that leads to the formation of polaritons oscillating between photonic and excitonic states with frequency ΩR /h, ΩR being the Rabi frequency. Quantum mechanical analysis using polariton dynamics indicates that Kerr induced slowing down of group velocity of an optical pulse can be an alternative means to trap light in negative index medium by controlling the intensity of the light pulse unlike slow light, stopped light or stationary light generated conventionally through electromagnetically induced transparency(EIT) in atomic medium.

DOI
10.1364/opticaopen.26129932.v1

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Kerr non-linearity can induce epsilon-near-zero (ENZ) material characteristics in negative index material when incident pulse intensity I=Ith , the threshold intensity. Such Kerr induced ENZ regime in NIM, where group velocity approaches zero and phase velocity diverges, is ideal for strong exciton -photon interaction that leads to the formation of polaritons oscillating between photonic and excitonic states with frequency ΩR /h, ΩR being the Rabi frequency. Quantum mechanical analysis using polariton dynamics indicates that Kerr induced slowing down of group velocity of an optical pulse can be an alternative means to trap light in negative index medium by controlling the intensity of the light pulse unlike slow light, stopped light or stationary light generated conventionally through electromagnetically induced transparency(EIT) in atomic medium.
Kerr non-linearity can induce epsilon-near-zero (ENZ) material characteristics in negative index material when incident pulse intensity I=Ith , the threshold intensity. Such Kerr induced ENZ regime in NIM, where group velocity approaches zero and phase velocity diverges, is ideal for strong exciton -photon interaction that leads to the formation of polaritons oscillating between photonic and excitonic states with frequency ΩR /h, ΩR being the Rabi frequency. Quantum mechanical analysis using polariton dynamics indicates that Kerr induced slowing down of group velocity of an optical pulse can be an alternative means to trap light in negative index medium by controlling the intensity of the light pulse unlike slow light, stopped light or stationary light generated conventionally through electromagnetically induced transparency(EIT) in atomic medium.
We prove that it is possible to freeze a light pulse (i.e., to bring it to a full stop) or even to make its group velocity negative in a coherently driven Doppler broadened atomic medium via electromagnetically induced transparency (EIT). This remarkable phenomenon of the ultraslow EIT polariton is based on the spatial dispersion of the refraction index n(omega,k), i.e., its wave number dependence, which is due to atomic motion and provides a negative contribution to the group velocity. This is related to, but qualitatively different from, the recently observed light slowing caused by large temporal (frequency) dispersion.
A four-level N-type atomic medium is considered to study the effect of spontaneous generated coherence (SGC) and Kerr nonlinearity on light pulse propagation. A light pulse is propagating inside the medium where each atom follows four-level N-type atom-field configuration of rubidium ( 85 Rb) atom. The atom-field interaction leads to electromagnetically induced transparency (EIT) process. The atom-field interaction is accompanied by normal dispersion and in the presence of SGC and Kerr nonlinearity the dispersion property of the proposed atomic medium is modified, which leads to enhancement of positive group index of the medium. The enhancement of positive group index then leads to slow group velocity inside the medium. A more slow group velocity is also investigated by incorporated the collective effect of SGC and Kerr nonlinearity. The control of group velocity inside a four-level N-type atomic medium via collective effect of SGC and Kerr nonlinearity is the major part of this work.
In this work, we present an analytical method to achieve giant Kerr nonlinearity without absorption in a five-level atomic medium. By using iterative perturbation technique on density matrix equations, we have derived the analytical expressions of nonlinear susceptibility and Kerr nonlinear coefficient in the presence of spontaneously generated coherence (SGC) and relative phase between applied laser fields. It shows that, this five-level atomic medium exhibits multiple electromagnetically induced transparency (EIT) at three different frequencies, at the same time, the Kerr nonlinear coefficient is enhanced around three transparent spectral regions; in each such EIT region appears a pair of positive-negative peaks of Kerr nonlinear coefficient. In particular, these nonlinear peaks are moved to the center of the EIT windows via SGC. This means that the Kerr nonlinear coefficient is enhanced with completely suppressed absorption at different transparency frequencies. Furthermore, the magnitude and the sign of the Kerr nonlinear coefficient are easily controlled according to the SGC strength, the coupling laser intensity, and the relative phase between applied laser fields. Such a giant nonlinear medium can be useful for photonic devices working in the resonant frequency region without absorption. As a typical application, this giant Kerr nonlinear material has been applied to an interferometer for the formation of optical bistability, and showed the appearance of OB at the resonant frequency with significantly reduced threshold intensity and OB width.
Subluminal and superluminal propagation of a light pulse in Kerr materials has been investigated. Group velocities as slow as much less than 1 mm per second to as fast as negative several thousands meters per second can easily be obtained in the Kerr medium, which possesses a large nonlinear refractive index and long relaxation time, such as Cr3+-doped alexandrite, ruby, and GdAlO3. The physical mechanism is the strong highly dispersive coupling between different frequency components of the pulse.
The possibility of the direct excitation of surface polaritons (SPs) by the free-space laser fields at the interface of negative-index metamaterial (NIMM) layer and a bottom layer of cold double Lambda-type atomic medium is investigated. The giant field enhancement (up to |E/E0|2≈4.1), together with suppressed ohmic loss of the NIMM layer in a wide transparency window of a double electromagnetically induced transparency, results in the SPs generation. The excitation efficiency of these SPs can be effectively enhanced by applying the unidirectional atomic motion, modulation of the coupling laser characteristics, and using a probe laser with proper incident angle. Based on the special modulation of the driven fields parameters, the group velocity switching of the SPs is observed. In the nonlinear propagation regime of the SPs, a giant Kerr nonlinearity is produced by applying a negative unidirectional atomic velocity. The controllable optical Kerr effect in this coupler-free scheme results in the lossless propagation of the nonlinear SPs. It is revealed that the electromagnetically induced transparencybased system can be used for stable propagation of one-dimensional (1+1)D bright and dark superluminal polaritonic solitons. It is also shown that the proposed scheme could be easily realized in an experiment and hence can be used for various ultrafast optical devices.