Abstract

We report a synchronously pumped optical parametric oscillator that generates the sum frequency of the pump and the signal wavelengths. A single KTiOPO4 (KTP) crystal is used for both parametric generation and sum-frequency generation in which these two processes are simultaneously phase matched for the same direction of propagation. The parametric oscillator, pumped by a femtosecond Ti:sapphire laser at a wavelength of 827 nm, generates a blue output beam at 487 nm with 43% power-conversion efficiency. The polarization geometry of simultaneous phase matching requires rotation of the pump polarization before the cavity. Adjusting the group delay between the two orthogonally polarized pump components to compensate for the group-velocity mismatch in the KTP crystal increases the photon-conversion efficiency more than threefold. Angle tuning in conjunction with pump wavelength tuning provides output tunability in the 484–512-nm range. A plane-wave model that takes group-velocity mismatch into account is in good agreement with our experimental results.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. L. Byer and A. Piskarskas, eds., feature on optical parametric oscillation and amplification, J. Opt. Soc. Am. B 10, 1655–2243 (1993); W. R. Bosenberg and R. C. Eckardt, eds., feature on optical parametric devices, J. Opt. Soc. Am. B 12, 2083–2320 (1995); C. L. Tang, W. R. Bosenberg, T. Ukachi, R. J. Lane, and L. K. Cheng, “Optical parametric oscillators,” Proc. IEEE IEEPAD 80, 365–374 (1992).
    [CrossRef]
  2. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
    [CrossRef]
  3. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
    [CrossRef]
  4. H. M. van Driel, “Synchronously pumped optical parametric oscillators,” Appl. Phys. B 60, 411–420 (1995).
    [CrossRef]
  5. D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54, 1728–1730 (1989); W. S. Pelouch, P. E. Powers, and C. L. Tang, “Ti:sapphire pumped, high-repetition-rate femtosecond optical parametric oscillator,” Opt. Lett. 17, 1070–1072 (1992); Q. Fu, G. Mak, and H. M. van Driel, “High-power, 62-fs infrared optical parametric oscillator synchronously pumped by a 76-MHz Ti:sapphire laser,” Opt. Lett. OPLEDP 17, 1006–1008 (1992); G. Mak, Q. Fu, and H. M. van Driel, “Externally pumped high repetition rate femtosecond infrared optical parametric oscillator,” Appl. Phys. Lett. APPLAB 60, 542–544 (1992); P. E. Powers, C. L. Tang, and L. K. Cheng, “High-repetition-rate femtosecond optical parametric oscillator based on CsTiOAsO4,” Opt. Lett. OPLEDP 19, 37–39 (1994).
    [CrossRef] [PubMed]
  6. T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire 2nd-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
    [CrossRef]
  7. A. Nebel, H. Frost, R. Beigang, and R. Wallenstein, “Visible femtosecond pulses by second harmonic generation of a cw mode-locked KTP optical parametric oscillator,” Appl. Phys. B 60, 453–458 (1995).
    [CrossRef]
  8. R. J. Ellingson and C. L. Tang, “High-power high-repetition-rate femtosecond pulses tunable in the visible,” Opt. Lett. 18, 438–440 (1993); D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Efficient femtosecond pulse generation in the visible in a frequency-doubled optical parametric oscillator based on RbTiOAsO4,” J. Opt. Soc. Am. B 12, 1157–1163 (1995).
    [CrossRef] [PubMed]
  9. E. C. Cheung, K. Koch, and G. T. Moore, “Frequency upconversion by phase-matched sum-frequency generation in an optical parametric oscillator,” Opt. Lett. 19, 1967–1969 (1994).
    [CrossRef] [PubMed]
  10. A. Shirakawa, H. W. Mao, and T. Kobayashi, “Highly efficient generation of blue–orange femtosecond pulses from intracavity-frequency-mixed optical parametric oscillator,” Opt. Commun. 123, 121–128 (1996).
    [CrossRef]
  11. K. G. Köprülü, T. Kartaloğlu, and O. Aytür, “Single-crystal sum-frequency generating optical parametric oscillator,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 457–458.
  12. O. Aytür and Y. Dikmelik, “Plane wave theory of self-doubling optical parametric oscillators,” IEEE J. Quantum Electron. 34, 447–458 (1998); Y. Dikmelik, G. Akgün, and O. Aytür, “Plane-wave dynamics of optical parametric oscillation with simultaneous sum-frequency generation,” IEEE J. Quantum Electron. 35, 897–912 (1999).
    [CrossRef]
  13. K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
    [CrossRef]
  14. R. A. Andrews, H. Rabin, and C. L. Tang, “Coupled parametric downconversion and upconversion with simultaneous phase matching,” Phys. Rev. Lett. 25, 605–608 (1970).
    [CrossRef]
  15. T. Kartaloğlu, K. G. Köprülü, and O. Aytür, “Phase-matched self-doubling optical parametric oscillator,” Opt. Lett. 22, 280–282 (1997).
    [CrossRef]
  16. K. C. Burr, C. L. Tang, M. A. Arbore, and M. M. Fejer, “Broadly tunable mid-infrared femtosecond optical parametric oscillator using all-solid-state-pumped periodically poled lithium niobate,” Opt. Lett. 22, 1458–1460 (1997).
    [CrossRef]
  17. C. McGowan, D. T. Reid, Z. E. Penman, M. Ebrahimzadeh, W. Sibbett, and D. H. Jundt, “Femtosecond optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 15, 694–701 (1998).
    [CrossRef]
  18. D. T. Reid, G. T. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, “Widely tunable, near- to mid-infrared femtosecond and picosecond optical parametric oscillators using periodically poled LiNbO3 and RbTiOAsO4,” IEEE J. Sel. Top. Quantum Electron. 4, 238–248 (1998).
    [CrossRef]
  19. S. D. Butterworth, P. G. R. Smith, and D. C. Hanna, “Picosecond Ti:sapphire-pumped optical parametric oscillator based on periodically poled LiNbO3,” Opt. Lett. 22, 618–620 (1997).
    [CrossRef] [PubMed]
  20. M. Vaidyanathan, R. C. Eckardt, V. Dominic, L. E. Myers, and T. P. Grayson, “Cascaded optical parametric oscillations,” Opt. Express 1, 49–53 (1997), http://epubs.osa.org/opticsexpress.
    [CrossRef] [PubMed]
  21. V. Petrov and F. Noack, “Frequency upconversion of tunable femtosecond pulses by parametric amplification and sum-frequency generation in a single nonlinear crystal,” Opt. Lett. 20, 2171–2173 (1995).
    [CrossRef] [PubMed]
  22. O. Pfister, J. S. Wells, L. Hollberg, L. Zink, D. A. van Baak, M. D. Levenson, and W. R. Bosenberg, “Continuous-wave frequency tripling and quadrupling by simultaneous three-wave mixings in periodically poled crystals: application to a two-step 1.19–10.71-μm frequency bridge,” Opt. Lett. 22, 1211–1213 (1997).
    [CrossRef] [PubMed]

1998 (2)

C. McGowan, D. T. Reid, Z. E. Penman, M. Ebrahimzadeh, W. Sibbett, and D. H. Jundt, “Femtosecond optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 15, 694–701 (1998).
[CrossRef]

D. T. Reid, G. T. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, “Widely tunable, near- to mid-infrared femtosecond and picosecond optical parametric oscillators using periodically poled LiNbO3 and RbTiOAsO4,” IEEE J. Sel. Top. Quantum Electron. 4, 238–248 (1998).
[CrossRef]

1997 (5)

1996 (1)

A. Shirakawa, H. W. Mao, and T. Kobayashi, “Highly efficient generation of blue–orange femtosecond pulses from intracavity-frequency-mixed optical parametric oscillator,” Opt. Commun. 123, 121–128 (1996).
[CrossRef]

1995 (4)

1994 (2)

E. C. Cheung, K. Koch, and G. T. Moore, “Frequency upconversion by phase-matched sum-frequency generation in an optical parametric oscillator,” Opt. Lett. 19, 1967–1969 (1994).
[CrossRef] [PubMed]

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire 2nd-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

1992 (1)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

1991 (1)

K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
[CrossRef]

1970 (1)

R. A. Andrews, H. Rabin, and C. L. Tang, “Coupled parametric downconversion and upconversion with simultaneous phase matching,” Phys. Rev. Lett. 25, 605–608 (1970).
[CrossRef]

Andrews, R. A.

R. A. Andrews, H. Rabin, and C. L. Tang, “Coupled parametric downconversion and upconversion with simultaneous phase matching,” Phys. Rev. Lett. 25, 605–608 (1970).
[CrossRef]

Arbore, M. A.

Aytür, O.

Beigang, R.

A. Nebel, H. Frost, R. Beigang, and R. Wallenstein, “Visible femtosecond pulses by second harmonic generation of a cw mode-locked KTP optical parametric oscillator,” Appl. Phys. B 60, 453–458 (1995).
[CrossRef]

Bosenberg, W. R.

Burr, K. C.

Butterworth, S. D.

Byer, R. L.

Cheung, E. C.

Dominic, V.

Driscoll, T. J.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire 2nd-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

Ebrahimzadeh, M.

D. T. Reid, G. T. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, “Widely tunable, near- to mid-infrared femtosecond and picosecond optical parametric oscillators using periodically poled LiNbO3 and RbTiOAsO4,” IEEE J. Sel. Top. Quantum Electron. 4, 238–248 (1998).
[CrossRef]

C. McGowan, D. T. Reid, Z. E. Penman, M. Ebrahimzadeh, W. Sibbett, and D. H. Jundt, “Femtosecond optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 15, 694–701 (1998).
[CrossRef]

Eckardt, R. C.

Fejer, M. M.

Frost, H.

A. Nebel, H. Frost, R. Beigang, and R. Wallenstein, “Visible femtosecond pulses by second harmonic generation of a cw mode-locked KTP optical parametric oscillator,” Appl. Phys. B 60, 453–458 (1995).
[CrossRef]

Gale, G. M.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire 2nd-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

Grayson, T. P.

Hache, F.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire 2nd-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

Hanna, D. C.

Hollberg, L.

Jundt, D. H.

Kartaloglu, T.

Kato, K.

K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
[CrossRef]

Kennedy, G. T.

D. T. Reid, G. T. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, “Widely tunable, near- to mid-infrared femtosecond and picosecond optical parametric oscillators using periodically poled LiNbO3 and RbTiOAsO4,” IEEE J. Sel. Top. Quantum Electron. 4, 238–248 (1998).
[CrossRef]

Kobayashi, T.

A. Shirakawa, H. W. Mao, and T. Kobayashi, “Highly efficient generation of blue–orange femtosecond pulses from intracavity-frequency-mixed optical parametric oscillator,” Opt. Commun. 123, 121–128 (1996).
[CrossRef]

Koch, K.

Köprülü, K. G.

Levenson, M. D.

Mao, H. W.

A. Shirakawa, H. W. Mao, and T. Kobayashi, “Highly efficient generation of blue–orange femtosecond pulses from intracavity-frequency-mixed optical parametric oscillator,” Opt. Commun. 123, 121–128 (1996).
[CrossRef]

McGowan, C.

Miller, A.

D. T. Reid, G. T. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, “Widely tunable, near- to mid-infrared femtosecond and picosecond optical parametric oscillators using periodically poled LiNbO3 and RbTiOAsO4,” IEEE J. Sel. Top. Quantum Electron. 4, 238–248 (1998).
[CrossRef]

Moore, G. T.

Myers, L. E.

Nebel, A.

A. Nebel, H. Frost, R. Beigang, and R. Wallenstein, “Visible femtosecond pulses by second harmonic generation of a cw mode-locked KTP optical parametric oscillator,” Appl. Phys. B 60, 453–458 (1995).
[CrossRef]

Noack, F.

Penman, Z. E.

Petrov, V.

Pfister, O.

Pierce, J. W.

Rabin, H.

R. A. Andrews, H. Rabin, and C. L. Tang, “Coupled parametric downconversion and upconversion with simultaneous phase matching,” Phys. Rev. Lett. 25, 605–608 (1970).
[CrossRef]

Reid, D. T.

C. McGowan, D. T. Reid, Z. E. Penman, M. Ebrahimzadeh, W. Sibbett, and D. H. Jundt, “Femtosecond optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 15, 694–701 (1998).
[CrossRef]

D. T. Reid, G. T. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, “Widely tunable, near- to mid-infrared femtosecond and picosecond optical parametric oscillators using periodically poled LiNbO3 and RbTiOAsO4,” IEEE J. Sel. Top. Quantum Electron. 4, 238–248 (1998).
[CrossRef]

Roberts, D. A.

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

Shirakawa, A.

A. Shirakawa, H. W. Mao, and T. Kobayashi, “Highly efficient generation of blue–orange femtosecond pulses from intracavity-frequency-mixed optical parametric oscillator,” Opt. Commun. 123, 121–128 (1996).
[CrossRef]

Sibbett, W.

C. McGowan, D. T. Reid, Z. E. Penman, M. Ebrahimzadeh, W. Sibbett, and D. H. Jundt, “Femtosecond optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 15, 694–701 (1998).
[CrossRef]

D. T. Reid, G. T. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, “Widely tunable, near- to mid-infrared femtosecond and picosecond optical parametric oscillators using periodically poled LiNbO3 and RbTiOAsO4,” IEEE J. Sel. Top. Quantum Electron. 4, 238–248 (1998).
[CrossRef]

Smith, P. G. R.

Tang, C. L.

K. C. Burr, C. L. Tang, M. A. Arbore, and M. M. Fejer, “Broadly tunable mid-infrared femtosecond optical parametric oscillator using all-solid-state-pumped periodically poled lithium niobate,” Opt. Lett. 22, 1458–1460 (1997).
[CrossRef]

R. A. Andrews, H. Rabin, and C. L. Tang, “Coupled parametric downconversion and upconversion with simultaneous phase matching,” Phys. Rev. Lett. 25, 605–608 (1970).
[CrossRef]

Vaidyanathan, M.

van Baak, D. A.

van Driel, H. M.

H. M. van Driel, “Synchronously pumped optical parametric oscillators,” Appl. Phys. B 60, 411–420 (1995).
[CrossRef]

Wallenstein, R.

A. Nebel, H. Frost, R. Beigang, and R. Wallenstein, “Visible femtosecond pulses by second harmonic generation of a cw mode-locked KTP optical parametric oscillator,” Appl. Phys. B 60, 453–458 (1995).
[CrossRef]

Wells, J. S.

Zink, L.

Appl. Phys. B (2)

H. M. van Driel, “Synchronously pumped optical parametric oscillators,” Appl. Phys. B 60, 411–420 (1995).
[CrossRef]

A. Nebel, H. Frost, R. Beigang, and R. Wallenstein, “Visible femtosecond pulses by second harmonic generation of a cw mode-locked KTP optical parametric oscillator,” Appl. Phys. B 60, 453–458 (1995).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

D. T. Reid, G. T. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, “Widely tunable, near- to mid-infrared femtosecond and picosecond optical parametric oscillators using periodically poled LiNbO3 and RbTiOAsO4,” IEEE J. Sel. Top. Quantum Electron. 4, 238–248 (1998).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire 2nd-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

A. Shirakawa, H. W. Mao, and T. Kobayashi, “Highly efficient generation of blue–orange femtosecond pulses from intracavity-frequency-mixed optical parametric oscillator,” Opt. Commun. 123, 121–128 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. Lett. (1)

R. A. Andrews, H. Rabin, and C. L. Tang, “Coupled parametric downconversion and upconversion with simultaneous phase matching,” Phys. Rev. Lett. 25, 605–608 (1970).
[CrossRef]

Other (5)

K. G. Köprülü, T. Kartaloğlu, and O. Aytür, “Single-crystal sum-frequency generating optical parametric oscillator,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 457–458.

O. Aytür and Y. Dikmelik, “Plane wave theory of self-doubling optical parametric oscillators,” IEEE J. Quantum Electron. 34, 447–458 (1998); Y. Dikmelik, G. Akgün, and O. Aytür, “Plane-wave dynamics of optical parametric oscillation with simultaneous sum-frequency generation,” IEEE J. Quantum Electron. 35, 897–912 (1999).
[CrossRef]

R. L. Byer and A. Piskarskas, eds., feature on optical parametric oscillation and amplification, J. Opt. Soc. Am. B 10, 1655–2243 (1993); W. R. Bosenberg and R. C. Eckardt, eds., feature on optical parametric devices, J. Opt. Soc. Am. B 12, 2083–2320 (1995); C. L. Tang, W. R. Bosenberg, T. Ukachi, R. J. Lane, and L. K. Cheng, “Optical parametric oscillators,” Proc. IEEE IEEPAD 80, 365–374 (1992).
[CrossRef]

R. J. Ellingson and C. L. Tang, “High-power high-repetition-rate femtosecond pulses tunable in the visible,” Opt. Lett. 18, 438–440 (1993); D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Efficient femtosecond pulse generation in the visible in a frequency-doubled optical parametric oscillator based on RbTiOAsO4,” J. Opt. Soc. Am. B 12, 1157–1163 (1995).
[CrossRef] [PubMed]

D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54, 1728–1730 (1989); W. S. Pelouch, P. E. Powers, and C. L. Tang, “Ti:sapphire pumped, high-repetition-rate femtosecond optical parametric oscillator,” Opt. Lett. 17, 1070–1072 (1992); Q. Fu, G. Mak, and H. M. van Driel, “High-power, 62-fs infrared optical parametric oscillator synchronously pumped by a 76-MHz Ti:sapphire laser,” Opt. Lett. OPLEDP 17, 1006–1008 (1992); G. Mak, Q. Fu, and H. M. van Driel, “Externally pumped high repetition rate femtosecond infrared optical parametric oscillator,” Appl. Phys. Lett. APPLAB 60, 542–544 (1992); P. E. Powers, C. L. Tang, and L. K. Cheng, “High-repetition-rate femtosecond optical parametric oscillator based on CsTiOAsO4,” Opt. Lett. OPLEDP 19, 37–39 (1994).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Experimental setup for the SF-OPO. A mode-locked Ti:sapphire laser at a wavelength of 827 nm is used as the pump beam. Abbreviations are defined in text.

Fig. 2
Fig. 2

Power-conversion efficiency as a function of polarization rotation angle. The pump power is 515 mW, and the group delay is 2 ps.

Fig. 3
Fig. 3

Pump depletion for the p-polarized and the s-polarized components and the intracavity signal power (in relative units) as functions of polarization rotation angle. The pump power is 515 mW, and the group delay is 2 ps. r.u., Relative units.

Fig. 4
Fig. 4

Optimum polarization rotation angle and maximum power-conversion efficiency as functions of pump power.

Fig. 5
Fig. 5

Power-conversion efficiencies as functions of the group delay between the p- and the s-polarized pump components for 5- and 1.5-mm-long KTP crystals. The p-polarized component lags behind the s-polarized component for positive group-delay values.

Fig. 6
Fig. 6

Calculated tuning curves and measured values of output wavelength, pump wavelength, and output power across the tuning range for the SF-OPO. Angles are internal to the crystal. The filled circles represent experimental data points.

Fig. 7
Fig. 7

Autocorrelation trace (left) and spectrum (right) of the sum-frequency output beam.

Fig. 8
Fig. 8

Photon-conversion efficiency as a function of the polarization angle. Solid curve, theoretical plane-wave model; filled circles, experimental data points.

Equations (8)

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

aiz+1viait=-jκaapas*,
asz+1vsast=-j(κaapai*+κbafar*),
apz+1vpapt=-jκaaias,
arz+1vrart=-jκbafas*,
afz+1vfaft=-jκbasar,
am=(nmc0/2ωm)1/2Em,m=i, s, p, r, f,
κa=da2c301/2ωiωsωpninsnp1/2,
κb=db2c301/2ωsωrωfnsnrnf1/2,

Metrics