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Optical Instabilities in Sodium Vapor and Vertical Cavity Surface Emitting Lasers

Jeffrey W. Grantham

Published Jan 1, 1991• 0 citations
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Abstract

This dissertation investigates three different optical instabilities: cw conical emission, bifurcations of optical transverse solitary waves, and asymmetric gain modification in a vertical cavity surface emitting laser (VCSEL). The first two instabilities occur in sodium vapor while the third occurs in a new type of semiconductor laser. For the conical emission instability, the first comparison and agreement between theory and experiment is given. The conical emission process is modeled as a series of nonlinear effects including self-trapping of the pump beam, Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, propagational four-wave mixing, and diffraction and pump-induced refraction of the new frequencies. Each step of the emission process is thoroughly examined and explained. Detailed comparisons are made between experimental observables and numerical calculations including near-field and far-field spatial profiles, frequency spectra, and cone angles. All comparisons show good agreement. In a different but related experiment, bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations which result in transverse cell-exit profiles with the beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one-way computations. Evidence is also presented for the first observation of a double-peaked Raman gain. In the third experiment, a temporal instability is examined in a GaAs VCSEL. Strong evidence is presented for an asymmetric gain modification induced when a strong optical signal is injected into the Fabry-Perot transmission peak of the VCSEL while it is lasing. This gain modification results in increased absorption on the high frequency side of the injected signal and increased gain on the low frequency side as manifested by the formation of an optical sideband. The frequency of the sideband depends on the intensity of the injected signal with frequencies (> 50 GHz) well beyond the predicted relaxation oscillation frequency being observed. Very efficient nondegenerate four-wave mixing is also observed.

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Bifurcations of optical transverse solitary waves

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Bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations resulting in cell- exit profiles with beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one- way computations. Temporal and longitudinal development of the cell-exit profiles is shown, demonstrating both the instability nature of this phenomenon and its solitary wave nature. The first evidence is also presented for a double-peaked Raman gain

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 16, 1992•0 citations

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The gain spectrum of a semiconductor can be locally modified by a strong nearly resonant laser field through population pulsations.1,2 Rayleigh-gain, an asymmetric modification of the gain profile of an atom, has been investigated previously.3,4 Laser diode longitudinal modes have been used to show gain asymmetry1,5, but the mode spacing (75 GHz5) has limited the observation to the periphery of the curve. Mapping the more closely spaced gain peak and dip is important because they can significantly modify the output spectrum of a laser (creating new lasing lines at the new gain peak and extinguishing the original lasing with the gain dip). Pump/probe experiments in traveling wave amplifiers (TWA)6 have shown the gain to be asymmetric, but the gain peak and dip were broadened because the injected signal grew in power (from ≃ 87 μW to 4.4mW6) during propagation. Using a high Q vertical-cavity surface-emitting laser (VCSEL) as the gain medium we have intracavity powers at the injected frequency that do not grow with propagation and are much higher than the TWA experiments (up to 75 mW in a 5 μm spot), pushing the gain peak as far as 36.5 GHz from the injected frequency. Rather than using longitudinal modes to probe discretely the gain asymmetry, when the gain extrema are within 10 GHz of the injected frequency we directly observe localized dips and peaks in the continuous ouput spectrum of the VCSEL. As increased injected power pushes the gain extrema out further, we observe modification of the line shape and pushing of the lasing. We find that the detuning of the gain extrema from the injected frequency increases linearly with the intracavity intensity at the injected frequency (in contrast with relaxation oscillations and other effects that scale with the field level). Understanding local modifications of the cw gain profile is of crucial importance to elucidate instabilities in semiconductors lasers.

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Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.

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Conical emission and coherent sideband generation in laser propagation

Michael E. Crenshaw, Cyrus D. Cantrell

Computational results show that the conical emission and Rabi sidebands observed when a nearly resonant laser pulse propagates through an atomic vapor are the result of the breakup of the pulse into solitary waves. For an incident pulse with a transverse as well as a temporal profile, the crests and troughs of the 2-D solitary waves are curved in a time-radius plane. The temporal modulation associated with pulse breakup appears as Rabi sidebands in the spectrum, while the curvature of the solitary waves in the time-radius plane results in a transverse spatial modulation, resulting in conical emission in the far field. These results were obtained by performing detailed numerical calculations of the time-dependent paraxial propagation of a cylindrically symmetric laser pulse through a vapor of two-level atoms. Our results can be interpreted readily in terms of optical nutation on the Bloch sphere and in terms of noncollinear phase matching through the curvature of the solitary waves rather than through additional parametrically generated waves. The cone opening angle depends on the initial transverse profile of the pulse and the process of beam breakup as well as self-focusing.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
This dissertation investigates three different optical instabilities: cw conical emission, bifurcations of optical transverse solitary waves, and asymmetric gain modification in a vertical cavity surface emitting laser (VCSEL). The first two instabilities occur in sodium vapor while the third occurs in a new type of semiconductor laser. For the conical emission instability, the first comparison and agreement between theory and experiment is given. The conical emission process is modeled as a series of nonlinear effects including self-trapping of the pump beam, Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, propagational four-wave mixing, and diffraction and pump-induced refraction of the new frequencies. Each step of the emission process is thoroughly examined and explained. Detailed comparisons are made between experimental observables and numerical calculations including near-field and far-field spatial profiles, frequency spectra, and cone angles. All comparisons show good agreement. In a different but related experiment, bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations which result in transverse cell-exit profiles with the beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one-way computations. Evidence is also presented for the first observation of a double-peaked Raman gain. In the third experiment, a temporal instability is examined in a GaAs VCSEL. Strong evidence is presented for an asymmetric gain modification induced when a strong optical signal is injected into the Fabry-Perot transmission peak of the VCSEL while it is lasing. This gain modification results in increased absorption on the high frequency side of the injected signal and increased gain on the low frequency side as manifested by the formation of an optical sideband. The frequency of the sideband depends on the intensity of the injected signal with frequencies (> 50 GHz) well beyond the predicted relaxation oscillation frequency being observed. Very efficient nondegenerate four-wave mixing is also observed.
Bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations resulting in cell- exit profiles with beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one- way computations. Temporal and longitudinal development of the cell-exit profiles is shown, demonstrating both the instability nature of this phenomenon and its solitary wave nature. The first evidence is also presented for a double-peaked Raman gain
The gain spectrum of a semiconductor can be locally modified by a strong nearly resonant laser field through population pulsations.1,2 Rayleigh-gain, an asymmetric modification of the gain profile of an atom, has been investigated previously.3,4 Laser diode longitudinal modes have been used to show gain asymmetry1,5, but the mode spacing (75 GHz5) has limited the observation to the periphery of the curve. Mapping the more closely spaced gain peak and dip is important because they can significantly modify the output spectrum of a laser (creating new lasing lines at the new gain peak and extinguishing the original lasing with the gain dip). Pump/probe experiments in traveling wave amplifiers (TWA)6 have shown the gain to be asymmetric, but the gain peak and dip were broadened because the injected signal grew in power (from ≃ 87 μW to 4.4mW6) during propagation. Using a high Q vertical-cavity surface-emitting laser (VCSEL) as the gain medium we have intracavity powers at the injected frequency that do not grow with propagation and are much higher than the TWA experiments (up to 75 mW in a 5 μm spot), pushing the gain peak as far as 36.5 GHz from the injected frequency. Rather than using longitudinal modes to probe discretely the gain asymmetry, when the gain extrema are within 10 GHz of the injected frequency we directly observe localized dips and peaks in the continuous ouput spectrum of the VCSEL. As increased injected power pushes the gain extrema out further, we observe modification of the line shape and pushing of the lasing. We find that the detuning of the gain extrema from the injected frequency increases linearly with the intracavity intensity at the injected frequency (in contrast with relaxation oscillations and other effects that scale with the field level). Understanding local modifications of the cw gain profile is of crucial importance to elucidate instabilities in semiconductors lasers.
Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.
Experimentally observed near-field and far-field spatial profiles, frequency spectra, and cone angles are in good agreement with numerical computations of a theory that includes Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, four-wave mixing, propagational coupling, self-trapping of the pump beam, and diffraction and pump-induced refraction of the new frequencies. The use of a cw laser beam detuned from resonance by only a few gigahertz makes the computational problem tractable, leading to a simple physical model of this spatiotemporal instability.
Computational results show that the conical emission and Rabi sidebands observed when a nearly resonant laser pulse propagates through an atomic vapor are the result of the breakup of the pulse into solitary waves. For an incident pulse with a transverse as well as a temporal profile, the crests and troughs of the 2-D solitary waves are curved in a time-radius plane. The temporal modulation associated with pulse breakup appears as Rabi sidebands in the spectrum, while the curvature of the solitary waves in the time-radius plane results in a transverse spatial modulation, resulting in conical emission in the far field. These results were obtained by performing detailed numerical calculations of the time-dependent paraxial propagation of a cylindrically symmetric laser pulse through a vapor of two-level atoms. Our results can be interpreted readily in terms of optical nutation on the Bloch sphere and in terms of noncollinear phase matching through the curvature of the solitary waves rather than through additional parametrically generated waves. The cone opening angle depends on the initial transverse profile of the pulse and the process of beam breakup as well as self-focusing.