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Journal of the Optical Society of America B

Pulse propagation in a medium optically dressed by three fields forming a triangular loop configuration

Andrzej Raczyński, Jarosław Zaremba, Sylwia Zielińska‐Raczyńska

Published May 22, 2015• 6 citations
Publisher

Abstract

A probe pulse propagation is examined in a medium irradiated by three control fields which constitute a triangular loop system being, in general, out of resonance. As a consequence, the probe field interacts with the medium dressed in a time-dependent way. Coupled equations for the Floquet components of the probe field are written and solved by diagonalizing the coupling matrix. Examples of numerical solutions are presented and discussed.

DOI
10.1364/josab.32.001229

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A probe pulse propagation is examined in a medium irradiated by three control fields which constitute a triangular loop system being, in general, out of resonance. As a consequence, the probe field interacts with the medium dressed in a time-dependent way. Coupled equations for the Floquet components of the probe field are written and solved by diagonalizing the coupling matrix. Examples of numerical solutions are presented and discussed.
The subject of this work is the propagation of a weak probe pulse in an atomic medium in a three-level closed-loop configuration. An atomic system is irradiated with two strong control fields: optical and microwave. Two channels for the probe field are activated: (i) absorption of a probe photon and (ii) emission of a probe photon with the simultaneous absorption of two control and two microwave photons. We analyse in detail the pulse spectrum and its time–space evolution taking into account the generation of light by the atomic sample. In particular, we study interference effects due to the relative phase of the applied fields. In contrast to other papers, we do not make the assumption of net (three photon) resonance.
The light propagation of a probe field pulse in a four-level double-lambda type system driven by laser fields that form a closed interaction loop is studied. The finite frequency width of the probe pulse requires a time-dependent analysis beyond the multiphoton resonance assumption. We apply a Floquet decomposition to the equations of motion to solve this time-dependent problem and to identify the different scattering processes contributing to the medium response. We find that the response oscillating in phase with the probe field is phase-independent. The phase dependence arises from a scattering of the coupling fields into the probe field mode at a frequency which in general differs from the probe field frequency. In particular for short pulses with a large frequency width, inducing a closed loop interaction contour may lead to a distortion of the pulse shape via this phase-sensitive scattering. Finally, we demonstrate that both the closed loop and the nonclosed loop configuration allow for sub- and superluminal light propagation with small absorption or even gain, where one of the coupling field Rabi frequencies acts as a control parameter that enables one to switch between sub- and superluminal light propagation.
Weak probe-pulse propagation is studied in a three-level atomic system irradiated by a strong control laser field and a strong microwave field in the closed-loop triangular (Δ) configuration. In addition to the direct absorption channel, a second channel is activated in which a probe photon’s absorption is replaced by its emission accompanied by an absorption of two control and two microwave photons. The pulse can be considered a superposition of two components, each of which experiences a separated effective susceptibility, exhibiting its absorption/gain windows. The evolution of the pulse spectrum in space and the pulse evolution in space–time are discussed. In particular it is shown that the number and positions of the spectrum peaks change and the pulse exhibits beats. In addition to the propagating field, a stationary light generated by the sample is also discussed.
Light propagation is discussed in media with a cross coupling of the electric and magnetic component of an applied probe field. We derive the wave equations for a probe pulse propagating through such a medium and solve them analytically in Fourier space using the slowly varying envelope approximation. Our analysis reveals the influence of the different medium response coefficients on the propagation dynamics. We apply these results to a specific example system in which cross couplings are induced in an atomic medium by additional control fields. We show that the cross couplings render the propagation dynamics sensitive to the relative phase of the additional fields, and this phase dependence enables one to control the pulse during its propagation through the medium. Our results demonstrate that the magnetic field component of a probe beam can crucially influence the system dynamics already at experimentally accessible parameter ranges in dilute vapors.
Pulse propagation is studied in an atomic medium in the Λ configuration with the control field having a periodically varying phase (chirp). Numerical calculations of a probe-pulse shape have been performed and the results are compared with those for an approximate model neglecting absorption and nonadiabatic effects. It is shown that transparency occurs for probe pulses having a sufficiently narrow envelope and an appropriately suited chirp. For other chirped probe pulses the evolution of their spectra along a sample is studied. Using a projection method, one can divide a pulse into two components: one for which the medium is transparent and the remaining one for which it is opaque.
Nonlinear effects in pulse propagation through a medium consisting of four-level double-$\ensuremath{\Lambda}$-type systems are studied theoretically. We apply three continuous-wave driving fields and a pulsed probe field such that they form a closed interaction loop. Due to the closed loop and the finite frequency width of the probe pulses, the multiphoton resonance condition cannot be fulfilled, such that a time-dependent analysis is required. By identifying the different underlying physical processes we determine the parts of the solution relevant to calculate the linear and nonlinear response of the system. We find that the system can exhibit a strong intensity-dependent refractive index with small absorption over a range of several natural linewidths. For a realistic example we include Doppler and pressure broadening and calculate the nonlinear self-phase modulation in a gas cell with sodium vapor and argon buffer gas. We find that a self-phase modulation of $\ensuremath{\pi}$ is achieved after the propagation of a few centimeters through the medium while the absorption and pulse shape distortion in the corresponding spectral range is small.