A disk laser or active mirror (Fig.1) is a type of diode pumped solid-state laser characterized by a heat sink and laser output that are realized on opposite sides of a thin layer of active gain medium. [1] Despite their name, disk lasers do not have to be circular; other shapes have also been tried. The thickness of the disk is considerably smaller than the laser beam diameter. Initially this laser cavity configuration had been proposed [2] and realized experimentally for thin slice semiconductor lasers.[3]

Fig.1. An optically-pumped disk laser (active mirror).

The disk laser concepts allows very high average and peak powers[4] due to its large area leading to moderate power densities on the active material.

Active mirrors and disk lasersEdit

 
Fig.2. A disk laser (active mirror) configuration presented in 1992 at the SPIE conference.[5]

Initially, disk lasers were called active mirrors, because the gain medium of a disk laser is essentially an optical mirror with reflection coefficient greater than unity. An active mirror is a thin disk-shaped double-pass optical amplifier.

The first active mirrors were developed in the Laboratory for Laser Energetics (United States).[6] Scalable diode-end-pumped disk Nd:YAG laser had been proposed in [7] in Talbot active mirror configuration.[8]

Then, the concept was developed in various research groups, in particular, the University of Stuttgart (Germany)[9] for Yb:doped glasses.

In the disk laser, the heat sink does not have to be transparent, so, it can be extremely efficient even with large transverse size   of the device (Fig.1). The increase in size allows the power scaling to many kilowatts without significant modification of the design.[10]

Limit of power scaling for disk lasersEdit

 
Fig.3. Bouncing ray of ASE in a disk laser

The power of such lasers is limited not only by the power of pump available, but also by overheating, amplified spontaneous emission (ASE) and the background round-trip loss.[11] To avoid overheating, the size   should be increased with power scaling. Then, to avoid strong losses due to the exponential growth of the ASE, the transverse-trip gain   cannot be large. This requires reduction of the gain  ; this gain is determined by the reflectivity of the output coupler and thickness  . The round-trip gain   should remain larger than the round-trip loss   (the difference   determines the optical energy, which is output from the laser cavity at each round-trip). The reduction of gain  , in a given round-trip loss  , requires increasing the thickness  . Then, at some critical size, the disk becomes too thick and cannot be pumped above the threshold without overheating.

Some features of the power scaling can revealed from a simple model. Let   be the saturation intensity,[11][12] of the medium,   be the ratio of frequencies,   be the thermal loading parameter. The key parameter   determines the maximal power of the disk laser. The corresponding optimal thickness can be estimated with  . The corresponding optimal size  . Roughly, the round-trip loss should scale inversely proportionally to the cubic root of the power required.

An additional issue is the efficient delivery of pump energy. In low round-trip gain, the single-pass absorption of the pump is also low. Therefore, recycling of pump energy is required for efficient operation. (See the additional mirror M at the left-hand side of figure 2.) For power scaling, the medium should be optically thin, with many passes of pump energy required; the lateral delivery of pump energy [12] also might be a possible solution.

Scaling of disk lasers via self-imagingEdit

Thin disk diode-pumped solid-state lasers may be scaled by means of transverse mode-locking in Talbot cavities.[8] The remarkable feature of Talbot scaling is that Fresnel number   of the   element laser array phase-locked by self-imaging is given by:[7]

 

The limitation on a number of phase-locked emitters   is due to randomly distributed phase distortions across active mirror of the order  . [13]

Anti-ASE capEdit

 
Fig. 4. Uncovered disk laser and that with undoped cap.[14]

In order to reduce the impact of ASE, an anti-ASE cap consisting of undoped material on the surface of a disk laser has been suggested.[15][16] Such a cap allows spontaneously emitted photons to escape from the active layer and prevents them from resonating in the cavity. Rays cannot bounce (Figure 3) as in an uncovered disk. This could allow an order of magnitude increase in the maximum power achievable by a disk laser.[14] In both cases, the back reflection of the ASE from the edges of the disk should be suppressed. This can be done with absorbing layers, shown with green in Figure 4. At operation close to the maximal power, a significant part of the energy goes into ASE; therefore, the absorbing layers also should be supplied with heat sinks, which are not shown in the figure.

 
Fig. 5. Upper bound of loss   at which the output power   of a single disk laser is still achievable. Dashed line corresponds to uncovered disk; thick solid curve represents the case with undoped cap.[14]

Key parameter for laser materialsEdit

The estimate of maximal power achievable at given loss  , is very sensitive to  . The estimate of the upper bound of  , at which the desired output power   is achievable is robust. This estimate is plotted versus normalized power   in figure 5. Here,   is the output power of the laser, and   is dimensional scale of power; it is related with the key parameter  . The thick dashed line represents the estimate for the uncovered disk. The thick solid line shows the same for the disk with undoped cap. The thin solid line represents the qualitative estimate   without coefficients. Circles corresponds to the experimental data for the power achieved and corresponding estimates for the background loss  . All future experiments and numerical simulations and estimates are expected to give values of  , that are below the red dashed line in Fig.5 for the uncovered disks, and below the blue curve for the disks with anti-ASE cap. This can be interpreted as a scaling law for disk lasers .[17]

In the vicinity of the curves mentioned, the efficiency of the disk laser is low; most of the pumping power goes to ASE, and is absorbed at the edges of the device. In these cases, the distribution of the pump energy available among several disks may significantly improve the performance of the lasers. Indeed, some lasers reported using several elements combined in the same cavity.

Pulsed operationEdit

Similar scaling laws take place for pulsed operation. In quasi continuous wave regime, the maximal mean power can be estimated by scaling the saturation intensity with the fill factor of the pump, and the product of the duration of pump to the repetition rate. At short duration pulses, more detailed analysis is required .[18] At moderate values of the repetition rate (say, higher than 1 Hz), the maximal energy of the output pulses is roughly inversely proportional to the cube of the background loss  ; the undoped cap may provide an additional order of magnitude of mean output power, under the condition that this cap does not contribute to the background loss. At low repetition rate (and in the regime of single pulses) and sufficient pump power, there is no general limit of energy, but the required size of the device grows quickly with increase of the required pulse energy, setting the practical limit of energy; it is estimated that from a few joules to a few thousand joules can be extracted in an optical pulse from a single active element, dependently on the level of the background internal loss of the signal in the disk.[19]

See alsoEdit

ReferencesEdit

  1. ^ "Thin disk lasers". Encyclopedia of Laser Physics and Technology.
  2. ^ Basov, N G; Bogdankevich, OV; Grasiuk, AZ (1966). "Semiconductor lasers with radiating mirrors". IEEE Journal of QE. 2 (4): 9 B4. doi:10.1109/JQE.1966.1073948.
  3. ^ Bogdankevich, OV; Darznek, SA; Pechenov, A N; Vasiliev, BI; Zverev, MM (1973). "Semiconductor lasers with radiating mirrors". IEEE Journal of QE. 9 (2): 342–347. doi:10.1109/JQE.1973.1077470.
  4. ^ "All news in the overview | Institut für Strahlwerkzeuge | University of Stuttgart".
  5. ^ K. Ueda; N. Uehara (1993). Chung, Y. C (ed.). "Laser-diode-pumped solid state lasers for gravitational wave antenna". Proceedings of SPIE. Frequency-Stabilized Lasers and Their Applications. 1837: 336–345. Bibcode:1993SPIE.1837..336U. doi:10.1117/12.143686.[permanent dead link]
  6. ^ A.Abate; L.Lund; D.Brown; S.Jacobs; S.Refermat; J.Kelly; M.Gavin; J.Waldbillig; O.Lewis (1981). "Active mirror: a large-aperture medium-repetition rate Nd:glass amplifier". Applied Optics. 1837 (2): 351–361. Bibcode:1981ApOpt..20..351A. doi:10.1364/AO.20.000351. PMID 20309114.
  7. ^ a b Okulov, A Yu (1990). "Two-dimensional periodic structures in nonlinear resonator". JOSA B. 7 (6): 1045–1050. doi:10.1364/JOSAB.7.001045.
  8. ^ a b Okulov, A Yu (1993). "Scaling of diode-array-pumped solid-state lasers via self-imaging". Opt. Comm. 99 (5–6): 350–354. doi:10.1016/0030-4018(93)90342-3.
  9. ^ A. Giesen; H. Hügel; A. Voss; K. Wittig; U. Brauch; H. Opower (1994). "Scalable concept for diode-pumped high-power solid-state lasers". Applied Physics B. 58 (5): 365–372. Bibcode:1994ApPhB..58..365G. doi:10.1007/BF01081875.
  10. ^ C.Stewen; K.Contag; M.Larionov; A.Giesen; H.Hugel (2000). "A 1-kW CW thin disc laser". IEEE Journal of Selected Topics in Quantum Electronics. 6 (4): 650–657. Bibcode:2000IJSTQ...6..650S. doi:10.1109/2944.883380. ISSN 1077-260X. NSPEC Accession Number 6779337.
  11. ^ a b D. Kouznetsov; J.F. Bisson; J. Dong; K. Ueda (2006). "Surface loss limit of the power scaling of a thin-disk laser". JOSA B. 23 (6): 1074–1082. Bibcode:2006JOSAB..23.1074K. doi:10.1364/JOSAB.23.001074. S2CID 59505769.; [1][permanent dead link]
  12. ^ a b D.Kouznetsov; J.F.Bisson; K.Takaichi; K.Ueda (2005). "Single-mode solid-state laser with short wide unstable cavity". JOSA B. 22 (8): 1605–1619. Bibcode:2005JOSAB..22.1605K. doi:10.1364/JOSAB.22.001605.
  13. ^ Okulov, A Yu (1991). "The Effect of Roughness of Optical Elements on the Transverse Structure of a Light Field in a Nonlinear Talbot Cavity". Journal of Modern Optics. 38 (10): 1887–1890. doi:10.1080/09500349114551991.
  14. ^ a b c D.Kouznetsov; J.F.Bisson (2008). "Role of undoped cap in the scaling of thin-disk lasers". JOSA B. 25 (3): 338–345. Bibcode:2008JOSAB..25..338K. doi:10.1364/JOSAB.25.000338. S2CID 55659195.
  15. ^ Stephen A. Payne; William F. Krupke; Raymond J. Beach; Steven B. Sutton; Eric C. Honea; Camille Bibeau; Howard Powel (2002). "High average power scaleable thin-disk laser". US Patent. 6347109. Archived from the original on 2009-01-16.
  16. ^ Beach, Raymond J.; Honea, Eric C.; Bibeau, Camille; Payne, Stephen A.; Powell, Howard; Krupke, William F.; Sutton, Steven B. (2002). "High average power scaleable thin-disk laser". USA Patent. 6347109.
  17. ^ D.Kouznetsov; J.-F.Bisson, K.Ueda (2009). "Scaling laws of disk lasers" (PDF). Optical Materials. 31 (5): 754–759. Bibcode:2009OptMa..31..754K. CiteSeerX 10.1.1.694.3844. doi:10.1016/j.optmat.2008.03.017.
  18. ^ D.Kouznetsov (2008). "Storage of energy in disk-shaped laser materials". Research Letters in Physics. 2008: 1–5. Bibcode:2008RLPhy2008E..17K. doi:10.1155/2008/717414. Archived from the original on 2013-01-25.
  19. ^ J.Speiser (2009). "Scaling of thin-disk lasers--influence of amplified spontaneous emission". JOSA B. 26 (1): 26–35. Bibcode:2008JOSAB..26...26S. doi:10.1364/JOSAB.26.000026.