Abstract

We present an experimental demonstration of adaptive control of modal properties of optical beams. The control is achieved via heat-induced photothermal actuation of transmissive optical elements. We apply the heat using four electrical heaters in thermal contact with the element. The system is capable of controlling both symmetrical and astigmatic aberrations providing a powerful means for in situ correction and control of thermal aberrations in high power laser systems. We demonstrate a tunable lens with a focusing power varying from minus infinity to −10 m along two axes using SF57 optical glass. Applications of the proposed system include laser material processing, thermal compensation of high laser power radiation, and optical beam steering.

© 2010 OSA

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References

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  1. J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG Laser,” Appl. Opt. 41, 3656–3663 (1970).
  2. E. Greninger, “Thermally induced wave-front distortions in laser windows,” Appl. Opts., 41, 549–552, (1986). A. E. Siegman, Lasers, University Science books, Sausalito, CA (1984).
  3. P. Hello and J. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. (France) 51, 1267–1282 (1990).
    [CrossRef]
  4. P. Hello and J. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power CW laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
    [CrossRef]
  5. G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
    [CrossRef]
  6. R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29(22), 2635–2637 (2004).
    [CrossRef] [PubMed]
  7. M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
    [CrossRef] [PubMed]
  8. R. Schmiedl, “Adaptive optics for CO2 laser material processing, ” in 2nd International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific Publishing Co Pte Ltd, 2000), pp. 32–36.
  9. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
    [CrossRef]
  10. W. L. IJzerman, S. T. de Zwart, and T. Dekker, “Design of 2D/3D switchable displays,” SID Symposium Digest, 36, 98–101 (2005).
  11. T. L. Kelly, A. F. Naumov, M. Yu. Loktev, and M. A. Rakhmatulin, “Focusing of astigmatic laser diode beam by combination of adaptive liquid crystal lenses,” Opt. Commun. 181(4-6), 295–301 (2000).
    [CrossRef]
  12. I. Kanno, T. Kunisawa, T. Suzuki, and H. Kotera, “Development of deformable mirror composed of piezoelectric thin films for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 155–161 (2007).
    [CrossRef]
  13. H. Ren and S.-T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14(23), 11292–11298 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11292 .
    [CrossRef] [PubMed]
  14. T.-Y. Chen, C.-H. Li, J.-L. Wang, C. E. Chiu, and G. J. Su, “A MEMS-based Organic Deformable Mirror with Tunable Focal Length,”2007 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, July 16 (2007), pp. 103–104.
  15. M. Smith, and P. Willems, Auxiliary Optics Support System Conceptual Design Document, Volume 1 Thermal Compensation System, LIGO-T060083–00-D, http://docuserv.ligo.caltech.edu/docs/public/T/T060083-00/T060083-00.pdf
  16. M. A. Arain, V. Quetschke, L. F. Williams, G. Mueller, D. B. Tanner, and D. H. Reitze, “Elements for Future Gravitational Wave Interferometers,’ Frontiers in Optics, OSA meeting, San Jose, CA, September 2007.
  17. M. A. Arain, V. Quetschke, L. F. Williams, R. Martin, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive Optical Elements for Laser Beam Shaping,” US provisional patent, Serial No. 61/086,661, US patent pending.
  18. F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 5th ed., (John Wiley & Sons, USA, 2002).
  19. A. E. Siegman, “Defining, measuring, and optimizing laser beam quality,” Proc. SPIE 1868, 2 (1993).
    [CrossRef]

2007

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

I. Kanno, T. Kunisawa, T. Suzuki, and H. Kotera, “Development of deformable mirror composed of piezoelectric thin films for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 155–161 (2007).
[CrossRef]

2006

H. Ren and S.-T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14(23), 11292–11298 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11292 .
[CrossRef] [PubMed]

2004

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29(22), 2635–2637 (2004).
[CrossRef] [PubMed]

2002

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

2000

T. L. Kelly, A. F. Naumov, M. Yu. Loktev, and M. A. Rakhmatulin, “Focusing of astigmatic laser diode beam by combination of adaptive liquid crystal lenses,” Opt. Commun. 181(4-6), 295–301 (2000).
[CrossRef]

1993

A. E. Siegman, “Defining, measuring, and optimizing laser beam quality,” Proc. SPIE 1868, 2 (1993).
[CrossRef]

1990

P. Hello and J. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. (France) 51, 1267–1282 (1990).
[CrossRef]

P. Hello and J. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power CW laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
[CrossRef]

1979

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[CrossRef]

1970

J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG Laser,” Appl. Opt. 41, 3656–3663 (1970).

Amin, R. S.

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

Arain, M. A.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

Cruz, R. J.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

Foster, J. D.

J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG Laser,” Appl. Opt. 41, 3656–3663 (1970).

Fritschel, P.

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29(22), 2635–2637 (2004).
[CrossRef] [PubMed]

Gleason, J.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

Guagliardo, D.

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

Hello, P.

P. Hello and J. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power CW laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
[CrossRef]

P. Hello and J. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. (France) 51, 1267–1282 (1990).
[CrossRef]

Kanno, I.

I. Kanno, T. Kunisawa, T. Suzuki, and H. Kotera, “Development of deformable mirror composed of piezoelectric thin films for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 155–161 (2007).
[CrossRef]

Kelly, T. L.

T. L. Kelly, A. F. Naumov, M. Yu. Loktev, and M. A. Rakhmatulin, “Focusing of astigmatic laser diode beam by combination of adaptive liquid crystal lenses,” Opt. Commun. 181(4-6), 295–301 (2000).
[CrossRef]

Kotera, H.

I. Kanno, T. Kunisawa, T. Suzuki, and H. Kotera, “Development of deformable mirror composed of piezoelectric thin films for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 155–161 (2007).
[CrossRef]

Kunisawa, T.

I. Kanno, T. Kunisawa, T. Suzuki, and H. Kotera, “Development of deformable mirror composed of piezoelectric thin films for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 155–161 (2007).
[CrossRef]

Lawrence, R.

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29(22), 2635–2637 (2004).
[CrossRef] [PubMed]

Lee, J.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

Loktev, M. Yu.

T. L. Kelly, A. F. Naumov, M. Yu. Loktev, and M. A. Rakhmatulin, “Focusing of astigmatic laser diode beam by combination of adaptive liquid crystal lenses,” Opt. Commun. 181(4-6), 295–301 (2000).
[CrossRef]

Lundock, R.

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

McFeron, D.

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

Mueller, G.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

Naumov, A. F.

T. L. Kelly, A. F. Naumov, M. Yu. Loktev, and M. A. Rakhmatulin, “Focusing of astigmatic laser diode beam by combination of adaptive liquid crystal lenses,” Opt. Commun. 181(4-6), 295–301 (2000).
[CrossRef]

Osterink, L. M.

J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG Laser,” Appl. Opt. 41, 3656–3663 (1970).

Ottaway, D.

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29(22), 2635–2637 (2004).
[CrossRef] [PubMed]

Quetschke, V.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

Rakhmanov, M.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

Rakhmatulin, M. A.

T. L. Kelly, A. F. Naumov, M. Yu. Loktev, and M. A. Rakhmatulin, “Focusing of astigmatic laser diode beam by combination of adaptive liquid crystal lenses,” Opt. Commun. 181(4-6), 295–301 (2000).
[CrossRef]

Reitze, D. H.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

Ren, H.

H. Ren and S.-T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14(23), 11292–11298 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11292 .
[CrossRef] [PubMed]

Sato, S.

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “Defining, measuring, and optimizing laser beam quality,” Proc. SPIE 1868, 2 (1993).
[CrossRef]

Suzuki, T.

I. Kanno, T. Kunisawa, T. Suzuki, and H. Kotera, “Development of deformable mirror composed of piezoelectric thin films for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 155–161 (2007).
[CrossRef]

Tanner, D. B.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

Vinet, J.

P. Hello and J. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. (France) 51, 1267–1282 (1990).
[CrossRef]

P. Hello and J. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power CW laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
[CrossRef]

Williams, L. F.

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

Wu, S.-T.

H. Ren and S.-T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14(23), 11292–11298 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11292 .
[CrossRef] [PubMed]

Zucker, M.

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29(22), 2635–2637 (2004).
[CrossRef] [PubMed]

Appl. Opt.

J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG Laser,” Appl. Opt. 41, 3656–3663 (1970).

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007).
[CrossRef] [PubMed]

Class. Quantum Gravity

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Gravity 19(7), 1793–1801 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

I. Kanno, T. Kunisawa, T. Suzuki, and H. Kotera, “Development of deformable mirror composed of piezoelectric thin films for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 155–161 (2007).
[CrossRef]

J. Phys. (France)

P. Hello and J. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. (France) 51, 1267–1282 (1990).
[CrossRef]

P. Hello and J. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power CW laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
[CrossRef]

Jpn. J. Appl. Phys.

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[CrossRef]

Opt. Commun.

T. L. Kelly, A. F. Naumov, M. Yu. Loktev, and M. A. Rakhmatulin, “Focusing of astigmatic laser diode beam by combination of adaptive liquid crystal lenses,” Opt. Commun. 181(4-6), 295–301 (2000).
[CrossRef]

Opt. Express

H. Ren and S.-T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14(23), 11292–11298 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11292 .
[CrossRef] [PubMed]

Opt. Lett.

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29(22), 2635–2637 (2004).
[CrossRef] [PubMed]

Proc. SPIE

A. E. Siegman, “Defining, measuring, and optimizing laser beam quality,” Proc. SPIE 1868, 2 (1993).
[CrossRef]

Other

W. L. IJzerman, S. T. de Zwart, and T. Dekker, “Design of 2D/3D switchable displays,” SID Symposium Digest, 36, 98–101 (2005).

T.-Y. Chen, C.-H. Li, J.-L. Wang, C. E. Chiu, and G. J. Su, “A MEMS-based Organic Deformable Mirror with Tunable Focal Length,”2007 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, July 16 (2007), pp. 103–104.

M. Smith, and P. Willems, Auxiliary Optics Support System Conceptual Design Document, Volume 1 Thermal Compensation System, LIGO-T060083–00-D, http://docuserv.ligo.caltech.edu/docs/public/T/T060083-00/T060083-00.pdf

M. A. Arain, V. Quetschke, L. F. Williams, G. Mueller, D. B. Tanner, and D. H. Reitze, “Elements for Future Gravitational Wave Interferometers,’ Frontiers in Optics, OSA meeting, San Jose, CA, September 2007.

M. A. Arain, V. Quetschke, L. F. Williams, R. Martin, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive Optical Elements for Laser Beam Shaping,” US provisional patent, Serial No. 61/086,661, US patent pending.

F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 5th ed., (John Wiley & Sons, USA, 2002).

R. Schmiedl, “Adaptive optics for CO2 laser material processing, ” in 2nd International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific Publishing Co Pte Ltd, 2000), pp. 32–36.

E. Greninger, “Thermally induced wave-front distortions in laser windows,” Appl. Opts., 41, 549–552, (1986). A. E. Siegman, Lasers, University Science books, Sausalito, CA (1984).

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Figures (15)

Fig. 1
Fig. 1

Geometry of an optical element heated by an external heating band in direct thermal contact with the barrel. This heat can be applied by one or multiple elements positioned along the perimeter of the optical element.

Fig. 2
Fig. 2

Schematic diagram of SF57 with four independent heaters arranged symmetrically along the barrel of the optics. Here the direction marked as “No direct heat input” shows the axis of the gap between heaters.

Fig. 3
Fig. 3

Experimental setup to measure the thermal lensing of SF57 as a function of the applied heat. The four quadrant photodetector (QPD) is used to measure the beam angular drift. The beam scan gives an estimate of the thermal lensing by measuring the beam waist position and size and using ABCD matrices.

Fig. 4
Fig. 4

Beam z-scans for various heating powers. The solid lines are fits to the data points using Gaussian beam parameters. These fits are used to estimate the focal point shift enabling extraction of the induced focal length.

Fig. 5
Fig. 5

Computed lensing based upon the z-scan data calculated by means of ABCD matrices. The solid blue line shows the cumulative OPL change between the center and the edge of the lens while the dotted green line shows the simulated (using COMSOL) focal length (m) as a function of heating power. The measured data, shown as red points (with error bars) agrees well with the simulations.

Fig. 6
Fig. 6

A thermal image of the SF57 sample and its four heaters with 2.4 W per heater is shown on the left. Contours of constant temperature are indicated. A calculation from COMSOL is shown on the right.

Fig. 7
Fig. 7

Astigmatic lens generation using differential heating in SF57. Images of the beam taken at a fixed location show a) cold SF57, b) heating in the x-axis only, c) heating in the y-axis only, and d) heating in both axes.

Fig. 8
Fig. 8

Simulation of the temperature profile of SF57 with heating in the vertical direction only. Note the negative temperature gradient in the vertical direction where the heat is applied and the positive gradient appearing in the horizontal direction. This is attributed to the finite extent of the heaters. Here fx and fy represent focal length values in the x and y axes.

Fig. 9
Fig. 9

simulation showing the effect of the gap between adjacent heaters on the cross coupling between the two axes when heat is applied to one direction only.

Fig. 10
Fig. 10

Beam waist measured at a fixed location for various degrees of SF57 heating. The response time is measured as the average of five step changes and is found to be 500 ± 80 s calculated as average of the response time during four heating cycles and one cooling phase.

Fig. 11
Fig. 11

Simulation of the heating response showing the OPL change at two points—the center of the SF57 and a point 2 mm away from the center, corresponding to 2 mm waist beam size. The difference is shown as the red curve multiplied by 100.

Fig. 12
Fig. 12

Beam drift in the horizontal and vertical directions. The y-axis deviation is scaled to the 2.5 mm beam size at the QPD and shown as a percentage—a 0.1% deviation corresponds to a 2.5 μm shift. Various states of the SF57 heater are shown as separate grid blocks. The response time is on the order of 500 seconds calculated as average of the response time during four heating cycles and one cooling phase.

Fig. 13
Fig. 13

Temperature profile across the center line of the heating elements in y-direction and 45° to the axis of the heating elements.

Fig. 14
Fig. 14

Measured temperature profile across the center line of the heating elements in the y-direction and a quadratic fit to the data. The lower graph shows the residues of the quadratic fit to the measured data.

Fig. 15
Fig. 15

Simulated temperature profile and the resultant OPL as a function of radial distance. Quadratic fits and the corresponding Regression coefficient is also shown.

Tables (3)

Tables Icon

Table 1 Material properties of prospective optical elements for adaptive beam shaping

Tables Icon

Table 2 Astigmatic Lens Creation in SF57 via Differential Heating

Tables Icon

Table 3 Thermal Depolarization Measurement Summary

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

ρ   C   T   t = k 2 T + Q
k 2 T + Q = 0
q = q r a d + q e x t
q r a d = ε σ ( T 4 T a m b 4 )
k   T   r ( a , z , φ ) = ε   σ   T 4 + q ( a , z , φ ) ,
k   T   z ( r , h / 2 ) = ε   σ   T 4 ,
k   T   z ( r , h / 2 ) = ε   σ   T 4 .
T ( r ) = q e x t a 2 4 k ( r 2 a 2 1 ) + T 0 ,
  Δ OPL = h [ d n d T + α T ( 1 + υ ) × ( n 1 ) ]    q e x t r 2 4 k ,
f = 4 k h [ d n d T + α T ( 1 + υ ) × ( n 1 ) ]   1 q e x t .
F O M = [ d n d T + α T ( 1 + υ ) × ( n 1 ) ] / k

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