OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 21 — Oct. 13, 2008
  • pp: 16382–16389
« Show journal navigation

Picosecond master-oscillator, power-amplifier system based on a mixed vanadate phase conjugate bounce amplifier

Naoki Shiba, Yasuhito Morimoto, Kenji Furuki, Yuichi Tanaka, Kouji Nawata, Masahito Okida, and Takashige Omatsu  »View Author Affiliations


Optics Express, Vol. 16, Issue 21, pp. 16382-16389 (2008)
http://dx.doi.org/10.1364/OE.16.016382


View Full Text Article

Acrobat PDF (162 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate a high average power ~4 ps output from a phase conjugate laser system based on a diode-side-pumped Nd:Gd0.6Y0.4VO4 bounce amplifier. An average output power of 16.2 W with a peak power of 210 kW was achieved. A corresponding extraction efficiency of 23% was measured.

© 2008 Optical Society of America

1. Introduction

High average-power picosecond sources have been attracting intense attention for a variety of commercial and scientific applications, such as nonlinear frequency conversion processes, nonlinear microscopy and microfabrication [1

1. G. J. Sphler, R. Paschootta, U. Keller, M. Moser, M. J. P. Dymott, D. Kopf, J. Meyer, K. J. Weingarten, J. D. Kmetec, J. Alexander, and G. Truong, “Diode-pumped passively mode-locked Nd:YAG laser with 10-W average power in a diffraction-limited beam,” Opt. Lett. 24, 528–530 (1999). [CrossRef]

, 2

2. U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, IEEE J. Quantum Electron 2, 435 (1996). [CrossRef]

].

Nd-doped vanadate bounce amplifiers, wherein an intense inversion population can be produced below the pump face, have been successfully demonstrated to generate high average-power picosecond outputs without a conventional regenerative amplifier configuration at ultra-high efficiencies [3

3. J. E. Bernard and A. J. Alcock, “High-efficiency diode-pumped Nd:YVO4 slab laser,” Opt. Lett. 18, 968–970 (1993). [CrossRef] [PubMed]

-6

6. K. Nawata, Y. Ojima, M. Okida, T. Ogawa, and T. Omastu, “Power scaling of picosecond Nd:YVO4 maste-roscillator power amplifier with a phase-conjugate mirror,” Opt. Express 14, 10657–10662 (2006). [CrossRef] [PubMed]

]. To date, Nawata et al. have demonstrated highly intense, high-average-power, near-diffraction-limited picosecond output from a Nd-doped yttrium vanadate (Nd:YVO4) bounce amplifier with a photorefractive phase conjugate mirror in combination with a pulse selector formed by a RbTiPO4 (RTP) Pockels cell [7

7. K. Nawata, M. Okida, K. Furuki, and T. Omastu, “MW ps pulse generation at sub-MHz repetition rates from a phase conjugate Nd:YVO4 bounce amplifier,” Opt. Express 15, 9123–9128 (2007). [CrossRef] [PubMed]

]. A maximum output power of >25 W with a peak power of >5 MW was achieved at a pulse repetition frequency of 0.3-1 MHz. The pulse width of the output from the system was measured to be as much as ~8 ps, and was limited by the finite gain bandwidth of the Nd:YVO4 amplifier.

Mixed vanadate technology, in which, for example, a fraction of Gd ions in the gadolinium vanadate (GdVO4) are substituted by Y ions, allows for the customization of the fluorescence spectrum, thereby yielding adjustable laser parameters such as gain bandwidth and stimulated emission cross-section [8

8. J. Liu, Z. Wang, X. Meng, Z. Shao, B. Ozygus, A. Ding, and H. Weber, “Improvement of passive Qswitching performance reached with a new Nd-doped mixed vanadate crystal Nd:Gd0.64Y0.36VO4,” Opt. Lett 28, 2330–2332 (2003). [CrossRef] [PubMed]

-11

11. J. Liu, X. Meng, Z. Shao, and M. Jiang, “Pulse energy enhancement in passive Q-switching operation with a class of Nd:GdxY1-xVO4 crystals,” Appl. Phys. Lett. 83, 1289 (2003). [CrossRef]

]. Recently, we successfully demonstrated actively and passively Q-switched Nd-doped mixed gadolinium yttrium vanadate (Nd:GdxY1-xVO4) lasers with custom-made pulse repetition frequency and peak power ranges [12. 13]. The Nd-doped mixed vanadates are promising candidates for much shorter picosecond pulse generation, i.e., ~5 ps pulse, at high efficiencies.

In this paper, we demonstrate high average-power sub-5 ps (4 ps) output from a diode-side-pumped phase conjugate Nd:Gd0.6Y0.4VO4 amplifier, for the first time. The maximum average power of 16 W was obtained at a pump power of 70 W. The corresponding peak power of the output was 0.2 MW at the pulse repetition frequency of 20 MHz.

2. Experiments

2.1 Experimental setup

Figure 1 shows the experimental setup used in this study for the phase-conjugate amplifier system. The amplifiers used for the experiment were a-cut, 2 mm×5 mm×20 mm, 1.5at.% Nd-doped Gd-rich mixed vanadate Nd:Gd0.6Y0.4VO4 (Hortek Crystal Co., Ltd) slab and a 1.5at.% Nd-doped GdVO4 slab. The two end faces of the amplifiers were AR coated for a wavelength of 1 µm, and they were wedged to the normal of the pump face to prevent self-lasing within the crystal. A continuous-wave (CW) 808 nm pump diode array output was line-focused by a cylindrical lens CLD (f=12.7 mm) on the pump face of the amplifiers. The maximum pump power was 56 W.

The master laser used was a commercial 20 mW continuous-wave mode-locked Yb-doped fiber laser, having a pulse width of 5.1 ps and a pulse repetition frequency (PRF) of 20 MHz. Its lasing frequency was 1063.5 nm. A polarizing beam splitter (PBS), a Faraday rotator (FR), and a half-wave plate (HWP1) formed an optical isolator to prevent feedback to the master laser. The master laser beam was focused using cylindrical lenses, HCL1 (f=400 mm) and VCL (f=100 mm), so that the master laser beam spatially matched the ellipsoidal gain volume. The amplified master laser beam was retro-reflected, and it backed to the amplifier by 4f imaging optics formed by a prism mirror and a spherical lens L1 (f=100 mm). The external incident angles of the master laser beam and the amplified master laser beam with respect to the pump surface were 15° and 18°, respectively.

After passing through the amplifier twice, the amplified beam was collimated by two cylindrical lenses, VCL (f=100 mm) and HCL2 (f=200 mm), and was directed toward a phase-conjugate mirror based on a Rh:BaTiO3 crystal by imaging optics including two spherical lenses L2 (f=150 mm) and L3 (f=75 mm). The polarization of the amplified beam was rotated using a half-wave plate, HWP, and it lay in the extraordinary plane of the Rh:BaTiO3 crystal to maximize the two-wave mixing gain [14

14. T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a picosecond phase conjugate Nd:YVO4 laser system,” Jpn. J. Appl. Phys. 43, 2515–2518 (2004). [CrossRef]

]. The phase conjugation of the amplified beam was automatically fed back to the amplifier. After passing through the amplifier twice, it was ejected as an output by a PBS.

Fig. 1. Experimental setup of the phase-conjugate amplifier system.

2.2 Experimental results

Figure 2 shows the average output power in the Nd:Gd0.6Y0.4VO4 and Nd:GdVO4 amplifiers as a function of the pump power. Below the pump power of 30W, the Nd:Gd0.6Y0.4VO4 showed low output power when compared to Nd:GdVO4. Above the pump power of 30W, the Nd:Gd0.6Y0.4VO4 exhibited almost the same slope efficiency as that of Nd:GdVO4. The output power in the Nd:Gd0.6Y0.4VO4 and Nd:GdVO4 amplifiers reached 7.2 W and 8.5 W at the maximum pump level (56 W), respectively. As shown in Fig. 3, the output of the Nd:GdVO4 had a pulse duration of 6.3 ps, while the master laser had a pulse-duration of 5.1 ps. We assumed Gaussian-pulse shapes (Fourier transform product =0.441) for all autocorrelations, and thus, the corresponding Fourier-transform limit was 2.4ps. Pulse broadening was induced by the narrowing of the lasing frequency (Fig. 4) due to the finite gain-band of the Nd:GdVO4 [15

15. H. Jiang, H. Zhang, J. Wang, H. Xia, X. Hu, B. Teng, and C. Zhang, “Optical and laser properties of Nd:GdVO4 crystal,” Opt. Commun. 198, 447–452 (2001). [CrossRef]

].

On the other hand, the output in the Nd:Gd0.6Y0.4VO4 had almost the same spectral bandwidth (0.7 nm) as that of the master laser output, though its center frequency was shifted towards the red so that it matched spectrally the gain-band of the Nd:Gd0.6Y0.4VO4. The pulse-duration of the output was estimated to be 4.1 ps.

Fig. 2. Average output power in the Nd:GdVO4 and Nd:Gd0.6Y0.4VO4 amplifiers as a function of the pump power.
Fig. 3. The intensity autocorrelation trace of the output.
Fig. 4. The wavelength trace of the output.

The peak power estimated by using the measured pulse width of the output as a function of pump power is shown in Fig. 5. The maximum peak power of the output in Nd:Gd0.6Y0.4VO4 reached 87 kW, which was 1.2-times higher than that in Nd:GdVO4. The mixed vanadate is capable of generating higher peak power picosecond pulses when compared to conventional Nd:GdVO4.

Fig. 5. Estimated peak power with the measured pulse width of the outputs as a function of pump power.

2.3 Power scalability of Nd:Gd0.6Y0.4VO4 amplifier

Fig. 6. Output power as a function of pump power under three-bar diode stack pumping.
Fig. 7. Intensity autocorrelation trace of the output under three-bar diode stack pumping.

The output also exhibited a near Gaussian profile, as shown in Fig. 8, and the corresponding beam-propagation factors, M 2 x and M 2 y, were <1.4, and <1.3, respectively.

Fig. 8. The spatial profile of the output beam under three-bar diode stack pumping.

3. Discussion

The pulse width τ of the down-chirped pulse transmitted in the positive dispersive material is given by [16

16. J.-C. Diels and W. Rudolph, Ultrashort laser pulse phenomena : Fundamentals, Techniques, and Applications on a Femtosecond Time Scale (Academic, San Diego, Calif., 1996), 32–38.

]

τ=τ0[(1+2·Δωβτ0)2+(4ln2)2(βτ02)2]
(1),

where τ 0 is the pulse width of the incident pulse, Δω is the spectral bandwidth of the incident pulse, β is the second-order phase dispersion, respectively. The β of the 4 mm thick BaTiO3 determined from the Sellmeier equation [17

17. K. Buse, S. Riehemann, S. L. Oheide, H. Hesse, F. Mersch, and E. Kraetzig, “Refractive indices of single domain BaTiO3 for different wavelengths and temperatures,” Phys. Stat. Sol. (a) 135, K87–K89 (1993). [CrossRef]

], then, is estimated to be ~-1×10-25 s2. Assume that the master laser pulse with the pulse width of 5.1 ps and spectral bandwidth of 0.7 nm shows the negative frequency chirp. After passing though the BaTiO3 crystal, the master laser pulse will be compressed. And then, its pulse width will be expected to be ~4.5 ps in accordance with Eq. (1). Therefore, the unexpected pulse narrowing effect might be induced by that the negative frequency chirp of the master laser was compensated by the positive group velocity dispersion in the system including phase conjugate mirror formed by the BaTiO3 crystal. To understand fully the pulse narrowing effect observed in the output, frequency-resolved pulse analysis such as FROG will be needed.

Table 1. Physical parameters for numerical simulation.

table-icon
View This Table
Fig. 9. Numerically simulated model of the four pass amplifier.

Since the saturation gain intensity (4.8 kW/cm2) of the Nd:Gd0.6Y0.4VO4 amplifier was approximately higher by a factor of two than that of Nd:GdVO4 (2.0 kW/cm2), the Nd:Gd0.6Y0.4VO4 exhibited low output power at low pump level when compared to Nd:GdVO4. There is good agreement between the simulations and the experiments. We also simulated the output power under three-diode stack pumping, and obtained good consistency with experiments (Fig. 6).

4. Conclusions

We have demonstrated a picosecond master-oscillator, power-amplifier system based on a diode-side-pumped phase conjugate mixed gadolinium yttrium vanadate Nd:Gd0.6Y0.4VO4 amplifier, for the first time. The maximum average power of 16.2 W was achieved at a pump power of 70 W, and a corresponding peak power of >200 kW was estimated. The output also showed a pulse-duration of 4 ps as well as near-diffraction-limited spatial form. We believe that the mixed vanadate is promising and has great potential to produce higher peak power picosecond pulses in comparison with conventional vanadate crystals. This system, capable of achieving high quality and very intense sub-5 ps pulses, has potential for applications in various fields, including laser microfabrication and nonlinear optics.

Acknowledgments

The authors acknowledge support from a Scientific Research Grant-in-Aid (19018007, 18360031) from the Ministry of Education, Science and Culture of Japan and the Japan Society for the Promotion of Science.

References and links

1.

G. J. Sphler, R. Paschootta, U. Keller, M. Moser, M. J. P. Dymott, D. Kopf, J. Meyer, K. J. Weingarten, J. D. Kmetec, J. Alexander, and G. Truong, “Diode-pumped passively mode-locked Nd:YAG laser with 10-W average power in a diffraction-limited beam,” Opt. Lett. 24, 528–530 (1999). [CrossRef]

2.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, IEEE J. Quantum Electron 2, 435 (1996). [CrossRef]

3.

J. E. Bernard and A. J. Alcock, “High-efficiency diode-pumped Nd:YVO4 slab laser,” Opt. Lett. 18, 968–970 (1993). [CrossRef] [PubMed]

4.

M. J. Damzen, M. Trew, E. Ross, and G. J. Crofts, “Continuous-wave Nd:YVO4 grazing-incidence laser with 22.5 W output power and 64 % conversion efficiency,” Opt. Commun. 196, 237–241 (2001). [CrossRef]

5.

A. Agnesi, L. Carra, F. Pirzio, G. Reali, A. Tomaselli, D. Scarpa, and C. Vacchi, “Amplification of a low-power picosecond Nd:YVO4 laser by a diode-laser side-pumped grazing-incidence slab amplifier,” IEEE J. Quantum Electron 42, 772–776 (2006). [CrossRef]

6.

K. Nawata, Y. Ojima, M. Okida, T. Ogawa, and T. Omastu, “Power scaling of picosecond Nd:YVO4 maste-roscillator power amplifier with a phase-conjugate mirror,” Opt. Express 14, 10657–10662 (2006). [CrossRef] [PubMed]

7.

K. Nawata, M. Okida, K. Furuki, and T. Omastu, “MW ps pulse generation at sub-MHz repetition rates from a phase conjugate Nd:YVO4 bounce amplifier,” Opt. Express 15, 9123–9128 (2007). [CrossRef] [PubMed]

8.

J. Liu, Z. Wang, X. Meng, Z. Shao, B. Ozygus, A. Ding, and H. Weber, “Improvement of passive Qswitching performance reached with a new Nd-doped mixed vanadate crystal Nd:Gd0.64Y0.36VO4,” Opt. Lett 28, 2330–2332 (2003). [CrossRef] [PubMed]

9.

H. Zhang, J. Wang, C. Wang, L. Zhu, X. Meng, M. Jiang, and Y. T. Chow, “A comparative study of crystal growth and laser properties of Nd:YVO4, Nd:GdVO4 and Nd:GdxLa1-xVO4 (x=0.80, 0.60, 0.45) crystals,” Opt. Mater. 23, 449–454 (2003). [CrossRef]

10.

Y. F. Chen, M. L. Ku, L. Y. Tsai, and Y. C. Chen, “Diode-pumped passively Q-switched picosecond Nd:GDxY1-xVO4 self-stimulated Raman laser,” Opt. Lett. 29, 2279–2281 (2004). [CrossRef] [PubMed]

11.

J. Liu, X. Meng, Z. Shao, and M. Jiang, “Pulse energy enhancement in passive Q-switching operation with a class of Nd:GdxY1-xVO4 crystals,” Appl. Phys. Lett. 83, 1289 (2003). [CrossRef]

12.

T. Omatsu, M. Okida, A. Minassian, and M. J. Damzen, “High repetition rate Q-switching performance in transversely diode-pumped Nd doped mixed gadolinium yttrium vanadate bounce laser,” Opt. Express 14, 2727–2734 (2006). [CrossRef] [PubMed]

13.

T. Omatsu, M. Okida, A. Minassian, and M. J. Damzen, “Passive Q-switching of a diode-side-pumped Nd-doped mixed gadolinium yttrium vanadate bounce laser,” Appl. Phys. 90, 445–449 (2008). [CrossRef]

14.

T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a picosecond phase conjugate Nd:YVO4 laser system,” Jpn. J. Appl. Phys. 43, 2515–2518 (2004). [CrossRef]

15.

H. Jiang, H. Zhang, J. Wang, H. Xia, X. Hu, B. Teng, and C. Zhang, “Optical and laser properties of Nd:GdVO4 crystal,” Opt. Commun. 198, 447–452 (2001). [CrossRef]

16.

J.-C. Diels and W. Rudolph, Ultrashort laser pulse phenomena : Fundamentals, Techniques, and Applications on a Femtosecond Time Scale (Academic, San Diego, Calif., 1996), 32–38.

17.

K. Buse, S. Riehemann, S. L. Oheide, H. Hesse, F. Mersch, and E. Kraetzig, “Refractive indices of single domain BaTiO3 for different wavelengths and temperatures,” Phys. Stat. Sol. (a) 135, K87–K89 (1993). [CrossRef]

18.

Y. Ojima, K. Nawata, and T. Omatsu, “Over 10-watt picosecond diffraction-limited output from a Nd:YVO4 slab amplifier with a phase conjugate mirror,” Opt. Express 13, 8993–8998 (2005) [CrossRef] [PubMed]

OCIS Codes
(140.3280) Lasers and laser optics : Laser amplifiers
(140.3580) Lasers and laser optics : Lasers, solid-state
(190.5040) Nonlinear optics : Phase conjugation
(320.5390) Ultrafast optics : Picosecond phenomena

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 30, 2008
Revised Manuscript: August 25, 2008
Manuscript Accepted: August 25, 2008
Published: September 29, 2008

Citation
Naoki Shiba, Yasuhito Morimoto, Kenji Furuki, Yuichi Tanaka, Kouji Nawata, Masahito Okida, and Takashige Omatsu, "Picosecond master-oscillator, power-amplifier system based on a mixed vanadate phase conjugate bounce amplifier," Opt. Express 16, 16382-16389 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16382


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. J. Sphler, R. Paschootta, U. Keller, M. Moser, M. J. P. Dymott, D. Kopf, J. Meyer, K. J. Weingarten, J. D. Kmetec, J. Alexander, and G. Truong, "Diode-pumped passively mode-locked Nd:YAG laser with 10-W average power in a diffraction-limited beam," Opt. Lett. 24, 528-530 (1999). [CrossRef]
  2. U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, IEEE J. Quantum Electron 2, 435 (1996). [CrossRef]
  3. J. E. Bernard and A. J. Alcock, "High-efficiency diode-pumped Nd:YVO4 slab laser," Opt. Lett. 18, 968-970 (1993). [CrossRef] [PubMed]
  4. M. J. Damzen, M. Trew, E. Ross, and G. J. Crofts, "Continuous-wave Nd:YVO4 grazing-incidence laser with 22.5 W output power and 64% conversion efficiency," Opt. Commun. 196, 237-241 (2001). [CrossRef]
  5. A. Agnesi, L. Carra, F. Pirzio, G. Reali, A. Tomaselli, D. Scarpa, and C. Vacchi, "Amplification of a low-power picosecond Nd:YVO4 laser by a diode-laser side-pumped grazing-incidence slab amplifier," IEEE J. Quantum Electron 42, 772-776 (2006). [CrossRef]
  6. K. Nawata, Y. Ojima, M. Okida, T. Ogawa, and T. Omastu, "Power scaling of picosecond Nd:YVO4 master-oscillator power amplifier with a phase-conjugate mirror," Opt. Express 14, 10657-10662 (2006). [CrossRef] [PubMed]
  7. K. Nawata, M. Okida, K. Furuki, and T. Omastu, "MW ps pulse generation at sub-MHz repetition rates from a phase conjugate Nd:YVO4 bounce amplifier," Opt. Express 15, 9123-9128 (2007). [CrossRef] [PubMed]
  8. J. Liu, Z. Wang, X. Meng, Z. Shao, B. Ozygus, A. Ding, and H. Weber, "Improvement of passive Q-switching performance reached with a new Nd-doped mixed vanadate crystal Nd:Gd0.64Y0.36VO4," Opt. Lett 28, 2330-2332 (2003). [CrossRef] [PubMed]
  9. H. Zhang, J. Wang, C. Wang, L. Zhu, X. Meng, M. Jiang, and Y. T. Chow, "A comparative study of crystal growth and laser properties of Nd:YVO4, Nd:GdVO4 and Nd:GdxLa1-xVO4 (x = 0.80, 0.60, 0.45) crystals," Opt. Mater. 23, 449-454 (2003). [CrossRef]
  10. Y. F. Chen, M. L. Ku, L. Y. Tsai, and Y. C. Chen, "Diode-pumped passively Q-switched picosecond Nd:GDxY1-xVO4 self-stimulated Raman laser," Opt. Lett. 29, 2279-2281 (2004). [CrossRef] [PubMed]
  11. J. Liu, X. Meng, Z. Shao, and M. Jiang, "Pulse energy enhancement in passive Q-switching operation with a class of Nd:GdxY1-xVO4 crystals," Appl. Phys. Lett. 83, 1289 (2003). [CrossRef]
  12. T. Omatsu, M. Okida, A. Minassian, and M. J. Damzen, "High repetition rate Q-switching performance in transversely diode-pumped Nd doped mixed gadolinium yttrium vanadate bounce laser," Opt. Express 14, 2727-2734 (2006). [CrossRef] [PubMed]
  13. T. Omatsu, M. Okida, A. Minassian, and M. J. Damzen, "Passive Q-switching of a diode-side-pumped Nd-doped mixed gadolinium yttrium vanadate bounce laser," Appl. Phys. 90, 445-449 (2008). [CrossRef]
  14. T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, "Characterization of a picosecond phase conjugate Nd:YVO4 laser system," Jpn. J. Appl. Phys. 43, 2515-2518 (2004). [CrossRef]
  15. H. Jiang, H. Zhang, J. Wang, H. Xia, X. Hu, B. Teng, and C. Zhang, "Optical and laser properties of Nd:GdVO4 crystal," Opt. Commun. 198, 447-452 (2001). [CrossRef]
  16. J.-C. Diels and W. Rudolph, Ultrashort laser pulse phenomena : Fundamentals, Techniques, and Applications on a Femtosecond Time Scale (Academic, San Diego, Calif., 1996), 32-38.
  17. K. Buse, S. Riehemann, S. L. Oheide, H. Hesse, F. Mersch, and E. Kraetzig, "Refractive indices of single domain BaTiO3 for different wavelengths and temperatures," Phys. Stat. Sol.(a) 135, K87-K89 (1993). [CrossRef]
  18. Y. Ojima, K. Nawata, and T. Omatsu, "Over 10-watt picosecond diffraction-limited output from a Nd:YVO4 slab amplifier with a phase conjugate mirror," Opt. Express 13, 8993-8998 (2005) [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited