- Email: [email protected]
Resonant absorption in LiNdP4O12 lasers
Volume 17, number 1
OPTICS COMMUNICATIONS
April 1976
RESONANT ABSORPTION IN LiNdP4012 LASERS Kenju OTSUKA and Tomoaki YAMADA
Musashino Electrical Communication Laboratory, Nippon Telegraph and Telephone Public Corporation, Musashino-shi, Tokyo, Japan Received 26 December 1975
Tile resonant loss in LiNdP4012 (LNP) lasers has been investigated. The effective resonant loss coefficient for the 1.047(7)/~m laser emission was measured to be 0.042 cm -1 . This value can be explained by resonant absorption due to the 4 i11/2 -~ 4 F3/2 transition including the reabsorption effect of the fluorescence resulting from the 4 i9/2 _~ 4 F3/2 transition.
In a Nd-laser material, there exists an intrinsic resonant loss due to the absorption resulting from the 4 I l l / 2 -+ 4F3/2 transition. The resonant loss is an important parameter to estimate the threshold pump power, as well as the slope efficiency of the laser oscillation. High Nd-concentration materials such as NdPsO14 and LiNdP4012 (LNP) have strong pump bands [1,2] but their high Nd-concentration also leads to the deleterious effect of high resonant losses [3]. In this letter, the resonant absorption in LNP lasers is reported. The experimental arrangement was as follows. A cw argon laser served as a pump. The LNP laser resonator is of nearly semiconcentric type with mirrors M 1 (radius of curvature R 1 = 0% transmission at 1.047 (7)/sin, T 1 = 0.1%) and M2 (R 2 = 9 cm, T 2 = 0.1, 1, 2, 3%) separated by about 9 cm. The LNP crystal was placed just in front of M 1 . The round-trip loss of the resonator was directly measured by the change of threshold with - I n (r lr2), where r 1 and r 2 are the mirror reflectivities (i.e. straightforward method). The measured longitudinally pumped threshold has been plotted as a function of - l n ( r 1r2) in fig. 1 for three polished LNP-crystals with different thickness cut out from the same boules of the as-grown crystal. The used crystals were 0.7, 2 and 3 mm thick (pseudo-orthorhombic a-axis) and the LNP-laser emission was linearly polarized along the c-axis of the crystal. The absorption coefficient of the LNP for 5145 A was 23 cm - I , therefore the pump light was absorbed about 100% within an absorption length of 24
9.8 ram. The population inversion distribution in the crystal is illustrated in fig. 1, and regions over 0.8 mm in the crystal are not pumped. From the difference of measured round-trip losses shown in fig. 1, the absorption loss coefficient for the unpumped LNP crystal which corresponds to the passive resonant loss is obtained to be ap = (0.11 +-0.001) cm -1 . The nonresonant loss except the mirror transmission loss is estimated to be 0.025.
s,,s
popu,.tion 0 -M1 LNP M2 o04L thickness " | 0.7 2 3 (rnm) o
-002L / / / ,.re..o,d
2r// -0 . 0 8 [ ~ -
O
J
O
I
-
Fig. 1. Laser threshold as a function of -In (rlr2) for 0.7, 2, and 3 mm thick, LNP crystals. The spot size of the pump beam, which was focused by the lens of 5-cm focal-length, was adjusted to that of the oscillating beam.
V o l u m e 17, n u m b e r 1
OPTICS COMMUNICATIONS
Then we pumped platelet-like LNP crystals which are thinner than the penetration depth for the pump light with the same cavity configuration. The used crystals were 0.3 and 0.8 mm thick a-plates and the laser emission was also linearly polarized along the c-axis. The round-trip losses were measured by the straightforward method described above as a function of the oscillating beam spot size averaged over the crystal length. The oscillating beam spot size in the crystal was changed by moving the mirror M 2 or the LNP crystals along the laser axis using the motor-driven micrometer screw and calculated from the output laser beam divergence [4]. The pump light (5145 A) was focused on the LNP crystal by the lens of 5-cm focal-length, longitudinally and the averaged pump beam spot size in the crystal, Wp, was (20 + 5) ~m. The measured absorption loss coefficient Cta for the pumped LNP crystal which corresponds to the active resonant loss is shown in fig. 2 as a function of the oscillating beam spot size, wa. From fig. 2 it is found that the absorption loss coefficient for the pumped crystal o~a is smaller than the passive resonant loss coefficient ap of0.11 cm -1 , and c~a = (0.042 + 0.006) cm -1 for the mode-matching condition, i.e., w a = Wp = (20 + 5) ~tm. The loss coefficient increases with the increase of the beam spot size w a. A possible explanation of this result is that the pump beam does not match the oscillating beam for larger spot sizes (w a > Wp) and the passive loss overlaps the resonant loss. To confirm the reduction of the resonant loss in the pumped LNP crystal, we have carried out two experiments described below.
April 1976
First, we pumped the LNP crystal of 2.57 mm thickness longitudinally with the argon laser of different wavelengths (5145, 4765 and 4579 A). The absorption coefficients of the LNP crystal for these wavelengths are 23 cm -1 (5145 A), 6.3 cm -1 (4765 A) and 4.7 cm -1 (4579 A), respectively. The pump light was absorbed about 80% and 70% for the 4765 A and 4579 A pump respectively, therefore the LNP crystals were uniformly pumped for these wavelengths compared with the 5145 A pump. The measured absorbed threshold power is plotted as a function of the pump wavelength in fig. 3. The solid line show the theoretical value calculated from the threshold power for the 5145 A pump, assuming that the resonant loss is constant. The observed threshold powers for the 4765 A and 4579 A pump are smaller than the theoretical value. This indicates that the resonant losses for these pumpings are effectively smaller than the resonant loss for the 5145 A pump. Second, the LNP crystal of 2.57 mm thickness was pumped longitudinally as well as transversely with the 5145 A argon laser and the round-trip loss of the resonator was measured by the straightforward method. The results are shown in fig. 4. Since the aperture of the pump beam which was focused by the cylindrical lens was adjusted to the crystal length in the case of transverse pumping, the pump light was absorbed uniformly over the crystal length compared with the longitudinal pumping. From fig. 4, it is found that the resonant loss for the transverse pumping is smaller than that for the longitudinal pumping. pump population A
514s~,
2.57mm thick LNP
o rl o°'at°n [1 motor drive
A
"5 c
/theory
.... 60
E
oo o o
--~ 0.10 .u
~o~O
o 0.05 --
0 Q.
"o 80
% 0.15
I/I 0
LNP
~I00
LNP
¢-
o % %
"10
o 4.7
o 6.3
absorption
coeffi. 23cn~
¢n
2o .£1
0
40
i
I
i
i
i
10
20
30
40
50
ed
60
spot size, Wa(lam) Fig. 2. T h e loss coefficient of the u n i f o r m l y p u m p e d LNP laser as a f u n c t i o n of the oscillating b e a m spot size.
0
&o
4~0
560
520
p u m p w a v e l e n g t h (nm) Fig. 3. Laser threshold as a function o f the p u m p wavelength (4579 A, 4765 A, 5145 A).
25
Volume 1 7, number 1
0.04
OPTICS COMMUNICATIONS
2.57mmthickLNP(5145~pump) end side
April 1976
4F~2
-
[1 12
0.02 C
T
o
40 80
-0.02 / ~ -0.04
I?.0 160 200 /threshold pumppower(rnW)
reabsorption 4Illt2
,,E2
1,
-OD6 -0.08
41912
1
-0.I 0
Fig. 4. Laser threshold for longitudinal and transverse pumping as a function of -In (rlr2). The transverse pump light was focused on the crystal by the cylindiical lens of 2-cm focallength. F r o m these experimental results, it is shown that the active resonant loss of the LNP crystal is smaller than the passive one. A plausible explanation of the above experimental results is presented in the following. In the LNP crystal, the absorption coefficient for the inverse 419] 2 ~ 4F3/2 transition is 410 cm - I [2] and the fluorescence corresponding to 4 F 3/2 ~ 4 i912 transition is reabsorbed about 100% within the absorption length of 30/~m. This process is shown in the level scheme of fig. 5. Taking into account the excess pumping effect in the pumped crystal due to the 419/2 ~ 4F3/2 reabsorption of the fluorescence, the threshold pump power for the uniformly pumped LNP laser is approximately given by the rate equation as follows
Pth = huTrw2(Lo + 2~pl)/2°ITf(1 +/39J2),
(1)
~p = N0(o/1 +a2ol2)al/Z,
(2)
where Pth is the threshold pump power, h Planck's constant, v the pump frequency, L 0 the non-resonant loss of the resonator, o l the effective emission cross section, rf the fluorescence lifetime,/39/2 the branching ratio for the 4F3/2 -+ 419/2 transition, N O the Nd-ion density, Oll 2 the emission cross sections for the l 1 and l 2 lines [2] ~a l , 2 = exp(-z2xE1,2/kT), i.e., the Boltzmann factor, Z = 2;i exp ( - ( E i - Eo)/kT} is the partition function. Eq. (2) represents the passive resonant loss coefficient and 2C~p/the resonant loss of the 26
Fig. 5. 419/2 --~4F3/2 reabsorption of the fluorescence and the laser transition in LNP lasers. crystal, where l is the crystal length. Converting the
excess pumping term (1 +/]9/2) in the resonant loss, the active resonant loss coefficient is given by ~a = O~p/(1 +/39/2). The round-trip loss measured by the straightforward method corresponds to (L 0 + 2C~pl) X (1 +~9/2) -1 . In short, the active resonant loss is smaller than the passive one as a consequence of the reabsorption effect of the fluorescence. The observed resonant loss as well as that calculated from eqs. (1) and (2) are summarized in table 1 together with the spectroscopic parameters [2]. In conclusion, we have examined the resonant absorption loss in the LNP laser. It is found that the effective resonant loss is reduced due to the reabsorption effect of the fluorescence corresponding to the inverse 4 i9/2 ~ 4 F3/2 transition. The effective active resonant loss was measured to be about one half of the passive resonant loss for the unpumped crystal. Table 1 Spectroscopic parameters and resonant loss coefficients of LNP lasers, al, a2 and Z are calculated from the energy levels reported in ref. [2]. No all
0/2 al
a2 Z 139/2 C~p c~a
4.37 X 1021 cm -3 5.1 X 10 -19 cm2 0.8 X 10 19 cm2 0.736 0.760 2.48 0.36 0.11 cm -1 (obs.), 0.09 cm -1 (talc.) 0.042 cm -I (obs.), 0.066 cm -I (ealc.)
(ref. [21) (ref. [2]) (ref. [2])
(ref. [2])
Volume 17, number 1
OPTICS COMMUNICATIONS
The authors wish to acknowledge Dr. H. Iwasaki for valuable discussions and criticism.
References
April 1976
[2] K. Otsuka, T. Yamada, M. Saruwatari and T. Kimura, IEEE J. Quantum Electron. QE-11 (1975) 330. [3] S. Singh, D.C. Miller, J.R. Potowicz and L.K. Shick, J. Appl. Phys. 46 (1975) 1191. [4] K. Otsuka and T. Yamada, IEEE J. Quantum Electron. QE-11 (1975) 845.
[1] H.G. Danielmeyer and H.P. Weber, IEEE J. Quantum Electron. QE-8 (1972) 805.
27
OPTICS COMMUNICATIONS
April 1976
RESONANT ABSORPTION IN LiNdP4012 LASERS Kenju OTSUKA and Tomoaki YAMADA
Musashino Electrical Communication Laboratory, Nippon Telegraph and Telephone Public Corporation, Musashino-shi, Tokyo, Japan Received 26 December 1975
Tile resonant loss in LiNdP4012 (LNP) lasers has been investigated. The effective resonant loss coefficient for the 1.047(7)/~m laser emission was measured to be 0.042 cm -1 . This value can be explained by resonant absorption due to the 4 i11/2 -~ 4 F3/2 transition including the reabsorption effect of the fluorescence resulting from the 4 i9/2 _~ 4 F3/2 transition.
In a Nd-laser material, there exists an intrinsic resonant loss due to the absorption resulting from the 4 I l l / 2 -+ 4F3/2 transition. The resonant loss is an important parameter to estimate the threshold pump power, as well as the slope efficiency of the laser oscillation. High Nd-concentration materials such as NdPsO14 and LiNdP4012 (LNP) have strong pump bands [1,2] but their high Nd-concentration also leads to the deleterious effect of high resonant losses [3]. In this letter, the resonant absorption in LNP lasers is reported. The experimental arrangement was as follows. A cw argon laser served as a pump. The LNP laser resonator is of nearly semiconcentric type with mirrors M 1 (radius of curvature R 1 = 0% transmission at 1.047 (7)/sin, T 1 = 0.1%) and M2 (R 2 = 9 cm, T 2 = 0.1, 1, 2, 3%) separated by about 9 cm. The LNP crystal was placed just in front of M 1 . The round-trip loss of the resonator was directly measured by the change of threshold with - I n (r lr2), where r 1 and r 2 are the mirror reflectivities (i.e. straightforward method). The measured longitudinally pumped threshold has been plotted as a function of - l n ( r 1r2) in fig. 1 for three polished LNP-crystals with different thickness cut out from the same boules of the as-grown crystal. The used crystals were 0.7, 2 and 3 mm thick (pseudo-orthorhombic a-axis) and the LNP-laser emission was linearly polarized along the c-axis of the crystal. The absorption coefficient of the LNP for 5145 A was 23 cm - I , therefore the pump light was absorbed about 100% within an absorption length of 24
9.8 ram. The population inversion distribution in the crystal is illustrated in fig. 1, and regions over 0.8 mm in the crystal are not pumped. From the difference of measured round-trip losses shown in fig. 1, the absorption loss coefficient for the unpumped LNP crystal which corresponds to the passive resonant loss is obtained to be ap = (0.11 +-0.001) cm -1 . The nonresonant loss except the mirror transmission loss is estimated to be 0.025.
s,,s
popu,.tion 0 -M1 LNP M2 o04L thickness " | 0.7 2 3 (rnm) o
-002L / / / ,.re..o,d
2r// -0 . 0 8 [ ~ -
O
J
O
I
-
Fig. 1. Laser threshold as a function of -In (rlr2) for 0.7, 2, and 3 mm thick, LNP crystals. The spot size of the pump beam, which was focused by the lens of 5-cm focal-length, was adjusted to that of the oscillating beam.
V o l u m e 17, n u m b e r 1
OPTICS COMMUNICATIONS
Then we pumped platelet-like LNP crystals which are thinner than the penetration depth for the pump light with the same cavity configuration. The used crystals were 0.3 and 0.8 mm thick a-plates and the laser emission was also linearly polarized along the c-axis. The round-trip losses were measured by the straightforward method described above as a function of the oscillating beam spot size averaged over the crystal length. The oscillating beam spot size in the crystal was changed by moving the mirror M 2 or the LNP crystals along the laser axis using the motor-driven micrometer screw and calculated from the output laser beam divergence [4]. The pump light (5145 A) was focused on the LNP crystal by the lens of 5-cm focal-length, longitudinally and the averaged pump beam spot size in the crystal, Wp, was (20 + 5) ~m. The measured absorption loss coefficient Cta for the pumped LNP crystal which corresponds to the active resonant loss is shown in fig. 2 as a function of the oscillating beam spot size, wa. From fig. 2 it is found that the absorption loss coefficient for the pumped crystal o~a is smaller than the passive resonant loss coefficient ap of0.11 cm -1 , and c~a = (0.042 + 0.006) cm -1 for the mode-matching condition, i.e., w a = Wp = (20 + 5) ~tm. The loss coefficient increases with the increase of the beam spot size w a. A possible explanation of this result is that the pump beam does not match the oscillating beam for larger spot sizes (w a > Wp) and the passive loss overlaps the resonant loss. To confirm the reduction of the resonant loss in the pumped LNP crystal, we have carried out two experiments described below.
April 1976
First, we pumped the LNP crystal of 2.57 mm thickness longitudinally with the argon laser of different wavelengths (5145, 4765 and 4579 A). The absorption coefficients of the LNP crystal for these wavelengths are 23 cm -1 (5145 A), 6.3 cm -1 (4765 A) and 4.7 cm -1 (4579 A), respectively. The pump light was absorbed about 80% and 70% for the 4765 A and 4579 A pump respectively, therefore the LNP crystals were uniformly pumped for these wavelengths compared with the 5145 A pump. The measured absorbed threshold power is plotted as a function of the pump wavelength in fig. 3. The solid line show the theoretical value calculated from the threshold power for the 5145 A pump, assuming that the resonant loss is constant. The observed threshold powers for the 4765 A and 4579 A pump are smaller than the theoretical value. This indicates that the resonant losses for these pumpings are effectively smaller than the resonant loss for the 5145 A pump. Second, the LNP crystal of 2.57 mm thickness was pumped longitudinally as well as transversely with the 5145 A argon laser and the round-trip loss of the resonator was measured by the straightforward method. The results are shown in fig. 4. Since the aperture of the pump beam which was focused by the cylindrical lens was adjusted to the crystal length in the case of transverse pumping, the pump light was absorbed uniformly over the crystal length compared with the longitudinal pumping. From fig. 4, it is found that the resonant loss for the transverse pumping is smaller than that for the longitudinal pumping. pump population A
514s~,
2.57mm thick LNP
o rl o°'at°n [1 motor drive
A
"5 c
/theory
.... 60
E
oo o o
--~ 0.10 .u
~o~O
o 0.05 --
0 Q.
"o 80
% 0.15
I/I 0
LNP
~I00
LNP
¢-
o % %
"10
o 4.7
o 6.3
absorption
coeffi. 23cn~
¢n
2o .£1
0
40
i
I
i
i
i
10
20
30
40
50
ed
60
spot size, Wa(lam) Fig. 2. T h e loss coefficient of the u n i f o r m l y p u m p e d LNP laser as a f u n c t i o n of the oscillating b e a m spot size.
0
&o
4~0
560
520
p u m p w a v e l e n g t h (nm) Fig. 3. Laser threshold as a function o f the p u m p wavelength (4579 A, 4765 A, 5145 A).
25
Volume 1 7, number 1
0.04
OPTICS COMMUNICATIONS
2.57mmthickLNP(5145~pump) end side
April 1976
4F~2
-
[1 12
0.02 C
T
o
40 80
-0.02 / ~ -0.04
I?.0 160 200 /threshold pumppower(rnW)
reabsorption 4Illt2
,,E2
1,
-OD6 -0.08
41912
1
-0.I 0
Fig. 4. Laser threshold for longitudinal and transverse pumping as a function of -In (rlr2). The transverse pump light was focused on the crystal by the cylindiical lens of 2-cm focallength. F r o m these experimental results, it is shown that the active resonant loss of the LNP crystal is smaller than the passive one. A plausible explanation of the above experimental results is presented in the following. In the LNP crystal, the absorption coefficient for the inverse 419] 2 ~ 4F3/2 transition is 410 cm - I [2] and the fluorescence corresponding to 4 F 3/2 ~ 4 i912 transition is reabsorbed about 100% within the absorption length of 30/~m. This process is shown in the level scheme of fig. 5. Taking into account the excess pumping effect in the pumped crystal due to the 419/2 ~ 4F3/2 reabsorption of the fluorescence, the threshold pump power for the uniformly pumped LNP laser is approximately given by the rate equation as follows
Pth = huTrw2(Lo + 2~pl)/2°ITf(1 +/39J2),
(1)
~p = N0(o/1 +a2ol2)al/Z,
(2)
where Pth is the threshold pump power, h Planck's constant, v the pump frequency, L 0 the non-resonant loss of the resonator, o l the effective emission cross section, rf the fluorescence lifetime,/39/2 the branching ratio for the 4F3/2 -+ 419/2 transition, N O the Nd-ion density, Oll 2 the emission cross sections for the l 1 and l 2 lines [2] ~a l , 2 = exp(-z2xE1,2/kT), i.e., the Boltzmann factor, Z = 2;i exp ( - ( E i - Eo)/kT} is the partition function. Eq. (2) represents the passive resonant loss coefficient and 2C~p/the resonant loss of the 26
Fig. 5. 419/2 --~4F3/2 reabsorption of the fluorescence and the laser transition in LNP lasers. crystal, where l is the crystal length. Converting the
excess pumping term (1 +/]9/2) in the resonant loss, the active resonant loss coefficient is given by ~a = O~p/(1 +/39/2). The round-trip loss measured by the straightforward method corresponds to (L 0 + 2C~pl) X (1 +~9/2) -1 . In short, the active resonant loss is smaller than the passive one as a consequence of the reabsorption effect of the fluorescence. The observed resonant loss as well as that calculated from eqs. (1) and (2) are summarized in table 1 together with the spectroscopic parameters [2]. In conclusion, we have examined the resonant absorption loss in the LNP laser. It is found that the effective resonant loss is reduced due to the reabsorption effect of the fluorescence corresponding to the inverse 4 i9/2 ~ 4 F3/2 transition. The effective active resonant loss was measured to be about one half of the passive resonant loss for the unpumped crystal. Table 1 Spectroscopic parameters and resonant loss coefficients of LNP lasers, al, a2 and Z are calculated from the energy levels reported in ref. [2]. No all
0/2 al
a2 Z 139/2 C~p c~a
4.37 X 1021 cm -3 5.1 X 10 -19 cm2 0.8 X 10 19 cm2 0.736 0.760 2.48 0.36 0.11 cm -1 (obs.), 0.09 cm -1 (talc.) 0.042 cm -I (obs.), 0.066 cm -I (ealc.)
(ref. [21) (ref. [2]) (ref. [2])
(ref. [2])
Volume 17, number 1
OPTICS COMMUNICATIONS
The authors wish to acknowledge Dr. H. Iwasaki for valuable discussions and criticism.
References
April 1976
[2] K. Otsuka, T. Yamada, M. Saruwatari and T. Kimura, IEEE J. Quantum Electron. QE-11 (1975) 330. [3] S. Singh, D.C. Miller, J.R. Potowicz and L.K. Shick, J. Appl. Phys. 46 (1975) 1191. [4] K. Otsuka and T. Yamada, IEEE J. Quantum Electron. QE-11 (1975) 845.
[1] H.G. Danielmeyer and H.P. Weber, IEEE J. Quantum Electron. QE-8 (1972) 805.
27