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Physical Review A

Spatial distortions of laser pulses in coherent on-resonance propagation: Large-scale self-focusing

Jacques de Lamare, Michel Comte, Ph.J. Kupecek

Published Oct 1, 1994• 11 citations
Publisher

Abstract

When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a ${\mathrm{Tm}}^{169}$ vapor.

DOI
10.1103/physreva.50.3366

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Spatial distortions of laser pulses in coherent on-resonance propagation: Small-scale self-focusing

Jacques de Lamare, Ph.J. Kupecek, Michel Comte

We present a quantitative model for coherent on-resonance small-scale self-focusing of laser pulses in atomic media. A vapor-induced diaphragm effect at the edge of the pulse generates a pattern of diffraction rings that modulates the initial transverse profile of the pulse. Practically, because of the spatial asymmetry of the original pulse, this diffraction pattern is perturbed and dots appear superimposed upon the rings. A large-scale self-focusing phenomenon is then initiated from each individual dot and the global transverse energy profile of the pulse evolves in a hot-spot pattern. This final pattern is characteristic of what is usually called small-scale self-focusing. Our theoretical predictions are compared with both the results of an experiment on a $^{169}\mathrm{Tm}$ vapor and the predictions of existing models.

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On-resonance self-focusing of coherent optical pulses in absorbers

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Analytic and numerical solutions of the Maxwell–Bloch equations, including transverse and timedependent phase variations, predict on-resonance self-focusing (SF) and elucidate its formation due to the combined effect of diffraction and inertial response of the medium. This new SF can be characterized by a simple parameter in terms of the beam and medium parameters. Recently, two independent experiments on SF in Na and Ne demonstrated convincingly this new SF effect for spatially nonuniform self-induced transparency pulses propagating in thick resonant absorbers.

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Self-focusing of spatially nonuniform coherent pulses has been seen in the center of Na and Ne transitions. Self-focusing and temporal reshaping were studied as a function of laser detuning in Na. The dependence of on-resonance self-focusing upon input pulse area was observed in Ne. Numerical solutions of the Maxwell-Bloch equations including transverse variations predict coherent self-focusing and yield a single parameter for estimating its importance for a given beam diameter and sample absorption.

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Analytical and numerical methods are used to study the transverse reshaping that occurs when ultrashort optical pulses propagate through media resonant to the pulse-carrier frequency. The field is described by the scalar quasi-optic equation, and the material system by the full Bloch equations describing a distribution of homogeneously broadened two-level molecules. Transverse derivatives in the field equation provide the coupling leading to the development of radially dependent frequency variations and phase curvature. We have studied the origin and evolution of transverse energy flow and investigated the conditions under which this leads to significant coherent self-focusing. The physical mechanisms responsible for the onset and development of the focusing phenomenon are discussed and related to other types of self-confinement of optical pulses.

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Dispersive self-focusing in atomic media

A. W. McCord, R. J. Ballagh, J. Cooper

An analytic model based on a single encoding–diffraction sequence is developed to describe the first main region of focusing that occurs when a cw off-resonant monochromatic Gaussian beam enters a medium of two-state atoms. A quantitative definition of the dispersive regime for self-focusing is given, and an explicit form is obtained for the field encoding produced by the initial propagation. The phase profile of this encoded field incorporates the effects of both the medium and diffraction, and we find a simple expression for the fundamental length scale, which determines where diffractive effects become dominant. An analytic expression is obtained for the on-axis field, which results once the encoded field begins to diffract freely, and simple expressions for the position and size of the main enhancement are given. We give a simple interpretation of the focusing and the two parameters required for its characterization. The model gives excellent agreement to the full numeric solution over a wide parameter range and, in particular, explains the rapid on-axis oscillations at the outset of focusing.

Journal of the Optical Society of America B•Jun 1, 1988•18 citations

Simultaneous generation of N coherent pulses of various areas under self-diffraction in87Rb vapors

Sergey N. Bagaev, Igor B. Mekhov, Чехонин Игорь Анатольевич +1 more

Subject of study. The self-diffraction process of a resonant pulse in a dense extended resonant medium was studied for the first time to our knowledge. This process leads to an angular deflection of the output radiation and sequential emission of a large series of N pulses with a variable area in the range (−3π,…,0,…,3π). The pulses are emitted from a small focusing region (0.1–1 mm) of the pump pulse in a dense extended resonant medium. The pulse wavelength corresponds to the resonant transition D287Rb (wavelength 780.24 nm). Aim of study. The nonlinear effect of the self-diffraction of a laser pulse with a cylindrical wavefront is studied in an extended resonant medium of rubidium vapor to develop new resonant microwave photonics devices using laser signal-processing methods in the microwave spectrum. Method. A transverse spatial profile of the electric field strength of a special shape f(x) is created in the caustic of a focused beam of a laser pump pulse with a cylindrical wavefront. The pump pulse must have a converging (for example, cylindrical) wavefront. Computer-synthesized holograms developed by us are used to create an arbitrary f(x) profile. Main results. The effect of the self-diffraction of a pump pulse is studied. This is accompanied by the emission of a series of N coherent resonant pulses with different areas in the range (−3π,…,0,…,3π) from a short focusing region (0.1–1 mm) of a resonant laser pump pulse. The self-diffraction of the pump pulse resulted in 16 emitted pulses with different areas. The distribution of series pulses over the diffraction angle was observed in the angle range from −5∘ to +4∘. The nonlinear generation of 0π-pulses was observed at some angles. The results verify the nonlinear generation of 0π-pulses over a short interaction length between light and a resonant medium for the first time to our knowledge. Practical significance. The obtained results on the effect of the self-diffraction of a resonant pulse with a transverse spatial profile f(x) will serve as a basis for the development of prototype devices for signal-processing problems using low-power laser diodes.

Journal of Optical Technology•May 1, 2023•0 citations
When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a Tm169{\mathrm{Tm}}^{169}Tm169 vapor.
We present a quantitative model for coherent on-resonance small-scale self-focusing of laser pulses in atomic media. A vapor-induced diaphragm effect at the edge of the pulse generates a pattern of diffraction rings that modulates the initial transverse profile of the pulse. Practically, because of the spatial asymmetry of the original pulse, this diffraction pattern is perturbed and dots appear superimposed upon the rings. A large-scale self-focusing phenomenon is then initiated from each individual dot and the global transverse energy profile of the pulse evolves in a hot-spot pattern. This final pattern is characteristic of what is usually called small-scale self-focusing. Our theoretical predictions are compared with both the results of an experiment on a 169Tm^{169}\mathrm{Tm}169Tm vapor and the predictions of existing models.
Analytic and numerical solutions of the Maxwell–Bloch equations, including transverse and timedependent phase variations, predict on-resonance self-focusing (SF) and elucidate its formation due to the combined effect of diffraction and inertial response of the medium. This new SF can be characterized by a simple parameter in terms of the beam and medium parameters. Recently, two independent experiments on SF in Na and Ne demonstrated convincingly this new SF effect for spatially nonuniform self-induced transparency pulses propagating in thick resonant absorbers.
Self-focusing of spatially nonuniform coherent pulses has been seen in the center of Na and Ne transitions. Self-focusing and temporal reshaping were studied as a function of laser detuning in Na. The dependence of on-resonance self-focusing upon input pulse area was observed in Ne. Numerical solutions of the Maxwell-Bloch equations including transverse variations predict coherent self-focusing and yield a single parameter for estimating its importance for a given beam diameter and sample absorption.
Analytical and numerical methods are used to study the transverse reshaping that occurs when ultrashort optical pulses propagate through media resonant to the pulse-carrier frequency. The field is described by the scalar quasi-optic equation, and the material system by the full Bloch equations describing a distribution of homogeneously broadened two-level molecules. Transverse derivatives in the field equation provide the coupling leading to the development of radially dependent frequency variations and phase curvature. We have studied the origin and evolution of transverse energy flow and investigated the conditions under which this leads to significant coherent self-focusing. The physical mechanisms responsible for the onset and development of the focusing phenomenon are discussed and related to other types of self-confinement of optical pulses.
An analytic model based on a single encoding–diffraction sequence is developed to describe the first main region of focusing that occurs when a cw off-resonant monochromatic Gaussian beam enters a medium of two-state atoms. A quantitative definition of the dispersive regime for self-focusing is given, and an explicit form is obtained for the field encoding produced by the initial propagation. The phase profile of this encoded field incorporates the effects of both the medium and diffraction, and we find a simple expression for the fundamental length scale, which determines where diffractive effects become dominant. An analytic expression is obtained for the on-axis field, which results once the encoded field begins to diffract freely, and simple expressions for the position and size of the main enhancement are given. We give a simple interpretation of the focusing and the two parameters required for its characterization. The model gives excellent agreement to the full numeric solution over a wide parameter range and, in particular, explains the rapid on-axis oscillations at the outset of focusing.
Subject of study. The self-diffraction process of a resonant pulse in a dense extended resonant medium was studied for the first time to our knowledge. This process leads to an angular deflection of the output radiation and sequential emission of a large series of N pulses with a variable area in the range (−3π,…,0,…,3π). The pulses are emitted from a small focusing region (0.1–1 mm) of the pump pulse in a dense extended resonant medium. The pulse wavelength corresponds to the resonant transition D287Rb (wavelength 780.24 nm). Aim of study. The nonlinear effect of the self-diffraction of a laser pulse with a cylindrical wavefront is studied in an extended resonant medium of rubidium vapor to develop new resonant microwave photonics devices using laser signal-processing methods in the microwave spectrum. Method. A transverse spatial profile of the electric field strength of a special shape f(x) is created in the caustic of a focused beam of a laser pump pulse with a cylindrical wavefront. The pump pulse must have a converging (for example, cylindrical) wavefront. Computer-synthesized holograms developed by us are used to create an arbitrary f(x) profile. Main results. The effect of the self-diffraction of a pump pulse is studied. This is accompanied by the emission of a series of N coherent resonant pulses with different areas in the range (−3π,…,0,…,3π) from a short focusing region (0.1–1 mm) of a resonant laser pump pulse. The self-diffraction of the pump pulse resulted in 16 emitted pulses with different areas. The distribution of series pulses over the diffraction angle was observed in the angle range from −5∘ to +4∘. The nonlinear generation of 0π-pulses was observed at some angles. The results verify the nonlinear generation of 0π-pulses over a short interaction length between light and a resonant medium for the first time to our knowledge. Practical significance. The obtained results on the effect of the self-diffraction of a resonant pulse with a transverse spatial profile f(x) will serve as a basis for the development of prototype devices for signal-processing problems using low-power laser diodes.