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Measurement of nonradiative relaxation of rare earths in glasses using selective laser excitation
HIGH POWER LASER SYSTEMS
V8
References I l ] E.S. Bliss, D . R . S p e c k , and W.W. S i m m o n s , A p p l . P h y s . L e t t . 25 ( 1 9 7 4 ) 7 2 7 .
12 J M.J. Moran, C.Y. She and R.L. Carman, IFEE. J. Quant. Electron QE-11 (1975) 259. [3 I N.L. Boling, A. O w y o u n g , and A.J. Glass, UCRL 75628 (1974).
MEASUREMENT OF N O N R A D I A T I V E R E L A X A T I O N OF R A R E EARTHS IN GLASSES USING SELECTIVE LASER EXCITATION C.B. LAYNE, W.H. LOWDERMILK and M.J. WEBER
V8
Lawrence Livermore Laboratory, Livermore, CA 94550, USA Nonradiative decay rates from excited states o f rare-earth ions determine three i m p o r t a n t properties o f rare-earth lasers: p u m p conversion efficiency, radiative q u a n t u m efficiency, and lifetime of the terminal laser level. When the energy gap between an excited level and the next-lower level is greater than the energy o f the m o s t energetic lattice vibration, the nonradiative decay m u s t involve the emission o f several p h o n o n s . This multip h o n o n relaxation a m o n g the 4 f n levels o f rare earths has been investigated in crystals. It has been s h o w n that the decay is de-
Nd4G7/2]0 8
10 7
J
.
106
lr) 5
o
g
104
? ]03
102 1000
2000
3000
4000
Energy gap to next lower level
5000
(ciu - I )
Fig. 1. M u l t i p h o n o n d e c a y rates of rare-earth ions in five oxide glasses as a function of energy gap to next lower level. The ions and energy levels whose decays were measured are indicated at the top of the figure.
scribed in m a n y cases by the stimulated emission o f p h o n o n s , all of a single frequency 03, leading to a decay rate o f the form Wnr=Cexp(
o~AXE)[n(03,T)+l]P.
(1)
The constants C and c~ are characteristic o f the host material, AxE is the energy gap to the next-lower electronic level, and p is the n u m b e r o f p h o n o n s which m u s t be emitted to conserve energy. The temperature dependence of Wnr, given by the B o s e - E i n s t e i n occupation n u m b e r n = [exp (h03/kT) 1] t provides a way to experimentally determine the n u m b e r and energy o f the p h o n o n s involved in the decay. It h a s b e c n established that the highest energy vibrations o f the crystal lattice are d o m i n a n t in the relaxation. Comparable results might be expected for glasses, since crystals and their vitreous p o l y m o r p h s have similar vibrational spectra. We have investigated m u l t i p h o n o n relaxation of rare earths in glasses to determine the dependence of the rates on the energy gap and on glass composition. The relaxation rates were determined from m e a s u r e m e n t s o f transient fluorescence following pulses selective excitation of various electronic energy levels. Excitation was accomplished using l-ns pulses at the second and third harmonic frequencies o f a Nd : YAG laser. Decay rates for seven different energy gaps in Nd 3+, Er 3+, and T m 3+ were determined for five oxide glasses: borate, phosphate, silicate, germanate, and tellurite. Fig. 1 summarizes the measured multipfionon relaxation rates. These vary from 10 8 to 10 3 s -I for electronic energy gaps ranging from 1500 to 5000 cm -1 . The rates for each glass exhibit an exponential dependence on energy gap, independent of rare-earth ion or electronic state. This result indicates that the single frequency model of m u l t i p h o n o n decay [eq. (1)] does apply to glasses. To e x a m i n e the dependence of the m u l t i p h o n o n emission rates on glass composition, vibrational spectra of the glasses were determined by s p o n t a n e o u s R a m a n scattering. The multip h o n o n rates were found to increase in the same order as the energy o f the highest frequency vibrations in the glasses. For a particular energy gap, the rates vary with glass composition by as m u c h as 10 3 from the fastest (borate) to the slowest (tellurite). The variations o f the m u l t i p h o n o n decay rates with temperature were measured for each glass and compared to the behavior predicted by eq. (1). The good agreement of the theory and experiment confirms that the highest energy p h o n o n s are responsible for m u l t i p h o n o n decay, and proves that the ion decays by exciting several of the high energy vibrational m o d e s rather than by relaxing to a single highly excited mode. T h e strength o f coupling of the rare earth to the lattice is found to be approximately equal for the oxide glasses, so that the differences in the rates between glasses are accounted for by the differences in p h o n o n energies. Similar results obtained for fluoride glasses, where a different coupling strength is expected, will be discussed and compared to the results for oxide glasses. Predictions of q u a n t u m efficiencies and excited state lifetimes o f interest for rare-earth lasers will also be presented.
1 '73
V8
References I l ] E.S. Bliss, D . R . S p e c k , and W.W. S i m m o n s , A p p l . P h y s . L e t t . 25 ( 1 9 7 4 ) 7 2 7 .
12 J M.J. Moran, C.Y. She and R.L. Carman, IFEE. J. Quant. Electron QE-11 (1975) 259. [3 I N.L. Boling, A. O w y o u n g , and A.J. Glass, UCRL 75628 (1974).
MEASUREMENT OF N O N R A D I A T I V E R E L A X A T I O N OF R A R E EARTHS IN GLASSES USING SELECTIVE LASER EXCITATION C.B. LAYNE, W.H. LOWDERMILK and M.J. WEBER
V8
Lawrence Livermore Laboratory, Livermore, CA 94550, USA Nonradiative decay rates from excited states o f rare-earth ions determine three i m p o r t a n t properties o f rare-earth lasers: p u m p conversion efficiency, radiative q u a n t u m efficiency, and lifetime of the terminal laser level. When the energy gap between an excited level and the next-lower level is greater than the energy o f the m o s t energetic lattice vibration, the nonradiative decay m u s t involve the emission o f several p h o n o n s . This multip h o n o n relaxation a m o n g the 4 f n levels o f rare earths has been investigated in crystals. It has been s h o w n that the decay is de-
Nd4G7/2]0 8
10 7
J
.
106
lr) 5
o
g
104
? ]03
102 1000
2000
3000
4000
Energy gap to next lower level
5000
(ciu - I )
Fig. 1. M u l t i p h o n o n d e c a y rates of rare-earth ions in five oxide glasses as a function of energy gap to next lower level. The ions and energy levels whose decays were measured are indicated at the top of the figure.
scribed in m a n y cases by the stimulated emission o f p h o n o n s , all of a single frequency 03, leading to a decay rate o f the form Wnr=Cexp(
o~AXE)[n(03,T)+l]P.
(1)
The constants C and c~ are characteristic o f the host material, AxE is the energy gap to the next-lower electronic level, and p is the n u m b e r o f p h o n o n s which m u s t be emitted to conserve energy. The temperature dependence of Wnr, given by the B o s e - E i n s t e i n occupation n u m b e r n = [exp (h03/kT) 1] t provides a way to experimentally determine the n u m b e r and energy o f the p h o n o n s involved in the decay. It h a s b e c n established that the highest energy vibrations o f the crystal lattice are d o m i n a n t in the relaxation. Comparable results might be expected for glasses, since crystals and their vitreous p o l y m o r p h s have similar vibrational spectra. We have investigated m u l t i p h o n o n relaxation of rare earths in glasses to determine the dependence of the rates on the energy gap and on glass composition. The relaxation rates were determined from m e a s u r e m e n t s o f transient fluorescence following pulses selective excitation of various electronic energy levels. Excitation was accomplished using l-ns pulses at the second and third harmonic frequencies o f a Nd : YAG laser. Decay rates for seven different energy gaps in Nd 3+, Er 3+, and T m 3+ were determined for five oxide glasses: borate, phosphate, silicate, germanate, and tellurite. Fig. 1 summarizes the measured multipfionon relaxation rates. These vary from 10 8 to 10 3 s -I for electronic energy gaps ranging from 1500 to 5000 cm -1 . The rates for each glass exhibit an exponential dependence on energy gap, independent of rare-earth ion or electronic state. This result indicates that the single frequency model of m u l t i p h o n o n decay [eq. (1)] does apply to glasses. To e x a m i n e the dependence of the m u l t i p h o n o n emission rates on glass composition, vibrational spectra of the glasses were determined by s p o n t a n e o u s R a m a n scattering. The multip h o n o n rates were found to increase in the same order as the energy o f the highest frequency vibrations in the glasses. For a particular energy gap, the rates vary with glass composition by as m u c h as 10 3 from the fastest (borate) to the slowest (tellurite). The variations o f the m u l t i p h o n o n decay rates with temperature were measured for each glass and compared to the behavior predicted by eq. (1). The good agreement of the theory and experiment confirms that the highest energy p h o n o n s are responsible for m u l t i p h o n o n decay, and proves that the ion decays by exciting several of the high energy vibrational m o d e s rather than by relaxing to a single highly excited mode. T h e strength o f coupling of the rare earth to the lattice is found to be approximately equal for the oxide glasses, so that the differences in the rates between glasses are accounted for by the differences in p h o n o n energies. Similar results obtained for fluoride glasses, where a different coupling strength is expected, will be discussed and compared to the results for oxide glasses. Predictions of q u a n t u m efficiencies and excited state lifetimes o f interest for rare-earth lasers will also be presented.
1 '73