Abstract

An adaptive simulated annealing optimization algorithm is used to derive laser rate equation and waveguiding models with which the best design for a diode-pumped fiber-coupled, Yb:Er glass waveguide laser can be determined. Material parameters that correspond to commercially available laser-glass and diode-pump sources are used in this study. Given a continuous-wave 300-mW pump at 977 nm, approximately 48 mW of power at 1540 nm can be coupled into the LP01 mode of an optical fiber. Fabrication and alignment tolerance analyses are presented.

© 2000 Optical Society of America

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References

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  1. P. M. Peters, S. N. Houde-Walter, “New rare earth hosts: OH in laser glass,” in Optical Devices for Optical Communication, M. J. Digonnet, ed., Proc. SPIE3847, 35–43 (1999).
  2. D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).
  3. D. L. Veasey, D. S. Funk, N. A. Sanford, “Arrays of distributed-Bragg-reflector waveguide lasers at 1536 nm in Yb/Er codoped phosphate glass,” Appl. Phys. Lett. 74, 789–791 (1999).
    [CrossRef]
  4. Ridge waveguide laser in development at Spectracom, 4459 White Bear Parkway, White Bear Lake, Minn. 55110. Specifications from Spectracom are used to allow the reader to reproduce the results reported here and do not imply endorsement by the National Institute of Standards and Technology.
  5. IOG-1 laser glass, Schott Glass Technologies, Inc., 400 York Ave., Duryea, Pa. The IOG-1 trade name is used to allow the reader to reproduce the results reported here and does not imply endorsement by the National Institute of Standards and Technology.
  6. M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, A. J. Bruce, G. Nykolak, J. Smulovich, “Uniform upconversion in high-concentration Er3+-doped soda lime silicate and aluminosilicate glasses,” Opt. Lett. 22, 772–774 (1997).
    [CrossRef] [PubMed]
  7. D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.
  8. Corning SMF-28, Corning, Inc., Corning, N.Y. The SMF-28 trade name is used to allow the reader to reproduce the results reported here and does not imply endorsement by the National Institute of Standards and Technology.
  9. J. Crank, The Mathematics of Diffusion, 2nd ed. (Clarendon, Oxford, 1979), Chap. 1.
  10. S. Houde-Walter, D. Moore, “Gradient index profile control by field-assisted ion exchange in glass,” Appl. Opt. 24, 4326–4333 (1985).
    [CrossRef]
  11. L. Ingber, “Adaptive simulated annealing (ASA),” C-code (Lester Ingber Research, Chicago, Ill., 1993); URL http://www.ingber.com/#ASA-CODE .
  12. R. E. Smith, S. N. Houde-Walter, G. W. Forbes, “Numerical determination of planar waveguide modes using the analyticity of the dispersion relation,” Opt. Lett. 16, 1316–1318 (1991).
    [CrossRef] [PubMed]
  13. D. L. Veasey, J. M. Gary, J. Amin, “Rigorous scalar modeling of Er and Er/Yb-doped waveguide lasers,” in Rare-Earth-Doped Devices, S. Honkanen, ed., Proc. SPIE2996, 109–120 (1997).
    [CrossRef]
  14. H. Kogelnik, “Theory of optical waveguide,” in Guide-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988), Chap. 2.
    [CrossRef]
  15. D. L. Veasey, J. M. Gary, J. Amin, J. A. Aust, “Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm,” IEEE J. Quantum Electron. 33, 1647–1662 (1997).
    [CrossRef]
  16. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
    [CrossRef]
  17. R. E. Smith, S. N. Houde-Walter, “Leaky guiding in nontransparent waveguides,” J. Opt. Soc. Am. A 12, 715–724 (1995).
    [CrossRef]
  18. S. E. Stokowski, R. A. Saroyan, M. J. Weber, eds., Laser Glass: Nd-Doped Glass Spectroscopic and Physical Properties, document M-095, Rev. 2 (Lawrence Livermore National Laboratory, Livermore, Calif., 1981), Vol. 1., Chap. 2.

2000 (1)

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

1999 (1)

D. L. Veasey, D. S. Funk, N. A. Sanford, “Arrays of distributed-Bragg-reflector waveguide lasers at 1536 nm in Yb/Er codoped phosphate glass,” Appl. Phys. Lett. 74, 789–791 (1999).
[CrossRef]

1997 (2)

D. L. Veasey, J. M. Gary, J. Amin, J. A. Aust, “Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm,” IEEE J. Quantum Electron. 33, 1647–1662 (1997).
[CrossRef]

M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, A. J. Bruce, G. Nykolak, J. Smulovich, “Uniform upconversion in high-concentration Er3+-doped soda lime silicate and aluminosilicate glasses,” Opt. Lett. 22, 772–774 (1997).
[CrossRef] [PubMed]

1995 (1)

1991 (1)

1985 (1)

1977 (1)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

Amin, J.

D. L. Veasey, J. M. Gary, J. Amin, J. A. Aust, “Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm,” IEEE J. Quantum Electron. 33, 1647–1662 (1997).
[CrossRef]

D. L. Veasey, J. M. Gary, J. Amin, “Rigorous scalar modeling of Er and Er/Yb-doped waveguide lasers,” in Rare-Earth-Doped Devices, S. Honkanen, ed., Proc. SPIE2996, 109–120 (1997).
[CrossRef]

Aust, J. A.

D. L. Veasey, J. M. Gary, J. Amin, J. A. Aust, “Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm,” IEEE J. Quantum Electron. 33, 1647–1662 (1997).
[CrossRef]

Bruce, A. J.

Cockroft, N. J.

Crank, J.

J. Crank, The Mathematics of Diffusion, 2nd ed. (Clarendon, Oxford, 1979), Chap. 1.

Fontaine, N.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

Fontaine, N. H.

D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.

Forbes, G. W.

Funk, D. S.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

D. L. Veasey, D. S. Funk, N. A. Sanford, “Arrays of distributed-Bragg-reflector waveguide lasers at 1536 nm in Yb/Er codoped phosphate glass,” Appl. Phys. Lett. 74, 789–791 (1999).
[CrossRef]

D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.

Gary, J. M.

D. L. Veasey, J. M. Gary, J. Amin, J. A. Aust, “Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm,” IEEE J. Quantum Electron. 33, 1647–1662 (1997).
[CrossRef]

D. L. Veasey, J. M. Gary, J. Amin, “Rigorous scalar modeling of Er and Er/Yb-doped waveguide lasers,” in Rare-Earth-Doped Devices, S. Honkanen, ed., Proc. SPIE2996, 109–120 (1997).
[CrossRef]

Gosnell, T. R.

Hayden, J. S.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.

Hehlen, M. P.

Houde-Walter, S.

Houde-Walter, S. N.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

R. E. Smith, S. N. Houde-Walter, “Leaky guiding in nontransparent waveguides,” J. Opt. Soc. Am. A 12, 715–724 (1995).
[CrossRef]

R. E. Smith, S. N. Houde-Walter, G. W. Forbes, “Numerical determination of planar waveguide modes using the analyticity of the dispersion relation,” Opt. Lett. 16, 1316–1318 (1991).
[CrossRef] [PubMed]

P. M. Peters, S. N. Houde-Walter, “New rare earth hosts: OH in laser glass,” in Optical Devices for Optical Communication, M. J. Digonnet, ed., Proc. SPIE3847, 35–43 (1999).

Kogelnik, H.

H. Kogelnik, “Theory of optical waveguide,” in Guide-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988), Chap. 2.
[CrossRef]

Liu, W.-C.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

Moore, D.

Nykolak, G.

Obarski, G. E.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

Peskin, A. P.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

Peters, P. M.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

P. M. Peters, S. N. Houde-Walter, “New rare earth hosts: OH in laser glass,” in Optical Devices for Optical Communication, M. J. Digonnet, ed., Proc. SPIE3847, 35–43 (1999).

D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.

Sanford, N. A.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

D. L. Veasey, D. S. Funk, N. A. Sanford, “Arrays of distributed-Bragg-reflector waveguide lasers at 1536 nm in Yb/Er codoped phosphate glass,” Appl. Phys. Lett. 74, 789–791 (1999).
[CrossRef]

D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.

Smith, R. E.

Smulovich, J.

Veasey, D. L.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

D. L. Veasey, D. S. Funk, N. A. Sanford, “Arrays of distributed-Bragg-reflector waveguide lasers at 1536 nm in Yb/Er codoped phosphate glass,” Appl. Phys. Lett. 74, 789–791 (1999).
[CrossRef]

D. L. Veasey, J. M. Gary, J. Amin, J. A. Aust, “Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm,” IEEE J. Quantum Electron. 33, 1647–1662 (1997).
[CrossRef]

D. L. Veasey, J. M. Gary, J. Amin, “Rigorous scalar modeling of Er and Er/Yb-doped waveguide lasers,” in Rare-Earth-Doped Devices, S. Honkanen, ed., Proc. SPIE2996, 109–120 (1997).
[CrossRef]

D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.

Young, M.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. L. Veasey, D. S. Funk, N. A. Sanford, “Arrays of distributed-Bragg-reflector waveguide lasers at 1536 nm in Yb/Er codoped phosphate glass,” Appl. Phys. Lett. 74, 789–791 (1999).
[CrossRef]

Bell Syst. Tech. J. (1)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. L. Veasey, J. M. Gary, J. Amin, J. A. Aust, “Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm,” IEEE J. Quantum Electron. 33, 1647–1662 (1997).
[CrossRef]

J. Non-Cryst. Solids (1)

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263/264, 369–381 (2000).

J. Opt. Soc. Am. A (1)

Opt. Lett. (2)

Other (10)

P. M. Peters, S. N. Houde-Walter, “New rare earth hosts: OH in laser glass,” in Optical Devices for Optical Communication, M. J. Digonnet, ed., Proc. SPIE3847, 35–43 (1999).

L. Ingber, “Adaptive simulated annealing (ASA),” C-code (Lester Ingber Research, Chicago, Ill., 1993); URL http://www.ingber.com/#ASA-CODE .

S. E. Stokowski, R. A. Saroyan, M. J. Weber, eds., Laser Glass: Nd-Doped Glass Spectroscopic and Physical Properties, document M-095, Rev. 2 (Lawrence Livermore National Laboratory, Livermore, Calif., 1981), Vol. 1., Chap. 2.

Ridge waveguide laser in development at Spectracom, 4459 White Bear Parkway, White Bear Lake, Minn. 55110. Specifications from Spectracom are used to allow the reader to reproduce the results reported here and do not imply endorsement by the National Institute of Standards and Technology.

IOG-1 laser glass, Schott Glass Technologies, Inc., 400 York Ave., Duryea, Pa. The IOG-1 trade name is used to allow the reader to reproduce the results reported here and does not imply endorsement by the National Institute of Standards and Technology.

D. S. Funk, D. L. Veasey, P. M. Peters, N. A. Sanford, N. H. Fontaine, M. Young, J. S. Hayden, “Erbium/ytterbium-co-doped glass waveguide laser producing 170 mW of output power at 1540 nm,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 157–159.

Corning SMF-28, Corning, Inc., Corning, N.Y. The SMF-28 trade name is used to allow the reader to reproduce the results reported here and does not imply endorsement by the National Institute of Standards and Technology.

J. Crank, The Mathematics of Diffusion, 2nd ed. (Clarendon, Oxford, 1979), Chap. 1.

D. L. Veasey, J. M. Gary, J. Amin, “Rigorous scalar modeling of Er and Er/Yb-doped waveguide lasers,” in Rare-Earth-Doped Devices, S. Honkanen, ed., Proc. SPIE2996, 109–120 (1997).
[CrossRef]

H. Kogelnik, “Theory of optical waveguide,” in Guide-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988), Chap. 2.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Yb:Er energy levels and excitation scheme for the glass waveguide laser: W ij , A ij , pump and spontaneous decay rates for the ith and jth levels, respectively; C Cr, forward energy transfer rate; C up, cooperative upconversion rate from 4 I 13/2 to 4 I 9/2 level.

Fig. 2
Fig. 2

Schematic illustration of the waveguide laser with diode-laser pump and output fiber, showing the fabrication and alignment parameters that are varied in the design.

Fig. 3
Fig. 3

Simplified flow chart: the laser model is the coupled beam propagation and laser rate-equation model. The ASA algorithm, the Cauchy waveguide solver, and the laser rate-equation solver are linked together with a Perl script called optdrive.

Fig. 4
Fig. 4

Optimization results for two waveguide laser types. Top, the laser is single mode at both 977 and 1540 nm, fabricated by thermal ion exchange: (a) power coupled into the LP01 fiber mode as a function of channel width, height, and refractive index at 977 nm, (b) power coupled into LP01 fiber mode as a function of laser mode width, height, and refractive index at 977 nm. Bottom, the laser is two-mode at 977 nm and single mode at 1540 nm, fabricated by field-assisted ion exchange: (c) power coupled into LP01 fiber mode as a function of channel width, height, and refractive index at 977 nm; (d) power coupled into LP01 fiber mode as a function of laser mode width, height, and refractive index at 977 nm. The power in the fiber mode is indicated by color, as shown. See text for further description.

Fig. 5
Fig. 5

TE mode field contours for laser mode at 1540 nm and lowest-order pump mode at 977 nm, corresponding to the best overall solution. Numbers on contours indicate intensities.

Fig. 6
Fig. 6

Power coupled into LP01 mode of single-mode fiber as a function of diode pump power (not launched power) for the best overall solution.

Tables (4)

Tables Icon

Table 1 Fixed and Varying Design Parametersa

Tables Icon

Table 2 Spectroscopic Parametersa

Tables Icon

Table 3 Best Configuration (FAIE, Two Pump Modes)

Tables Icon

Table 4 Tolerances on Waveguide, Cavity, and Alignment Parameters for a 10% (4.8-mW) Drop in LP01 Mode Power for the Configuration in Table 3

Equations (2)

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

n(λ)=nd-nd-1νd1.5079-523604λ2,
nLnp=ns,Lns,p.

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