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An investigation of CaF2:Dy2+ system to determine its potential as continuously tunable far-infrared laser∗
0020-0891~82/01M)51-06M)3 Oil/O Pergamon Press Ltd
AN INVESTIGATION OF CaF, : Dy2+ SYSTEM TO DETERMINE ITS POTENTIAL AS CONTINUOUSLY TUNABLE FAR-INFRARED LASER* H. DAVIS, R. W. STIMETS~and J. WALDMAN~ ‘North ’ University
Carolma Central University, Department of Physics, Durham, NC 27707, of Lowell, Department of Physics and Applied Physics, Lowell. MA 01854 and ‘Lincoln Laboratory, Lexington, MA 02173. U.S.A. (Rrcei~etl 29 July
1981)
-An investigation has been carried out on the CaF,:Dy*’ system to determine its potential as a tunable source of far infrared (FIR) radiation. High resolution laser magnetospectroscopy using optically pumped FIR lasers has been performed on the (E2 - T2)-type transitions of CaF,: Dy’+ to determine the radiative and non-radiative lifetimes of 1 - 7, 1 - 8, and 2 + 7 transitions. The variation of the transition strengths with magnetic field and orientation has been calculated theoretically for all transitions. The experimental and theoretical work has shown that potentially workable pumping schemes. capable of providing tunable FIR radiation with tunability of several cm- ‘. exist. The threshold power for the best pumping scheme is estimated.
Abstract
INTRODUCTION
A continuously tunable coherent source of far infrared (FIR) radiation would be a very useful spectroscopic tool. One possible way of achieving tunability would be to utilize the Zeeman tuning of the energy levels of a rare-earth doped paramagnetic material such as CaF2 :Dy2+. J. Waldman et ul. (‘I have suggested possible pumping schemes in CaF,:Dy’+, utilizing the variation of energy levels with magnetic field and orientation. It is very important to have a quantitative knowledge of both radiative and non-radiative transition strengths of both pump and lasing transitions. In the present work, we have calculated the transition strengths as a function of magnetic field and orientation and have predicted several pumping schemes which might produce continuously tunable FIR radiation. Experimental results for the strengths are compared with theoretical calculations. The threshold pump power for the best scheme is estimated. EXPERIMENTAL
PROCEDURE
AND
RESULTS
The experimental setup for laser magnetospectroscopy with an optically-pumped FIR laser is shown in Fig. 1. The NH3 FIR laser line of interest at 35.6cm-’ is pumped by the 1 MW pulsed CO1 laser. The FIR output power is of the order of a few kilowatts. The photoconductive GaAs detector, the sample and the magnet are confined in a double wall dewar in liquid He. The FIR radiation is fed to the sample via a qin. brass light pipe. The magnetic field is then swept slowly and the desired transitions are brought into resonance with the nearly monochromatic radiation (Av < 0.001 cm- ‘). The transmitted signal is plotted on an x-y chart recorder. Typically, the overall S/N ratio is about 50. Due to the weak response of the GaAs detector below 25 cm-‘, the spectra with D20 (25.97 cm- I) and CH3F (20.16 cm- ‘) cannot be observed clearly. The samples used in the experiment were cylindrical in shape and measured 10 mm in diameter and 15 mm in length. The chemical reduction technique’2.3J was used to reduce the DY+~ which occurs naturally to Dy’+. Figures 2, 3 and 4 show transmission traces of the 35.6 cm- 1 NH3 laser radiation through a 15 mm thick sample of CaF, : Dy2 ’ which was oriented with the (111) axis parallel to the magnetic field. The magnetic field was fairly homogeneous and no field broadening occurred for fields less than 50 kG when the sample was carefully centered in the magnet. For the 1 -+ 8 transmission a triple splitting *Work
supported
by National
Science Foundation
under grant 51
ENG-77-24030.
H. DAVY. R. W. Slinw1.s and J. W WALIIMAU
52
1
w
I
Boxcar integrator
Chort recorder
I Dlffractton grating
l-b
Magnet
Detector
Experimental
setup
is observed due to the different hype&e interaction terms for the different isotopes of natural dysprosium. For the magnetic field along one of the principal orientations. the transition is allowed only for either left ( - ) or right ( + ) circular polarization. Therefore. only half the unpolarized probe radiation incident on the sample is effective in absorpThe 1 4 7 transition is tion. This is graphically depicted in Fig. 3 for the 1 --f 7 transition. The crystal absorbs the right very strong compared to the I ---) 8 and 2 -+ 7 transitions. circularly polarized component of radiation completely while the left circularly polarized component propagates through crystal unattenuated. The flat region indicates the level
CaF, Bol
Qy” [Ill1
N H 3 Laser X = 35
6 cm-’
d = 15mm
15 2
Magnetic Fig. 2. Trace of the NH,
laser transmission
I
I
I
14 14
I6 26
field
1
18 38
(kG)
as the magnetic B,, (III).
I7 32
field sweeps the
I - X transition
with
CaF‘,: Dy’+
as continuously
tunable
FIR
53
laser
5 ._
.-z E z E
: ._
NH 3 Laser
Leakoge t
X = 35.6cm”’ d = 15mm
.z &
1
24 56
24 79
250
Magnetic Fig. 3. Trace of the NH,
laser transmission
25
field
21
25.42
(kG)
as the magnetic
1--+7 transition
field sweeps the
with
Bo ‘Ii 1111.
of approximately 50% the transmission. Additional transmitted signal is attributed to the leakage around the sample. Assuming the lineshape to be Lorentzian. the integrated absorption may be calculated by the relation
where Av is the full width at half maximum of the absorption line and c((vO)is the peak absorption coefficient. Table 1 summarizes the values of cc(vo),Av and integrated absorption obtained for the various transitions. The HCN data are taken from J. Waldman et al”) for analysis. The increase in linewidth with magnetic field is due to an increased non-radiative transition rate at larger level separation.
CoFp: 2-7
Dyzt
Boll
Gill
NHs
Laser
X = 35.6 d=
I
44
t
5
46
Magnetic Fig. 4. Trace of the NH,
laser transmission
field
cm-’
15mm
/
16
L
4’7 86
(kGf
as the magnetic B13!lU 11).
field sweeps the 2 --+ 7 transition
with
54
H. DAVE, R. W. STIMETS and J. W. WALIIMAN
Table
I. Comparison
of experimental
Ion
Pump laser
NH, 35.6cm
’
1011
of
,ons in lower state
0.555
I-X (111)1+7 2+7
2.54
I-X
2.54
(IlOJ
Et-act
concentration ( x IO”cm .’ 1
TransItion
and theoretical
0.746 0.04x
Integraled
absorption _______
Integrated (cm
Exp. 0.1 13 0.706 0.064
Z)
Thcoq O.OXY 0.6 13
o.oio
Kclatiic Integrated absorption Theor! F\P
h.YO 0.i’)
1.oo I.21
1.oo I 0-I
0.53x 0.200
2-7
__-
(100) I
+x
2+X
0.396 0.384
i.XI
.oo
I 00 625 0 57
I .oo
0 30
I
___~
I .oo 0.30
HCN 29.7 cm~
’
I-X (111)1-7 2-7
0.3Y2 0.4 I Y 0.377
1.01
0.0 I 5
I .oo I.27 I .30
O.OlY 0.01x
THEORETICAL CALCULATIONS TRANSITION STRENGTH
I .oo
I i .i 1.7s
OF
Previously J. Waldman rt ul (‘) have suggested possible pumping schemes for a tunable laser using the variation of transition energies with magnetic field and crystal orientation. In order to determine the feasibility of these schemes. it is essential to calculate the strength of various transitions involved. In a workable scheme it is important that both the pump and the laser transition strengths be large over a fairly broad range of orientation and magnetic field. Radiative transitions within the ground state manifold ‘I8 of CaF,: Dy’I proceed bq magnetic dipole process. The transition strength, i.e. transition probability per unit time between an initial state i and final statef’is given by
where g is the Landi: g-factor, h is the direction of polarization of the magnetic vector of the incident electromagnetic radiation and t1 is the index of refraction of the crystal. The transition strengths for all possible transitions within the ground manifold were calculated as a function of magnetic field and orientation for both polarizations. The eigen energies and eigen vectors were obtained by diagonalization of an 8 x 8 complex matrixt4’ using the wave functions given by Kiss. (5’ The transition strength calculations were used to obtain the integrated absorption for the 1 -+ 8, 1 + 7. and 2 ----f7 transitions and were compared with values derived from experiment. Theoretically the integrated absorption is obtained by ‘M(Y)ds =
Ni wi/ ~JYI?\~~/.
where Ni is the concentration of ions in the initial state i and vif. is the pump frequency in cm-‘. The caluclated strengths were also used to assess the feasibility of various pumping schemes and to choose the best scheme. Figure 5 shows plots of transition strength as a function of orientation in (110) plane for the (NH,. 1 + 5, 5 ----t2) scheme. The magnetic field is varied in such a way that the pump transition energy remains constant and equal to the transition energy of the pump laser, i.e. 35.6 cm- ‘. DISCUSSION
The experimental and theoretical values of the integrated absorption are summarized for the 1 + 8, 1 + 7, and 2 -+ 7 transitions in different crystals with (111). ( 1 IO), and (I 00)
CaF,
: Dy2+ as continuously
tunable
NH3
Laser
X1+5=
Lose
0
20
35.6
II I II Angle 8 in
[ 1103
- 305 cm-’
5+2
60
40
IOOII
55
FIR laser
80
c I 101
plane
Fig 5. Variation of the pump transition probability per unit time (W, _ 5), laser transition probabihty per unit time ( W, _ *) and laser transition energy (vg _ *) with angle in the (I 10) plane. The magnetic field is varied such that the pump transition energy remains constant and is equal to that of the pump laser (NH,. 35.6 cm- ‘).
orientations in Table 1. In general the agreement between experiment and theory is very good for the 1 + 8 and 1 -+ 7 transitions. The discrepancy for 2 + 7 can be attributed to inaccuracies in the second order perturbation theory treatment of transition strengths at high magnetic field. However, with one exception, the agreement obtained is very good and makes us believe that the present calculations are correct at least up to 40 kG. The theoretical and experimental integrated absorption for HCN differs by an order of magnitude because the samples used for acquiring those data were irradiated with y-rays and the y-ray irradiation technique (‘) effectively converts only about 10% of the ions. Many of the pumping schemes with large tuning range are rejected due to very weak transition strengths. The best scheme is the one in which an optically-pumped NH3 laser at 35.6 cm-’ is used to pump the 1 + 5 transition and lasing action is achieved in the 5 ---+2 transition (NH,, 1 + 5, 5 -+ 2). Figure 5 is a plot of the transition strengths of the pump and laser transition as well as the output wavelength as a function of orientation in the (110) plane. The transition strengths for pump (1 - 5) and laser (5 + 2) are reasonably strong over the range from 15 to 45” in the (110) plane, corresponding to a variation of magnetic field from 54 kG to 65 kG. An output tunability of approximately 4 cm- ’ (from 29.5 to 25 cm-‘) is achieved. The threshold pump power for the (NH,, 1 -+ 5, 5 -+ 2) scheme can be estimated from the radiative lifetime r, and non-radiative lifetime rnr. At the peak strength r, for the 5 + 2 transition is = lo4 sec. r, should be comparable with that for level 8, i.e. z 1.5 x 10-i’ sec. If we assume that the linewidth is due to natural broadening, i.e. Av = ~/XT,, then the threshold intensity is given by I ‘I-H
87~Vn3hv, = zc
T, 2 Tn,
(4)
where V is the laser volume, hv, the pump transition energy and the cavity lifetime rc. Using the above values of T, and r,,*, we obtain ZTH z 100 kW/cm’. This value is almost an order of magnitude more than currently available optically-pumped lasers. CONCLUSIONS
The strong dependence of transition strength on magnetic field and orientation suggests that before attempting a particular scheme, its dependency on magnetic field and
56
H. DAVE. R. W. STIMETSand J. W. WALDMAN
orientation be studied carefully. There exist several workable schemes for achieving tunable lasing action in CaF, : Dy2 ’ which would provide a tuning range of several cm- ’ about a center frequency in the range 5-30 cm- ‘. The best pumping scheme seems to be (NH,, 1 + 5, 5 + 2) which yields a tunability of about 4 cm- ‘. Agreement between experimental data and theory indicates that the understanding of radiative processes of the transitions is reasonably good and present calculations could be extended to other materials. The short non-radiative lifetime is the main difficulty in achieving lasing action at reasonable power levels. The lifetimes should be at least a factor of three greater than those of CaFz:Dy2’, i.e. rnr 2 6 x IO- lo set and Av < 0.02 cm~ ’ in order to achieve lasing action with currently optically-pumped lasers. REFERENCES I. WALIIMAN J.. R. W. S,II~~~TS.S. ZOIJ’LY MAI)AN & T. S. CIIAUG. /r~f,‘wtd /-‘/I\ ,. IX. 111 (107X1 2. DAVY H. Ph.D. Thesis. University of Lowell (1980). 3. Few F. K. & M. A. HIL.L.CR.J. Plop. C‘hrm 71. 2X.54 (l967l. 4. MERCFRIAN D.. 1. H. HARROP. M. P. STOMRIXR & K. C. KIRKORI,\N. P/IL\. Rec.. 153, 3-1’9(19671 5. KISS Z. J. P/IV\. Rr,r. 137, A 1749 (19651.
AN INVESTIGATION OF CaF, : Dy2+ SYSTEM TO DETERMINE ITS POTENTIAL AS CONTINUOUSLY TUNABLE FAR-INFRARED LASER* H. DAVIS, R. W. STIMETS~and J. WALDMAN~ ‘North ’ University
Carolma Central University, Department of Physics, Durham, NC 27707, of Lowell, Department of Physics and Applied Physics, Lowell. MA 01854 and ‘Lincoln Laboratory, Lexington, MA 02173. U.S.A. (Rrcei~etl 29 July
1981)
-An investigation has been carried out on the CaF,:Dy*’ system to determine its potential as a tunable source of far infrared (FIR) radiation. High resolution laser magnetospectroscopy using optically pumped FIR lasers has been performed on the (E2 - T2)-type transitions of CaF,: Dy’+ to determine the radiative and non-radiative lifetimes of 1 - 7, 1 - 8, and 2 + 7 transitions. The variation of the transition strengths with magnetic field and orientation has been calculated theoretically for all transitions. The experimental and theoretical work has shown that potentially workable pumping schemes. capable of providing tunable FIR radiation with tunability of several cm- ‘. exist. The threshold power for the best pumping scheme is estimated.
Abstract
INTRODUCTION
A continuously tunable coherent source of far infrared (FIR) radiation would be a very useful spectroscopic tool. One possible way of achieving tunability would be to utilize the Zeeman tuning of the energy levels of a rare-earth doped paramagnetic material such as CaF2 :Dy2+. J. Waldman et ul. (‘I have suggested possible pumping schemes in CaF,:Dy’+, utilizing the variation of energy levels with magnetic field and orientation. It is very important to have a quantitative knowledge of both radiative and non-radiative transition strengths of both pump and lasing transitions. In the present work, we have calculated the transition strengths as a function of magnetic field and orientation and have predicted several pumping schemes which might produce continuously tunable FIR radiation. Experimental results for the strengths are compared with theoretical calculations. The threshold pump power for the best scheme is estimated. EXPERIMENTAL
PROCEDURE
AND
RESULTS
The experimental setup for laser magnetospectroscopy with an optically-pumped FIR laser is shown in Fig. 1. The NH3 FIR laser line of interest at 35.6cm-’ is pumped by the 1 MW pulsed CO1 laser. The FIR output power is of the order of a few kilowatts. The photoconductive GaAs detector, the sample and the magnet are confined in a double wall dewar in liquid He. The FIR radiation is fed to the sample via a qin. brass light pipe. The magnetic field is then swept slowly and the desired transitions are brought into resonance with the nearly monochromatic radiation (Av < 0.001 cm- ‘). The transmitted signal is plotted on an x-y chart recorder. Typically, the overall S/N ratio is about 50. Due to the weak response of the GaAs detector below 25 cm-‘, the spectra with D20 (25.97 cm- I) and CH3F (20.16 cm- ‘) cannot be observed clearly. The samples used in the experiment were cylindrical in shape and measured 10 mm in diameter and 15 mm in length. The chemical reduction technique’2.3J was used to reduce the DY+~ which occurs naturally to Dy’+. Figures 2, 3 and 4 show transmission traces of the 35.6 cm- 1 NH3 laser radiation through a 15 mm thick sample of CaF, : Dy2 ’ which was oriented with the (111) axis parallel to the magnetic field. The magnetic field was fairly homogeneous and no field broadening occurred for fields less than 50 kG when the sample was carefully centered in the magnet. For the 1 -+ 8 transmission a triple splitting *Work
supported
by National
Science Foundation
under grant 51
ENG-77-24030.
H. DAVY. R. W. Slinw1.s and J. W WALIIMAU
52
1
w
I
Boxcar integrator
Chort recorder
I Dlffractton grating
l-b
Magnet
Detector
Experimental
setup
is observed due to the different hype&e interaction terms for the different isotopes of natural dysprosium. For the magnetic field along one of the principal orientations. the transition is allowed only for either left ( - ) or right ( + ) circular polarization. Therefore. only half the unpolarized probe radiation incident on the sample is effective in absorpThe 1 4 7 transition is tion. This is graphically depicted in Fig. 3 for the 1 --f 7 transition. The crystal absorbs the right very strong compared to the I ---) 8 and 2 -+ 7 transitions. circularly polarized component of radiation completely while the left circularly polarized component propagates through crystal unattenuated. The flat region indicates the level
CaF, Bol
Qy” [Ill1
N H 3 Laser X = 35
6 cm-’
d = 15mm
15 2
Magnetic Fig. 2. Trace of the NH,
laser transmission
I
I
I
14 14
I6 26
field
1
18 38
(kG)
as the magnetic B,, (III).
I7 32
field sweeps the
I - X transition
with
CaF‘,: Dy’+
as continuously
tunable
FIR
53
laser
5 ._
.-z E z E
: ._
NH 3 Laser
Leakoge t
X = 35.6cm”’ d = 15mm
.z &
1
24 56
24 79
250
Magnetic Fig. 3. Trace of the NH,
laser transmission
25
field
21
25.42
(kG)
as the magnetic
1--+7 transition
field sweeps the
with
Bo ‘Ii 1111.
of approximately 50% the transmission. Additional transmitted signal is attributed to the leakage around the sample. Assuming the lineshape to be Lorentzian. the integrated absorption may be calculated by the relation
where Av is the full width at half maximum of the absorption line and c((vO)is the peak absorption coefficient. Table 1 summarizes the values of cc(vo),Av and integrated absorption obtained for the various transitions. The HCN data are taken from J. Waldman et al”) for analysis. The increase in linewidth with magnetic field is due to an increased non-radiative transition rate at larger level separation.
CoFp: 2-7
Dyzt
Boll
Gill
NHs
Laser
X = 35.6 d=
I
44
t
5
46
Magnetic Fig. 4. Trace of the NH,
laser transmission
field
cm-’
15mm
/
16
L
4’7 86
(kGf
as the magnetic B13!lU 11).
field sweeps the 2 --+ 7 transition
with
54
H. DAVE, R. W. STIMETS and J. W. WALIIMAN
Table
I. Comparison
of experimental
Ion
Pump laser
NH, 35.6cm
’
1011
of
,ons in lower state
0.555
I-X (111)1+7 2+7
2.54
I-X
2.54
(IlOJ
Et-act
concentration ( x IO”cm .’ 1
TransItion
and theoretical
0.746 0.04x
Integraled
absorption _______
Integrated (cm
Exp. 0.1 13 0.706 0.064
Z)
Thcoq O.OXY 0.6 13
o.oio
Kclatiic Integrated absorption Theor! F\P
h.YO 0.i’)
1.oo I.21
1.oo I 0-I
0.53x 0.200
2-7
__-
(100) I
+x
2+X
0.396 0.384
i.XI
.oo
I 00 625 0 57
I .oo
0 30
I
___~
I .oo 0.30
HCN 29.7 cm~
’
I-X (111)1-7 2-7
0.3Y2 0.4 I Y 0.377
1.01
0.0 I 5
I .oo I.27 I .30
O.OlY 0.01x
THEORETICAL CALCULATIONS TRANSITION STRENGTH
I .oo
I i .i 1.7s
OF
Previously J. Waldman rt ul (‘) have suggested possible pumping schemes for a tunable laser using the variation of transition energies with magnetic field and crystal orientation. In order to determine the feasibility of these schemes. it is essential to calculate the strength of various transitions involved. In a workable scheme it is important that both the pump and the laser transition strengths be large over a fairly broad range of orientation and magnetic field. Radiative transitions within the ground state manifold ‘I8 of CaF,: Dy’I proceed bq magnetic dipole process. The transition strength, i.e. transition probability per unit time between an initial state i and final statef’is given by
where g is the Landi: g-factor, h is the direction of polarization of the magnetic vector of the incident electromagnetic radiation and t1 is the index of refraction of the crystal. The transition strengths for all possible transitions within the ground manifold were calculated as a function of magnetic field and orientation for both polarizations. The eigen energies and eigen vectors were obtained by diagonalization of an 8 x 8 complex matrixt4’ using the wave functions given by Kiss. (5’ The transition strength calculations were used to obtain the integrated absorption for the 1 -+ 8, 1 + 7. and 2 ----f7 transitions and were compared with values derived from experiment. Theoretically the integrated absorption is obtained by ‘M(Y)ds =
Ni wi/ ~JYI?\~~/.
where Ni is the concentration of ions in the initial state i and vif. is the pump frequency in cm-‘. The caluclated strengths were also used to assess the feasibility of various pumping schemes and to choose the best scheme. Figure 5 shows plots of transition strength as a function of orientation in (110) plane for the (NH,. 1 + 5, 5 ----t2) scheme. The magnetic field is varied in such a way that the pump transition energy remains constant and equal to the transition energy of the pump laser, i.e. 35.6 cm- ‘. DISCUSSION
The experimental and theoretical values of the integrated absorption are summarized for the 1 + 8, 1 + 7, and 2 -+ 7 transitions in different crystals with (111). ( 1 IO), and (I 00)
CaF,
: Dy2+ as continuously
tunable
NH3
Laser
X1+5=
Lose
0
20
35.6
II I II Angle 8 in
[ 1103
- 305 cm-’
5+2
60
40
IOOII
55
FIR laser
80
c I 101
plane
Fig 5. Variation of the pump transition probability per unit time (W, _ 5), laser transition probabihty per unit time ( W, _ *) and laser transition energy (vg _ *) with angle in the (I 10) plane. The magnetic field is varied such that the pump transition energy remains constant and is equal to that of the pump laser (NH,. 35.6 cm- ‘).
orientations in Table 1. In general the agreement between experiment and theory is very good for the 1 + 8 and 1 -+ 7 transitions. The discrepancy for 2 + 7 can be attributed to inaccuracies in the second order perturbation theory treatment of transition strengths at high magnetic field. However, with one exception, the agreement obtained is very good and makes us believe that the present calculations are correct at least up to 40 kG. The theoretical and experimental integrated absorption for HCN differs by an order of magnitude because the samples used for acquiring those data were irradiated with y-rays and the y-ray irradiation technique (‘) effectively converts only about 10% of the ions. Many of the pumping schemes with large tuning range are rejected due to very weak transition strengths. The best scheme is the one in which an optically-pumped NH3 laser at 35.6 cm-’ is used to pump the 1 + 5 transition and lasing action is achieved in the 5 ---+2 transition (NH,, 1 + 5, 5 -+ 2). Figure 5 is a plot of the transition strengths of the pump and laser transition as well as the output wavelength as a function of orientation in the (110) plane. The transition strengths for pump (1 - 5) and laser (5 + 2) are reasonably strong over the range from 15 to 45” in the (110) plane, corresponding to a variation of magnetic field from 54 kG to 65 kG. An output tunability of approximately 4 cm- ’ (from 29.5 to 25 cm-‘) is achieved. The threshold pump power for the (NH,, 1 -+ 5, 5 -+ 2) scheme can be estimated from the radiative lifetime r, and non-radiative lifetime rnr. At the peak strength r, for the 5 + 2 transition is = lo4 sec. r, should be comparable with that for level 8, i.e. z 1.5 x 10-i’ sec. If we assume that the linewidth is due to natural broadening, i.e. Av = ~/XT,, then the threshold intensity is given by I ‘I-H
87~Vn3hv, = zc
T, 2 Tn,
(4)
where V is the laser volume, hv, the pump transition energy and the cavity lifetime rc. Using the above values of T, and r,,*, we obtain ZTH z 100 kW/cm’. This value is almost an order of magnitude more than currently available optically-pumped lasers. CONCLUSIONS
The strong dependence of transition strength on magnetic field and orientation suggests that before attempting a particular scheme, its dependency on magnetic field and
56
H. DAVE. R. W. STIMETSand J. W. WALDMAN
orientation be studied carefully. There exist several workable schemes for achieving tunable lasing action in CaF, : Dy2 ’ which would provide a tuning range of several cm- ’ about a center frequency in the range 5-30 cm- ‘. The best pumping scheme seems to be (NH,, 1 + 5, 5 + 2) which yields a tunability of about 4 cm- ‘. Agreement between experimental data and theory indicates that the understanding of radiative processes of the transitions is reasonably good and present calculations could be extended to other materials. The short non-radiative lifetime is the main difficulty in achieving lasing action at reasonable power levels. The lifetimes should be at least a factor of three greater than those of CaFz:Dy2’, i.e. rnr 2 6 x IO- lo set and Av < 0.02 cm~ ’ in order to achieve lasing action with currently optically-pumped lasers. REFERENCES I. WALIIMAN J.. R. W. S,II~~~TS.S. ZOIJ’LY MAI)AN & T. S. CIIAUG. /r~f,‘wtd /-‘/I\ ,. IX. 111 (107X1 2. DAVY H. Ph.D. Thesis. University of Lowell (1980). 3. Few F. K. & M. A. HIL.L.CR.J. Plop. C‘hrm 71. 2X.54 (l967l. 4. MERCFRIAN D.. 1. H. HARROP. M. P. STOMRIXR & K. C. KIRKORI,\N. P/IL\. Rec.. 153, 3-1’9(19671 5. KISS Z. J. P/IV\. Rr,r. 137, A 1749 (19651.