Abstract

We use analytic expressions and simulations to examine a model laser gain element formed by integrating diamond and a solid state laser material, such as, Ti:sapphire. The gain element is designed to provide in a single composite structure the thermal management capabilities of diamond and the optical amplification of the laser material. The model results indicate low temperature and a specific radial dependence of the heat transfer coefficient at the material interfaces are needed to access the highest average powers and highest quality optical fields. We outline paths designed to increase average output power of a lowest order mode laser oscillator based on these gain elements to megawatt levels. The long term goal is economically viable solar power delivered safely from space. The short term goal is a design strategy that will facilitate “proof of principle” demonstrations using currently accessible optical pump and thermal management capabilities.

© 2003 Optical Society of America

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References

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  1. See, e.g., Matthew H. Smith, Richard L. Fork and Spencer T. Cole, �??Safe delivery of optical power from space,�?? Opt. Express 8, 537-546 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-10-537">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-10-537</a>
    [CrossRef] [PubMed]
  2. See, e.g., �??Mid Infra-Red Advanced Chemical Laser,�?? Journal of Aerospace and Defense Industry News, Dec. (1997).
  3. W. Koechner, Solid-State Laser Engineering, 5th Ed, (Springer-Verlag, Berlin, 1999).
  4. �??High temperature superconductor power transformer,�?? Superconductivity Program Overview, <a href=http://www.nrel.gov/docs/fy02osti/31252.pdf>http://www.nrel.gov/docs/fy02osti/31252.pdf</a>.
  5. Dan Marker and Mark Gruneisen, �??Thirty meter diameter large space telescope�?? <a href=" http://www.afrlhorizons.com/Briefs/Sept01/DE0102.html">http://www.afrlhorizons.com/Briefs/Sept01/DE0102.html</a>.
  6. James E. Butler, �??Chemical Vapor Deposited Diamond - Maturity and Diversity,�?? The Electrochemical Society Interface, Spring 2003.
  7. James E. Butler and Henry Windischmann, �??Developments in CVD Diamond Synthesis During the Past Decade,�?? MRS Bulletin, September 1998.
  8. T. Sato, K. Ohashi, T. Sudoh, K. Haruna, and H. Maeta, �??Thermal expansion of a high purity synthetic diamond single crystal at low temperatures,�?? Phys. Rev. B 65 092102(R), 1-4 (2002).
    [CrossRef]
  9. L. Wei, P. K. Kuo, R. L. Thomas, T.R. Anthony, and W.F. Banholzer, �??Thermal conductivity of isotopically modified single crystal diamond,�?? Phys. Rev. Lett. 70, 3764-3767 (1993).
    [CrossRef] [PubMed]
  10. F. Nitsche and B. Schumann, �??Heat Transfer Between Sapphire and Lead,�?? J. Low Temperature Phys. 39, 119-130 (1980).
    [CrossRef]
  11. O. Meissner, Onyx Optics, Inc., private communication.
  12. M. N. Ozisik, Basic Heat Transfer, (McGraw-Hill, New York, 1977).
  13. G. Myers, Analytical Methods in Conduction Heat Transfer, (Genium Publishing Corp., Schenectady, 1987).
  14. See, e.g., J. T. Verdeyen, Laser Electronics 3rd ed., (Prentice Hall, Englewood Cliffs, 1995).
  15. R. L. Fork, O. E. Martinez, J. P. Gordon, �??Negative dispersion using pairs of prisms,�?? Opt. Lett. 9, 150-152 (1984).
    [CrossRef] [PubMed]
  16. A. M. Zaitsev, Handbook of Industrial Diamonds and Diamond Films, M.A. Prelas, G. Popovici, and L.K. Bigelow, eds. (Marcel Dekker, Inc., New York, 1998)
  17. M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, �??Thermal modeling of continuouswave end-pumped solid-state lasers,�?? Appl. Phys. Lett. 56, 1831-1833 (1990).
    [CrossRef]
  18. L. M. Osterink and J. D. Foster, �??Thermal effects and transverse mode control in a Nd:YAG laser,�?? Appl. Phys. Lett. 12, 128-131 (1968).
    [CrossRef]
  19. T. Y. Fan and J. Daneu, �??Thermal coefficients of the optical path length and refractive index in YAG,�?? Appl. Opt. 37, 1635-1637 (1998).
    [CrossRef]
  20. A. C. DeFranzo and B. G. Pazol, �??Index of refraction measurement on sapphire at low temperatures and visible wavelengths,�?? Appl. Opt. 32, 2236 (1993).
    [CrossRef]
  21. D. Yang, M. E. Thomas, W. J. Tropf, and S. G. Kaplan, �??Infrared refractive index measurements using a new method,�?? in Optical Diagnostic Methods for Inorganic Materials II, ed., Leonard M Hanssen, SPIE 4103, 42-52 (2000).
    [CrossRef]
  22. P. Schulz and S. Henion, �??Liquid-Nitrogen-Cooled Ti:Al2O3 Laser,�?? IEEE J. Quant. Elect. 27, 1039-1047 (1991).
    [CrossRef]
  23. T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, �??Temperature dependence of the refractive index of diamond up to 925 K,�?? Phys. Rev. B 2, 16578-16581 (2000).
    [CrossRef]
  24. R. W. Dixon, �??Photoelastic Properties of Selected Materials and Their Relevance for Applications to Acoustic Light Modulators and Scanners,�?? J. Appl. Phys. 38, 5149-5153 (1967).
    [CrossRef]
  25. M. H. Grimsditch, E. Anastassakis, and M. Cardona, �??Piezobirefringence in diamond,�?? Phys. Rev. B 19, 3240-3243 (1979).
    [CrossRef]
  26. F. Benabid, M. Notcutt, L. Ju, and D. G. Blair, �??Birefringence measurements of sapphire test masses for laser interferometer gravitational wave detector,�?? Phys. Lett. A 237, 337-342 (1998).
    [CrossRef]
  27. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw Hill, New York, 1970).
  28. W. C. Scott and M. de Wit, �??Birefringence Compensation and TEM00 Mode Enhancement in a Nd:YAG Laser,�?? Appl. Phys. Lett. 18, 3-4 (1971).
    [CrossRef]
  29. George R. Neil, Thomas Jefferson National Accelerator Facility, private communication.
  30. Michael Landry, �??LIGO Commissioning and Initial Science Runs: Current Status,�?? <a href="http://www.slac.stanford.edu/gen/meeting/ssi/2003/landry/landry.pdf">http://www.slac.stanford.edu/gen/meeting/ssi/2003/landry/landry.pdf</a>.
  31. O. Albert and G. Mourou, �??Single optical cycle laser pulse in the visible and near-infrared spectral range,�?? Appl. Phys. B 69, 207-209 (1999).
    [CrossRef]
  32. A. Kaplan, �??Diffraction-Induced Transformation of Near-Cycle and Subcycle Pulses,�?? J. Opt. Soc. Am. B 14, 951-956 (1998).
    [CrossRef]
  33. Richard L. Fork, Spencer T. Cole, Wesley W. Walker, Rustin L. Laycock, and Jason J. A. Green, �??High Average and Peak Power Integrated Laser for Propulsion,�?? NASA Advanced Space Propulsion Workshop, April, Huntsville, AL (2003).

Appl. Opt.

T. Y. Fan and J. Daneu, �??Thermal coefficients of the optical path length and refractive index in YAG,�?? Appl. Opt. 37, 1635-1637 (1998).
[CrossRef]

A. C. DeFranzo and B. G. Pazol, �??Index of refraction measurement on sapphire at low temperatures and visible wavelengths,�?? Appl. Opt. 32, 2236 (1993).
[CrossRef]

Appl. Phys. B

O. Albert and G. Mourou, �??Single optical cycle laser pulse in the visible and near-infrared spectral range,�?? Appl. Phys. B 69, 207-209 (1999).
[CrossRef]

Appl. Phys. Lett.

W. C. Scott and M. de Wit, �??Birefringence Compensation and TEM00 Mode Enhancement in a Nd:YAG Laser,�?? Appl. Phys. Lett. 18, 3-4 (1971).
[CrossRef]

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, �??Thermal modeling of continuouswave end-pumped solid-state lasers,�?? Appl. Phys. Lett. 56, 1831-1833 (1990).
[CrossRef]

L. M. Osterink and J. D. Foster, �??Thermal effects and transverse mode control in a Nd:YAG laser,�?? Appl. Phys. Lett. 12, 128-131 (1968).
[CrossRef]

IEEE J. Quant. Elect.

P. Schulz and S. Henion, �??Liquid-Nitrogen-Cooled Ti:Al2O3 Laser,�?? IEEE J. Quant. Elect. 27, 1039-1047 (1991).
[CrossRef]

J. Aerospace and Def. Ind. News

See, e.g., �??Mid Infra-Red Advanced Chemical Laser,�?? Journal of Aerospace and Defense Industry News, Dec. (1997).

J. Appl. Phys.

R. W. Dixon, �??Photoelastic Properties of Selected Materials and Their Relevance for Applications to Acoustic Light Modulators and Scanners,�?? J. Appl. Phys. 38, 5149-5153 (1967).
[CrossRef]

J. Low Temperature Phys.

F. Nitsche and B. Schumann, �??Heat Transfer Between Sapphire and Lead,�?? J. Low Temperature Phys. 39, 119-130 (1980).
[CrossRef]

J. Opt. Soc. Am. B

A. Kaplan, �??Diffraction-Induced Transformation of Near-Cycle and Subcycle Pulses,�?? J. Opt. Soc. Am. B 14, 951-956 (1998).
[CrossRef]

MRS Bulletin

James E. Butler and Henry Windischmann, �??Developments in CVD Diamond Synthesis During the Past Decade,�?? MRS Bulletin, September 1998.

NASA Advanced Space Propulsion Workshop

Richard L. Fork, Spencer T. Cole, Wesley W. Walker, Rustin L. Laycock, and Jason J. A. Green, �??High Average and Peak Power Integrated Laser for Propulsion,�?? NASA Advanced Space Propulsion Workshop, April, Huntsville, AL (2003).

Opt. Diag. Methods for Inorganic Mat. II

D. Yang, M. E. Thomas, W. J. Tropf, and S. G. Kaplan, �??Infrared refractive index measurements using a new method,�?? in Optical Diagnostic Methods for Inorganic Materials II, ed., Leonard M Hanssen, SPIE 4103, 42-52 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

F. Benabid, M. Notcutt, L. Ju, and D. G. Blair, �??Birefringence measurements of sapphire test masses for laser interferometer gravitational wave detector,�?? Phys. Lett. A 237, 337-342 (1998).
[CrossRef]

Phys. Rev. B

M. H. Grimsditch, E. Anastassakis, and M. Cardona, �??Piezobirefringence in diamond,�?? Phys. Rev. B 19, 3240-3243 (1979).
[CrossRef]

T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, �??Temperature dependence of the refractive index of diamond up to 925 K,�?? Phys. Rev. B 2, 16578-16581 (2000).
[CrossRef]

T. Sato, K. Ohashi, T. Sudoh, K. Haruna, and H. Maeta, �??Thermal expansion of a high purity synthetic diamond single crystal at low temperatures,�?? Phys. Rev. B 65 092102(R), 1-4 (2002).
[CrossRef]

Phys. Rev. Lett.

L. Wei, P. K. Kuo, R. L. Thomas, T.R. Anthony, and W.F. Banholzer, �??Thermal conductivity of isotopically modified single crystal diamond,�?? Phys. Rev. Lett. 70, 3764-3767 (1993).
[CrossRef] [PubMed]

Superconductivity Program Overview

�??High temperature superconductor power transformer,�?? Superconductivity Program Overview, <a href=http://www.nrel.gov/docs/fy02osti/31252.pdf>http://www.nrel.gov/docs/fy02osti/31252.pdf</a>.

The Electrochem. Soc. Interface Spr. 03

James E. Butler, �??Chemical Vapor Deposited Diamond - Maturity and Diversity,�?? The Electrochemical Society Interface, Spring 2003.

Other

Dan Marker and Mark Gruneisen, �??Thirty meter diameter large space telescope�?? <a href=" http://www.afrlhorizons.com/Briefs/Sept01/DE0102.html">http://www.afrlhorizons.com/Briefs/Sept01/DE0102.html</a>.

W. Koechner, Solid-State Laser Engineering, 5th Ed, (Springer-Verlag, Berlin, 1999).

A. M. Zaitsev, Handbook of Industrial Diamonds and Diamond Films, M.A. Prelas, G. Popovici, and L.K. Bigelow, eds. (Marcel Dekker, Inc., New York, 1998)

O. Meissner, Onyx Optics, Inc., private communication.

M. N. Ozisik, Basic Heat Transfer, (McGraw-Hill, New York, 1977).

G. Myers, Analytical Methods in Conduction Heat Transfer, (Genium Publishing Corp., Schenectady, 1987).

See, e.g., J. T. Verdeyen, Laser Electronics 3rd ed., (Prentice Hall, Englewood Cliffs, 1995).

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw Hill, New York, 1970).

George R. Neil, Thomas Jefferson National Accelerator Facility, private communication.

Michael Landry, �??LIGO Commissioning and Initial Science Runs: Current Status,�?? <a href="http://www.slac.stanford.edu/gen/meeting/ssi/2003/landry/landry.pdf">http://www.slac.stanford.edu/gen/meeting/ssi/2003/landry/landry.pdf</a>.

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of a pair of diamond and gain material disks. Heat (yellow arrows) generated in gain disk (red-orange), propagates axially into the adjacent diamond disk (green-blue) and then leaves diamond in an outward radial direction. The gain disk is insulated at the outer edge (gray bar), the diamond is not so insulated. Color indicates temperature (red highest, blue lowest).

Fig. 2.
Fig. 2.

Temperature in the sapphire Ts (r,z) (red-orange) and in diamond Td (z,r) (green-blue) as described by the analytic expressions. The variable discontinuous change in temperature at the interface results from the radially dependent heat transfer coefficient discussed in Section 2.5.

Fig. 3.
Fig. 3.

Log of the stress fracture limit P/L vs. temperature for diamond (blue), sapphire (curved red), and YAG (green). To avoid stress fracture the value of P/L must exceed the value indicated by the straight horizontal line (red).

Fig. 4.
Fig. 4.

Log of the thermal lens focal length for diamond, sapphire, and YAG given a cylindrical rod having length L=1 cm and radius of 0.6 cm continuously removing waste heat at a uniform density of 30 kW/cm3 from the rod. The straight horizontal line (red) corresponds to a thermal lens having a focal length equal to the 35 m Rayleigh length of the representative resonator.

Fig. 5.
Fig. 5.

Log of the loss (expressed in percentage of total incident power) caused by thermal stress induced birefringence. The horizontal red line corresponds to a fractional loss of 0.1% for a rod of length 1 cm and radius 0.6 cm at γo =30 kW/cm2.

Fig. 6.
Fig. 6.

Comparison of temperature distributions in: (a) a continuous cylindrical rod of sapphire (b) alternating disks of sapphire and diamond having a radially constant heat transfer coefficient. Note the difference in the two different color coded temperature scales.

Fig. 7.
Fig. 7.

Temperature of diamond and Ti:sapphire gain element for h(r) chosen to yield constant temperature Tsr (r)=To in the Ti:sapphire. The upper limits on power are set by thermal shock, lensing, and birefringence in diamond as opposed to those in sapphire.

Fig. 8.
Fig. 8.

Cross sectional view of integrated diamond and solid state material laser gain elements. Examples are: (a) “Brewster” configuration, (b) “Prism” configuration. The laser beam is shown in dark red.

Fig. 9.
Fig. 9.

Laser configuration where N≤2zo /Li “Brewster window” gain elements are included in a single symmetric confocal laser oscillator resonator.

Fig. 10.
Fig. 10.

Laser oscillator including N≤2zo /Lp “Prism” gain elements. The regions of the optical path labeled Lp, produce negative dispersion useful for compensating the positive material dispersion of the gain elements.

Equations (10)

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d 2 T sz d z 2 + γ o κ s = 0
T s ( z ) = T d ( 0 , 0 ) + Δ T ds 0 + Δ T sz [ 1 ( z + ) 2 2 ] Δ T sz = γ o 2 2 κ s
( a ) d 2 T dz dz 2 γ o κ d = 0 ( b ) d 2 T dr d r 2 + ( 1 r ) d T dr dr + γ o κ d = 0
T dz ( z ) = Δ T dz [ 1 ( z ) 2 2 ] , Δ T dz = γ o 2 2 κ d , T dr ( r ) = Δ T dr r 2 r o 2 , Δ T dr = γ o r o 2 4 κ d
T s ( r ) = Δ T sr r 2 r o 2 Δ T sr = + ( γ o r o 2 4 κ d ) [ ( dn dT ) d ( dn dT ) s ]
q ds ( r ) = h ( r ) Δ T ds ( r )
h ( r ) = γ o [ Δ T ds 0 + γ o r 2 ( 4 κ d ) ]
P = γ o π 2 r o 4 m λ
I L I o = 0.25 [ 1 + 16 ( C T 2 P h 2 ) ]
C T = 2 n o 3 α C B ( λ κ ) C B = 0.5 ( p 11 p 12 ) E [ 16 ( 1 ν ) ( c 11 c 12 ) ]

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