## Transporting continuous quantum variables of individual light pulses |

Optics Express, Vol. 19, Issue 2, pp. 1360-1366 (2011)

http://dx.doi.org/10.1364/OE.19.001360

Acrobat PDF (926 KB)

### Abstract

We experimentally demonstrate transporting continuous quantum variables of individual light pulses at telecommunication wavelengths by using continuous-variable Bell measurements and post-processing displacement techniques. Time-domain pulsed homodyne detectors are used in the Bell measurements and the quantum variables of input light are transported pulse-by-pulse. Fidelity of *F* = 0.57 ± 0.03 is experimentally achieved with the aid of entanglement, which is higher than the bound (*F _{c}* = 0.5) of the classical case in the absence of entanglement.

© 2011 Optical Society of America

## 1. Introduction

1. L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A **49**, 1473–1476 (1994). [CrossRef] [PubMed]

2. S. L. Braunstein and H. J. Kimble, “Teleportation of Continuous Quantum Variables,” Phys. Rev. Lett. **80**, 869–872 (1998). [CrossRef]

3. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. **69**, 2881–2884 (1992). [CrossRef] [PubMed]

4. S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A **61**, 042302 (2000). [CrossRef]

5. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. **67**, 661–663 (1991). [CrossRef] [PubMed]

6. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science **282**, 706–709 (1998). [CrossRef] [PubMed]

8. T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A **67**, 033802 (2003). [CrossRef]

9. X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam,” Phys. Rev. Lett. **88**, 047904 (2002). [CrossRef] [PubMed]

10. J. Mizuno, K. Wakui, A. Furusawa, and M. Sasaki, “Experimental demonstration of entanglement-assisted coding using a two-mode squeezed vacuum state,” Phys. Rev. A **71**, 012304 (2005). [CrossRef]

11. H. Hansen, T. Aichele, C. Hettich, P. Lodahl, A. I. Lvovsky, J. Mlynek, and S. Schiller, “Ultrasensitive pulsed, balanced homodyne detector: application to time-domain quantum measurements,” Opt. Lett. **26**, 1714–1716 (2001). [CrossRef]

12. R. Okubo, M. Hirano, Y. Zhang, and T. Hirano, “Pulse-resolved measurement of quadrature phase amplitudes of squeezed pulse trains at a repetition rate of 76 MHz,” Opt. Lett. **33**, 1458–1460 (2008). [CrossRef] [PubMed]

13. Y. Eto, A. Nonaka, Y. Zhang, and T. Hirano, “Stable generation of quadrature entanglement using a ring interferometer,” Phys. Rev. A **79**, 050302 (2009). [CrossRef]

14. D. T. Smithey, M. Beck, and M. G. Raymer, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. **70**, 1244–1247 (1993). [CrossRef] [PubMed]

*F*= 0.57 ± 0.03 is higher than the 0.5 of the classical case without entanglement.

## 2. Scheme for transporting continuous quantum variables

*x̄*and

*p̂*, which obey the commutation relationship, [

*x̄*,

*p̂*] =

*i*/2.

*a*and

*b*in Fig. 1) is created by combining two squeezed states, which are generated by optical parametric amplification (OPA), on a half beamsplitter (50/50 BS) [6

6. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science **282**, 706–709 (1998). [CrossRef] [PubMed]

*π*/2, the amplitude and phase quadratures of the two output beams can be expressed as

*r*is a squeezing parameter. The following correlations are derived as the features of quadrature entanglement: Maximum correlations are obtained in the limit of infinite squeezing.

*a*, the canonically conjugate quadratures are jointly measured. They can be expressed as

*x*and

_{u}*p*that are random for each light pulse. The instruments used in these CV Bell measurements consist of the 50/50 BS and two PHDs, as shown in Fig. 1. The quadrature component of entangled beam

_{v}*b*in any local oscillator (LO) phase

*ϕ*can be expressed by using the measured values

_{b}*x*and

_{u}*p*as [15

_{v}15. P. van Loock, S. L. Braunstein, and H. J. Kimble, “Broadband teleportation,” Phys. Rev. A **62**, 022309 (2000). [CrossRef]

*X̂*(

_{b}*ϕ*) is defined by

_{b}*x̄*cos

_{b}*ϕ*+

_{b}*p̂*sin

_{b}*ϕ*. This state is identical to the input state,

_{b}*x̄*

_{in}cos

*ϕ*+

_{b}*p̂*

_{in}sin

*ϕ*, for the ideal case (

_{b}*r*

_{1},

*r*

_{2}→ ∞) except for the classical phase-space displacement of

*b*is displaced in phase space by amplitude and phase modulators. We did not displace entangled beam

*b*in the present experiment, but we displaced the measured value,

*X*(

_{b}*ϕ*), for individual light pulses by using the random

_{b}*x*and

_{u}*p*obtained from CV Bell measurements after measuring

_{v}*X̂*(

_{b}*ϕ*) by using PHD. The values after displacement

_{b}*X*

_{out}(

*ϕ*) can be expressed as This posterior displacement can easily be achieved for pulsed-light CV entanglement where each pulse can be regarded as a single mode and the correspondence between entangled pairs is well identified. The quality of transportation is evaluated by using the variance of

_{b}*X*

_{out}(

*ϕ*). When a vacuum state or coherent state is used as the input state, 〈Δ

_{b}^{2}

*X*

_{out}(

*ϕ*)〉 at any

_{b}*ϕ*is at least three times larger than the vacuum state variance for classical transportation without entanglement [2

_{b}2. S. L. Braunstein and H. J. Kimble, “Teleportation of Continuous Quantum Variables,” Phys. Rev. Lett. **80**, 869–872 (1998). [CrossRef]

*b*). Therefore, measurements of observables other than quadrature-phase amplitudes will give completely different results from measurements on the input state except for when the results of the CV Bell measurements (

*x*and

_{u}*p*) are close to zero. When both

_{v}*x*and

_{u}*p*are close to zero, there is no need for unitary operation to transport quantum states analogous to obtaining |

_{v}*ψ*

^{−}> out of four Bell states for quantum teleportation of discrete variables [16

16. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental Quantum Teleportation,” Nature **390**, 575–579 (1997). [CrossRef]

17. Ch. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum Key Distribution with Bright Entangled Beams,” Phys. Rev. Lett. **88**, 167902 (2002). [CrossRef] [PubMed]

## 3. Experimental setup

*Q*-switched erbium-doped glass laser, which produces optical pulses at a wavelength of 1.535

*μ*m with a duration of 3.9 ns and a repetition rate of 2.7 kHz (Cobolt model Tango). A small fraction of FW is used as the LO for homodyne detection, and the most of this is frequency doubled in a periodically poled LiNbO

_{3}waveguide (PPLN-WG, not shown in Fig. 2) [18

18. Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, “Pulsed Homodyne Detection of Squeezed Light at Telecommunication Wavelength,” Jpn. J. Appl. Phys. **45**(Part 2), L821–L823 (2006). [CrossRef]

19. Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, “Observation of squeezed light at 1.535 *μ*m using a pulsed homodyne detector,” Opt. Lett. **32**, 1698–1700 (2007). [CrossRef] [PubMed]

13. Y. Eto, A. Nonaka, Y. Zhang, and T. Hirano, “Stable generation of quadrature entanglement using a ring interferometer,” Phys. Rev. A **79**, 050302 (2009). [CrossRef]

*μ*m. The two harmonic wave plates (HWP1 and 2) serve as

*λ*/2 plates at a wavelength of 1.535

*μ*m and as a

*λ*plate at 767 nm. The two dual-wavelength beamsplitters (DBS1 and 2) divide the horizontally polarized beam at wavelengths of both 1.535

*μ*m and 767 nm (transmissivity/reflectivity for 1.535

*μ*m is 50/50, and that for 767 nm is 52/48). After passing through the DPBS1 and HWP1, the horizontally polarized SHW (the red dotted line in Fig. 1) and the vertically polarized FW (the solid line) are introduced into the ring interferometer. The SHW is divided into two beams, and is used to pump the PPLN-WG from both sides. The two counter-propagating squeezed beams (dashed line) are generated by bidirectional pumping. Entanglement is generated from the DBS1 by controlling the relative phase between squeezed beams

*θ*to

*π*/2 using BK7 plates. The vertically polarized FW is reflected by DBS1 and propagated into three PHDs (PHD1-3) after passing through the ring interferometer.

*x*and

_{u}*p*, are simultaneously measured in PHD1 and PHD2 by shifting the relative phase using a properly designed birefringence plate (BP). The quadrature values,

_{v}*X*(

_{b}*ϕ*), of the other entangled beam are measured in PHD3. The relative phase,

_{b}*ϕ*, between the other entangled beam and LO can be adjusted by displacing one of the wedged BK7 plates.

_{b}## 4. Results and discussion

*x*or

_{u}*p*and

_{v}*X*(

_{b}*ϕ*) are measured, before the quantum transportation experiment was done. Figure 3 shows the measured noise variance in the sum and difference in quadratures while the LO phase in PHD3 is scanned. Each point is calculated from the quadrature values of pairs of 2000 pulses. As seen in Fig. 3(a),

_{b}*ϕ*= 0 and 2

_{b}*π*are defined for the minimum variance of 〈Δ

^{2}[

*x*+

_{u}*X*(

_{b}*ϕ*)]〉. The quantum correlation of 〈Δ

_{b}^{2}[

*x*+

_{u}*X*(0)]〉 = 0.40 (−0.9 dB compared to the corresponding vacuum variances of 0.5) is obtained after correcting for electronic noise. The electronic noise levels of PHD1, PHD2, and PHD3 are 8.8 dB, 9.5 dB, and 11.0 dB below the shot noise levels (SNLs). When

_{b}*ϕ*is chosen as

_{b}*π*/2,

*π*, and 3/2

*π*, the quantum correlations of 〈Δ

^{2}[

*p*+

_{v}*X*(

_{b}*π*/2)]〉 = 〈Δ

^{2}[

*x*−

_{u}*X*(

_{b}*π*)]〉 = 〈Δ

^{2}[

*p*−

_{u}*X*(3

_{b}*π*/2)]〉 = 0.40 (−0.9 dB) are also respectively observed. The output pump average powers from PPLN-WG are 80 and 70

*μ*W (corresponding to peak powers of 7.6 and 6.6 W). The squeezing parameters of

*r*

_{1}= 1.16 and

*r*

_{2}= 1.38 are estimated from these powers. Taking into account the loss in ring interferometer (

*ξ*

_{1}= 0.77 and

*ξ*

_{2}= 0.68) and the total detection efficiencies (

*η*

_{1}=

*η*

_{2}= 0.60,

*η*

_{3}= 0.58 for PHD1, 2, and 3, respectively), 〈Δ

^{2}[

*x*+

_{u}*X*(0)]〉 = 〈Δ

_{b}^{2}[

*p*+

_{v}*X*(

_{b}*π*/2)]〉 = 〈Δ

^{2}[

*x*−

_{u}*X*(

_{b}*π*)]〉 = 〈Δ

^{2}[

*p̂*−

_{u}*X*(3

_{b}*π*/2)]〉 = 0.41 (−0.9 dB) are calculated, and the black solid lines in Fig. 3 represent theoretical curves (no fitting parameters) [13

13. Y. Eto, A. Nonaka, Y. Zhang, and T. Hirano, “Stable generation of quadrature entanglement using a ring interferometer,” Phys. Rev. A **79**, 050302 (2009). [CrossRef]

*r*

_{1}≠

*r*

_{2}). By using these parameters, the inseparability,

20. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. **84**, 2722–2725 (2000). [CrossRef] [PubMed]

21. R. Simon, “Peres-Horodecki Separability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. **84**, 2726–2729 (2000). [CrossRef] [PubMed]

*X*

_{out}(

*ϕ*) as a function of

_{b}*ϕ*. With the use of entanglement, the variance 〈Δ

_{b}^{2}

*X*

_{out}〉 obtained by averaging over all

*ϕ*is 0.63 ± 0.04 (4.0 ±0.3 dB compared to the corresponding vacuum variance of 0.25), and fidelity

_{b}*F*is achieved as 0.57 ± 0.03. For classical transportation in the absence of entanglement, the measured noise variance, 〈Δ

^{2}

*X*

_{out}〉 = 0.75 ± 0.01 (4.8 ± 0.1 dB), is measured, which corresponds to

*F*= 0.50 ± 0.01. The fidelity of

_{c}*F*= 0.57 ± 0.03 is beyond the classical bound of

*F*. Thus, quantum transportation for individual pulses is experimentally demonstrated.

_{c}22. S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, “7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO_{4},” Appl. Phys. Lett. **89**, 061116 (2006). [CrossRef]

*r*

_{eff}is the effective squeezing parameter. In our experiments, considering the loss in the ring interferometer and the total detection efficiencies,

*r*

_{eff}= 0.25, and thus

*F*

_{eff}= 0.62 was expected. This value is slightly higher than the experimentally obtained fidelity of

*F*= 0.57 ± 0.03. One possible cause for this discrepancy is due to the temporal fluctuations in

*ϕ*during the measuring time of 2 minutes when measurement were done [8

_{b}8. T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A **67**, 033802 (2003). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A |

2. | S. L. Braunstein and H. J. Kimble, “Teleportation of Continuous Quantum Variables,” Phys. Rev. Lett. |

3. | C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. |

4. | S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A |

5. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. |

6. | A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science |

7. | W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H.-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A |

8. | T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A |

9. | X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam,” Phys. Rev. Lett. |

10. | J. Mizuno, K. Wakui, A. Furusawa, and M. Sasaki, “Experimental demonstration of entanglement-assisted coding using a two-mode squeezed vacuum state,” Phys. Rev. A |

11. | H. Hansen, T. Aichele, C. Hettich, P. Lodahl, A. I. Lvovsky, J. Mlynek, and S. Schiller, “Ultrasensitive pulsed, balanced homodyne detector: application to time-domain quantum measurements,” Opt. Lett. |

12. | R. Okubo, M. Hirano, Y. Zhang, and T. Hirano, “Pulse-resolved measurement of quadrature phase amplitudes of squeezed pulse trains at a repetition rate of 76 MHz,” Opt. Lett. |

13. | Y. Eto, A. Nonaka, Y. Zhang, and T. Hirano, “Stable generation of quadrature entanglement using a ring interferometer,” Phys. Rev. A |

14. | D. T. Smithey, M. Beck, and M. G. Raymer, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. |

15. | P. van Loock, S. L. Braunstein, and H. J. Kimble, “Broadband teleportation,” Phys. Rev. A |

16. | D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental Quantum Teleportation,” Nature |

17. | Ch. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum Key Distribution with Bright Entangled Beams,” Phys. Rev. Lett. |

18. | Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, “Pulsed Homodyne Detection of Squeezed Light at Telecommunication Wavelength,” Jpn. J. Appl. Phys. |

19. | Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, “Observation of squeezed light at 1.535 |

20. | L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. |

21. | R. Simon, “Peres-Horodecki Separability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. |

22. | S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, “7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO |

**OCIS Codes**

(270.6570) Quantum optics : Squeezed states

(270.5565) Quantum optics : Quantum communications

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 15, 2010

Revised Manuscript: December 19, 2010

Manuscript Accepted: January 11, 2011

Published: January 12, 2011

**Citation**

Yujiro Eto, Yun Zhang, and Takuya Hirano, "Transporting continuous quantum variables of individual light pulses," Opt. Express **19**, 1360-1366 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1360

Sort: Year | Journal | Reset

### References

- L. Vaidman, "Teleportation of quantum states," Phys. Rev. A 49, 1473-1476 (1994). [CrossRef] [PubMed]
- S. L. Braunstein, and H. J. Kimble, "Teleportation of Continuous Quantum Variables," Phys. Rev. Lett. 80, 869-872 (1998). [CrossRef]
- C. H. Bennett, and S. J. Wiesner, "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states," Phys. Rev. Lett. 69, 2881-2884 (1992). [CrossRef] [PubMed]
- S. L. Braunstein, and H. J. Kimble, "Dense coding for continuous variables," Phys. Rev. A 61, 042302 (2000). [CrossRef]
- A. K. Ekert, "Quantum cryptography based on Bell’s theorem," Phys. Rev. Lett. 67, 661-663 (1991). [CrossRef] [PubMed]
- A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional Quantum Teleportation," Science 282, 706-709 (1998). [CrossRef] [PubMed]
- W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H.-A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003). [CrossRef]
- T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003). [CrossRef]
- X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam," Phys. Rev. Lett. 88, 047904 (2002). [CrossRef] [PubMed]
- J. Mizuno, K. Wakui, A. Furusawa, and M. Sasaki, "Experimental demonstration of entanglement-assisted coding using a two-mode squeezed vacuum state," Phys. Rev. A 71, 012304 (2005). [CrossRef]
- H. Hansen, T. Aichele, C. Hettich, P. Lodahl, A. I. Lvovsky, J. Mlynek, and S. Schiller, "Ultrasensitive pulsed, balanced homodyne detector: application to time-domain quantum measurements," Opt. Lett. 26, 1714-1716 (2001). [CrossRef]
- R. Okubo, M. Hirano, Y. Zhang, and T. Hirano, "Pulse-resolved measurement of quadrature phase amplitudes of squeezed pulse trains at a repetition rate of 76 MHz," Opt. Lett. 33, 1458-1460 (2008). [CrossRef] [PubMed]
- Y. Eto, A. Nonaka, Y. Zhang, and T. Hirano, "Stable generation of quadrature entanglement using a ring interferometer," Phys. Rev. A 79, 050302 (2009). [CrossRef]
- D. T. Smithey, M. Beck, and M. G. Raymer, "Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum," Phys. Rev. Lett. 70, 1244-1247 (1993). [CrossRef] [PubMed]
- P. van Loock, S. L. Braunstein, and H. J. Kimble, "Broadband teleportation," Phys. Rev. A 62, 022309 (2000). [CrossRef]
- D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental Quantum Teleportation," Nature 390, 575-579 (1997). [CrossRef]
- Ch. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum Key Distribution with Bright Entangled Beams," Phys. Rev. Lett. 88, 167902 (2002). [CrossRef] [PubMed]
- Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Pulsed Homodyne Detection of Squeezed Light at Telecommunication Wavelength," Jpn. J. Appl. Phys. 45(Part 2), L821-L823 (2006). [CrossRef]
- Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Observation of squeezed light at 1.535 μm using a pulsed homodyne detector," Opt. Lett. 32, 1698-1700 (2007). [CrossRef] [PubMed]
- L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability Criterion for Continuous Variable Systems," Phys. Rev. Lett. 84, 2722-2725 (2000). [CrossRef] [PubMed]
- R. Simon, "Peres-Horodecki Separability Criterion for Continuous Variable Systems," Phys. Rev. Lett. 84, 2726-2729 (2000). [CrossRef] [PubMed]
- S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116 (2006). [CrossRef]

## 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.