Abstract

Optical coatings with circularly symmetric graded reflectance are used as laser mirrors in unstable resonators. A proper design of such coatings permits any maximum central reflectance to be obtained along with a null external reflectance. Different design approaches are discussed, and an optimized design that gives negligible distortion of the reflected and transmitted wave front is proposed. Coatings with super-Gaussian and step reflectance profiles are examined as two different solutions for improving laser beam quality.

© 1993 Optical Society of America

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References

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  1. P. Lavigne, N. McCarthy, J.-G. Demers, “Design and characterization of complementary Gaussian reflectivity mirrors,” Appl. Opt. 24, 2581–2586 (1985).
    [CrossRef] [PubMed]
  2. S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with taperedreflectivity mirrors: the supergaussian approach,” IEEE J. Quantum Electron. 42, 1172–1177 (1988).
    [CrossRef]
  3. A. Parent, P. Lavigne, “Variable reflectivity unstable resonators for coherent laser radar emitters,” Appl. Opt. 28, 901–903 (1989).
    [CrossRef] [PubMed]
  4. P. Sona, P. Muys, G. Sherman, Ch. Leys, “High-power fast-axial-flow CO2 laser with a variable reflectivity output coupler,” Opt. Lett. 15, 1452–1454 (1990).
    [CrossRef] [PubMed]
  5. S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, “Q-switched Nd:YAG laser with supergaussian resonators,” Opt. Lett. 16, 642–644 (1991).
    [CrossRef] [PubMed]
  6. M. Perrone, C. Cali, C. Pace, “Performance of XeCl laser with supergaussian reflectivity unstable resonators,” Opt. Commun. 92, 93–97 (1992).
    [CrossRef]
  7. K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21, (1989).
    [CrossRef]
  8. A. Cutolo, G. Calafiore, S. Solimeno, “Optoelectronic super-gaussian mirrors based on the thermo-optical effect,” Opt. Commun. 93, 163–168 (1992).
    [CrossRef]
  9. A. Piegari, A. Tirabassi, G. Emiliani, “Thin films for special laser mirrors with radially variable reflectance: production techniques and laser testing,” in Thin Films in Optics, T. T. Tschudi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1125, 68–73 (1989).
  10. C. Zizzo, C. Arnone, C. Cali, S. Sciortino, “Fabrication and characterization of tuned Gaussian mirrors for the visible and near infrared,” Opt. lett. 13, 342–344 (1988).
    [CrossRef] [PubMed]
  11. A. Piegari, S. Scaglione, G. Emiliani, “Optical coatings for improving laser beam quality,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1782, 145–155 (1992).
    [CrossRef]
  12. H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Macmillan, New York, 1986), Chap. 2.
    [CrossRef]
  13. K. Yasui, S. Yagi, M. Tanaka, “Negative-branch unstable resonator with a phase-unifying output coupler for high power Nd:YAG laser,” Appl. Opt. 29, 1277–1280 (1990).
    [CrossRef] [PubMed]
  14. Y. Takenaka, M. Kuzumoto, K. Yasui, S. Yagi, M. Tagashira, “High power and high focusing cw CQ2 laser using an unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. 27, 2482–2487 (1991).
    [CrossRef]

1992 (2)

M. Perrone, C. Cali, C. Pace, “Performance of XeCl laser with supergaussian reflectivity unstable resonators,” Opt. Commun. 92, 93–97 (1992).
[CrossRef]

A. Cutolo, G. Calafiore, S. Solimeno, “Optoelectronic super-gaussian mirrors based on the thermo-optical effect,” Opt. Commun. 93, 163–168 (1992).
[CrossRef]

1991 (2)

S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, “Q-switched Nd:YAG laser with supergaussian resonators,” Opt. Lett. 16, 642–644 (1991).
[CrossRef] [PubMed]

Y. Takenaka, M. Kuzumoto, K. Yasui, S. Yagi, M. Tagashira, “High power and high focusing cw CQ2 laser using an unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. 27, 2482–2487 (1991).
[CrossRef]

1990 (2)

1989 (2)

A. Parent, P. Lavigne, “Variable reflectivity unstable resonators for coherent laser radar emitters,” Appl. Opt. 28, 901–903 (1989).
[CrossRef] [PubMed]

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21, (1989).
[CrossRef]

1988 (2)

C. Zizzo, C. Arnone, C. Cali, S. Sciortino, “Fabrication and characterization of tuned Gaussian mirrors for the visible and near infrared,” Opt. lett. 13, 342–344 (1988).
[CrossRef] [PubMed]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with taperedreflectivity mirrors: the supergaussian approach,” IEEE J. Quantum Electron. 42, 1172–1177 (1988).
[CrossRef]

1985 (1)

Arnone, C.

Calafiore, G.

A. Cutolo, G. Calafiore, S. Solimeno, “Optoelectronic super-gaussian mirrors based on the thermo-optical effect,” Opt. Commun. 93, 163–168 (1992).
[CrossRef]

Cali, C.

M. Perrone, C. Cali, C. Pace, “Performance of XeCl laser with supergaussian reflectivity unstable resonators,” Opt. Commun. 92, 93–97 (1992).
[CrossRef]

C. Zizzo, C. Arnone, C. Cali, S. Sciortino, “Fabrication and characterization of tuned Gaussian mirrors for the visible and near infrared,” Opt. lett. 13, 342–344 (1988).
[CrossRef] [PubMed]

Cutolo, A.

A. Cutolo, G. Calafiore, S. Solimeno, “Optoelectronic super-gaussian mirrors based on the thermo-optical effect,” Opt. Commun. 93, 163–168 (1992).
[CrossRef]

De Silvestri, S.

S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, “Q-switched Nd:YAG laser with supergaussian resonators,” Opt. Lett. 16, 642–644 (1991).
[CrossRef] [PubMed]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with taperedreflectivity mirrors: the supergaussian approach,” IEEE J. Quantum Electron. 42, 1172–1177 (1988).
[CrossRef]

Demers, J.-G.

Emiliani, G.

A. Piegari, S. Scaglione, G. Emiliani, “Optical coatings for improving laser beam quality,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1782, 145–155 (1992).
[CrossRef]

A. Piegari, A. Tirabassi, G. Emiliani, “Thin films for special laser mirrors with radially variable reflectance: production techniques and laser testing,” in Thin Films in Optics, T. T. Tschudi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1125, 68–73 (1989).

Kuzumoto, M.

Y. Takenaka, M. Kuzumoto, K. Yasui, S. Yagi, M. Tagashira, “High power and high focusing cw CQ2 laser using an unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. 27, 2482–2487 (1991).
[CrossRef]

Laporta, P.

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with taperedreflectivity mirrors: the supergaussian approach,” IEEE J. Quantum Electron. 42, 1172–1177 (1988).
[CrossRef]

Lavigne, P.

Leys, Ch.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Macmillan, New York, 1986), Chap. 2.
[CrossRef]

Magni, V.

S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, “Q-switched Nd:YAG laser with supergaussian resonators,” Opt. Lett. 16, 642–644 (1991).
[CrossRef] [PubMed]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with taperedreflectivity mirrors: the supergaussian approach,” IEEE J. Quantum Electron. 42, 1172–1177 (1988).
[CrossRef]

McCarthy, N.

Muys, P.

Pace, C.

M. Perrone, C. Cali, C. Pace, “Performance of XeCl laser with supergaussian reflectivity unstable resonators,” Opt. Commun. 92, 93–97 (1992).
[CrossRef]

Parent, A.

Perrone, M.

M. Perrone, C. Cali, C. Pace, “Performance of XeCl laser with supergaussian reflectivity unstable resonators,” Opt. Commun. 92, 93–97 (1992).
[CrossRef]

Piegari, A.

A. Piegari, A. Tirabassi, G. Emiliani, “Thin films for special laser mirrors with radially variable reflectance: production techniques and laser testing,” in Thin Films in Optics, T. T. Tschudi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1125, 68–73 (1989).

A. Piegari, S. Scaglione, G. Emiliani, “Optical coatings for improving laser beam quality,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1782, 145–155 (1992).
[CrossRef]

Scaglione, S.

A. Piegari, S. Scaglione, G. Emiliani, “Optical coatings for improving laser beam quality,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1782, 145–155 (1992).
[CrossRef]

Sciortino, S.

Sherman, G.

Solimeno, S.

A. Cutolo, G. Calafiore, S. Solimeno, “Optoelectronic super-gaussian mirrors based on the thermo-optical effect,” Opt. Commun. 93, 163–168 (1992).
[CrossRef]

Sona, P.

Svelto, O.

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with taperedreflectivity mirrors: the supergaussian approach,” IEEE J. Quantum Electron. 42, 1172–1177 (1988).
[CrossRef]

Taccheo, S.

Tagashira, M.

Y. Takenaka, M. Kuzumoto, K. Yasui, S. Yagi, M. Tagashira, “High power and high focusing cw CQ2 laser using an unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. 27, 2482–2487 (1991).
[CrossRef]

Takenaka, Y.

Y. Takenaka, M. Kuzumoto, K. Yasui, S. Yagi, M. Tagashira, “High power and high focusing cw CQ2 laser using an unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. 27, 2482–2487 (1991).
[CrossRef]

Tanaka, M.

K. Yasui, S. Yagi, M. Tanaka, “Negative-branch unstable resonator with a phase-unifying output coupler for high power Nd:YAG laser,” Appl. Opt. 29, 1277–1280 (1990).
[CrossRef] [PubMed]

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21, (1989).
[CrossRef]

Tirabassi, A.

A. Piegari, A. Tirabassi, G. Emiliani, “Thin films for special laser mirrors with radially variable reflectance: production techniques and laser testing,” in Thin Films in Optics, T. T. Tschudi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1125, 68–73 (1989).

Valentini, G.

Yagi, S.

Y. Takenaka, M. Kuzumoto, K. Yasui, S. Yagi, M. Tagashira, “High power and high focusing cw CQ2 laser using an unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. 27, 2482–2487 (1991).
[CrossRef]

K. Yasui, S. Yagi, M. Tanaka, “Negative-branch unstable resonator with a phase-unifying output coupler for high power Nd:YAG laser,” Appl. Opt. 29, 1277–1280 (1990).
[CrossRef] [PubMed]

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21, (1989).
[CrossRef]

Yasui, K.

Y. Takenaka, M. Kuzumoto, K. Yasui, S. Yagi, M. Tagashira, “High power and high focusing cw CQ2 laser using an unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. 27, 2482–2487 (1991).
[CrossRef]

K. Yasui, S. Yagi, M. Tanaka, “Negative-branch unstable resonator with a phase-unifying output coupler for high power Nd:YAG laser,” Appl. Opt. 29, 1277–1280 (1990).
[CrossRef] [PubMed]

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21, (1989).
[CrossRef]

Zizzo, C.

Appl. Opt. (3)

IEEE J. Quantum Electron. (2)

Y. Takenaka, M. Kuzumoto, K. Yasui, S. Yagi, M. Tagashira, “High power and high focusing cw CQ2 laser using an unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. 27, 2482–2487 (1991).
[CrossRef]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with taperedreflectivity mirrors: the supergaussian approach,” IEEE J. Quantum Electron. 42, 1172–1177 (1988).
[CrossRef]

J. Appl. Phys. (1)

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21, (1989).
[CrossRef]

Opt. Commun. (2)

A. Cutolo, G. Calafiore, S. Solimeno, “Optoelectronic super-gaussian mirrors based on the thermo-optical effect,” Opt. Commun. 93, 163–168 (1992).
[CrossRef]

M. Perrone, C. Cali, C. Pace, “Performance of XeCl laser with supergaussian reflectivity unstable resonators,” Opt. Commun. 92, 93–97 (1992).
[CrossRef]

Opt. lett. (1)

Other (3)

A. Piegari, S. Scaglione, G. Emiliani, “Optical coatings for improving laser beam quality,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1782, 145–155 (1992).
[CrossRef]

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Macmillan, New York, 1986), Chap. 2.
[CrossRef]

A. Piegari, A. Tirabassi, G. Emiliani, “Thin films for special laser mirrors with radially variable reflectance: production techniques and laser testing,” in Thin Films in Optics, T. T. Tschudi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1125, 68–73 (1989).

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Figures (14)

Fig. 1
Fig. 1

Coatings for a CO2 laser (λ = 10.6 μm) that give radially graded reflectance: (a) R0 = 74%, Rmin = 1%; (b) R0 = 80%, Rmin = 0.

Fig. 2
Fig. 2

Coatings for a Nd:YAG laser (λ = 1.06 μm) that contain only one variable layer. Refractive indices and geometric thicknesses are reported. q.w.'s, Quarter-wave layers.

Fig. 3
Fig. 3

Reflectance as a function of wavelength: solid curve, quarter-wave multilayer stack (reference wavelength λ0 = 3080 Å); dotted curve, optimized coating for obtaining R0) = 75% and Rmin = 0 (nH = 2, nL = 1.395, ns = 1.486).

Fig. 4
Fig. 4

Variable reflectance coating for a XeCl laser (λ = 3080 Å) with all profiled layers (the maximum thickness is reported). The central reflectance as function of wavelength is as shown in Fig. 3. R0 = 75%, Rmin = 0 (all thicknesses divided by 1.22).

Fig. 5
Fig. 5

Super-Gaussian reflectance profile obtained with the coating of Fig. 4 when the thicknesses profile is as shown in the inset of the figure.

Fig. 6
Fig. 6

Variable reflectance coating for a XeCl laser that contains only one variable layer and is able to give the reflectance profile of Fig. 5. R0 = 75%, Rmin = 0 (null thickness of the profiled layer).

Fig. 7
Fig. 7

Masks for deposition of profiled layers for obtaining the reflectance profile shown in Fig. 5 (the hollow area is slashed and the rotation axis is indicated by a cross): (a) typical mask for fabricating the coating of Fig. 4, (b) typical mask corresponding to the coating of Fig. 6.

Fig. 8
Fig. 8

Phase shift of the beam reflected by a double-layer AR coating: dependence on layer thicknesses. λ = 3080 Å, R = 1 × 10−7.

Fig. 9
Fig. 9

Phase shift of the beam reflected by a variable reflectance coating (λ = 3080 Å, R0 = 35%) along the substrate radius. The two curves correspond to slightly different AR coating thicknesses.

Fig. 10
Fig. 10

Schematic of a profiled layer as a reference for the calculation of the phase front profile.

Fig. 11
Fig. 11

Phase variations along the radius associated with the transmitted and the reflected beams (intensity profile of Fig. 5): (a) coating of Fig. 4, (b) coating of Fig. 6.

Fig. 12
Fig. 12

Effect of thickness errors on performance of coatings of (a) Fig. 4 and (b) Fig. 6 (solid curve). Dashed curve, random variations in the range ±3%; dotted curve, all thicknesses increased by 3%; dotted–dashed curve, all thicknesses decreased by 3%.

Fig. 13
Fig. 13

Various coating structures (for a CO2 laser) that give step-shaped reflectance and no phase front distortion. λ = 10.6 μm, R0 = 50%.

Fig. 14
Fig. 14

Phase-unifying mirror for a high-power CO2 laser. λ = 10.6 μm, R0 = 80%, Rmin = 1 × 10−3.

Equations (3)

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ρ = | ρ | exp ( i ϕ ) = ( y 0 Y ) / ( y 0 + Y ) , Y = C / B ,
( B C ) = j [ cos δ j i sin δ j / n j i n j sin δ j cos δ j ] ( 1 n s ) ,
Δ ϕ R ( r ) = ϕ R ( 0 ) [ ϕ R ( r ) + 2 ϕ air ( r ) ] , Δ ϕ T ( r ) = ϕ T ( 0 ) [ ϕ T ( r ) + ϕ air ( r ) ] ϕ air = 2 π [ d ( r ) d ( 0 ) ] / λ ,

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