Comment on "Surface loss limit of the power scaling of a thin-disk laser"
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Comment on “Surface loss limit of the power scaling of a thin-disk laser” Rüdiger Paschotta, 1, * Jochen Speiser, 2 and Adolf Giesen 2,3 1 RP Photonics Consulting GmbH, Kurfirstenstr. 63, 8002 Zürich, Switzerland 2 Deutsches Zentrum für Luft- und Raumfahrt, Institut für Technische Physik, Pfaffenwaldring 38–40, 70569 Stuttgart, Germany 3 E-mail: [email protected] * Corresponding author: [email protected] Received August 21, 2006; accepted February 9, 2007; posted July 9, 2007 (Doc. ID 74302); published September 21, 2007 A recent paper [J. Opt. Soc. Am. B 23, 1074 (2006)] on power-scaling aspects of thin-disk lasers is based on a wrong assumption concerning the impact of amplified spontaneous emission, which is greatly overestimated. As a consequence of this and two other issues, the evaluated power-scaling limits—which are close to already realized performance values—are substantially too low. © 2007 Optical Society of America OCIS codes: 140.3580, 140.3430. A recent paper [1] contains an interesting discussion of the power-scaling limits of thin-disk lasers. Unfortu- nately, much of it is affected by a wrong assumption con- cerning the effect of amplified spontaneous emission (ASE). This assumption is that the decay rate of the up- per laser level is increased relative to its intrinsic value by a factor of expGL (see Eq. (1) in [1]), i.e., the power- amplification factor for a path from one end of the disk to the opposite end. This factor would only apply for an yt- terbium ion that is surrounded by a sphere with radius L of excited gain medium, so that rays reaching that ion from any direction would have experienced the mentioned gain. However, if bouncing modes are suppressed by a suitable design of the reflecting coating (as assumed in [1]), this high gain applies only to radiation coming from a quite limited solid angle, so that the actual increase of the decay rate is significantly smaller. Furthermore, even this reduced additional decay would apply only to laser ions near the edge of the disk, whereas the effect on ions near the center of the disk would be much smaller. (Reference 6 cited in [1] gives more details on how to calculate the actual decay rate.) Taking these considerations into ac- count, we can expect that a significantly larger transverse gain factor expGL should not have a strong impact on the effective upper-state lifetime. As a rough estimate, the corresponding correction, which is related to the term e u / u 2 in Eq. (20), is equivalent to increasing the param- eter R 2 by more than 1 order of magnitude. The same in- crease then applies to the achievable output power P s,max . Even for the much-less-favorable situation with bounc- ing modes, having a total path length of up to 2L in the disk, one can show that the resulting effect on the upper- state lifetime is much weaker than estimated in [1], al- lowing for output powers that are roughly 1 order of mag- nitude higher. The authors intend to present a comprehensive discussion of such calculations in a forth- coming publication. Another comment concerns the value of the loss param- eter , which has been assumed to be 1%. This is rather pessimistic, given that several-times-lower values have already been achieved. As the possible output power de- pends on the third power of that parameter, the limits are again increased by perhaps 2 orders of magnitude. Furthermore, the assumed limit for the parameter R is also quite pessimistic. A temperature rise of 100 K (in- stead of 50 K) can be handled; the thermal shock issue is also much less severe, because the corresponding assump- tions of [1] apply only to a mechanically unsupported disk, while the mechanical support provided either by the cooling finger or by an undoped piece of YAG crystal on top of the doped part can strongly mitigate stress effects. We expect that a higher R parameter allows for another factor of 4 in the output power. As the authors of [1] noted, their results would indicate that already-realized thin-disk lasers operate close to the scaling limits. However, the indicated corrections show that there should be room for a further increase of power by several orders of magnitude, even without use of an undoped cap. This result appears to be quite important, e.g., for anyone comparing the potentials of thin-disk la- sers and fiber lasers. Of course, one should be aware that the entire analysis is fairly simplified and that various disregarded issues (e.g., heating of the gain medium by absorbed ASE) and unexpected technical problems may make it difficult to realize the full theoretical potential. Two smaller corrections to [1] are that the denominator in Eq. (18) must be 2h instead of 2g, and that Eq. (23) must contain the term R 2 instead of R 4 . REFERENCES 1. D. Kouznetsov, J.-F. Bisson, J. Dong, and K. Ueda, “Surface loss limit of the power scaling of a thin-disk laser,” J. Opt. Soc. Am. B 23, 1074–1082 (2006). 2658 J. Opt. Soc. Am. B/Vol. 24, No. 10/October 2007 0740-3224/07/102658-1/$15.00 © 2007 Optical Society of America
Transcript of Comment on "Surface loss limit of the power scaling of a thin-disk laser"
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2658 J. Opt. Soc. Am. B/Vol. 24, No. 10 /October 2007
Comment on “Surface loss limit of the powerscaling of a thin-disk laser”
Rüdiger Paschotta,1,* Jochen Speiser,2 and Adolf Giesen2,3
1RP Photonics Consulting GmbH, Kurfirstenstr. 63, 8002 Zürich, Switzerland2Deutsches Zentrum für Luft- und Raumfahrt, Institut für Technische Physik, Pfaffenwaldring 38–40, 70569
Stuttgart, Germany3E-mail: [email protected]
*Corresponding author: [email protected]
Received August 21, 2006; accepted February 9, 2007;posted July 9, 2007 (Doc. ID 74302); published September 21, 2007
A recent paper [J. Opt. Soc. Am. B 23, 1074 (2006)] on power-scaling aspects of thin-disk lasers is based on awrong assumption concerning the impact of amplified spontaneous emission, which is greatly overestimated.As a consequence of this and two other issues, the evaluated power-scaling limits—which are close to alreadyrealized performance values—are substantially too low. © 2007 Optical Society of America
OCIS codes: 140.3580, 140.3430.
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recent paper [1] contains an interesting discussion ofhe power-scaling limits of thin-disk lasers. Unfortu-ately, much of it is affected by a wrong assumption con-erning the effect of amplified spontaneous emissionASE). This assumption is that the decay rate of the up-er laser level is increased relative to its intrinsic valuey a factor of exp�GL� (see Eq. (1) in [1]), i.e., the power-mplification factor for a path from one end of the disk tohe opposite end. This factor would only apply for an yt-erbium ion that is surrounded by a sphere with radius Lf excited gain medium, so that rays reaching that ionrom any direction would have experienced the mentionedain. However, if bouncing modes are suppressed by auitable design of the reflecting coating (as assumed in1]), this high gain applies only to radiation coming from auite limited solid angle, so that the actual increase of theecay rate is significantly smaller. Furthermore, even thiseduced additional decay would apply only to laser ionsear the edge of the disk, whereas the effect on ions nearhe center of the disk would be much smaller. (Reference
cited in [1] gives more details on how to calculate thectual decay rate.) Taking these considerations into ac-ount, we can expect that a significantly larger transverseain factor exp�GL� should not have a strong impact onhe effective upper-state lifetime. As a rough estimate, theorresponding correction, which is related to the termu /u2 in Eq. (20), is equivalent to increasing the param-ter R2 by more than 1 order of magnitude. The same in-rease then applies to the achievable output power Ps,max.
Even for the much-less-favorable situation with bounc-ng modes, having a total path length of up to �2L in theisk, one can show that the resulting effect on the upper-tate lifetime is much weaker than estimated in [1], al-owing for output powers that are roughly 1 order of mag-itude higher. The authors intend to present aomprehensive discussion of such calculations in a forth-oming publication.
0740-3224/07/102658-1/$15.00 © 2
Another comment concerns the value of the loss param-ter �, which has been assumed to be 1%. This is ratheressimistic, given that several-times-lower values havelready been achieved. As the possible output power de-ends on the third power of that parameter, the limits aregain increased by perhaps 2 orders of magnitude.Furthermore, the assumed limit for the parameter R is
lso quite pessimistic. A temperature rise of 100 K (in-tead of 50 K) can be handled; the thermal shock issue islso much less severe, because the corresponding assump-ions of [1] apply only to a mechanically unsupportedisk, while the mechanical support provided either by theooling finger or by an undoped piece of YAG crystal onop of the doped part can strongly mitigate stress effects.e expect that a higher R parameter allows for another
actor of 4 in the output power.As the authors of [1] noted, their results would indicate
hat already-realized thin-disk lasers operate close to thecaling limits. However, the indicated corrections showhat there should be room for a further increase of powery several orders of magnitude, even without use of anndoped cap. This result appears to be quite important,.g., for anyone comparing the potentials of thin-disk la-ers and fiber lasers. Of course, one should be aware thathe entire analysis is fairly simplified and that variousisregarded issues (e.g., heating of the gain medium bybsorbed ASE) and unexpected technical problems mayake it difficult to realize the full theoretical potential.Two smaller corrections to [1] are that the denominator
n Eq. (18) must be 2h instead of 2g, and that Eq. (23)ust contain the term R2 instead of R4.
EFERENCES1. D. Kouznetsov, J.-F. Bisson, J. Dong, and K. Ueda, “Surface
loss limit of the power scaling of a thin-disk laser,” J. Opt.Soc. Am. B 23, 1074–1082 (2006).
007 Optical Society of America
