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Applied Optics

Realization of an all-optical triode and diode with a two-level-atom–loaded diffraction grating

Richard W. Ziolkowski

Published Nov 20, 1997• 9 citations
Publisher

Abstract

A finite-difference time-domain full-wave vector Maxwell equation solver is coupled with a two-level-atom model to simulate the scattering of an ultrafast pulsed Gaussian beam from a finite-length, metallic lamellar grating loaded with two-level atoms. The atomic medium is taken to be resonant at or near the frequency of the incident optical radiation. The highly resonant material and grating behaviors are then combined to realize an all-optical triode at low powers and an all-optical diode at high powers. Simulation results demonstrate the operating characteristics of these triode and diode configurations.

DOI
10.1364/ao.36.008547

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A finite-difference time-domain full-wave vector Maxwell equation solver is coupled with a two-level-atom model to simulate the scattering of an ultrafast pulsed Gaussian beam from a finite-length, metallic lamellar grating loaded with two-level atoms. The atomic medium is taken to be resonant at or near the frequency of the incident optical radiation. The highly resonant material and grating behaviors are then combined to realize an all-optical triode at low powers and an all-optical diode at high powers. Simulation results demonstrate the operating characteristics of these triode and diode configurations.
Recent progress in ultrafast technology has led to the generation of optical pulses as short as 8 fs. The propagation of such short pulses in nonlinear optical media requires new computational techniques in which the standard approximations such as the slowly-varying envelope approximation (SVEA) and rotating-wave approximation (RWA) are not made while using the Maxwell-Bloch equations [1]. Previous calculations, which used the finite-difference time-domain (FDTD) method, found that for a a Kerr-like instantaneous nonlinearity [2] significant differences can occur when the full vector Maxwell equations are used instead of the nonlinear Schrodinger equation. Recently, the FDTD method has been extended to the case of a homogeneously broadened two-level atomic system [3].
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.
We propose a scheme for effectively creating a type of all optical device called electromagnetically induced two-dimensional grating by utilizing a four-level coherent atomic medium, which is coherently driven by two orthogonal standing-wave fields. With a far-off resonant trigger field, a spatially modulated cross-phase modulation takes place accompanied by vanishing absorption. The resulting phase grating can diffract the probe beam into high-order directions. When a resonant trigger field is applied on the atoms, the probe obtains gain without inversion due to the atomic coherence effect. And then a gain-phase grating is formed. The diffraction efficiency can be significantly improved compared with that of phase grating. The results show that the diffraction efficiencies attainable by the gratings strongly depend on the interaction length, coherent field intensity, probe field detuning and coherent field detuning. Therefore, the proposed gratings can be used as two-dimensional multi-channel beam splitter which have potential application in optical networking and communication.
The efficient light-matter interaction and discrete level structure of atomic vapors made possible numerous seminal scientific achievements including time-keeping, extreme non-linear interactions, and strong coupling to electric and magnetic fields in quantum sensors. As such, atomic systems can be regarded as a highly resourceful quantum material platform. Recently, the field of thin optical elements with miniscule features has been extensively studied demonstrating an unprecedented ability to control photonic degrees of freedom. Hybridization of atoms with such thin optical devices may offer a material system enhancing the functionality of traditional vapor cells. Here, we demonstrate chip-scale, quantum diffractive optical elements which map atomic states to the spatial distribution of diffracted light. Two foundational diffractive elements, lamellar gratings and Fresnel lenses, are hybridized with atomic vapors demonstrating exceptionally strong frequency-dependent, non-linear and magneto-optic behaviors. Providing the design tools for chip-scale atomic diffractive optical elements develops a path for compact thin quantum-optical elements.
An iterative predictor-corrector finite-difference time-domain method is used to solve the semiclassical Maxwell-Bloch system numerically without invoking any of the standard approximations such as the rotating-wave approximation. This approach permits a more exact study of self-induced transparency effects in a two-level atom. In addition to recovering the standard results, for instance, for \ensuremath{\pi}, 2\ensuremath{\pi}, and 4\ensuremath{\pi} pulses, several features in the results appear at the zeros of the driving pulse, where its time derivatives are maximum. Several ultrafast-pulse examples demonstrate that time-derivative-driven nonlinearities have a significant impact on the time evolution of a two-level atom system. Moreover, typical small-signal gain results are also obtained with our Maxwell-Bloch simulator. We illustrate that these time-derivative effects can be used to design an ultrafast, single-cycle pump pulse that completely inverts the two-level atom population. A pump-probe signal set is then used to illustrate gain in the probe signal.
We demonstrate a scheme for coherently induced grating based on a mixture of two three-level atomic species interacting with two standing-wave fields. As a result of interaction between the absorptive and amplified Raman resonances, the refractive index of the medium can be enhanced and modulated periodically. Then a sinusoidal grating, which can diffract the probe field into high-order directions, is coherently formed in the medium. The proposed scheme is theoretically investigated in a mixture of atomic isotopes of rubidium. The results show that the diffraction efficiency depends strongly on the two two-photon detunings of the two Raman transitions and the intensities of the two driving standing-wave fields. The proposed electromagnetically induced grating scheme may be applied to the all-optical switching and beam splitting in optical networking and communication.