Abstract

We demonstrate a stable Q-switched single-longitudinal-mode (SLM) Nd:YAG laser using a volume Bragg grating as the output coupler. The reflective volume Bragg grating, serving as a longitudinal selector and passive frequency stabilizer, effectively eliminates the mode hopping effect of the laser. The maximum output energy of the SLM obtained from the current experimental setup is 18.5mJ. The maximum separation of frequencies is significantly less than the longitudinal mode separation, indicating that a stable SLM laser is achieved.

© 2011 Optical Society of America

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  1. Y. C. Chen, S. Q. Li, K. K. Lee, and S. H. Zhou, “Self-stabilized single-longitudinal-mode operation in a self-Q-switched Cr, Nd:YAG laser,” Opt. Lett. 18, 1418–1419 (1993).
    [CrossRef] [PubMed]
  2. B. Song, W. Zhao, D. Ren, Y. Qu, H. Zhang, L. Qian, and X. Hu, “Passively Q-switched laser with single longitudinal mode based on the frequency selection of grating and F-P etalon in twisted-mode folded cavity,” Chin. Opt. Lett. 7, 805–808(2009).
    [CrossRef]
  3. C. T. Wu, Y. L. Ju, and Z. G. Wang, “Diode-pumped single frequency Tm:YAG laser at room temperature,” Laser Phys. Lett. 5, 793–796 (2008).
    [CrossRef]
  4. Y. Y. Lin, S. Y. Chen, A. C. Chiang, R. Y. Tu, and Y. C. Huang, “Single-longitudinal-mode, tunable dualwavelength CW Nd:YVO4 laser,” Opt. Express 14, 5329–5334 (2006).
    [CrossRef] [PubMed]
  5. J. E. Bernard, V. D. Lokhnygin, and A. J. Alcock, “Grating-tuned, single-longitudinal-mode, diode-pumped Nd:YVO4laser,” Opt. Lett. 18, 2020–2021 (1993).
    [CrossRef] [PubMed]
  6. T. Chung, A. Rapaport, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror,” Opt. Lett. 31, 229–231 (2006).
    [CrossRef] [PubMed]
  7. I. Ciapurin, V. Smirnov, G. Venus, L. Glebova, E. Rotari, and L. Glebov, “High-power laser beam control by PTR Bragg gratings,” Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuP51.
  8. N. Vorobiev, L. Glebov, and V. Smirnov, “Single-frequency-mode Q-switched Nd:YAG and Er:glass lasers controlled by volume Bragg gratings,” Opt. Express 16, 9199–9204 (2008).
    [CrossRef] [PubMed]
  9. N. Vorobiev, V. Smirnov, and L. Glebov, “Single-frequency-mode Q-switched Nd:YAG laser controlled by volume Bragg gratings,” Proc. SPIE 6952, 69520G (2008).
    [CrossRef]
  10. B. Jacobsson, “Valdas Pasiskevicius, Fredrik Laurell, Single- longitudinal-mode Nd-laser with a Bragg-grating Fabry-Perot cavity,” Opt. Express 14, 9284–9292 (2006).
    [CrossRef] [PubMed]
  11. M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
    [PubMed]
  12. B. L. Volodin, S. V. Dolgy, and E. D. Melnik, “Wavelength stabilization and spectrum narrowing of high-power multimode laser diodes and arrays by use of volume Bragg gratings,” Opt. Lett. 29, 1891–1893 (2004).
    [CrossRef] [PubMed]
  13. B. Song, W. Zhao, D. Ren, Y. Qu, and X. Hu, “Smooth-pulse of the single longitudinal mode obtained with twisted mode and passive Q-switch,” J. Optoelectron. Laser 19, 1328–1331(2008).
    [CrossRef]
  14. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  15. I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of Gaussian beam diffraction on volume Bragg grating in PTR glass,” Proc. SPIE 5742, 183–194 (2005).
    [CrossRef]
  16. B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
    [CrossRef]

2009 (1)

2008 (5)

C. T. Wu, Y. L. Ju, and Z. G. Wang, “Diode-pumped single frequency Tm:YAG laser at room temperature,” Laser Phys. Lett. 5, 793–796 (2008).
[CrossRef]

N. Vorobiev, L. Glebov, and V. Smirnov, “Single-frequency-mode Q-switched Nd:YAG and Er:glass lasers controlled by volume Bragg gratings,” Opt. Express 16, 9199–9204 (2008).
[CrossRef] [PubMed]

N. Vorobiev, V. Smirnov, and L. Glebov, “Single-frequency-mode Q-switched Nd:YAG laser controlled by volume Bragg gratings,” Proc. SPIE 6952, 69520G (2008).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, and X. Hu, “Smooth-pulse of the single longitudinal mode obtained with twisted mode and passive Q-switch,” J. Optoelectron. Laser 19, 1328–1331(2008).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

2006 (3)

2005 (1)

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of Gaussian beam diffraction on volume Bragg grating in PTR glass,” Proc. SPIE 5742, 183–194 (2005).
[CrossRef]

2004 (1)

1993 (2)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Alcock, A. J.

Bass, M.

T. Chung, A. Rapaport, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror,” Opt. Lett. 31, 229–231 (2006).
[CrossRef] [PubMed]

M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
[PubMed]

Bernard, J. E.

Chen, S. Y.

Chen, Y.

M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
[PubMed]

Chen, Y. C.

Chiang, A. C.

Chung, T.

Chung, T. Y.

M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
[PubMed]

Ciapurin, I.

I. Ciapurin, V. Smirnov, G. Venus, L. Glebova, E. Rotari, and L. Glebov, “High-power laser beam control by PTR Bragg gratings,” Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuP51.

Ciapurin, I. V.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of Gaussian beam diffraction on volume Bragg grating in PTR glass,” Proc. SPIE 5742, 183–194 (2005).
[CrossRef]

Dolgy, S. V.

Glebov, L.

N. Vorobiev, L. Glebov, and V. Smirnov, “Single-frequency-mode Q-switched Nd:YAG and Er:glass lasers controlled by volume Bragg gratings,” Opt. Express 16, 9199–9204 (2008).
[CrossRef] [PubMed]

N. Vorobiev, V. Smirnov, and L. Glebov, “Single-frequency-mode Q-switched Nd:YAG laser controlled by volume Bragg gratings,” Proc. SPIE 6952, 69520G (2008).
[CrossRef]

T. Chung, A. Rapaport, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror,” Opt. Lett. 31, 229–231 (2006).
[CrossRef] [PubMed]

I. Ciapurin, V. Smirnov, G. Venus, L. Glebova, E. Rotari, and L. Glebov, “High-power laser beam control by PTR Bragg gratings,” Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuP51.

M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
[PubMed]

Glebov, L. B.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of Gaussian beam diffraction on volume Bragg grating in PTR glass,” Proc. SPIE 5742, 183–194 (2005).
[CrossRef]

Glebova, L.

I. Ciapurin, V. Smirnov, G. Venus, L. Glebova, E. Rotari, and L. Glebov, “High-power laser beam control by PTR Bragg gratings,” Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuP51.

Hemmer, M.

M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
[PubMed]

Hu, X.

B. Song, W. Zhao, D. Ren, Y. Qu, H. Zhang, L. Qian, and X. Hu, “Passively Q-switched laser with single longitudinal mode based on the frequency selection of grating and F-P etalon in twisted-mode folded cavity,” Chin. Opt. Lett. 7, 805–808(2009).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, and X. Hu, “Smooth-pulse of the single longitudinal mode obtained with twisted mode and passive Q-switch,” J. Optoelectron. Laser 19, 1328–1331(2008).
[CrossRef]

Huang, Y. C.

Jacobsson, B.

Ju, Y. L.

C. T. Wu, Y. L. Ju, and Z. G. Wang, “Diode-pumped single frequency Tm:YAG laser at room temperature,” Laser Phys. Lett. 5, 793–796 (2008).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Lee, K. K.

Li, S. Q.

Lin, Y. Y.

Lokhnygin, V. D.

Melnik, E. D.

Mo, S.

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

Qian, L.

Qu, Y.

B. Song, W. Zhao, D. Ren, Y. Qu, H. Zhang, L. Qian, and X. Hu, “Passively Q-switched laser with single longitudinal mode based on the frequency selection of grating and F-P etalon in twisted-mode folded cavity,” Chin. Opt. Lett. 7, 805–808(2009).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, and X. Hu, “Smooth-pulse of the single longitudinal mode obtained with twisted mode and passive Q-switch,” J. Optoelectron. Laser 19, 1328–1331(2008).
[CrossRef]

Rapaport, A.

Ren, D.

B. Song, W. Zhao, D. Ren, Y. Qu, H. Zhang, L. Qian, and X. Hu, “Passively Q-switched laser with single longitudinal mode based on the frequency selection of grating and F-P etalon in twisted-mode folded cavity,” Chin. Opt. Lett. 7, 805–808(2009).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, and X. Hu, “Smooth-pulse of the single longitudinal mode obtained with twisted mode and passive Q-switch,” J. Optoelectron. Laser 19, 1328–1331(2008).
[CrossRef]

Richardson, M.

T. Chung, A. Rapaport, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror,” Opt. Lett. 31, 229–231 (2006).
[CrossRef] [PubMed]

M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
[PubMed]

Rotari, E.

I. Ciapurin, V. Smirnov, G. Venus, L. Glebova, E. Rotari, and L. Glebov, “High-power laser beam control by PTR Bragg gratings,” Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuP51.

Smirnov, V.

N. Vorobiev, V. Smirnov, and L. Glebov, “Single-frequency-mode Q-switched Nd:YAG laser controlled by volume Bragg gratings,” Proc. SPIE 6952, 69520G (2008).
[CrossRef]

N. Vorobiev, L. Glebov, and V. Smirnov, “Single-frequency-mode Q-switched Nd:YAG and Er:glass lasers controlled by volume Bragg gratings,” Opt. Express 16, 9199–9204 (2008).
[CrossRef] [PubMed]

T. Chung, A. Rapaport, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror,” Opt. Lett. 31, 229–231 (2006).
[CrossRef] [PubMed]

I. Ciapurin, V. Smirnov, G. Venus, L. Glebova, E. Rotari, and L. Glebov, “High-power laser beam control by PTR Bragg gratings,” Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuP51.

M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
[PubMed]

Smirnov, V. I.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of Gaussian beam diffraction on volume Bragg grating in PTR glass,” Proc. SPIE 5742, 183–194 (2005).
[CrossRef]

Song, B.

B. Song, W. Zhao, D. Ren, Y. Qu, H. Zhang, L. Qian, and X. Hu, “Passively Q-switched laser with single longitudinal mode based on the frequency selection of grating and F-P etalon in twisted-mode folded cavity,” Chin. Opt. Lett. 7, 805–808(2009).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, and X. Hu, “Smooth-pulse of the single longitudinal mode obtained with twisted mode and passive Q-switch,” J. Optoelectron. Laser 19, 1328–1331(2008).
[CrossRef]

Tu, R. Y.

Venus, G.

I. Ciapurin, V. Smirnov, G. Venus, L. Glebova, E. Rotari, and L. Glebov, “High-power laser beam control by PTR Bragg gratings,” Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuP51.

Volodin, B. L.

Vorobiev, N.

N. Vorobiev, L. Glebov, and V. Smirnov, “Single-frequency-mode Q-switched Nd:YAG and Er:glass lasers controlled by volume Bragg gratings,” Opt. Express 16, 9199–9204 (2008).
[CrossRef] [PubMed]

N. Vorobiev, V. Smirnov, and L. Glebov, “Single-frequency-mode Q-switched Nd:YAG laser controlled by volume Bragg gratings,” Proc. SPIE 6952, 69520G (2008).
[CrossRef]

Wang, Z. G.

C. T. Wu, Y. L. Ju, and Z. G. Wang, “Diode-pumped single frequency Tm:YAG laser at room temperature,” Laser Phys. Lett. 5, 793–796 (2008).
[CrossRef]

Wu, C. T.

C. T. Wu, Y. L. Ju, and Z. G. Wang, “Diode-pumped single frequency Tm:YAG laser at room temperature,” Laser Phys. Lett. 5, 793–796 (2008).
[CrossRef]

Zhang, H.

Zhang, S.

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

Zhao, W.

B. Song, W. Zhao, D. Ren, Y. Qu, H. Zhang, L. Qian, and X. Hu, “Passively Q-switched laser with single longitudinal mode based on the frequency selection of grating and F-P etalon in twisted-mode folded cavity,” Chin. Opt. Lett. 7, 805–808(2009).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

B. Song, W. Zhao, D. Ren, Y. Qu, and X. Hu, “Smooth-pulse of the single longitudinal mode obtained with twisted mode and passive Q-switch,” J. Optoelectron. Laser 19, 1328–1331(2008).
[CrossRef]

Zhou, S. H.

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Chin. Opt. Lett. (1)

Infrared Laser Eng. (1)

B. Song, W. Zhao, D. Ren, Y. Qu, S. Mo, S. Zhang, and X. Hu, “Spectral measurement method for stability of pulse laser frequency,” Infrared Laser Eng. 37, 660–662 (2008).
[CrossRef]

J. Optoelectron. Laser (1)

B. Song, W. Zhao, D. Ren, Y. Qu, and X. Hu, “Smooth-pulse of the single longitudinal mode obtained with twisted mode and passive Q-switch,” J. Optoelectron. Laser 19, 1328–1331(2008).
[CrossRef]

Laser Phys. Lett. (1)

C. T. Wu, Y. L. Ju, and Z. G. Wang, “Diode-pumped single frequency Tm:YAG laser at room temperature,” Laser Phys. Lett. 5, 793–796 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Proc. SPIE (2)

N. Vorobiev, V. Smirnov, and L. Glebov, “Single-frequency-mode Q-switched Nd:YAG laser controlled by volume Bragg gratings,” Proc. SPIE 6952, 69520G (2008).
[CrossRef]

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of Gaussian beam diffraction on volume Bragg grating in PTR glass,” Proc. SPIE 5742, 183–194 (2005).
[CrossRef]

Other (2)

M. Hemmer, T. Y. Chung, Y. Chen, V. Smirnov, L. Glebov, M. Richardson, and M. Bass, “Spectral narrowing in a dual volume Bragg grating Ti:Sapphire oscillator,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper cThE5.
[PubMed]

I. Ciapurin, V. Smirnov, G. Venus, L. Glebova, E. Rotari, and L. Glebov, “High-power laser beam control by PTR Bragg gratings,” Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuP51.

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Figures (8)

Fig. 1
Fig. 1

Efficiency of the RVBG about deviation from Bragg wavelength.

Fig. 2
Fig. 2

Spectral profile of the diffraction efficiency of RVBG.

Fig. 3
Fig. 3

Laser schematic of the SLM Nd:YAG laser. HR, high reflectivity; QWP, quarter-wave plate; P, Polaroid.

Fig. 4
Fig. 4

Structure scheme of the displaying SLM laser.

Fig. 5
Fig. 5

Output energy of the SLM.

Fig. 6
Fig. 6

Time evolution of the passive Q-switched laser pulse.

Fig. 7
Fig. 7

Interference ring of the SLM.

Fig. 8
Fig. 8

Frequency difference of 170 samples captured in the CCD.

Equations (2)

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η = [ 1 + 1 ( λ f 2 Δ λ 2 n av δ n ) 2 sinh 2 ( 2 π n av d δ n λ 2 f ) 2 ( π f d Δ λ λ ) 2 ] 1 ,
Δ ν = ν r Δ r f 2 ,

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