Rigrod theory was used to model outcoupled power from a low-gain laser with good accuracy. For a low-gain overtone cw HF chemical laser, Rigrod theory shows that a higher medium saturation yields a higher overall overtone efficiency, but does not necessarily yield a higher measurable power (power in the bucket). For low-absorption–scattering loss overtone mirrors and a 5% penalty in outcoupled power, the intracavity flux and hence the mirror loading may be reduced by more than a factor of 2 when the gain length is long enough to saturate the medium well. For the University of Illinois at Urbana-Champaign overtone laser that has an extensive database with well-characterized mirrors for which the Rigrod parameters g0 and Isat were firmly established, the accuracy to which the reflectivities of high-reflectivity overtone mirrors can be deduced by using measured mirror transmissivities, measured outcoupled power, and Rigrod theory is approximatly ±0.07%. This method of accurately deducing mirror reflectivities may be applicable to other low-gain laser systems that use high-reflectivity mirrors at different wavelengths. The maximum overtone efficiency is estimated to be approximately 80%–100%.
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List of Fundamental and Overtone Mirror Sets Used for the UIUC SSL Experimentsa
Mirror
Mirror #1
Mirror #2
Reflectivity
Trans.
Abs./Scat.
Mirror
Reflectivity
Trans.
Abs./Scat.
Fundamental
2mCC
0.38
0.62
0
2mCC
0.995
0.005
0
2mCC
0.50
0.50
0
2mCC
0.995
0.005
0
2mCC
0.63
0.37
0
2mCC
0.995
0.005
0
2mCC
0.73
0.27
0
2mCC
0.995
0.005
0
2mCC
0.93
0.07
0
2mCC
0.995
0.005
0
2mCC
0.96
0.04
0
2mCC
0.995
0.005
0
Overtone
4mCC #7
0.980
0.0113
0.0087
4mCC #2
0.9967
0.00067
0.00263
4mCC #1-ad
0.9968
0.00064
0.00256
4mCC #2
0.9967
0.00067
0.00263
4mCC #1-ad
0.9968
0.00064
0.00256
Flat #2
0.9970
0.00071
0.00229
30mCC #2
0.9970
0.00078
0.00222
Flat #2
0.9970
0.00071
0.00229
4mCC #3
0.9970
0.00073
0.00227
4mCC #4
0.9970
0.00080
0.00220
4mCC #5-ad
0.9970
0.00081
0.00219
4mCC #6-ad
0.9970
0.00074
0.00226
30mCC #1
0.9970
0.00084
0.00216
30mCC #2
0.9970
0.00078
0.00222
8mCC #1
0.99.70
0.00084
0.00216
8mCC #2
0.9970
0.00080
0.00220
4mCC #1-bd
0.9978
0.00064
0.00156
4mCC #2
0.9967
0.00067
0.00263
4mCC #9
0.9971
0.00044
0.00246
4mCC #10
0.9980
0.00047
0.00153
4mCC #5-bd
0.9975
0.00081
0.00169
4mCC #6-bd
0.9975
0.00074
0.00176
4mCC #10
0.9980
0.00047
0.00153
4mCC#ll
0.9986
0.00049
0.00091
ad, After degradation; bd, before degradation.
Table 2
List of the Different Overtone Mirror Combinations, Their Effective Reflectivity, Their Total Transmission, and Their Total Mirror Absorption-Scattering Lossa
Mirror 1
Mirror 2
(R1*R2)1/2
T1 + T2
AS1 + AS2
Reg. He Injection Outcoupled Power (W)
CSS He Injection Outcoupled Power (W)
4mCC #7
4mCC #2
0.98831
0.01197
0.01133
2.7
1.0
4mCC #1-ad
4mCC #2
0.99675
0.00131
0.00519
8.1
7.6
4mCC #1-ad
Flat #2
0.99690
0.00135
0.00485
12.1
9.9
30mCC #2
Flat #2
0.99700
0.00149
0.00451
12.5
12.7
4mCC #3
4mCC #4
0.99700
0.00153
0.00447
11.0
11.7
4mCC #5-ad
4mCC #6-ad
0.99700
0.00155
0.00445
14.6
14.1
30mmCC #1
30mCC #2
0.99700
0.00162
0.00438
12.4
12.4
8mCC#1
8mCC #2
0.99700
0.00164
0.00436
11.9
14.2
4mCC #1-bd
4mCC #2
0.99725
0.00131
0.00419
11.5
nm
4mCC #9
4mCC #10
0.99755
0.00091
0.00399
10.5
nm
4mCC #5-bd
4mCC #6-bd
0.99750
0.00155
0.00345
19.9
nm
4mCC #10
4mCC#11
0.99830
0.00096
0.00244
11.9
nm
ad, After degradation; bd, before degradation; nm, not measured.
Table 3
Overtone Outcoupled Power and Efficiency as a Function of Reflectivity and Gain Length as Predicted by Rigrod Theory
The calculations are done for one pair of 99.7% reflective, 0.05% transmissive, 0.25% absorption–scattering loss mirrors, a pair of 99.4% reflective, 0.35% transmissive, 0.25% absorption–scattering loss mirrors, a pair of 99.7% reflective, 0.25% transmissive, 0.05% absorption–scattering loss mirrors, and a pair of 99.4% reflective, 0.55% transmissive, 0.05% absorption–scattering loss mirrors.
The overtone efficiency estimates are based on a maximum fundamental power of 63–76.2 W for the 30-cm device and an estimated maximum fundamental power of 126–152.4 W with the proposed 60-cm device.
Tables (3)
Table 1
List of Fundamental and Overtone Mirror Sets Used for the UIUC SSL Experimentsa
Mirror
Mirror #1
Mirror #2
Reflectivity
Trans.
Abs./Scat.
Mirror
Reflectivity
Trans.
Abs./Scat.
Fundamental
2mCC
0.38
0.62
0
2mCC
0.995
0.005
0
2mCC
0.50
0.50
0
2mCC
0.995
0.005
0
2mCC
0.63
0.37
0
2mCC
0.995
0.005
0
2mCC
0.73
0.27
0
2mCC
0.995
0.005
0
2mCC
0.93
0.07
0
2mCC
0.995
0.005
0
2mCC
0.96
0.04
0
2mCC
0.995
0.005
0
Overtone
4mCC #7
0.980
0.0113
0.0087
4mCC #2
0.9967
0.00067
0.00263
4mCC #1-ad
0.9968
0.00064
0.00256
4mCC #2
0.9967
0.00067
0.00263
4mCC #1-ad
0.9968
0.00064
0.00256
Flat #2
0.9970
0.00071
0.00229
30mCC #2
0.9970
0.00078
0.00222
Flat #2
0.9970
0.00071
0.00229
4mCC #3
0.9970
0.00073
0.00227
4mCC #4
0.9970
0.00080
0.00220
4mCC #5-ad
0.9970
0.00081
0.00219
4mCC #6-ad
0.9970
0.00074
0.00226
30mCC #1
0.9970
0.00084
0.00216
30mCC #2
0.9970
0.00078
0.00222
8mCC #1
0.99.70
0.00084
0.00216
8mCC #2
0.9970
0.00080
0.00220
4mCC #1-bd
0.9978
0.00064
0.00156
4mCC #2
0.9967
0.00067
0.00263
4mCC #9
0.9971
0.00044
0.00246
4mCC #10
0.9980
0.00047
0.00153
4mCC #5-bd
0.9975
0.00081
0.00169
4mCC #6-bd
0.9975
0.00074
0.00176
4mCC #10
0.9980
0.00047
0.00153
4mCC#ll
0.9986
0.00049
0.00091
ad, After degradation; bd, before degradation.
Table 2
List of the Different Overtone Mirror Combinations, Their Effective Reflectivity, Their Total Transmission, and Their Total Mirror Absorption-Scattering Lossa
Mirror 1
Mirror 2
(R1*R2)1/2
T1 + T2
AS1 + AS2
Reg. He Injection Outcoupled Power (W)
CSS He Injection Outcoupled Power (W)
4mCC #7
4mCC #2
0.98831
0.01197
0.01133
2.7
1.0
4mCC #1-ad
4mCC #2
0.99675
0.00131
0.00519
8.1
7.6
4mCC #1-ad
Flat #2
0.99690
0.00135
0.00485
12.1
9.9
30mCC #2
Flat #2
0.99700
0.00149
0.00451
12.5
12.7
4mCC #3
4mCC #4
0.99700
0.00153
0.00447
11.0
11.7
4mCC #5-ad
4mCC #6-ad
0.99700
0.00155
0.00445
14.6
14.1
30mmCC #1
30mCC #2
0.99700
0.00162
0.00438
12.4
12.4
8mCC#1
8mCC #2
0.99700
0.00164
0.00436
11.9
14.2
4mCC #1-bd
4mCC #2
0.99725
0.00131
0.00419
11.5
nm
4mCC #9
4mCC #10
0.99755
0.00091
0.00399
10.5
nm
4mCC #5-bd
4mCC #6-bd
0.99750
0.00155
0.00345
19.9
nm
4mCC #10
4mCC#11
0.99830
0.00096
0.00244
11.9
nm
ad, After degradation; bd, before degradation; nm, not measured.
Table 3
Overtone Outcoupled Power and Efficiency as a Function of Reflectivity and Gain Length as Predicted by Rigrod Theory
The calculations are done for one pair of 99.7% reflective, 0.05% transmissive, 0.25% absorption–scattering loss mirrors, a pair of 99.4% reflective, 0.35% transmissive, 0.25% absorption–scattering loss mirrors, a pair of 99.7% reflective, 0.25% transmissive, 0.05% absorption–scattering loss mirrors, and a pair of 99.4% reflective, 0.55% transmissive, 0.05% absorption–scattering loss mirrors.
The overtone efficiency estimates are based on a maximum fundamental power of 63–76.2 W for the 30-cm device and an estimated maximum fundamental power of 126–152.4 W with the proposed 60-cm device.