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Continuous-wave mirrorless lasing at 221 μm in sodium vapors

A. M. Akulshin, Felipe Pedreros Bustos, Dmitry Budker

Published Jan 1, 2018• 20 citations
OpenAlex

Abstract

We demonstrate backward-directed continuous-wave (cw) emission at 2.21 {\mu}m generated on the 4P3/2-4S1/2 population-inverted transition in Na vapors two-photon excited with resonant laser light at 589 and 569 nm. Our study of power and atom-number-density threshold characteristics shows that lasing occurs at sub-10 mW total power of the applied laser light. The observed 6 mrad divergence is defined mainly by the aspect ratio of the gain region. We find that mirrorless lasing at 2.21 {\mu}m is magnetic field and polarization dependent that may be useful for remote magnetometry. The presented results could help determine the requirements for obtaining directional return from sodium atoms in the mesosphere

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Continuous-wave mirrorless lasing at 221 μm in sodium vapors

Alexander M. Akulshin, Felipe Pedreros Bustos, Dmitry Budker

population-inverted transition in Na vapors that are two-photon excited with resonant laser light at 589 and 569 nm. Our study of power and atom-number-density threshold characteristics shows that lasing occurs at sub-10 mW total power of the applied laser light. The observed 6 mrad divergence is defined mainly by the aspect ratio of the gain region. We find that mirrorless lasing at 2.21 μm is magnetic field and polarization dependent and this may be useful for remote magnetometry. The presented results could help determine the requirements for obtaining directional return from sodium atoms in the mesosphere.

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Population inversion on the 7S1/2− 6P3/2transition of cesium atoms is built by 455 nm diode laser pumping, and continuous-wave (cw) lasing is observed without the feedback on the gain medium from cavity mirrors. The stimulated emission at 1.47 µm infrared wavelength is restricted to a narrow angle along the direction of propagation of the pumping laser. Evidence of threshold-like characteristic is demonstrated in the cw mirrorless lasing dependence on pumping laser detuning, atomic density, and pumping light intensity. This compact structure can be used to generate mirrorless laser in a number of infrared wavelengths applied for the communication area. Moreover, it is expected to realize the narrow-linewidth optical frequency standard from an ultralow-finesse optical cavity.

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Mirrorless lasing from the mesospheric sodium layer could transform laser-guide-star emission into a directional, gain-driven source. Here we convert this possibility into quantitative requirements, using a ten-level velocity-resolved rate-equation model and an exact compression--irradiance equivalence. Continuous-wave operation remains below threshold across the accessible parameter space. The transient 4D5/2-4P3/2 channel at 2339 nm reaches threshold at pulsed irradiances of 104-105 Wm-2, given six- to ten-fold velocity compression. The obstacle is therefore not laser power but momentum transfer: spontaneous scattering delivers at most one recoil per event at a bounded rate, leaving chirp-driven compression an order of magnitude short. This gap defines the technological challenge for mesospheric mirrorless lasing.

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We report second-order intensity correlations g ( 2 ) ( τ ) of directional midinfrared emissions from sodium vapor under bichromatic continuous-wave excitation. Directional emission at 2.34 µ m in the forward direction and at 2.21 µ m in both forward and backward directions exhibits g ( 2 ) ( 0 ) values that exceed unity yet remain well below the thermal limit of 2, indicating subthermal photon bunching characteristics of a multimode collectively driven process rather than purely independent amplified spontaneous emission. Cross-correlation measurements reveal that the counterpropagating 2.21 − µ m beams are positively correlated, demonstrating dynamic coupling between the two emission channels. Persistent oscillations in g ( 2 ) ( τ ) , observed across a broad range of pump powers, shift systematically to higher frequencies with increasing excitation power, consistent with ac Stark shifts of hyperfine sublevels. Together, these observations establish that the emission arises from a phase-matched, continuous-wave collective process combining features of mirrorless lasing and amplified spontaneous emission, with long-range dipole coherence and velocity-selective coupling governing the photon statistics and the forward-backward emission symmetry. The experiment uses a 10-cm buffer-gas-free sodium vapor cell under bichromatic excitation at 589.2 and 569.0 nm; the emitted midinfrared light is detected in a Hanbury Brown–Twiss configuration. The demonstrated backward emission is of particular interest for applications in laser guide star generation and mesospheric remote sensing, where understanding the statistical properties of the emitted light is essential for optimizing sodium-based light sources.

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Population-inversion map of the mesospheric sodium ladder: continuous-wave and pulsed pumping schemes for directed emission

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Directed mirrorless lasing from the mesospheric sodium layer has been proposed as a way to overcome the isotropy of laser guide star fluorescence, with demonstrated cell-scale analogues and a demonstrated stand-off magnetometry application. Several transition paths on the Na ladder compete for the same pump photons. We build a ten-level rate-equation model of the ladder from NIST transition probabilities and evaluate every electric-dipole line under four continuous-wave pumping schemes, both in a Doppler-averaged treatment and in a velocity-selective treatment appropriate for the collision-poor mesosphere. Three design-relevant results emerge. At practically accessible continuous-wave irradiances the column-gain exponents remain far below unity, consistent with published feasibility estimates; the value of the classification is to identify which lines, schemes, and pulse formats merit further study.

arXiv:2608.09037•Aug 10, 2026•0 citations
We demonstrate backward-directed continuous-wave (cw) emission at 2.21 {\mu}m generated on the 4P3/2-4S1/2 population-inverted transition in Na vapors two-photon excited with resonant laser light at 589 and 569 nm. Our study of power and atom-number-density threshold characteristics shows that lasing occurs at sub-10 mW total power of the applied laser light. The observed 6 mrad divergence is defined mainly by the aspect ratio of the gain region. We find that mirrorless lasing at 2.21 {\mu}m is magnetic field and polarization dependent that may be useful for remote magnetometry. The presented results could help determine the requirements for obtaining directional return from sodium atoms in the mesosphere
population-inverted transition in Na vapors that are two-photon excited with resonant laser light at 589 and 569 nm. Our study of power and atom-number-density threshold characteristics shows that lasing occurs at sub-10 mW total power of the applied laser light. The observed 6 mrad divergence is defined mainly by the aspect ratio of the gain region. We find that mirrorless lasing at 2.21 μm is magnetic field and polarization dependent and this may be useful for remote magnetometry. The presented results could help determine the requirements for obtaining directional return from sodium atoms in the mesosphere.
Population inversion on the 7S1/2− 6P3/2transition of cesium atoms is built by 455 nm diode laser pumping, and continuous-wave (cw) lasing is observed without the feedback on the gain medium from cavity mirrors. The stimulated emission at 1.47 µm infrared wavelength is restricted to a narrow angle along the direction of propagation of the pumping laser. Evidence of threshold-like characteristic is demonstrated in the cw mirrorless lasing dependence on pumping laser detuning, atomic density, and pumping light intensity. This compact structure can be used to generate mirrorless laser in a number of infrared wavelengths applied for the communication area. Moreover, it is expected to realize the narrow-linewidth optical frequency standard from an ultralow-finesse optical cavity.
Mirrorless lasing from the mesospheric sodium layer could transform laser-guide-star emission into a directional, gain-driven source. Here we convert this possibility into quantitative requirements, using a ten-level velocity-resolved rate-equation model and an exact compression--irradiance equivalence. Continuous-wave operation remains below threshold across the accessible parameter space. The transient 4D5/2-4P3/2 channel at 2339 nm reaches threshold at pulsed irradiances of 104-105 Wm-2, given six- to ten-fold velocity compression. The obstacle is therefore not laser power but momentum transfer: spontaneous scattering delivers at most one recoil per event at a bounded rate, leaving chirp-driven compression an order of magnitude short. This gap defines the technological challenge for mesospheric mirrorless lasing.
Mirrorless lasing from the mesospheric sodium layer could transform laser-guide-star emission into a directional, gain-driven source. Here we convert this possibility into quantitative requirements, using a ten-level velocity-resolved rate-equation model and an exact compression--irradiance equivalence. Continuous-wave operation remains below threshold across the accessible parameter space. The transient 4D5/2-4P3/2 channel at 2339 nm reaches threshold at pulsed irradiances of 104-105 W/m-2, given six- to ten-fold velocity compression. The obstacle is therefore not laser power but momentum transfer: spontaneous scattering delivers at most one recoil per event at a bounded rate, leaving chirp-driven compression an order of magnitude short. This gap defines the technological challenge for mesospheric mirrorless lasing.
We report second-order intensity correlations g ( 2 ) ( τ ) of directional midinfrared emissions from sodium vapor under bichromatic continuous-wave excitation. Directional emission at 2.34 µ m in the forward direction and at 2.21 µ m in both forward and backward directions exhibits g ( 2 ) ( 0 ) values that exceed unity yet remain well below the thermal limit of 2, indicating subthermal photon bunching characteristics of a multimode collectively driven process rather than purely independent amplified spontaneous emission. Cross-correlation measurements reveal that the counterpropagating 2.21 − µ m beams are positively correlated, demonstrating dynamic coupling between the two emission channels. Persistent oscillations in g ( 2 ) ( τ ) , observed across a broad range of pump powers, shift systematically to higher frequencies with increasing excitation power, consistent with ac Stark shifts of hyperfine sublevels. Together, these observations establish that the emission arises from a phase-matched, continuous-wave collective process combining features of mirrorless lasing and amplified spontaneous emission, with long-range dipole coherence and velocity-selective coupling governing the photon statistics and the forward-backward emission symmetry. The experiment uses a 10-cm buffer-gas-free sodium vapor cell under bichromatic excitation at 589.2 and 569.0 nm; the emitted midinfrared light is detected in a Hanbury Brown–Twiss configuration. The demonstrated backward emission is of particular interest for applications in laser guide star generation and mesospheric remote sensing, where understanding the statistical properties of the emitted light is essential for optimizing sodium-based light sources.
Directed mirrorless lasing from the mesospheric sodium layer has been proposed as a way to overcome the isotropy of laser guide star fluorescence, with demonstrated cell-scale analogues and a demonstrated stand-off magnetometry application. Several transition paths on the Na ladder compete for the same pump photons. We build a ten-level rate-equation model of the ladder from NIST transition probabilities and evaluate every electric-dipole line under four continuous-wave pumping schemes, both in a Doppler-averaged treatment and in a velocity-selective treatment appropriate for the collision-poor mesosphere. Three design-relevant results emerge. At practically accessible continuous-wave irradiances the column-gain exponents remain far below unity, consistent with published feasibility estimates; the value of the classification is to identify which lines, schemes, and pulse formats merit further study.