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Annual Meeting Optical Society of America

Lasing without population inversion in ruby

Cunkai Wu, Yang Zhao

Published Jan 1, 1993• 0 citations
Publisher

Abstract

Lasing without population inversion was studied in a three-level solid state medium of ruby. The two closely-spaced lower levels are the Zeeman split sublevels of the ground state 4A2 of ruby, corresponding to M=−3/2 and M=+l/2. The transition between the lower levels is the electric dipole-forbidden. When the angle between the constant magnetic field and C-axis of ruby is 90°, the transition matrix element of the electric dipole-forbidden transition is quite large.1 A strong microwave field which operates at K-band coherently couples the two lower levels.2 Changing the constant magnetic field intensity or adjusting the frequency of the pumping microwave field, the exact resonant excitation can be established. The upper level of the lasing process is the Zeeman split sub-level M=−l/2 of 2E state. The ruby crystal, with about 0.05% chromium concentration, is placed at the center of a cylindrical cavity and cooled by liquid helium. With 500 Gauss magnetic field, the coupling microwave frequency is 13.1 Ghz and the required power is around 100 W/cm2.

DOI
10.1364/oam.1993.thq.5

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Direct relaxation within the optically excited $\overline{E}(^{2}E)$ level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the $c$ axis. At low pump intensities, the experimental relaxation rates are found to be in excellent agreement with the theory by Blume et al., predicting a fifth-power dependence on field and a ${cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}$ dependence on orientation. The observed proportionality constant of 4.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}19}$ ${\mathrm{G}}^{\ensuremath{-}5}$${\mathrm{s}}^{\ensuremath{-}1}$ is close to the theoretical estimate based on static experiments in ruby. When increasing optical pumping, the phonon-bath conduction is demonstrated to become the limiting process due to resonant trapping of the phonons. Following pulsed excitation, a prolonging of the decay time by a factor up to 13 is attained at excited-state concentrations ${N}^{*}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. In stationary experiments, a nonlinear increase with ${N}^{*}$ is observed of the equilibrium population of the upper Zeeman level of $\overline{E}$ to over a decade above the nonbottlenecked value, corresponding to bottlenecking factors of over \ensuremath{\sim}200. Under the assumption of a constant phonon lifetime of the order of the flight time through the illuminated region, rate equations appear to consistently account for the experiments. A Gaussian-type resonance line, fully homogenized supposedly by magnetic interactions with the surrounding Al nuclei and ${\mathrm{Cr}}^{3+}$ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the $\overline{E}$ direct transition in ruby as a tunable phonon generator and detector with bandwidth 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the practical frequency range of 2-15 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Physical review. B, Condensed matter•Sep 1, 1979•19 citations
Lasing without population inversion was studied in a three-level solid state medium of ruby. The two closely-spaced lower levels are the Zeeman split sublevels of the ground state 4A2 of ruby, corresponding to M=−3/2 and M=+l/2. The transition between the lower levels is the electric dipole-forbidden. When the angle between the constant magnetic field and C-axis of ruby is 90°, the transition matrix element of the electric dipole-forbidden transition is quite large.1 A strong microwave field which operates at K-band coherently couples the two lower levels.2 Changing the constant magnetic field intensity or adjusting the frequency of the pumping microwave field, the exact resonant excitation can be established. The upper level of the lasing process is the Zeeman split sub-level M=−l/2 of 2E state. The ruby crystal, with about 0.05% chromium concentration, is placed at the center of a cylindrical cavity and cooled by liquid helium. With 500 Gauss magnetic field, the coupling microwave frequency is 13.1 Ghz and the required power is around 100 W/cm2.
Ruby exhibits the Zeeman effect in the energy levels responsible for the absorption of the R1line. When a ruby laser is directed to pass through a section of unexcited ruby rod, the intensity of the transmitted beam is strongly dependent upon the magnetic field applied to the absorber. This effect was used to modulate the amplitude of a pulsed ruby laser in the microwave frequency region. The experimental modulator consisted of a 0.2- inch long ruby absorber located at one end of anS-band TE111mode cylindrical cavity pumped by a 3.2-Gc/s microwave source. A dc bias magnetic field was also applied to the absorber. When both the laser and the absorber rods were cooled to 80°K, the modulated beam attained maximum modulation index with a bias field of 2.5 kOe. This and other experimental results agree well with calculations made from theoretical analysis of this modulation technique, and indicate that the various known relaxation mechanisms in the spin system of ruby do not impose a frequency limit to this method of modulation.
Population trapping in the ground state spin sublevels of Cr 3+ in ruby at liquid helium temperature is considered. It is proposed to excite the R 1 -transition by a bichromatic laser beam with an optical frequency difference matching the ground state spin sublevels splitting. If the excitation is strong enough to decouple Cr 3+ from its environment, responsible for dephasing, an appreciable amount of the population is trapped in a particular superposition of the spin sublevels. This superposition state does not interact with the laser beam because of the destructive interference of the quantum paths constituting the transition. Population trapping can be detected by the reduced luminescence from the excited state and by the magnetization ringing originating from the ground state spin coherence.
Summary form only given. We study a model for an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity and producing two laser fields, one of them without population inversion. Each laser field couples to only one of the transitions of the three-level medium. We have studied our model for parameters appropriate to two real atomic systems (i) a cascade scheme in atomic /sup 138/Ba looking for lasing with (without) inversion at /spl lambda//sub /spl beta//=554 nm (/spl lambda//sub /spl alpha//=821 nm), and (ii) a V-scheme in atomic /sup 85/Rb with ordinary lasing at /spl lambda//sub /spl alpha//=780 nm and lasing without inversion (LWI) at /spl lambda//sub /spl alpha//=4216 nm. These two cases are qualitatively different in that two-photon processes are responsible for inversionless gain in case (i) while LWI in case (ii) arises from one-photon processes. Moreover, the frequency up-conversion ratio is R=0.67 for the case of /sup 138/Ba and it is R=1.88 for the case of /sup 85/Rb. In spite of the fact that the frequencies of the two laser fields are relatively different, our results show that dual-wavelength lasing extends up to Doppler broadening values typical for optical transitions of atoms in a vapor cell. In case (i) /spl alpha/-lasing occurs without two-photon inversion only for approximately the lower half of the domain of Doppler-broadening values. However, in case (ii) one has LWI in all the domains. Some considerations for a practical realization of the dual-wavelength inversionless-conventional laser are discussed.
The spectral character of the stimulated emission from ruby has been investigated; we found that the zero-field splitting (0.38 cm−1) of the 4A2 ground level and the cavity optical length and its reflectivity determine the spectral character of this emission. At 300°K the system is induced into oscillation in a number of cavity modes separated by Δv = (2le12)−1, where l is the length of the resonator and e12 is the index of refraction for the ordinary ray. At T≅80°K the Ē(2E) → ±32(A2) and the Ē(2E) → ±12(4A2) transitions were identified in the stimulated emission spectrum. Each can oscillate in an axial cavity mode (or modes) plus an off-axis mode at the center of the transition. At 4.2°K the system oscillates in off-axis modes, unless the length of the cavity l is such that it has axial resonances coincident with the transition frequencies. An analysis of the temperature dependence of the oscillation threshold for the separate transitions is presented and is compared with the observed behavior.
Coherent population trapping (CPT) in a three-level atomic medium pumped by two subsequent short optical pulses is considered under the condition of negligible population decay from the excited optical state. It is shown that the amount of atomic population transferred to the excited state by the combined action of the pulses strongly depends on the phase of the ground-state coherence excited by the first pulse at the arrival time of the second pulse. Oscillatory behavior of optical excitation efficiency on the time delay between the pulses is predicted. It is also shown that saturating optical pulses can produce population inversion in a resonantly pumped quasi-two-level system. A class of solid materials in which the predicted phenomena can be observed at room temperature is found. It includes some rare-earth and transition-metal doped dielectric crystals where Orbach relaxation between ground-state Zeeman states is suppressed: ruby, alexandrite, and several others. On the basis of the theoretical predictions, experimental observation of Ramsey fringes in CPT spectrum of ruby is reported.
Direct relaxation within the optically excited E‾(2E)\overline{E}(^{2}E)E(2E) level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the ccc axis. At low pump intensities, the experimental relaxation rates are found to be in excellent agreement with the theory by Blume et al., predicting a fifth-power dependence on field and a ${cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}$ dependence on orientation. The observed proportionality constant of 4.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}19}$ ${\mathrm{G}}^{\ensuremath{-}5}$${\mathrm{s}}^{\ensuremath{-}1}$ is close to the theoretical estimate based on static experiments in ruby. When increasing optical pumping, the phonon-bath conduction is demonstrated to become the limiting process due to resonant trapping of the phonons. Following pulsed excitation, a prolonging of the decay time by a factor up to 13 is attained at excited-state concentrations ${N}^{*}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. In stationary experiments, a nonlinear increase with N∗{N}^{*}N∗ is observed of the equilibrium population of the upper Zeeman level of E‾\overline{E}E to over a decade above the nonbottlenecked value, corresponding to bottlenecking factors of over \ensuremath{\sim}200. Under the assumption of a constant phonon lifetime of the order of the flight time through the illuminated region, rate equations appear to consistently account for the experiments. A Gaussian-type resonance line, fully homogenized supposedly by magnetic interactions with the surrounding Al nuclei and Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the E‾\overline{E}E direct transition in ruby as a tunable phonon generator and detector with bandwidth 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the practical frequency range of 2-15 ${\mathrm{cm}}^{\ensuremath{-}1}$.