Abstract

We report on the performance of a multipass diode-pumped amplifier design to provide a combination of high gain and efficiency with high stability. A simple rod-cavity design and the establishment of quasi-steady-state operation resulted in a saturated gain of over 6000 at an average output intensity during the pulse train of 7 kW/cm2. The amplifier showed an output stability of 0.2% rms in the short term and 0.7% rms in the long term and an output intensity insensitive to input power changes. Zernike analysis of the measurements of pump distortion showed an almost pure astigmatic phase error that can be compensated up to high average power levels.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Beach, P. Reichert, W. Benett, B. Freitas, S. Mitchell, A. Velsko, J. Davin, R. Solarz, “Scalable diode-end-pumping technology applied to a 100-mJ Q-switched Nd3+:YLF oscillator,” Opt. Lett. 18, 1326–1328 (1993).
    [CrossRef]
  2. S. Lee, S. K. Kim, M. Yun, H. S. Kim, B. H. Cha, H.-J. Moon, “Design and fabrication of a diode-side-pumped Nd:YAG laser with a diffusive optical cavity for 500-W output power,” Appl. Opt. 41, 1089–1094 (2002).
    [CrossRef] [PubMed]
  3. S. Konno, T. Kojima, S. Fujikawa, K. Yasui, “High-brightness 138-W green laser on an intracavity-frequency-doubled diode-side-pumped Q-switched Nd:YAG laser,” Opt. Lett. 25, 105–107 (2000).
    [CrossRef]
  4. Y. Hirano, T. Yanagisawa, S. Ueno, T. Tajime, O. Uchino, T. Nagai, C. Nagasawa, “All-solid-state high-power conduction-cooled Nd:YLF rod laser,” Opt. Lett. 25, 1168–1170 (2000).
    [CrossRef]
  5. K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
    [CrossRef]
  6. D. R. Walker, C. J. Flood, H. M. van Driel, U. J. Greiner, H. H. Klingenberg, “High power diode-pumped Nd:YAG regerative amplifier for picosecond pulses,” Appl. Phys. Lett. 65, 1992–1994 (1994).
    [CrossRef]
  7. M. J. P. Dymott, K. J. Weingarten, “Picosecond diode-pumped laser system with 9.3-W average power and 2.3-mJ pulse energy,” Appl. Opt. 40, 3042–3045 (2001).
    [CrossRef]
  8. I. Will, A. Liero, D. Mertins, W. Sandner, “Feedback-stabilized Nd:YLF amplifier system for generation of picosecond pulse trains of an exactly rectangular envelope,” IEEE J. Quantum Electron. 34, 2020–2028 (1998).
    [CrossRef]
  9. A. R. Fry, M. J. Fitch, A. C. Melissinos, B. D. Taylor, “Laser system for a high duty cycle photoinjector,” Nucl. Instrum. Methods Phys. Res. A 430, 180–188 (1999).
    [CrossRef]
  10. Y. Hirano, Y. Koyata, S. Yamamoto, K. Kasahara, T. Tajime, “208-W TEM00 operation of a diode-pumped Nd:YAG rod laser,” Opt. Lett. 24, 679–681 (1999).
    [CrossRef]
  11. T. H. Graf, A. I. Ferguson, E. Bente, D. Burns, M. D. Dawson, “Multi-watt Nd:YVO4 laser, mode locked by a semiconductor saturable absorber mirror and side-pumped by a diode-laser bar,” Opt. Commun. 159, 84–87 (1999).
    [CrossRef]
  12. G. Cerullo, S. De Silvestri, V. Magni, “High efficiency, 40 W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 17, 77–81 (1992).
    [CrossRef]
  13. K. J. Weingarten, D. C. Shannon, R. W. Wallace, U. Keller, “Two-gigahertz repetition-rate, diode-pumped, mode-locked Nd:YLF laser,” Opt. Lett. 15, 962–964 (1990).
    [CrossRef] [PubMed]
  14. J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–696 (1985).
    [CrossRef]
  15. I. N. Ross, E. J. Divall, J. M. D. Lister, “A high gain multipass titanium sapphire amplifier,” Annual Rep. TR-96-066 (Central Laser Facility, Rutherford Appleton Laboratory, 1996), pp. 101–103.
  16. N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–568 (1990).
    [CrossRef]
  17. J. J. Kasinski, R. L. Burnham, “Near-diffraction-limited, high-energy, high-power, diode-pumped laser using thermal aberration correction with aspheric diamond-turned optics,” Appl. Opt. 35, 5949–5954 (1996).
    [CrossRef] [PubMed]
  18. J. E. Murray, “Pulsed gain and thermal lensing of Nd:LiYF4,” IEEE J. Quantum Electron. 19, 488–491 (1983).
    [CrossRef]

2002 (1)

2001 (1)

2000 (2)

1999 (3)

A. R. Fry, M. J. Fitch, A. C. Melissinos, B. D. Taylor, “Laser system for a high duty cycle photoinjector,” Nucl. Instrum. Methods Phys. Res. A 430, 180–188 (1999).
[CrossRef]

Y. Hirano, Y. Koyata, S. Yamamoto, K. Kasahara, T. Tajime, “208-W TEM00 operation of a diode-pumped Nd:YAG rod laser,” Opt. Lett. 24, 679–681 (1999).
[CrossRef]

T. H. Graf, A. I. Ferguson, E. Bente, D. Burns, M. D. Dawson, “Multi-watt Nd:YVO4 laser, mode locked by a semiconductor saturable absorber mirror and side-pumped by a diode-laser bar,” Opt. Commun. 159, 84–87 (1999).
[CrossRef]

1998 (1)

I. Will, A. Liero, D. Mertins, W. Sandner, “Feedback-stabilized Nd:YLF amplifier system for generation of picosecond pulse trains of an exactly rectangular envelope,” IEEE J. Quantum Electron. 34, 2020–2028 (1998).
[CrossRef]

1996 (1)

1994 (2)

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

D. R. Walker, C. J. Flood, H. M. van Driel, U. J. Greiner, H. H. Klingenberg, “High power diode-pumped Nd:YAG regerative amplifier for picosecond pulses,” Appl. Phys. Lett. 65, 1992–1994 (1994).
[CrossRef]

1993 (1)

1992 (1)

G. Cerullo, S. De Silvestri, V. Magni, “High efficiency, 40 W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 17, 77–81 (1992).
[CrossRef]

1990 (2)

K. J. Weingarten, D. C. Shannon, R. W. Wallace, U. Keller, “Two-gigahertz repetition-rate, diode-pumped, mode-locked Nd:YLF laser,” Opt. Lett. 15, 962–964 (1990).
[CrossRef] [PubMed]

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–568 (1990).
[CrossRef]

1985 (1)

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–696 (1985).
[CrossRef]

1983 (1)

J. E. Murray, “Pulsed gain and thermal lensing of Nd:LiYF4,” IEEE J. Quantum Electron. 19, 488–491 (1983).
[CrossRef]

Akatsuka, M.

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

Barnes, N. P.

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–568 (1990).
[CrossRef]

Beach, R.

Benett, W.

Bente, E.

T. H. Graf, A. I. Ferguson, E. Bente, D. Burns, M. D. Dawson, “Multi-watt Nd:YVO4 laser, mode locked by a semiconductor saturable absorber mirror and side-pumped by a diode-laser bar,” Opt. Commun. 159, 84–87 (1999).
[CrossRef]

Burnham, R. L.

Burns, D.

T. H. Graf, A. I. Ferguson, E. Bente, D. Burns, M. D. Dawson, “Multi-watt Nd:YVO4 laser, mode locked by a semiconductor saturable absorber mirror and side-pumped by a diode-laser bar,” Opt. Commun. 159, 84–87 (1999).
[CrossRef]

Cerullo, G.

G. Cerullo, S. De Silvestri, V. Magni, “High efficiency, 40 W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 17, 77–81 (1992).
[CrossRef]

Cha, B. H.

Cross, P. L.

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–568 (1990).
[CrossRef]

Davin, J.

Dawson, M. D.

T. H. Graf, A. I. Ferguson, E. Bente, D. Burns, M. D. Dawson, “Multi-watt Nd:YVO4 laser, mode locked by a semiconductor saturable absorber mirror and side-pumped by a diode-laser bar,” Opt. Commun. 159, 84–87 (1999).
[CrossRef]

De Silvestri, S.

G. Cerullo, S. De Silvestri, V. Magni, “High efficiency, 40 W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 17, 77–81 (1992).
[CrossRef]

Divall, E. J.

I. N. Ross, E. J. Divall, J. M. D. Lister, “A high gain multipass titanium sapphire amplifier,” Annual Rep. TR-96-066 (Central Laser Facility, Rutherford Appleton Laboratory, 1996), pp. 101–103.

Dymott, M. J. P.

Ferguson, A. I.

T. H. Graf, A. I. Ferguson, E. Bente, D. Burns, M. D. Dawson, “Multi-watt Nd:YVO4 laser, mode locked by a semiconductor saturable absorber mirror and side-pumped by a diode-laser bar,” Opt. Commun. 159, 84–87 (1999).
[CrossRef]

Fitch, M. J.

A. R. Fry, M. J. Fitch, A. C. Melissinos, B. D. Taylor, “Laser system for a high duty cycle photoinjector,” Nucl. Instrum. Methods Phys. Res. A 430, 180–188 (1999).
[CrossRef]

Flood, C. J.

D. R. Walker, C. J. Flood, H. M. van Driel, U. J. Greiner, H. H. Klingenberg, “High power diode-pumped Nd:YAG regerative amplifier for picosecond pulses,” Appl. Phys. Lett. 65, 1992–1994 (1994).
[CrossRef]

Freitas, B.

Fry, A. R.

A. R. Fry, M. J. Fitch, A. C. Melissinos, B. D. Taylor, “Laser system for a high duty cycle photoinjector,” Nucl. Instrum. Methods Phys. Res. A 430, 180–188 (1999).
[CrossRef]

Fujikawa, S.

Graf, T. H.

T. H. Graf, A. I. Ferguson, E. Bente, D. Burns, M. D. Dawson, “Multi-watt Nd:YVO4 laser, mode locked by a semiconductor saturable absorber mirror and side-pumped by a diode-laser bar,” Opt. Commun. 159, 84–87 (1999).
[CrossRef]

Greiner, U. J.

D. R. Walker, C. J. Flood, H. M. van Driel, U. J. Greiner, H. H. Klingenberg, “High power diode-pumped Nd:YAG regerative amplifier for picosecond pulses,” Appl. Phys. Lett. 65, 1992–1994 (1994).
[CrossRef]

Hirano, Y.

Ishikawa, K.

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

Kasahara, K.

Kasinski, J. J.

Keller, U.

Kim, H. S.

Kim, S. K.

Klingenberg, H. H.

D. R. Walker, C. J. Flood, H. M. van Driel, U. J. Greiner, H. H. Klingenberg, “High power diode-pumped Nd:YAG regerative amplifier for picosecond pulses,” Appl. Phys. Lett. 65, 1992–1994 (1994).
[CrossRef]

Kojima, T.

Konno, S.

Koyata, Y.

Lee, S.

Liero, A.

I. Will, A. Liero, D. Mertins, W. Sandner, “Feedback-stabilized Nd:YLF amplifier system for generation of picosecond pulse trains of an exactly rectangular envelope,” IEEE J. Quantum Electron. 34, 2020–2028 (1998).
[CrossRef]

Lister, J. M. D.

I. N. Ross, E. J. Divall, J. M. D. Lister, “A high gain multipass titanium sapphire amplifier,” Annual Rep. TR-96-066 (Central Laser Facility, Rutherford Appleton Laboratory, 1996), pp. 101–103.

Magni, V.

G. Cerullo, S. De Silvestri, V. Magni, “High efficiency, 40 W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 17, 77–81 (1992).
[CrossRef]

Marion, J.

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–696 (1985).
[CrossRef]

Melissinos, A. C.

A. R. Fry, M. J. Fitch, A. C. Melissinos, B. D. Taylor, “Laser system for a high duty cycle photoinjector,” Nucl. Instrum. Methods Phys. Res. A 430, 180–188 (1999).
[CrossRef]

Mertins, D.

I. Will, A. Liero, D. Mertins, W. Sandner, “Feedback-stabilized Nd:YLF amplifier system for generation of picosecond pulse trains of an exactly rectangular envelope,” IEEE J. Quantum Electron. 34, 2020–2028 (1998).
[CrossRef]

Mitchell, S.

Moon, H.-J.

Murray, J. E.

J. E. Murray, “Pulsed gain and thermal lensing of Nd:LiYF4,” IEEE J. Quantum Electron. 19, 488–491 (1983).
[CrossRef]

Nagai, T.

Nagasawa, C.

Naito, K.

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

Nakai, S.

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

Nakatsuka, M.

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

Ohmi, M.

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

Reichert, P.

Ross, I. N.

I. N. Ross, E. J. Divall, J. M. D. Lister, “A high gain multipass titanium sapphire amplifier,” Annual Rep. TR-96-066 (Central Laser Facility, Rutherford Appleton Laboratory, 1996), pp. 101–103.

Sandner, W.

I. Will, A. Liero, D. Mertins, W. Sandner, “Feedback-stabilized Nd:YLF amplifier system for generation of picosecond pulse trains of an exactly rectangular envelope,” IEEE J. Quantum Electron. 34, 2020–2028 (1998).
[CrossRef]

Shannon, D. C.

Skolaut, M. W.

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–568 (1990).
[CrossRef]

Solarz, R.

Storm, M. E.

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–568 (1990).
[CrossRef]

Tajime, T.

Taylor, B. D.

A. R. Fry, M. J. Fitch, A. C. Melissinos, B. D. Taylor, “Laser system for a high duty cycle photoinjector,” Nucl. Instrum. Methods Phys. Res. A 430, 180–188 (1999).
[CrossRef]

Uchino, O.

Ueno, S.

van Driel, H. M.

D. R. Walker, C. J. Flood, H. M. van Driel, U. J. Greiner, H. H. Klingenberg, “High power diode-pumped Nd:YAG regerative amplifier for picosecond pulses,” Appl. Phys. Lett. 65, 1992–1994 (1994).
[CrossRef]

Velsko, A.

Walker, D. R.

D. R. Walker, C. J. Flood, H. M. van Driel, U. J. Greiner, H. H. Klingenberg, “High power diode-pumped Nd:YAG regerative amplifier for picosecond pulses,” Appl. Phys. Lett. 65, 1992–1994 (1994).
[CrossRef]

Wallace, R. W.

Weingarten, K. J.

Will, I.

I. Will, A. Liero, D. Mertins, W. Sandner, “Feedback-stabilized Nd:YLF amplifier system for generation of picosecond pulse trains of an exactly rectangular envelope,” IEEE J. Quantum Electron. 34, 2020–2028 (1998).
[CrossRef]

Yamamoto, S.

Yamanaka, M.

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

Yanagisawa, T.

Yasui, K.

Yun, M.

Appl. Opt. (3)

Appl. Phys. Lett. (3)

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–696 (1985).
[CrossRef]

K. Naito, M. Ohmi, K. Ishikawa, M. Akatsuka, M. Yamanaka, M. Nakatsuka, S. Nakai, “Demonstration of high energy extraction efficiency in a laser-diode-pumped high gain Nd:YAG regenerative amplifier,” Appl. Phys. Lett. 64, 1186–1188 (1994).
[CrossRef]

D. R. Walker, C. J. Flood, H. M. van Driel, U. J. Greiner, H. H. Klingenberg, “High power diode-pumped Nd:YAG regerative amplifier for picosecond pulses,” Appl. Phys. Lett. 65, 1992–1994 (1994).
[CrossRef]

IEEE J. Quantum Electron. (3)

I. Will, A. Liero, D. Mertins, W. Sandner, “Feedback-stabilized Nd:YLF amplifier system for generation of picosecond pulse trains of an exactly rectangular envelope,” IEEE J. Quantum Electron. 34, 2020–2028 (1998).
[CrossRef]

J. E. Murray, “Pulsed gain and thermal lensing of Nd:LiYF4,” IEEE J. Quantum Electron. 19, 488–491 (1983).
[CrossRef]

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–568 (1990).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

A. R. Fry, M. J. Fitch, A. C. Melissinos, B. D. Taylor, “Laser system for a high duty cycle photoinjector,” Nucl. Instrum. Methods Phys. Res. A 430, 180–188 (1999).
[CrossRef]

Opt. Commun. (2)

T. H. Graf, A. I. Ferguson, E. Bente, D. Burns, M. D. Dawson, “Multi-watt Nd:YVO4 laser, mode locked by a semiconductor saturable absorber mirror and side-pumped by a diode-laser bar,” Opt. Commun. 159, 84–87 (1999).
[CrossRef]

G. Cerullo, S. De Silvestri, V. Magni, “High efficiency, 40 W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 17, 77–81 (1992).
[CrossRef]

Opt. Lett. (5)

Other (1)

I. N. Ross, E. J. Divall, J. M. D. Lister, “A high gain multipass titanium sapphire amplifier,” Annual Rep. TR-96-066 (Central Laser Facility, Rutherford Appleton Laboratory, 1996), pp. 101–103.

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 (14)

Fig. 1
Fig. 1

Basic design of a photoinjector laser system. PC, Pockels cell, CYL, cylindrical; FHG, fourth-harmonic generator.

Fig. 2
Fig. 2

Schematic of the amplifier head.

Fig. 3
Fig. 3

(a) Experimental arrangement for the diode-pumped amplifier system. (b) The four-pass amplifier geometry.

Fig. 4
Fig. 4

Variation of the efficiency of extraction of pump power with the amplifier gain.

Fig. 5
Fig. 5

Calculated amplified intensity during the pumping period.

Fig. 6
Fig. 6

Fluorescence distribution across the rod that is due to the diode arrays individually and the saturated gain distribution with all diode arrays together. The contour interval is 12.5%.

Fig. 7
Fig. 7

Calculated and measured small signal gain of the amplifier.

Fig. 8
Fig. 8

Calculated and measured gain for the amplifier under strong saturation.

Fig. 9
Fig. 9

Unamplified and amplified output beam distributions showing the effect of strong saturation, which generates a flattop from a Gaussian profile. The contour interval is 6% for the unamplified beam and 20% for the amplified beam.

Fig. 10
Fig. 10

Dependence of the amplified signal on different coolant temperatures.

Fig. 11
Fig. 11

Short-term and long-term stability of the amplified signal with strong saturation.

Fig. 12
Fig. 12

Low sensitivity of the amplified signal to a large attenuation of the input signal.

Fig. 13
Fig. 13

Interferograms showing the thermal optical distortion of the amplifier for a heat deposition rate of 10 W: (a) and (b) show the interferograms for orthogonal orientations without and with pumping, respectively.

Fig. 14
Fig. 14

Strehl ratio calculated from the measured optical distortions and extrapolated up to the fracture limit of the amplifier rod.

Tables (1)

Tables Icon

Table 1 Photocathode Specifications for the CERN Linear Collider Photoinjector

Equations (12)

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

Ip=Iout-Iin+Fsat ln GηR1+Bτfl,
BP=fα rodexpαr4πr2dV,
Ip=f1gIin+f2G,
f1G=1-L3G4+1-L2LG3+1-L2LG2+LG-1, f2G=Fsat ln GηR1+Bτfl,
B=0.05d/l0.3G
ηex=Iout-IinIp.
dIp=f1Iin+f2dG+f1dIin.
IpdIpIp=G4f2+f1IindIoutIout-G4f2+f1Iin-f1IindIinIin,
dIoutIout=1.85 dIpIp+0.163 dIinIin.
Δαz,t=ηRFsatIpz,tτsl-αz,tτs1+Bτfl-αz,tηRFz,tFsat,
Fz,t=Fin exp0z αz,dz;
Fz,t=Fintexp0z αz,tdz+L exp0l αz,tdz+zl αz,tdz+L2 exp0l αz,tdz+0z αz,tdz+L3 exp3 0l αz,tdz+zl αz,tdz.

Metrics