Abstract

We first present the fabrication technique of apodizing holographic gratings. Gratings with a spatially variable reflectivity profile were obtained by the interference of two Gaussian beams on a glass plate covered with a photoresist. When the exposure time was short enough to avoid saturation of the photoresist, gratings with a quasi-Gaussian reflectivity profile for the beam reflected in the -1 order were produced; the reflectivity at the center could be as high as 71%, and the half-width of the reflectivity profile at the e -1 position could be as small as 180 µm. Apodizing gratings were used as the end mirror of the external cavity of a broad-area semiconductor laser. Single longitudinal- and lateral-mode operation was observed over the full range of allowed injection currents.

© 1997 Optical Society of America

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  1. H. Zucker, “Optical resonators with variable reflectivity mirrors,” Bell Syst. Tech. J. 49, 2349–2376 (1970).
    [CrossRef]
  2. 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]
  3. N. McCarthy, P. Lavigne, “Large-size Gaussian mode in unstable resonators using Gaussian mirrors,” Opt. Lett. 10, 553–555 (1985).
    [CrossRef] [PubMed]
  4. E. Armandillo, G. Giuliani, “Large-size TEM00 mode XeCl laser achieved with a novel apoditic filter,” in Conference on Lasers and Electro-Optics, 1985 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1985), p. 116.
  5. 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]
  6. S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
    [CrossRef]
  7. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1985), Chap. 23.
  8. R. A. Bartolini, “Photoresists,” in Holographic Recording Materials, H. M. Smith, ed. (Springer–Verlag, Berlin, 1977), pp. 209–227.
    [CrossRef]
  9. M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
    [CrossRef]
  10. J. E. Bjorkholm, L. Eichner, “Monitoring of the growth of nonuniform gratings written holographically by Gaussian laser beams,” J. Appl. Phys. 57, 2402–2405 (1985).
    [CrossRef]
  11. C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
    [CrossRef]
  12. B. W. Hakki, T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
    [CrossRef]
  13. N. McCarthy, P. Lavigne, J.-G. Demers, A. Parent, “Design and characterization of graded reflectivity mirrors,” in Optical Testing and Metrology, C. Grover, ed., Proc. SPIE661, 365–371 (1986).
    [CrossRef]

1990 (1)

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

1988 (1)

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 (3)

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

M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
[CrossRef]

J. E. Bjorkholm, L. Eichner, “Monitoring of the growth of nonuniform gratings written holographically by Gaussian laser beams,” J. Appl. Phys. 57, 2402–2405 (1985).
[CrossRef]

1980 (1)

1975 (1)

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

1970 (1)

H. Zucker, “Optical resonators with variable reflectivity mirrors,” Bell Syst. Tech. J. 49, 2349–2376 (1970).
[CrossRef]

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, 1985 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1985), p. 116.

Ballman, A. A.

M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
[CrossRef]

Bartolini, R. A.

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

Bjorkholm, J. E.

J. E. Bjorkholm, L. Eichner, “Monitoring of the growth of nonuniform gratings written holographically by Gaussian laser beams,” J. Appl. Phys. 57, 2402–2405 (1985).
[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. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Byer, R. L.

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]

Demers, J.-G.

N. McCarthy, P. Lavigne, J.-G. Demers, A. Parent, “Design and characterization of graded reflectivity mirrors,” in Optical Testing and Metrology, C. Grover, ed., Proc. SPIE661, 365–371 (1986).
[CrossRef]

Eichner, L.

J. E. Bjorkholm, L. Eichner, “Monitoring of the growth of nonuniform gratings written holographically by Gaussian laser beams,” J. Appl. Phys. 57, 2402–2405 (1985).
[CrossRef]

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, 1985 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1985), p. 116.

Glass, A. M.

M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
[CrossRef]

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. 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]

Kohl, P. A.

M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
[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]

N. McCarthy, P. Lavigne, J.-G. Demers, A. Parent, “Design and characterization of graded reflectivity mirrors,” in Optical Testing and Metrology, C. Grover, ed., Proc. SPIE661, 365–371 (1986).
[CrossRef]

Logan, R. A.

M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
[CrossRef]

Lum, M.

M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
[CrossRef]

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]

McCarthy, N.

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]

N. McCarthy, P. Lavigne, J.-G. Demers, A. Parent, “Design and characterization of graded reflectivity mirrors,” in Optical Testing and Metrology, C. Grover, ed., Proc. SPIE661, 365–371 (1986).
[CrossRef]

Ostermayer, F. W.

M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
[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]

Parent, A.

N. McCarthy, P. Lavigne, J.-G. Demers, A. Parent, “Design and characterization of graded reflectivity mirrors,” in Optical Testing and Metrology, C. Grover, ed., Proc. SPIE661, 365–371 (1986).
[CrossRef]

Park, Y. K.

Piché, M.

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. 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. 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. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1985), Chap. 23.

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]

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]

Zucker, H.

H. Zucker, “Optical resonators with variable reflectivity mirrors,” Bell Syst. Tech. J. 49, 2349–2376 (1970).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Zucker, “Optical resonators with variable reflectivity mirrors,” Bell Syst. Tech. J. 49, 2349–2376 (1970).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Appl. Phys. (3)

M. Lum, A. M. Glass, F. W. Ostermayer, P. A. Kohl, A. A. Ballman, R. A. Logan, “Holographic photoelectrochemical etching of diffraction gratings in n-InP and n-GaInAsP for distributed feedback lasers,” J. Appl. Phys. 57, 39–44 (1985).
[CrossRef]

J. E. Bjorkholm, L. Eichner, “Monitoring of the growth of nonuniform gratings written holographically by Gaussian laser beams,” J. Appl. Phys. 57, 2402–2405 (1985).
[CrossRef]

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

Opt. Commun. (1)

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. (2)

Other (5)

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

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1985), Chap. 23.

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

N. McCarthy, P. Lavigne, J.-G. Demers, A. Parent, “Design and characterization of graded reflectivity mirrors,” in Optical Testing and Metrology, C. Grover, ed., Proc. SPIE661, 365–371 (1986).
[CrossRef]

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

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Figures (9)

Fig. 1
Fig. 1

Geometry that was used to write the variable reflectivity gratings. The surface is covered with a thin layer of photoresist. The writing wavelength is 457.9 nm.

Fig. 2
Fig. 2

Illustration of the variable reflectivity grating surface. Vertical and horizontal scales are different; the groove depth is typically smaller than the grating period.

Fig. 3
Fig. 3

Measured reflectivity profiles for gratings A, B, C, and D.

Fig. 4
Fig. 4

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

Fig. 5
Fig. 5

Experimental setup used for the measurement of resolved near-field spectra.

Fig. 6
Fig. 6

Near-field spectrum of the laser diode operated with an external cavity terminated by a conventional plane mirror. The injection current is 375 mA and the output power is 46 mW.

Fig. 7
Fig. 7

Near-field spectrum of the laser diode operated with an external cavity terminated by grating A for different values of the injection current: 378, 405, 413, and 445 mA from top to bottom.

Fig. 8
Fig. 8

Near-field spectrum of the laser diode operated with an external cavity terminated by grating B for different values of the injection current: 405, 430, 450, and 456 mA from top to bottom.

Fig. 9
Fig. 9

Near-field spectrum of the laser diode operated with an external cavity terminated by grating C for different values of the injection current: 430, 440, 450, and 459 mA from top to bottom.

Tables (1)

Tables Icon

Table 1 Main Characteristics and Fabrication Parameters of Four Apodizing Gratings

Equations (7)

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E1=A1 exp- r2/w2exp-iky sin ψ,E2=A2 exp- r2/w2exp-iky sin ψ,
I=A12+A22+2A1A2 cos2ky sin ψexp-2r2/w2.
I=4A12 exp-2r2/w2cos2ky sin ψ.
sin ϕm=mλ/d+sin β,
d=λw/2 sin ψ.
1/3<λ/λwsinψ<1.
Rx=R0 exp-x2/wr2,

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