Electric-dipole vector model of the ruby laser transition taking account of the crystal structure

Experiments are described in which a dilute ruby crystal is found to emit spontaneously a short pulse of light, the photon echo, at a time $\ensuremath{\approx}{\ensuremath{\tau}}_{s}$ after irradiation by two successive ruby-laser pulses separated by ${\ensuremath{\tau}}_{s}$. The phenomenon is explained in terms of a macroscopic oscillating electric dipole moment, which is momentarily reformed at the time the photon echo is observed. The analysis predicts the echo polarization as well as the propagation direction relative to the input pulses. A necessary condition for obtaining echoes in ruby is the application of a moderate magnetic field close to the optic axis of the crystal, and a simple model based on ${\mathrm{Cr}}^{3+}$ -Al interactions is offered to account for this magnetic-field behavior. The relaxation time of the echo is found to exceed 250 nsec at 4.2\ifmmode^\circ\else\textdegree\fi{}K but to be less than 70 nsec at 14\ifmmode^\circ\else\textdegree\fi{}K, and is thought to be due to phonon-induced transitions in the excited $^{2}E(\overline{E})$ level. Multiple echo formation is also described.Experiments are described in which a dilute ruby crystal is found to emit spontaneously a short pulse of light, the photon echo, at a time $\ensuremath{\approx}{\ensuremath{\tau}}_{s}$ after irradiation by two successive ruby-laser pulses separated by ${\ensuremath{\tau}}_{s}$. The phenomenon is explained in terms of a macroscopic oscillating electric dipole moment, which is momentarily reformed at the time the photon echo is observed. The analysis predicts the echo polarization as well as the propagation direction relative to the input pulses. A necessary condition for obtaining echoes in ruby is the application of a moderate magnetic field close to the optic axis of the crystal, and a simple model based on ${\mathrm{Cr}}^{3+}$-Al interactions is offered to account for this magnetic-field behavior. The relaxation time of the echo is found to exceed 250 nsec at 4.2\ifmmode^\circ\else\textdegree\fi{}K but to be less than 70 nsec at 14\ifmmode^\circ\else\textdegree\fi{}K, and is thought to be due to phonon-induced transitions in the excited $^{2}E(\overline{E})$ level. Multiple echo formation is also described.

Physical ReviewJan 7, 1966689 citations

Photoelectric domain structure in ruby crystals

S. A. Basun, A. A. Kaplyanskiy, S.P. Feofilov

RpPhMFeb 1, 19861 citation

Effects of an electric field on the laser emission of ruby

W. Kaiser, H.E. Lessing

The European Physical Journal ADec 1, 19634 citations

Spontaneous emission rates of a single-impurity molecule in dependence on its orientation in biaxial host crystal

Inna Rebane

The spontaneous emission rate (SER) of a single impurity molecule for the electric dipole transition has been found in the case where the birefringence of a host crystal is taken into account. SER depends on the orientation of the dipole moment with respect to the principal axes of the dielectric (permittivity) tensor of the host crystal and on the principal refractive indices of the crystal. We use the model where the average electromagnetic field in the crystal is classical and effective electric field vectors at the site of the impurity molecule are found for the interstitial impurity which is located in the center of the crystal cell. The results of calculations for seven biaxial host crystals (anthracene, chrysene, diphenyl, fluorine, naphthalene, phenanthrene, terphenyl) are presented. It is shown that values of SER form in the space a three- axial ellipsoid. Differences in the values of SER for the electric dipole transition in the same host crystal are up to 34%.The spontaneous emission rate (SER) of a single impurity molecule for the electric dipole transition has been found in the case where the birefringence of a host crystal is taken into account. SER depends on the orientation of the dipole moment with respect to the principal axes of the dielectric (permittivity) tensor of the host crystal and on the principal refractive indices of the crystal. We use the model where the average electromagnetic field in the crystal is classical and effective electric field vectors at the site of the impurity molecule are found for the interstitial impurity which is located in the center of the crystal cell. The results of calculations for seven biaxial host crystals (anthracene, chrysene, diphenyl, fluorine, naphthalene, phenanthrene, terphenyl) are presented. It is shown that values of SER form in the space a three- axial ellipsoid. Differences in the values of SER for the electric dipole transition in the same host crystal are up to 34%.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEAug 3, 20051 citation

The Coherence and Directivity of Emission from a Ruby Laser

M. D. Galanin, Aleksandr M Leontovich, Zoya A Chizhikova

Journal of Experimental and Theoretical PhysicsJan 1, 19630 citations

Observation of the 5p3/2→6p3/2 electric-dipole-forbidden transition in atomic rubidium using optical-optical double-resonance spectroscopy

F. Ponciano-Ojeda, Santiago Hernández-Gómez, O López-Hernández +7 more

Direct evidence of excitation of the $5{p}_{3/2}\ensuremath{\rightarrow}6{p}_{3/2}$ electric-dipole-forbidden transition in atomic rubidium is presented. The experiments were performed in a room-temperature rubidium cell with continuous-wave external cavity diode lasers. Optical-optical double-resonance spectroscopy with counterpropagating beams allows the detection of the nondipole transition free of Doppler broadening. The $5{p}_{3/2}$ state is prepared by excitation with a laser locked to the maximum $F$ cyclic transition of the ${D}_{2}$ line, and the forbidden transition is produced by excitation with a 911 nm laser. Production of the forbidden transition is monitored by detection of the 420 nm fluorescence that results from decay of the $6{p}_{3/2}$ state. Spectra with three narrow lines ($\ensuremath{\approx}13$ MHz FWHM) with the characteristic $F\ensuremath{-}1, F$, and $F+1$ splitting of the $6{p}_{3/2}$ hyperfine structure in both rubidium isotopes were obtained. The results are in very good agreement with a direct calculation that takes into account the $5s\ensuremath{\rightarrow}5{p}_{3/2}$ preparation dynamics, the $5{p}_{3/2}\ensuremath{\rightarrow}6{p}_{3/2}$ nondipole excitation geometry, and the $6{p}_{3/2}\ensuremath{\rightarrow}5{s}_{1/2}$ decay. The comparison also shows that the electric-dipole-forbidden transition is a very sensitive probe of the preparation dynamics.Direct evidence of excitation of the $5{p}_{3/2}\ensuremath{\rightarrow}6{p}_{3/2}$ electric-dipole-forbidden transition in atomic rubidium is presented. The experiments were performed in a room-temperature rubidium cell with continuous-wave external cavity diode lasers. Optical-optical double-resonance spectroscopy with counterpropagating beams allows the detection of the nondipole transition free of Doppler broadening. The $5{p}_{3/2}$ state is prepared by excitation with a laser locked to the maximum $F$ cyclic transition of the ${D}_{2}$ line, and the forbidden transition is produced by excitation with a 911 nm laser. Production of the forbidden transition is monitored by detection of the 420 nm fluorescence that results from decay of the $6{p}_{3/2}$ state. Spectra with three narrow lines ($\ensuremath{\approx}13$ MHz FWHM) with the characteristic $F\ensuremath{-}1, F$, and $F+1$ splitting of the $6{p}_{3/2}$ hyperfine structure in both rubidium isotopes were obtained. The results are in very good agreement with a direct calculation that takes into account the $5s\ensuremath{\rightarrow}5{p}_{3/2}$ preparation dynamics, the $5{p}_{3/2}\ensuremath{\rightarrow}6{p}_{3/2}$ nondipole excitation geometry, and the $6{p}_{3/2}\ensuremath{\rightarrow}5{s}_{1/2}$ decay. The comparison also shows that the electric-dipole-forbidden transition is a very sensitive probe of the preparation dynamics.

arXiv:1506.06105Physical Review AOct 20, 201518 citations

{\mathrm{Cr}}^{3+}

-Al interactions is offered to account for this magnetic-field behavior. The relaxation time of the echo is found to exceed 250 nsec at 4.2\ifmmode^\circ\else\textdegree\fi{}K but to be less than 70 nsec at 14\ifmmode^\circ\else\textdegree\fi{}K, and is thought to be due to phonon-induced transitions in the excited

^{2}E(\overline{E})

level. Multiple echo formation is also described.

5{p}_{3/2}

state is prepared by excitation with a laser locked to the maximum

F

cyclic transition of the

{D}_{2}

line, and the forbidden transition is produced by excitation with a 911 nm laser. Production of the forbidden transition is monitored by detection of the 420 nm fluorescence that results from decay of the

6{p}_{3/2}

state. Spectra with three narrow lines ($\ensuremath{\approx}13$ MHz FWHM) with the characteristic $F\ensuremath{-}1, F$, and

F+1

splitting of the

6{p}_{3/2}

hyperfine structure in both rubidium isotopes were obtained. The results are in very good agreement with a direct calculation that takes into account the $5s\ensuremath{\rightarrow}5{p}_{3/2}$ preparation dynamics, the $5{p}_{3/2}\ensuremath{\rightarrow}6{p}_{3/2}$ nondipole excitation geometry, and the $6{p}_{3/2}\ensuremath{\rightarrow}5{s}_{1/2}$ decay. The comparison also shows that the electric-dipole-forbidden transition is a very sensitive probe of the preparation dynamics.