Abstract

We examine wave-front distortion caused by high-power lasers on transmissive optics using a Shack–Hartmann wave-front sensor. The coupling coefficient for a thermally aberrated Gaussian beam to the TEM00 mode of a cavity was determined as a function of magnitude of the thermally induced aberration. One wave of thermally induced phase aberration between the Gaussian intensity peak and the 1/e 2 radius of the intensity profile reduces the power-coupling coefficient to the TEM00 mode of the cavity to 4.5% with no compensation. With optimal focus compensation the power coupling is increased to 79%. The theoretical shape of the thermally induced optical phase aberration is compared with measurements made in a neutral-density filter glass, Faraday glass, and lithium niobate. The agreement between the theoretical and the measured thermal aberration profiles is within the rms wave-front measurement sensitivity of the Shack–Hartmann wave-front sensor, which is a few nanometers.

© 2001 Optical Society of America

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References

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  1. A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
    [CrossRef] [PubMed]
  2. R. Q. Fugate, B. L. Ellerbroek, C. H. Higgins, M. P. Jelonek, W. J. Lange, A. C. Slavin, W. J. Wild, D. M. Winker, J. M. Wynia, J. M. Spinhirne, B. R. Boeke, R. E. Ruane, J. F. Moroney, M. D. Oliker, D. W. Swindle, R. A. Cleis, “Two generations of laser-guide-star adaptive-optics experiments at the Starfire Optical Range,” J. Opt. Soc. Am. A 11, 310–324 (1994).
    [CrossRef]
  3. R. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, New York, 1998).
  4. J. Hartmann, “Bemerkungen uber den Bau und die Justirung von Spektrographen,” Z. Instrumentenkd. 20, 47 (1900).
  5. The cubic spline reconstructor is provided in the CLAS-2D software by WaveFront Sciences, Inc., Albuquerque, N.M. 87123.
  6. D. R. Neal, D. J. Armstrong, W. T. Turner, “Wave-front sensors for control and process monitoring in optics manufacture,” in Lasers as Tools for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 1–10 (1997).
  7. W. M. Rohsenow, J. P. Hartnett, E. N. Ganic, eds., Handbook of Heat Transfer Fundamentals, 2nd ed. (McGraw-Hill, New York, 1985), Chap. 4.
  8. K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
    [CrossRef]
  9. M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), pp. 227–231.
  10. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 318–323.
  11. A. Alexandrovski, Research Associate, Stanford University, Stanford Calif. (personal communication, 1998).
  12. M. M. Fejer, P. F. Bordiu, “Inorganic crystals for nonlinear optical frequency conversion,” Annu. Rev. Mater. Sci. 23, 321–379 (1993).
    [CrossRef]
  13. J. Storms, Hoya Corporation, 101 Metro Dr., Suite 500, San Jose, Calif. 95110 (personal communication, 1998).
  14. B. Scheller, Schott Glass Technologies Inc., 400 York Ave., Duryea, Pa. 18642-2026 (personal communication, 1998).
  15. R. Waynant, E. Marwood, Electro-optics Handbook (McGraw-Hill, New York, 1994), pp. 11.13–11.83.
  16. H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Symposium on Qusi-Optics (Polytechnic Institute of Brooklyn, Brooklyn, N.Y., 1964), 333–347.
  17. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [CrossRef]
  18. N. Uehara, E. K. Gustafson, M. M. Fejer, R. L. Byer, “Modeling of efficient mode matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukh, S. Basu, eds., Proc. SPIE2989, 57–68 (1997).
    [CrossRef]

1994

1993

M. M. Fejer, P. F. Bordiu, “Inorganic crystals for nonlinear optical frequency conversion,” Annu. Rev. Mater. Sci. 23, 321–379 (1993).
[CrossRef]

1992

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

1980

1900

J. Hartmann, “Bemerkungen uber den Bau und die Justirung von Spektrographen,” Z. Instrumentenkd. 20, 47 (1900).

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Alexandrovski, A.

A. Alexandrovski, Research Associate, Stanford University, Stanford Calif. (personal communication, 1998).

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Armstrong, D. J.

D. R. Neal, D. J. Armstrong, W. T. Turner, “Wave-front sensors for control and process monitoring in optics manufacture,” in Lasers as Tools for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 1–10 (1997).

Boeke, B. R.

Bordiu, P. F.

M. M. Fejer, P. F. Bordiu, “Inorganic crystals for nonlinear optical frequency conversion,” Annu. Rev. Mater. Sci. 23, 321–379 (1993).
[CrossRef]

Byer, R. L.

N. Uehara, E. K. Gustafson, M. M. Fejer, R. L. Byer, “Modeling of efficient mode matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukh, S. Basu, eds., Proc. SPIE2989, 57–68 (1997).
[CrossRef]

Cleis, R. A.

Danzmann, K.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

Drever, R. W. P.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Ellerbroek, B. L.

Fejer, M. M.

M. M. Fejer, P. F. Bordiu, “Inorganic crystals for nonlinear optical frequency conversion,” Annu. Rev. Mater. Sci. 23, 321–379 (1993).
[CrossRef]

N. Uehara, E. K. Gustafson, M. M. Fejer, R. L. Byer, “Modeling of efficient mode matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukh, S. Basu, eds., Proc. SPIE2989, 57–68 (1997).
[CrossRef]

Fugate, R. Q.

Gursel, Y.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Gustafson, E. K.

N. Uehara, E. K. Gustafson, M. M. Fejer, R. L. Byer, “Modeling of efficient mode matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukh, S. Basu, eds., Proc. SPIE2989, 57–68 (1997).
[CrossRef]

Hartmann, J.

J. Hartmann, “Bemerkungen uber den Bau und die Justirung von Spektrographen,” Z. Instrumentenkd. 20, 47 (1900).

Higgins, C. H.

Jelonek, M. P.

Kawamura, S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Kogelnik, H.

H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Symposium on Qusi-Optics (Polytechnic Institute of Brooklyn, Brooklyn, N.Y., 1964), 333–347.

Lange, W. J.

Marwood, E.

R. Waynant, E. Marwood, Electro-optics Handbook (McGraw-Hill, New York, 1994), pp. 11.13–11.83.

Mizuno, J.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

Moroney, J. F.

Neal, D. R.

D. R. Neal, D. J. Armstrong, W. T. Turner, “Wave-front sensors for control and process monitoring in optics manufacture,” in Lasers as Tools for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 1–10 (1997).

Nelson, P. G.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

Oliker, M. D.

Raab, F. J.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Ruane, R. E.

Rudiger, A.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

Scheller, B.

B. Scheller, Schott Glass Technologies Inc., 400 York Ave., Duryea, Pa. 18642-2026 (personal communication, 1998).

Schilling, R.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

Shoemaker, D.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Sievers, L.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Slavin, A. C.

Southwell, W. H.

Spero, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Spinhirne, J. M.

Storms, J.

J. Storms, Hoya Corporation, 101 Metro Dr., Suite 500, San Jose, Calif. 95110 (personal communication, 1998).

Strain, K. A.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

Swindle, D. W.

Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Turner, W. T.

D. R. Neal, D. J. Armstrong, W. T. Turner, “Wave-front sensors for control and process monitoring in optics manufacture,” in Lasers as Tools for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 1–10 (1997).

Tyson, R.

R. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, New York, 1998).

Uehara, N.

N. Uehara, E. K. Gustafson, M. M. Fejer, R. L. Byer, “Modeling of efficient mode matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukh, S. Basu, eds., Proc. SPIE2989, 57–68 (1997).
[CrossRef]

Vogt, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Waynant, R.

R. Waynant, E. Marwood, Electro-optics Handbook (McGraw-Hill, New York, 1994), pp. 11.13–11.83.

Weiss, R.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Whitcomb, S. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Wild, W. J.

Winker, D. M.

Winkler, W.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

Wynia, J. M.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 318–323.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 318–323.

Zucker, M. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Annu. Rev. Mater. Sci.

M. M. Fejer, P. F. Bordiu, “Inorganic crystals for nonlinear optical frequency conversion,” Annu. Rev. Mater. Sci. 23, 321–379 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Phys. Lett. A

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, A. Rudiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

Science

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Z. Instrumentenkd.

J. Hartmann, “Bemerkungen uber den Bau und die Justirung von Spektrographen,” Z. Instrumentenkd. 20, 47 (1900).

Other

The cubic spline reconstructor is provided in the CLAS-2D software by WaveFront Sciences, Inc., Albuquerque, N.M. 87123.

D. R. Neal, D. J. Armstrong, W. T. Turner, “Wave-front sensors for control and process monitoring in optics manufacture,” in Lasers as Tools for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 1–10 (1997).

W. M. Rohsenow, J. P. Hartnett, E. N. Ganic, eds., Handbook of Heat Transfer Fundamentals, 2nd ed. (McGraw-Hill, New York, 1985), Chap. 4.

M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), pp. 227–231.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 318–323.

A. Alexandrovski, Research Associate, Stanford University, Stanford Calif. (personal communication, 1998).

R. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, New York, 1998).

N. Uehara, E. K. Gustafson, M. M. Fejer, R. L. Byer, “Modeling of efficient mode matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukh, S. Basu, eds., Proc. SPIE2989, 57–68 (1997).
[CrossRef]

J. Storms, Hoya Corporation, 101 Metro Dr., Suite 500, San Jose, Calif. 95110 (personal communication, 1998).

B. Scheller, Schott Glass Technologies Inc., 400 York Ave., Duryea, Pa. 18642-2026 (personal communication, 1998).

R. Waynant, E. Marwood, Electro-optics Handbook (McGraw-Hill, New York, 1994), pp. 11.13–11.83.

H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Symposium on Qusi-Optics (Polytechnic Institute of Brooklyn, Brooklyn, N.Y., 1964), 333–347.

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Figures (7)

Fig. 1
Fig. 1

Calculation of the transmissive optic thermal lens shape in waves assuming five waves of aberration between the center and the Gaussian waist with respect to distance from the center of the heating beam. The Gaussian intensity is also plotted to show how much power is in the beam with respect to the radius.

Fig. 2
Fig. 2

Two-dimensional power coupling κ between a Gaussian beam with a thermal lens and an ideal TEM00 beam with and without optimal focus compensation. The power coupling of the aberrated beam with optimal focus compensation to the TEM20 Hermite–Gaussian mode is also shown.

Fig. 3
Fig. 3

Schematic of the operation of the Shack–Hartmann wave-front sensor. (a) Light incident on the sensor propagates along the z axis. The CCD array and the lens array are shown tilted relative to each other only to illustrate the operation of the device. In reality, the lens array and the CCD array are parallel. (b) Schematic of the measured position change of the focal spots where Δx and Δy give the average wave-front tilt over a lens aperture when divided by the separation between the lens array and the CCD.

Fig. 4
Fig. 4

Diagram showing the setup used to measure thermal lensing. Light from the 700-mW Nd:YAG laser travels through a half-wave plate (HWP) and a polarizing beam splitter (PBS) to control the laser power in the test region. The lens adjusts the Nd:YAG beam size in the test region. The high-reflector mirrors (HR) at 1064 nm are used to bring the Nd:YAG laser into and out of the test region. The He–Ne beam passes through a HWP to control polarization and is aligned collinear with the Nd:YAG beam in the test region through the dielectric HR mirrors. The Shack–Hartmann wave-front sensor measures the spatial phase of the He–Ne laser.

Fig. 5
Fig. 5

Optical path-length difference versus the radius of the pump beam for NG5 Schott glass when exposed to a 190-mW Nd:YAG beam with a Gaussian waist of 1.02 mm. Shown is the measured data, the fit to the theoretical shape given by Eq. (2), and the absolute value of the difference between the two curves expanded 30 times to make the difference visible.

Fig. 6
Fig. 6

Schematic of the optical setup used to measure the effect of transmissive optic thermal lensing on coupling to the TEM00 mode of a cavity. Note that the wave-front conditioning optics are not shown. An absorbing piece of filter glass, also not shown, was placed at different locations relative to the cavity waist. HWP, half-wave plate; PD, photodiode; NPRO, nonplanar ring-oscillator; FI, Faraday isolator; PBS, polarizing beam splitter; EOM, electro-optic modulator.

Fig. 7
Fig. 7

Power coupling of a thermally distorted TEM00 mode to a ring Fabry–Perot mode-cleaner cavity versus the thermal lens magnitude induced in different types of filter glass (NG9 and NG5) at different distances from the cavity waist. For the measurement with the NG5, the thermal lens was reimaged into the cavity to eliminate any change in the Gaussian beam intensity profile. The thermal lens magnitude was calculated with the known material parameters and Eq. (11).

Tables (2)

Tables Icon

Table 1 Optical and Thermal Parameters of Selected Optical Materials

Tables Icon

Table 2 Calculated Optical Path-Length Changes

Equations (15)

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

2T+qkth=1DthTt,
ΔTr=|Tr-T0|=-aP4πkthΓ+ln2rw2+E12rw2=aP4πkthn=0-1n2 r2w2nnn!,
ΔTmag=|ΔT0-ΔTw|=1.32 aP4πkth=0.105 aPkth.
Λr=n0L+ΔnthermalrL+Δnstressr×L+n0ΔLthermalr,
ΔΛthermalr=dndT LΔTr,
ΔΛstressr-n032 ρ12αLΔTr,
ΔΛexpansionr2αnwΔTr,
ΔΛmag=|ΔΛ0-ΔΛw|,
cxΨaberrated, Ψm=-+ ΨmxΨaberrated*xdx.
κ=cxΨaberrated, Ψmcx*Ψaberrated, Ψm×cyΨaberrated, Ψncy*Ψaberrated, Ψn=κxκy.
ΔΛmag=|ΔΛ0-ΔΛw|=1.32 Pabs4πkthdndT=0.105 PabskthdndT,
xposition=-- Ix, yxdxdy-- Ix, ydxdy,
xposition=i=iminimaxj=jminjmax Ii, jii=iminimaxj=jminjmax Ii, j sx,
dϕx, ydx=Δxf,
ϕrmsFreconstructordf Δxrms,

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