Abstract

We present a compact and efficient KTA-based intracavity optical parametric oscillator (IOPO) driven by a diode-end-pumped Nd:GdVO4/Cr:YAG passively Q-switched laser. At the incident diode pump power of 9.2W, signal (1.53μm) and idler (3.47μm) average output powers of up to 744 and 356mW, respectively, have been obtained. The total (signal+idler) optical-to-optical conversion efficiency is as high as 12%. By using the knife-edge method, near-diffraction-limited signal and idler beams have been detected, and the M2 factors are well within 1.2. In addition, based on the ABCD matrix theory, the impact of mode matching and the thermal lens effect on the OPO output have been analyzed.

© 2008 Optical Society of America

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  1. Y. Yashkir and H. M. van Driel, “Passively Q-switched 1.57-μm intracavity optical parametric oscillator,” Appl. Opt. 38, 2554-2559 (1999).
    [CrossRef]
  2. W. Zendzian, J. K. Jabczynski, P. Wachulak, and J. Kwiatkowski, “High-repetition-rate, intracavity-pumped KTP OPO at 1572 nm,” Appl. Phys. B 80, 329-332 (2005).
    [CrossRef]
  3. A. Dubois, S. Victori, T. Lepine, P. Georges, and A. Brun, “High-repetition-rate eyesafe intracavity optical parametric oscillator,” Appl. Phys. B 67, 181-183 (1998).
    [CrossRef]
  4. J. Miao, B. Wang, J. Peng, H. Tan, and H. Bian, “Highly stable and efficient KTP-based intracavity optical parametric oscillator with a diode-pumped passively Q-switched laser,” Appl. Phys. B 88, 193-196 (2007).
    [CrossRef]
  5. J. D. Bierlein, H. Vanherzeele, and A. A. Ballman, “Linear and nonlinear optical properties of flux-grown KTiOAsO4,” Appl. Phys. Lett. 54, 783-785 (1989).
    [CrossRef]
  6. W. R. Bosenberg, L. K. Cheng, and J. D. Bierlein, “Optical parametric frequency conversion properties of KTiOAsO4,” Appl. Phys. Lett. 65, 2765-2767 (1994).
    [CrossRef]
  7. S. French, M. Ebrahimzadeh, and A. Miller, “High power, high-repetition-rate picosecond optical parametric oscillator for the near- to mid-infrared,” Opt. Lett. 21, 131-133 (1996).
    [CrossRef] [PubMed]
  8. C. McGowan, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Femtosecond pulses tunable beyond 4 μm from a KTA-based optical parametric oscillator,” Opt. Commun. 134, 186-190(1997).
    [CrossRef]
  9. R. F. Wu, K. S. Lai, H. F. Wong, W. J. Xie, Y. L. Lim, and E. Lau, “Multiwatt mid-IR output from a Nd:YALO laser pumped intracavity KTA OPO,” Opt. Express 8, 694-698 (2001).
    [CrossRef] [PubMed]
  10. X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
    [CrossRef]
  11. J. Liu and D. Kim, “Optimization of intracavity doubled passively Q-switched solid-state laser,” IEEE J. Quantum Electron. 35, 1724-1730 (1999).
    [CrossRef]
  12. A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
    [CrossRef]
  13. Y. F. Chen, “Pump-to-mode size ratio dependence of thermal loading in diode-end-pumped solid-state lasers,” J. Opt. Soc. Am. B 17, 1835-1840 (2000).
    [CrossRef]
  14. B. Lü, Laser Optics (Higher Education Press, 2003) (in Chinese).
  15. G. Xiao, M. Bass, and M. Acharekar, “Passively Q-switched solid-state lasers with intracavity optical parametric oscillators,” IEEE J. Quantum Electron. 34, 2241-2245 (1998).
    [CrossRef]
  16. W. Zendzian, J. K. Jabczynski, and J. Kwiatkowski, “Intracavity optical parametric oscillator at 1572-nm wavelength pumped by passively Q-switched diode-pumped Nd:YAG laser,” Appl. Phys. B 76, 355-358 (2003).
    [CrossRef]
  17. T. Debuisschert, J. Raffy, J.-P. Pocholle, and M. Papuchon, “Intracavity optical parametric oscillator: study of the dynamics in pulsed regime,” J. Opt. Soc. Am. B 13, 1569-1587 (1996).
    [CrossRef]

2007 (1)

J. Miao, B. Wang, J. Peng, H. Tan, and H. Bian, “Highly stable and efficient KTP-based intracavity optical parametric oscillator with a diode-pumped passively Q-switched laser,” Appl. Phys. B 88, 193-196 (2007).
[CrossRef]

2005 (1)

W. Zendzian, J. K. Jabczynski, P. Wachulak, and J. Kwiatkowski, “High-repetition-rate, intracavity-pumped KTP OPO at 1572 nm,” Appl. Phys. B 80, 329-332 (2005).
[CrossRef]

2003 (1)

W. Zendzian, J. K. Jabczynski, and J. Kwiatkowski, “Intracavity optical parametric oscillator at 1572-nm wavelength pumped by passively Q-switched diode-pumped Nd:YAG laser,” Appl. Phys. B 76, 355-358 (2003).
[CrossRef]

2001 (1)

2000 (1)

1999 (2)

J. Liu and D. Kim, “Optimization of intracavity doubled passively Q-switched solid-state laser,” IEEE J. Quantum Electron. 35, 1724-1730 (1999).
[CrossRef]

Y. Yashkir and H. M. van Driel, “Passively Q-switched 1.57-μm intracavity optical parametric oscillator,” Appl. Opt. 38, 2554-2559 (1999).
[CrossRef]

1998 (2)

A. Dubois, S. Victori, T. Lepine, P. Georges, and A. Brun, “High-repetition-rate eyesafe intracavity optical parametric oscillator,” Appl. Phys. B 67, 181-183 (1998).
[CrossRef]

G. Xiao, M. Bass, and M. Acharekar, “Passively Q-switched solid-state lasers with intracavity optical parametric oscillators,” IEEE J. Quantum Electron. 34, 2241-2245 (1998).
[CrossRef]

1997 (2)

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

C. McGowan, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Femtosecond pulses tunable beyond 4 μm from a KTA-based optical parametric oscillator,” Opt. Commun. 134, 186-190(1997).
[CrossRef]

1996 (2)

1994 (1)

W. R. Bosenberg, L. K. Cheng, and J. D. Bierlein, “Optical parametric frequency conversion properties of KTiOAsO4,” Appl. Phys. Lett. 65, 2765-2767 (1994).
[CrossRef]

1992 (1)

A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
[CrossRef]

1989 (1)

J. D. Bierlein, H. Vanherzeele, and A. A. Ballman, “Linear and nonlinear optical properties of flux-grown KTiOAsO4,” Appl. Phys. Lett. 54, 783-785 (1989).
[CrossRef]

Acharekar, M.

G. Xiao, M. Bass, and M. Acharekar, “Passively Q-switched solid-state lasers with intracavity optical parametric oscillators,” IEEE J. Quantum Electron. 34, 2241-2245 (1998).
[CrossRef]

Ballman, A. A.

J. D. Bierlein, H. Vanherzeele, and A. A. Ballman, “Linear and nonlinear optical properties of flux-grown KTiOAsO4,” Appl. Phys. Lett. 54, 783-785 (1989).
[CrossRef]

Bass, M.

G. Xiao, M. Bass, and M. Acharekar, “Passively Q-switched solid-state lasers with intracavity optical parametric oscillators,” IEEE J. Quantum Electron. 34, 2241-2245 (1998).
[CrossRef]

Bian, H.

J. Miao, B. Wang, J. Peng, H. Tan, and H. Bian, “Highly stable and efficient KTP-based intracavity optical parametric oscillator with a diode-pumped passively Q-switched laser,” Appl. Phys. B 88, 193-196 (2007).
[CrossRef]

Bierlein, J. D.

W. R. Bosenberg, L. K. Cheng, and J. D. Bierlein, “Optical parametric frequency conversion properties of KTiOAsO4,” Appl. Phys. Lett. 65, 2765-2767 (1994).
[CrossRef]

J. D. Bierlein, H. Vanherzeele, and A. A. Ballman, “Linear and nonlinear optical properties of flux-grown KTiOAsO4,” Appl. Phys. Lett. 54, 783-785 (1989).
[CrossRef]

Bosenberg, W. R.

W. R. Bosenberg, L. K. Cheng, and J. D. Bierlein, “Optical parametric frequency conversion properties of KTiOAsO4,” Appl. Phys. Lett. 65, 2765-2767 (1994).
[CrossRef]

Brun, A.

A. Dubois, S. Victori, T. Lepine, P. Georges, and A. Brun, “High-repetition-rate eyesafe intracavity optical parametric oscillator,” Appl. Phys. B 67, 181-183 (1998).
[CrossRef]

Chen, Y. F.

Cheng, L. K.

W. R. Bosenberg, L. K. Cheng, and J. D. Bierlein, “Optical parametric frequency conversion properties of KTiOAsO4,” Appl. Phys. Lett. 65, 2765-2767 (1994).
[CrossRef]

Debuisschert, T.

Dubois, A.

A. Dubois, S. Victori, T. Lepine, P. Georges, and A. Brun, “High-repetition-rate eyesafe intracavity optical parametric oscillator,” Appl. Phys. B 67, 181-183 (1998).
[CrossRef]

Ebrahimzadeh, M.

C. McGowan, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Femtosecond pulses tunable beyond 4 μm from a KTA-based optical parametric oscillator,” Opt. Commun. 134, 186-190(1997).
[CrossRef]

S. French, M. Ebrahimzadeh, and A. Miller, “High power, high-repetition-rate picosecond optical parametric oscillator for the near- to mid-infrared,” Opt. Lett. 21, 131-133 (1996).
[CrossRef] [PubMed]

French, S.

Georges, P.

A. Dubois, S. Victori, T. Lepine, P. Georges, and A. Brun, “High-repetition-rate eyesafe intracavity optical parametric oscillator,” Appl. Phys. B 67, 181-183 (1998).
[CrossRef]

Huber, G.

A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
[CrossRef]

Jabczynski, J. K.

W. Zendzian, J. K. Jabczynski, P. Wachulak, and J. Kwiatkowski, “High-repetition-rate, intracavity-pumped KTP OPO at 1572 nm,” Appl. Phys. B 80, 329-332 (2005).
[CrossRef]

W. Zendzian, J. K. Jabczynski, and J. Kwiatkowski, “Intracavity optical parametric oscillator at 1572-nm wavelength pumped by passively Q-switched diode-pumped Nd:YAG laser,” Appl. Phys. B 76, 355-358 (2003).
[CrossRef]

Jensen, T.

A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
[CrossRef]

Kim, D.

J. Liu and D. Kim, “Optimization of intracavity doubled passively Q-switched solid-state laser,” IEEE J. Quantum Electron. 35, 1724-1730 (1999).
[CrossRef]

Kwiatkowski, J.

W. Zendzian, J. K. Jabczynski, P. Wachulak, and J. Kwiatkowski, “High-repetition-rate, intracavity-pumped KTP OPO at 1572 nm,” Appl. Phys. B 80, 329-332 (2005).
[CrossRef]

W. Zendzian, J. K. Jabczynski, and J. Kwiatkowski, “Intracavity optical parametric oscillator at 1572-nm wavelength pumped by passively Q-switched diode-pumped Nd:YAG laser,” Appl. Phys. B 76, 355-358 (2003).
[CrossRef]

Lai, K. S.

Lau, E.

Lepine, T.

A. Dubois, S. Victori, T. Lepine, P. Georges, and A. Brun, “High-repetition-rate eyesafe intracavity optical parametric oscillator,” Appl. Phys. B 67, 181-183 (1998).
[CrossRef]

Lim, Y. L.

Liu, J.

J. Liu and D. Kim, “Optimization of intracavity doubled passively Q-switched solid-state laser,” IEEE J. Quantum Electron. 35, 1724-1730 (1999).
[CrossRef]

Lü, B.

B. Lü, Laser Optics (Higher Education Press, 2003) (in Chinese).

McGowan, C.

C. McGowan, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Femtosecond pulses tunable beyond 4 μm from a KTA-based optical parametric oscillator,” Opt. Commun. 134, 186-190(1997).
[CrossRef]

Meyn, J. P.

A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
[CrossRef]

Miao, J.

J. Miao, B. Wang, J. Peng, H. Tan, and H. Bian, “Highly stable and efficient KTP-based intracavity optical parametric oscillator with a diode-pumped passively Q-switched laser,” Appl. Phys. B 88, 193-196 (2007).
[CrossRef]

Miller, A.

Ostroumov, V. G.

A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
[CrossRef]

Papuchon, M.

Peng, J.

J. Miao, B. Wang, J. Peng, H. Tan, and H. Bian, “Highly stable and efficient KTP-based intracavity optical parametric oscillator with a diode-pumped passively Q-switched laser,” Appl. Phys. B 88, 193-196 (2007).
[CrossRef]

Pocholle, J.-P.

Raffy, J.

Reid, D. T.

C. McGowan, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Femtosecond pulses tunable beyond 4 μm from a KTA-based optical parametric oscillator,” Opt. Commun. 134, 186-190(1997).
[CrossRef]

Shcherbarkov, I. A.

A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
[CrossRef]

Sibbett, W.

C. McGowan, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Femtosecond pulses tunable beyond 4 μm from a KTA-based optical parametric oscillator,” Opt. Commun. 134, 186-190(1997).
[CrossRef]

Sun, L.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Tan, H.

J. Miao, B. Wang, J. Peng, H. Tan, and H. Bian, “Highly stable and efficient KTP-based intracavity optical parametric oscillator with a diode-pumped passively Q-switched laser,” Appl. Phys. B 88, 193-196 (2007).
[CrossRef]

van Driel, H. M.

Vanherzeele, H.

J. D. Bierlein, H. Vanherzeele, and A. A. Ballman, “Linear and nonlinear optical properties of flux-grown KTiOAsO4,” Appl. Phys. Lett. 54, 783-785 (1989).
[CrossRef]

Victori, S.

A. Dubois, S. Victori, T. Lepine, P. Georges, and A. Brun, “High-repetition-rate eyesafe intracavity optical parametric oscillator,” Appl. Phys. B 67, 181-183 (1998).
[CrossRef]

Wachulak, P.

W. Zendzian, J. K. Jabczynski, P. Wachulak, and J. Kwiatkowski, “High-repetition-rate, intracavity-pumped KTP OPO at 1572 nm,” Appl. Phys. B 80, 329-332 (2005).
[CrossRef]

Wang, B.

J. Miao, B. Wang, J. Peng, H. Tan, and H. Bian, “Highly stable and efficient KTP-based intracavity optical parametric oscillator with a diode-pumped passively Q-switched laser,” Appl. Phys. B 88, 193-196 (2007).
[CrossRef]

Wang, Q.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Wong, H. F.

Wu, R. F.

Xiao, G.

G. Xiao, M. Bass, and M. Acharekar, “Passively Q-switched solid-state lasers with intracavity optical parametric oscillators,” IEEE J. Quantum Electron. 34, 2241-2245 (1998).
[CrossRef]

Xie, W. J.

Yashkir, Y.

Zagumennyi, A. I.

A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
[CrossRef]

Zendzian, W.

W. Zendzian, J. K. Jabczynski, P. Wachulak, and J. Kwiatkowski, “High-repetition-rate, intracavity-pumped KTP OPO at 1572 nm,” Appl. Phys. B 80, 329-332 (2005).
[CrossRef]

W. Zendzian, J. K. Jabczynski, and J. Kwiatkowski, “Intracavity optical parametric oscillator at 1572-nm wavelength pumped by passively Q-switched diode-pumped Nd:YAG laser,” Appl. Phys. B 76, 355-358 (2003).
[CrossRef]

Zhang, Q.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Zhang, S.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Zhang, X.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Zhao, S.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (4)

W. Zendzian, J. K. Jabczynski, P. Wachulak, and J. Kwiatkowski, “High-repetition-rate, intracavity-pumped KTP OPO at 1572 nm,” Appl. Phys. B 80, 329-332 (2005).
[CrossRef]

A. Dubois, S. Victori, T. Lepine, P. Georges, and A. Brun, “High-repetition-rate eyesafe intracavity optical parametric oscillator,” Appl. Phys. B 67, 181-183 (1998).
[CrossRef]

J. Miao, B. Wang, J. Peng, H. Tan, and H. Bian, “Highly stable and efficient KTP-based intracavity optical parametric oscillator with a diode-pumped passively Q-switched laser,” Appl. Phys. B 88, 193-196 (2007).
[CrossRef]

W. Zendzian, J. K. Jabczynski, and J. Kwiatkowski, “Intracavity optical parametric oscillator at 1572-nm wavelength pumped by passively Q-switched diode-pumped Nd:YAG laser,” Appl. Phys. B 76, 355-358 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

J. D. Bierlein, H. Vanherzeele, and A. A. Ballman, “Linear and nonlinear optical properties of flux-grown KTiOAsO4,” Appl. Phys. Lett. 54, 783-785 (1989).
[CrossRef]

W. R. Bosenberg, L. K. Cheng, and J. D. Bierlein, “Optical parametric frequency conversion properties of KTiOAsO4,” Appl. Phys. Lett. 65, 2765-2767 (1994).
[CrossRef]

IEEE J. Quantum Electron. (3)

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

J. Liu and D. Kim, “Optimization of intracavity doubled passively Q-switched solid-state laser,” IEEE J. Quantum Electron. 35, 1724-1730 (1999).
[CrossRef]

G. Xiao, M. Bass, and M. Acharekar, “Passively Q-switched solid-state lasers with intracavity optical parametric oscillators,” IEEE J. Quantum Electron. 34, 2241-2245 (1998).
[CrossRef]

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

Opt. Commun. (1)

C. McGowan, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Femtosecond pulses tunable beyond 4 μm from a KTA-based optical parametric oscillator,” Opt. Commun. 134, 186-190(1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Sov. J. Quantum Electron. (1)

A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbarkov, T. Jensen, J. P. Meyn, and G. Huber, “The Nd:GdVO4 crystal: a new material for diode-pumped lasers,” Sov. J. Quantum Electron. 22, 1071-1072 (1992).
[CrossRef]

Other (1)

B. Lü, Laser Optics (Higher Education Press, 2003) (in Chinese).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup of the KTA-IOPO. LDA, laser diode array; CO, coupling optics; S1, input mirror; LC, laser crystal; SA, Cr:YAG saturable absorber; NLC, KTA crystal; S2, output coupler; S3, OPO input mirror.

Fig. 2
Fig. 2

Equivalent cavity of the KTA-based IOPO with a thermally induced lens.

Fig. 3
Fig. 3

Variations of the product of G1 and G2 (a) and the mode beam radius in the active medium (b) as a function of the incident diode pump power with different cavity lengths.

Fig. 4
Fig. 4

Average output power of the IOPO with respect to the incident diode pump power.

Fig. 5
Fig. 5

Synchronous temporal profiles of the fundamental and signal pulses after the OPO began to oscillate.

Fig. 6
Fig. 6

Pulse repetition rate of the KTA-IOPO with respect to the incident diode pump power.

Fig. 7
Fig. 7

Output pulse energy of the signal and idler radiation as a function of the incident diode pump power.

Equations (7)

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

( a b c d ) = M 5 M kta M 4 M caf M 3 M cr M 2 M f M 1 ,
M f = ( 1 0 1 f 1 ) , M i = ( 1 L i 0 1 ) , i = 1 , 2 , 3 , 4 , 5 ,
M kta = ( 1 L kta n kta 0 1 ) , M cr = ( 1 L cr n cr 0 1 ) , M caf = ( 1 0 n caf 1 ρ 3 n caf ) ( 1 L caf n caf 0 1 ) ( 1 0 0 1 n caf ) .
1 f = ξ P abs 2 π K c ω p 2 [ d n / d T + ( n 1 ) ( 1 + ν ) α T ] ,
G 1 = a b / ρ 1 , G 2 = d b / ρ 2 ,
ω Nd = ω 1 [ ( 1 l ρ 1 ) 2 + ( λ l π ω 1 2 ) ] 1 / 2 ,
ω 1 2 = λ b π [ G 2 G 1 ( 1 G 1 G 2 ) ] 1 / 2 .

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