Physical review. B, Condensed matter

Stimulated emission of phonons in an acoustical cavity

Peter A. Fokker, J. I. Dijkhuis, H. W. de Wijn

Published Feb 1, 1997• 45 citations

Abstract

Stimulated emission is studied of phonons resonant with the metastable Zeeman-split E-bar${(}^{2}$E) doublet in ruby. Initial population inversion of this two-level system is prepared by selective pulsed optical pumping, and the ensuing stimulated emission of resonant phonons is observed via an accelerated growth of the luminescence intensity emanating from the lower level. Under favorable conditions, a periodic recurrence of the process of stimulated emission is observed, which points to a phonon cavity formed by the end faces of the crystal in combination with a limited interaction length of the resonant phonons. To analyze these phenomena in detail, use is made of rate equations for the phonon occupation and the level populations with explicit account of their position dependences. With plausible assumptions an analytic solution of these equations is achieved, which excellently fits the data. The effect of lattice anharmonicity is shown to depend on the phonon energy in agreement with the theoretical prediction.

DOI: 10.1103/physrevb.55.2925

Related papers

Coherent phonons generated by stimulated emission in ruby

Lieuwe Gijsbert Tilstra, A. F. M. Arts, H. W. de Wijn

The Zeeman-split (2E) doublet of Cr3+ in a single crystal of 500-at.ppm ruby (Al2O3:Cr3+) is population inverted by selective transient optical pumping, and the resulting avalanches of resonant phonons are measured and analyzed. Coherent Bloch equations governing the acoustic wave and the transverse spin polarizations are found to provide an excellent description. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physicsNov 1, 20041 citation

Optically excited ruby as a saser: Experiment and theory

Lieuwe Gijsbert Tilstra, A. F. M. Arts, H. W. de Wijn

Physical Review BJul 9, 200719 citations

Suppression of stimulated phonon emission in ruby by a magnetic-field gradient

Peter A. Fokker, Richard S. Meltzer, Y. P. Wang +2 more

Physical review. B, Condensed matterFeb 1, 199712 citations

SASER action in optically excited ruby: Angular and spectral distribution

Lieuwe Gijsbert Tilstra, A. F. M. Arts, H. W. de Wijn

Journal of Physics Conference SeriesDec 1, 20071 citation

Relaxation of an optically created phonon void in dilute ruby

Paul A. van Walree, A. F. M. Arts, H. W. de Wijn

Physical review. B, Condensed matterOct 3, 20011 citation

Stimulated emission of 0.2-THz phonons in La F3 : Er3+

D. J. Sox, John E. Rives, Richard S. Meltzer

Physical review. B, Condensed matterApr 15, 198218 citations

Physical review. B, Condensed matter

Stimulated emission of phonons in an acoustical cavity

Peter A. Fokker, J. I. Dijkhuis, H. W. de Wijn

Published Feb 1, 1997• 45 citations

Publisher

Abstract

Stimulated emission is studied of phonons resonant with the metastable Zeeman-split E-bar

{(}^{2}

E) doublet in ruby. Initial population inversion of this two-level system is prepared by selective pulsed optical pumping, and the ensuing stimulated emission of resonant phonons is observed via an accelerated growth of the luminescence intensity emanating from the lower level. Under favorable conditions, a periodic recurrence of the process of stimulated emission is observed, which points to a phonon cavity formed by the end faces of the crystal in combination with a limited interaction length of the resonant phonons. To analyze these phenomena in detail, use is made of rate equations for the phonon occupation and the level populations with explicit account of their position dependences. With plausible assumptions an analytic solution of these equations is achieved, which excellently fits the data. The effect of lattice anharmonicity is shown to depend on the phonon energy in agreement with the theoretical prediction.

DOI: 10.1103/physrevb.55.2925

Related papers

Coherent phonons generated by stimulated emission in ruby

Lieuwe Gijsbert Tilstra, A. F. M. Arts, H. W. de Wijn

Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physicsNov 1, 20041 citation

Optically excited ruby as a saser: Experiment and theory

Lieuwe Gijsbert Tilstra, A. F. M. Arts, H. W. de Wijn

Avalanches of phonons are generated following population inversion of the Zeeman-split $\overline{E}(^{2}E)$ Kramers doublet in a single crystal of dilute ruby $({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})$ at $1.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ . The inversion is achieved in a narrow zone of limited extent by selective pulsed optical pumping, and the phonons are detected via luminescence. The associated acoustic wave emanating from the zone propagates through the crystal, reverberates in the acoustic cavity formed by the crystalline end faces, and engages in further amplification each time it passes through the zone until the inversion becomes exhausted. The systems thus acts as a saser (sound amplification by stimulated emission of radiation). The avalanche is adequately described by coherent Bloch equations governing the acoustic wave and the interacting spin polarization, the losses being due to surface scattering and divergence. This conclusion holds good upon reducing the resonance length of the zone by a gradient magnetic field. Finally, the frequency and angular distributions of the avalanche are measured by using two disjunct zones located at opposite ends of the crystal, one serving as generator and the other as detector, in conjunction with a gradient field and lateral displacement. The frequency spread is found to be compatible with the inhomogeneously broadened transition within $\overline{E}(^{2}E)$ , while the angular divergence is determined by the geometry of the zone.Avalanches of phonons are generated following population inversion of the Zeeman-split $\overline{E}(^{2}E)$ Kramers doublet in a single crystal of dilute ruby $({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})$ at $1.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The inversion is achieved in a narrow zone of limited extent by selective pulsed optical pumping, and the phonons are detected via luminescence. The associated acoustic wave emanating from the zone propagates through the crystal, reverberates in the acoustic cavity formed by the crystalline end faces, and engages in further amplification each time it passes through the zone until the inversion becomes exhausted. The systems thus acts as a saser (sound amplification by stimulated emission of radiation). The avalanche is adequately described by coherent Bloch equations governing the acoustic wave and the interacting spin polarization, the losses being due to surface scattering and divergence. This conclusion holds good upon reducing the resonance length of the zone by a gradient magnetic field. Finally, the frequency and angular distributions of the avalanche are measured by using two disjunct zones located at opposite ends of the crystal, one serving as generator and the other as detector, in conjunction with a gradient field and lateral displacement. The frequency spread is found to be compatible with the inhomogeneously broadened transition within $\overline{E}(^{2}E)$, while the angular divergence is determined by the geometry of the zone.

Physical Review BJul 9, 200719 citations

Suppression of stimulated phonon emission in ruby by a magnetic-field gradient

Peter A. Fokker, Richard S. Meltzer, Y. P. Wang +2 more

It is demonstrated that a magnetic-field gradient can suppress amplified stimulated emission of phonons taking place within the Zeeman-split E-bar ${(}^{2}$ E) doublet of ${\mathrm{Cr}}^{3+}$ in 700 ppm ruby. The doublet is initially inverted by selective pulsed optical pumping. The field gradient produces a gradient in the transition frequency, thereby reducing the gain of the amplifying medium. The experiments are described with rate equations in which the gain is accounted for by the interaction length over which the phonons remain at resonance.It is demonstrated that a magnetic-field gradient can suppress amplified stimulated emission of phonons taking place within the Zeeman-split E-bar${(}^{2}$E) doublet of ${\mathrm{Cr}}^{3+}$ in 700 ppm ruby. The doublet is initially inverted by selective pulsed optical pumping. The field gradient produces a gradient in the transition frequency, thereby reducing the gain of the amplifying medium. The experiments are described with rate equations in which the gain is accounted for by the interaction length over which the phonons remain at resonance.

Physical review. B, Condensed matterFeb 1, 199712 citations

SASER action in optically excited ruby: Angular and spectral distribution

Lieuwe Gijsbert Tilstra, A. F. M. Arts, H. W. de Wijn

Selective pulsed optical excitation is used in 500-at.ppm ruby (Al 2 O 3 :Cr 3+ ) at 1.4 K to prepare complete population inversion of the Zeeman-split Ē( 2 E ) doublet in a zone of limited size. The inversion results in prolific stimulated emission of phonons resonant with the one-phonon transition connecting the doublet states. The phonons are detected via the R 1 luminescence. The angular and spectral distributions of the associated acoustic wave are measured using a geometry with inverted zones at either end of the crystal, one serving as generator and the other as detector. The divergence appears to be governed by the geometry of the zone, while the spectral distribution is, within errors, in keeping with the inhomogeneously broadened phonon transition.Selective pulsed optical excitation is used in 500-at.ppm ruby (Al 2 O 3 :Cr 3+ ) at 1.4 K to prepare complete population inversion of the Zeeman-split Ē( 2 E ) doublet in a zone of limited size. The inversion results in prolific stimulated emission of phonons resonant with the one-phonon transition connecting the doublet states. The phonons are detected via the R 1 luminescence. The angular and spectral distributions of the associated acoustic wave are measured using a geometry with inverted zones at either end of the crystal, one serving as generator and the other as detector. The divergence appears to be governed by the geometry of the zone, while the spectral distribution is, within errors, in keeping with the inhomogeneously broadened phonon transition.

Journal of Physics Conference SeriesDec 1, 20071 citation

Relaxation of an optically created phonon void in dilute ruby

Paul A. van Walree, A. F. M. Arts, H. W. de Wijn

A local frequency-selective depletion of phonons is created in dilute ruby at 1.8 K by optical pumping into the Zeeman-split metastable \ifmmode \bar{E}\else \={E}\fi{} ${(}^{2}$ E) doublet. This phonon ``void,'' which is in dynamic balance with the spin system, is observed to recover to thermal equilibrium by an inward flow of phonons supplied from regions beyond the void, and ultimately from the helium bath. Coupled rate equations of the level populations in the void as well as the phonon density throughout the crystal account for these effects. In particular, a quartic frequency dependence of the rate for phonon transport across the crystal boundary is found, in accordance with diffuse surface scattering.A local frequency-selective depletion of phonons is created in dilute ruby at 1.8 K by optical pumping into the Zeeman-split metastable \ifmmode \bar{E}\else \={E}\fi{}${(}^{2}$E) doublet. This phonon ``void,'' which is in dynamic balance with the spin system, is observed to recover to thermal equilibrium by an inward flow of phonons supplied from regions beyond the void, and ultimately from the helium bath. Coupled rate equations of the level populations in the void as well as the phonon density throughout the crystal account for these effects. In particular, a quartic frequency dependence of the rate for phonon transport across the crystal boundary is found, in accordance with diffuse surface scattering.

Physical review. B, Condensed matterOct 3, 20011 citation

Stimulated emission of 0.2-THz phonons in La F3 : Er3+

D. J. Sox, John E. Rives, Richard S. Meltzer

Stimulated emission of phonons in the 0.2-THz frequency range is observed in La ${\mathrm{F}}_{3}$ : ${\mathrm{Er}}^{3+}$ . The phonons are generated in the relaxation between the Kramers components of the $^{4}S_{\frac{3}{2}}(1)$ state of ${\mathrm{Er}}^{3+}$ split in a magnetic field after inverting the population with a pulsed tunable dye laser. The stimulated emission is identified from the temporal behavior of the luminescence from the upper Kramers component which shows a speedup in the relaxation during inversion. The population dynamics are analyzed with the rate equations for the system. Comparison with experiment indicates strong preferential stimulated emission along the axis of the cylindrically excited volume and a gain of up to 5 ${\mathrm{mm}}^{\ensuremath{-}1}$. The population inversion exists sufficiently long for phonon propagation over macroscopic distances and the phonon frequency is tunable with the magnetic field.Stimulated emission of phonons in the 0.2-THz frequency range is observed in La${\mathrm{F}}_{3}$:${\mathrm{Er}}^{3+}$. The phonons are generated in the relaxation between the Kramers components of the $^{4}S_{\frac{3}{2}}(1)$ state of ${\mathrm{Er}}^{3+}$ split in a magnetic field after inverting the population with a pulsed tunable dye laser. The stimulated emission is identified from the temporal behavior of the luminescence from the upper Kramers component which shows a speedup in the relaxation during inversion. The population dynamics are analyzed with the rate equations for the system. Comparison with experiment indicates strong preferential stimulated emission along the axis of the cylindrically excited volume and a gain of up to 5 ${\mathrm{mm}}^{\ensuremath{-}1}$. The population inversion exists sufficiently long for phonon propagation over macroscopic distances and the phonon frequency is tunable with the magnetic field.

Physical review. B, Condensed matterApr 15, 198218 citations

Stimulated emission is studied of phonons resonant with the metastable Zeeman-split E-bar

{(}^{2}

Avalanches of phonons are generated following population inversion of the Zeeman-split

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

Kramers doublet in a single crystal of dilute ruby

({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})

1.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}

. The inversion is achieved in a narrow zone of limited extent by selective pulsed optical pumping, and the phonons are detected via luminescence. The associated acoustic wave emanating from the zone propagates through the crystal, reverberates in the acoustic cavity formed by the crystalline end faces, and engages in further amplification each time it passes through the zone until the inversion becomes exhausted. The systems thus acts as a saser (sound amplification by stimulated emission of radiation). The avalanche is adequately described by coherent Bloch equations governing the acoustic wave and the interacting spin polarization, the losses being due to surface scattering and divergence. This conclusion holds good upon reducing the resonance length of the zone by a gradient magnetic field. Finally, the frequency and angular distributions of the avalanche are measured by using two disjunct zones located at opposite ends of the crystal, one serving as generator and the other as detector, in conjunction with a gradient field and lateral displacement. The frequency spread is found to be compatible with the inhomogeneously broadened transition within

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

, while the angular divergence is determined by the geometry of the zone.

It is demonstrated that a magnetic-field gradient can suppress amplified stimulated emission of phonons taking place within the Zeeman-split E-bar

{(}^{2}

E) doublet of

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

in 700 ppm ruby. The doublet is initially inverted by selective pulsed optical pumping. The field gradient produces a gradient in the transition frequency, thereby reducing the gain of the amplifying medium. The experiments are described with rate equations in which the gain is accounted for by the interaction length over which the phonons remain at resonance.

A local frequency-selective depletion of phonons is created in dilute ruby at 1.8 K by optical pumping into the Zeeman-split metastable \ifmmode \bar{E}\else \={E}\fi{}

{(}^{2}

E) doublet. This phonon ``void,'' which is in dynamic balance with the spin system, is observed to recover to thermal equilibrium by an inward flow of phonons supplied from regions beyond the void, and ultimately from the helium bath. Coupled rate equations of the level populations in the void as well as the phonon density throughout the crystal account for these effects. In particular, a quartic frequency dependence of the rate for phonon transport across the crystal boundary is found, in accordance with diffuse surface scattering.

Stimulated emission of phonons in the 0.2-THz frequency range is observed in La

{\mathrm{F}}_{3}

{\mathrm{Er}}^{3+}

. The phonons are generated in the relaxation between the Kramers components of the

^{4}S_{\frac{3}{2}}(1)

state of

{\mathrm{Er}}^{3+}

split in a magnetic field after inverting the population with a pulsed tunable dye laser. The stimulated emission is identified from the temporal behavior of the luminescence from the upper Kramers component which shows a speedup in the relaxation during inversion. The population dynamics are analyzed with the rate equations for the system. Comparison with experiment indicates strong preferential stimulated emission along the axis of the cylindrically excited volume and a gain of up to 5 ${\mathrm{mm}}^{\ensuremath{-}1}$. The population inversion exists sufficiently long for phonon propagation over macroscopic distances and the phonon frequency is tunable with the magnetic field.