Abstract

Apodizing holographic gratings are designed to have a Gaussian reflectivity profile in the -1 order and a complementary reflectivity profile in the specular (0) order. They are obtained by the interference of two Gaussian beams on a glass plate covered with a photoresist. These gratings are intended to be used as the coupler of the external cavity of a broad-area semiconductor laser. When the grating is oriented to get the -1 order counterpropagating with respect to the incident beam, single-longitudinal- and single-lateral-mode operation is obtained. We report on the fabrication technique of an apodizing holographic grating designed to allow lasing on two wavelengths simultaneously, with a preselected wavelength separation. The results obtained with a commercial broad-area laser are presented.

© 1998 Optical Society of America

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References

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  1. G. Giuliani, Y. K. Park, R. L. Byer, “Radial birefringent element and its application to laser resonator design,” Opt. Lett. 5, 491–493 (1980).
    [CrossRef] [PubMed]
  2. N. McCarthy, P. Lavigne, “Large-size Gaussian mode in unstable resonators using Gaussian mirrors,” Opt. Lett. 10, 553–555 (1985).
    [CrossRef] [PubMed]
  3. E. Armandillo, G. Giuliani, “Large-size TEM00 mode XeCl laser achieved with a novel apoditic filter,” in Conference on Lasers and Electro-Optics, Vol. 85.9 of 1985 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1985), p. 116.
  4. K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single-transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
    [CrossRef]
  5. S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
    [CrossRef]
  6. J.-F. Lepage, R. Massudi, G. Anctil, S. Gilbert, M. Piché, N. McCarthy, “Apodizing holographic gratings for the modal control of semiconductor lasers,” Appl. Opt. 36, 4993–4998 (1997).
    [CrossRef] [PubMed]
  7. R. A. Bartolini, “Photoresists,” in Holographic Recording Materials, H. M. Smith, ed. (Springer-Verlag, Berlin, 1977) pp. 209–227.
    [CrossRef]
  8. C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
    [CrossRef]
  9. S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
    [CrossRef]
  10. K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry–Perot grating–lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
    [CrossRef]
  11. C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
    [CrossRef]
  12. T. Hidaka, Y. Hatano, “Simultaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
    [CrossRef]
  13. P. de Groot, “Use of a multimode short-external-cavity laser diode for absolute-distance interferometry,” Appl. Opt. 32, 4193–4198 (1993).
    [CrossRef] [PubMed]
  14. B. W. Hakki, T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
    [CrossRef]

1997

J.-F. Lepage, R. Massudi, G. Anctil, S. Gilbert, M. Piché, N. McCarthy, “Apodizing holographic gratings for the modal control of semiconductor lasers,” Appl. Opt. 36, 4993–4998 (1997).
[CrossRef] [PubMed]

K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry–Perot grating–lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
[CrossRef]

1996

C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
[CrossRef]

1995

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

1993

1991

T. Hidaka, Y. Hatano, “Simultaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
[CrossRef]

1990

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

1988

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single-transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

1985

1980

1975

B. W. Hakki, T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
[CrossRef]

Anctil, G.

Armandillo, E.

E. Armandillo, G. Giuliani, “Large-size TEM00 mode XeCl laser achieved with a novel apoditic filter,” in Conference on Lasers and Electro-Optics, Vol. 85.9 of 1985 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1985), p. 116.

Bartolini, R. A.

R. A. Bartolini, “Photoresists,” in Holographic Recording Materials, H. M. Smith, ed. (Springer-Verlag, Berlin, 1977) pp. 209–227.
[CrossRef]

Budzinski, C.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Byer, R. L.

de Groot, P.

De Silvestri, S.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Gilbert, S.

Giuliani, G.

G. Giuliani, Y. K. Park, R. L. Byer, “Radial birefringent element and its application to laser resonator design,” Opt. Lett. 5, 491–493 (1980).
[CrossRef] [PubMed]

E. Armandillo, G. Giuliani, “Large-size TEM00 mode XeCl laser achieved with a novel apoditic filter,” in Conference on Lasers and Electro-Optics, Vol. 85.9 of 1985 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1985), p. 116.

Grunwald, R.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Hakki, B. W.

B. W. Hakki, T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
[CrossRef]

Hatano, Y.

T. Hidaka, Y. Hatano, “Simultaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
[CrossRef]

Hidaka, T.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

T. Hidaka, Y. Hatano, “Simultaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
[CrossRef]

Hirata, T.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

Iio, S.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

Lavigne, P.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single-transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

N. McCarthy, P. Lavigne, “Large-size Gaussian mode in unstable resonators using Gaussian mirrors,” Opt. Lett. 10, 553–555 (1985).
[CrossRef] [PubMed]

Lee, K.-S.

K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry–Perot grating–lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
[CrossRef]

Lepage, J.-F.

Magni, V.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Massudi, R.

McCarthy, N.

Pan, C.-L.

C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
[CrossRef]

Paoli, T. L.

B. W. Hakki, T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
[CrossRef]

Park, Y. K.

Piché, M.

J.-F. Lepage, R. Massudi, G. Anctil, S. Gilbert, M. Piché, N. McCarthy, “Apodizing holographic gratings for the modal control of semiconductor lasers,” Appl. Opt. 36, 4993–4998 (1997).
[CrossRef] [PubMed]

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single-transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

Pinz, I.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Schäfer, D.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Schönnagel, H.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Shu, C.

K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry–Perot grating–lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
[CrossRef]

Snell, K. J.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single-transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

Suehiro, M.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

Svelto, O.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Valentini, G.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Wang, C.-L.

C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
[CrossRef]

Appl. Opt.

Electron. Lett.

T. Hidaka, Y. Hatano, “Simultaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
[CrossRef]

IEEE J. Quantum Electron.

K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry–Perot grating–lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
[CrossRef]

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

J. Appl. Phys.

B. W. Hakki, T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
[CrossRef]

Opt. Commun.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single-transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
[CrossRef]

Other

R. A. Bartolini, “Photoresists,” in Holographic Recording Materials, H. M. Smith, ed. (Springer-Verlag, Berlin, 1977) pp. 209–227.
[CrossRef]

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

E. Armandillo, G. Giuliani, “Large-size TEM00 mode XeCl laser achieved with a novel apoditic filter,” in Conference on Lasers and Electro-Optics, Vol. 85.9 of 1985 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1985), p. 116.

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Figures (8)

Fig. 1
Fig. 1

Geometry used to write the double apodizing holographic grating. Dashed axes hold for the first exposure, whereas the solid axes hold for the second exposure.

Fig. 2
Fig. 2

Beam reflected in the -1 order for a He–Ne beam incident on the gratings A, B, C, and D.

Fig. 3
Fig. 3

Scheme of the diode laser with an external cavity terminated by an apodizing grating.

Fig. 4
Fig. 4

Setup used for the measurement of the spectrally resolved near field.

Fig. 5
Fig. 5

Near-field spectra of the diode laser with an external cavity terminated by a plane mirror.

Fig. 6
Fig. 6

Spectra of the diode laser with an external cavity terminated by the apodizing gratings A, B, C, and D.

Fig. 7
Fig. 7

Near-field spectra of the diode laser with an external cavity terminated by the apodizing gratings A, B, C, and D.

Fig. 8
Fig. 8

Intensity of one of the two wavelengths at the output of the spectrometer as a function of time.

Tables (2)

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Table 1 Grating Fabrication Parameters

Tables Icon

Table 2 Results Obtained with Gratings Used as Cavity Couplers

Equations (19)

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E 1 = A   exp - x 2 + y 2 cos 2   ψ / w 2 exp - jk + y   sin   ψ , E 2 = A   exp - x 2 + y 2 cos 2   ψ / w 2 exp - jk - y   sin   ψ .
I = 4 A 2   exp - 2 x 2 / w x 2 exp - 2 y 2 / w y 2 cos 2 ky   sin   ψ ,
w x = w , w y = w 2 1 + cos 2 ψ 1 / 2 ,
d = λ w 2   sin   ψ .
sin   ϕ m = m λ d + sin   β ,
sin   β L = λ 2 d .
1 3 < λ λ w sin   ψ < 1 .
I 4 A 2   exp - 2 x 2 / w x 2 exp - 2 y 2 / w y 2 ×   cos 2 ky   sin   ψ   cos   θ .
w x = w , w y = w 2 1 + cos 2 ψ cos 2 θ 1 / 2 .
d = λ w 2   sin   ψ   cos   θ = d cos   θ .
λ 2 d = λ + Δ λ 2 d = λ + Δ λ 2 d / cos   θ .
θ = arccos λ λ + Δ λ .
E 1 = A   exp - r 1 2 / w 2 exp - jky   sin ψ + θ , E 2 = A   exp - r 2 2 / w 2 exp + jky   sin ψ - θ ,
r 1 2 = x 2 + y 2   cos 2 ψ + θ , r 2 2 = x 2 + y 2   cos 2 ψ - θ .
I = E 1 + E 2 E 1 * + E 2 * = A 2   exp - 2 X ( exp - 2 Y   cos 2 ψ - θ + exp - 2 Y   cos 2 ψ + θ + 2   exp - Y cos 2 ψ - θ + cos 2 ψ + θ cos Δ ϕ )
X = x 2 / w 2 , Y = y 2 / w 2 , Δ ϕ = ky sin ψ + θ + sin ψ - θ .
I = A 2   exp - 2 X exp - Y cos 2 ψ - θ + cos 2 ψ + θ × { exp - Y cos 2 ψ - θ - cos 2 ψ + θ + exp + Y cos 2 ψ - θ - cos 2 ψ + θ + 2   cos 2 ky   sin   ψ   cos   θ } , I = A 2   exp - 2 X exp - Y cos 2 ψ - θ + cos 2 ψ + θ × { 2   cosh Y cos 2 ψ - θ - cos 2 ψ + θ + 2   cos 2 ky   sin   ψ   cos   θ } , I = 2 A 2   exp - 2 X exp - Y 1 + cos   2 ψ   cos   2 θ cosh Y   sin 2 ψ sin 2 θ + cos 2 ky   sin   ψ   cos   θ .
I 4 A 2   exp - 2 x 2 / w x 2 exp - 2 y 2 / w y 2 ×   cos 2 ky   sin   ψ   cos   θ
w x = w , w y = w 2 1 + cos 2 ψ cos 2 θ 1 / 2 .

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