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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 22333–22340
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Polarization measurements through space-to-ground atmospheric propagation paths by using a highly polarized laser source in space

Morio Toyoshima, Hideki Takenaka, Yozo Shoji, Yoshihisa Takayama, Yoshisada Koyama, and Hiroo Kunimori  »View Author Affiliations


Optics Express, Vol. 17, Issue 25, pp. 22333-22340 (2009)
http://dx.doi.org/10.1364/OE.17.022333


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Abstract

The polarization characteristics of an artificial laser source in space were measured through space-to-ground atmospheric transmission paths. An existing Japanese laser communication satellite and optical ground station were used to measure Stokes parameters and the degree of polarization of the laser beam transmitted from the satellite. As a result, the polarization was preserved within an rms error of 1.6°, and the degree of polarization was 99.4±4.4% through the space-to-ground atmosphere. These results contribute to the link estimation for quantum key distribution via space and provide the potential for enhancements in quantum cryptography worldwide in the future.

© 2009 OSA

1. Introduction

Recently, there have been many dangers and threats to society, such as frequent large-scale disasters and accidents, worldwide infectious diseases, recurrent terrorism, and the deterioration of homeland security. Besides being intellectual and industrial inventions and innovations, science and technology are also a means to create social values and can help provide answers for these crises that threaten the world’s security and safety [1

1. Ministry of Education, Culture, Sports, Science and Technology (MEXT) “Report on science and technology policy on contributing the secure and safety society,” http://www.mext.go.jp/a_menu/kagaku/anzen/houkoku/04042302/all.pdf (in Japanese, 2004)

]. Because of sophisticated eavesdropping technology, the information and communications technology sector needs to be able to prevent information leakage and illegal access; therefore, quantum cryptography technology has become more important to information security.

Novel methods have been studied that utilize the principles governing quantum cryptography to ensure unconditional security [2

2. C. H. Bennett, and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” Proc. International Conference on Computers, Systems & Signal Processing, Bangalore, India, (1984).

,3

3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 ( 2002). [CrossRef]

]; these include quantum teleportation between distant parties [4

4. D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information, (Springer, New York, 2000).

], which theoretically cannot be broken according to the laws of physics. Technologies for quantum teleportation and quantum channel coding that defeats the classical Shannon limit have been verified [5

5. M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90(16), 167906 ( 2003). [CrossRef] [PubMed]

]. Fiber-based quantum cryptography systems for commercial use are already being sold by some venture companies: Cerberis, Vectis, and Clavis from Id Quantique in Switzerland; MagiQ QPN Security Gateway 7505 from MagiQ Technologies in the USA; and SQBox from SmartQuantum in France [68]. In Switzerland, an Internet vote using quantum cryptography was conducted in October 2007 for the mayoral election in Geneva [9

9. M. E. Peck, “Geneva Vote Will Use Quantum Cryptography,” http://spectrum.ieee.org/oct07/5634

]. These details show the maturity of the technology level for quantum key distribution (QKD).

QKD using optical fibres is limited to a distance of approximately 100 km due to transmission losses, nonlinearity, and background noise. Using free-space QKD would enable the long-distance transmission of photons; therefore, satellite quantum cryptography is an ideal application of QKD [10

10. R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” N. J. Phys. 4, 43 ( 2002). [CrossRef]

]. It is important to investigate the feasibility of such satellite QKD for future space applications. A low earth orbit (LEO) satellite usually orbits the Earth at about 7 km/s, which causes the Doppler shift. The polarization is the best means for satellite QKD to be used under the Doppler shift comparing with the time-bin method. However, the depolarization from space to ground has never been measured precisely so far.

In this paper, a highly polarized artificial laser source with a degree of polarization (DOP) of more than 99% onboard a satellite is used for measuring the polarization and the obtained polarization characteristics through space to ground are presented.

2. Effect of atmospheric turbulence on the polarization

If the laser beam is polarized linearly at the transmitter output, the root-mean-square variation σφof the angle of polarization φ induced by atmospheric turbulence is given by [11

11. J. W. Strohbehn and S. F. Clifford, “Polarization and Angle-of -Arrival Fluctuatifoonr sa Plane Wave Propagated Through a Turbulent Medium,” IEEE Trans. on Antennas and Propagation, AP 15(3), 416–421 ( 1967). [CrossRef]

13

13. D. Höhn, “Depolarization of a Laser Beam at 6328 Ǻ due to Atmospheric Transmission,” Appl. Opt. 8(2), 367–369 ( 1969). [CrossRef] [PubMed]

]
σφ=12π3/4Δn21/2l3/2λ(L)1/2,
(1)
where Δn is the deviation of the refractive index of the atmosphere from its mean, normalized to unity; l is the scale factor of the Gaussian approximation of the three-dimensional spectral density of the refractive index used; λ is the wavelength; L is the range of propagation. The root-mean-square variation of the angle of polarization due to atmospheric turbulence is small enough, e.g., the depolarization of a linearly polarized laser beam was investigated with an optical path of 4.5 km and the values of depolarization found ranged between 10−7 rad and about 5x10−5 rad [13

13. D. Höhn, “Depolarization of a Laser Beam at 6328 Ǻ due to Atmospheric Transmission,” Appl. Opt. 8(2), 367–369 ( 1969). [CrossRef] [PubMed]

] and the detected depolarized light amounting to less than 10−8 rad over 600 m path was reported [14

14. J. N. Bradford and J. W. Tucker, “A Sensitive System for Measuring Atmospheric Depolarization of Light,” Appl. Opt. 8(3), 645–647 ( 1969). [CrossRef]

].

Polarimetry, which is a field in astronomy, has been conducted by measuring some polarized standard stars on the ground [15

15. M. Breger and J. C. Hsu, “On standard polarized stars,” Astrophys. J. 262, 732–738 ( 1982). [CrossRef]

,16

16. Interstellar-polarized standard stars, University of Arizona, http://chinadoll.as.arizona.edu/~schmidt/spol/polstds.html

]. The Hubble space telescope in space measured the polarized star by using the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) [17

17. D. Batcheldor, A. Robinson, D. Axon, D. C. Hines, W. Sparks, and C. Tadhunter, “The NICMOS polarimetric calibration,” Publ. Astron. Soc. Pac. 118(842), 642–650 ( 2006). [CrossRef]

] and the mean DOP of such polarized standard stars is less than 9.947% [18

18. G. D. Schmidt, R. Elston, and O. L. Lupie, “The Hubble Space Telescope northern-hemisphere grid of stellar polarimetric standards,” Astron. J. 104(4), 1563–1567 ( 1992). [CrossRef]

]. The comparison between the ground based and space based measurements was made [19

19. J. Grosinger, “Investigation of Polarization Modulation in Optical Free Space Communications through the Atmosphere,” Master Thesis, Technical University of Vienna, February, (2008).

], however, there has been no polarization measurement using a laser source from space so far.

The small ice crystals at the upper atmosphere induce the depolarization on the scattered light, which were done mainly not for the transmitted light but the scattered and reflected lights [20

20. S. R. Pal and A. I. Carswell, “The Polarization Characteristics of Lidar Scattering from Snow and Ice Crystals in the Atmosphere,” J. Appl. Meteorol. 16(1), 70–80 ( 1977). [CrossRef]

,21

21. Y. A. Kravtsov, “New effects in wave propagation and scattering in random media (a mini review),” Appl. Opt. 32(15), 2681–2691 ( 1993). [CrossRef] [PubMed]

]. The radiative transfer approach to measure the polarization through the atmosphere uses the scattered light as well [22

22. M. I. Mishchenko and L. D. Travis, “Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight,” J. Geophys. Res. 102(D14D14), 16989–17013 ( 1997). [CrossRef]

24

24. X. Guo, V. Natraj, D. R. Feldman, F. J. D. Spur, R.-L. Shia, S. P. Sander, and Y. L. Yung, “Retrieval of ozone profile from ground-based measurements with polarization: A synthetic study,” J. Quant. Spectrosc. Radiat. Transf. 103(1), 175–192 ( 2007). [CrossRef]

]. The influence of the small ice crystals at the upper atmosphere might cause some effects on the polarization for the transmitted light but has not been measured yet through space-ground atmospheric paths directly. Therefore, it needs to be confirmed whether the polarization characteristics and DOP can be maintained after the beam passes through the space-to-ground atmospheric paths.

3. Configuration of the ground-to-satellite laser communications experiments

The National Institute of Information and Communications Technology (NICT, formerly CRL) measured the polarization characteristics using an artificial laser source in space. A LEO satellite, the Optical Inter-Orbit Communications Engineering Test Satellite (OICETS) Kirari, was used for this purpose [25

25. M. Toyoshima, T. Takahashi, K. Suzuki, S. Kimura, K. Takizawa, T. Kuri, W. Klaus, M. Toyoda, H. Kunimori, T. Jono, Y. Takayama, and K. Arai, “Ground-to-satellite laser communication experiments,” IEEE AES Magazine 23, 10–18 ( 2008). [CrossRef]

]. The laser communications experiments between the optical ground station developed by NICT—located in Koganei of downtown Tokyo—and OICETS were conducted in cooperation with the Japan Aerospace Exploration Agency (JAXA) in March, May and September of 2006; these were called the Kirari Optical Communication Demonstration Experiments with the NICT optical ground station (KODEN).

After the first trials, NICT noticed that it would be important to measure the polarization characteristics through the atmosphere for satellite QKD. Then, NICT initiated the KODEN experiments again and conducted the revival experiments from October 2008 to February 2009 for the confirmation of the polarization characteristics through space-to-ground atmospheric paths. The OICETS satellite was controlled by JAXA from the Kirari operation center in Tsukuba, as shown in Fig. 1
Fig. 1 Configuration of ground-to-satellite laser communications experiments.
. The optical antenna onboard OICETS is a 26-cm diameter center-feed Cassegrain mirror-type telescope. The laser beam from the satellite is transmitted with a wavelength of 847 nm. The optical ground station has a 1.5-m telescope located in Koganei, Tokyo and operated by NICT.

4. Experimental results and discussions

4.1 System description

4.2 Polarization measurements on the ground before the launch

The polarization characteristics of the laser beam onboard the OICETS satellite was measured during the thermal vacuum test before launch [26

26. M. Toyoshima, T. Yamakawa, K. Yamawaki, and Arai, “Reconfirmation of the optical performances of the laser communications terminal onboard the OICETS satellite,” Acta Astronaut. 55(3-9), 261–269 ( 2004). [CrossRef]

]. The polarization of the emitted laser beam was right-handed circular polarization (RHCP|Optical) by the classical optics viewpoint, and the depolarization was within 0.49%. The definition of the polarization here is defined as Stokes parameters of (S0, S1, S2, S3) = (1, 0, 0, 1), which is RHCP|Optical by the classical optical viewpoint [27

27. M. Born, and E. Wolf, Principles of Optics–7th ed. (Cambridge University Press, London, 1999).

]. Circular polarization is usually used for laser communications terminals because the received weak laser beam can be isolated from the transmitted powerful laser beam with orthogonal polarization by using a quarter wave plate in front of the internal optics. If we follow the definition by the Institute of Electrical and Electronics Engineers (IEEE), the classical optics definition of circular polarization is just the opposite of the IEEE definition [28

28. D. Roddy, Satellite communications–2nd ed. (McGraw-Hill, New York, 1989).

]. The left-handed circular polarization for RF signals (LHCP|RF) is defined as the counterclockwise direction of the electro-magnetic field at the fixed observation plane from the back-side view of the propagation direction. This definition is common for satellite communications; however, LHCP|RF is regarded as RHCP|Optical and vice versa according to convention.

4.3 Polarization measurements through space-to-ground laser links

5. Conclusion

Acknowledgements

The authors express their appreciation to the team members of the Japan Aerospace Exploration Agency, Space Engineering Development Co. Ltd. and NEC Toshiba Space Systems, Ltd., for their support in conducting the experiments.

References and links

1.

Ministry of Education, Culture, Sports, Science and Technology (MEXT) “Report on science and technology policy on contributing the secure and safety society,” http://www.mext.go.jp/a_menu/kagaku/anzen/houkoku/04042302/all.pdf (in Japanese, 2004)

2.

C. H. Bennett, and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” Proc. International Conference on Computers, Systems & Signal Processing, Bangalore, India, (1984).

3.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 ( 2002). [CrossRef]

4.

D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information, (Springer, New York, 2000).

5.

M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90(16), 167906 ( 2003). [CrossRef] [PubMed]

6.

Specification sheet of Cerberis, http://www.idquantique.com/products/files/Cerberis-specs.pdf

7.

Data sheet of MAGIQ QPN 8505, http://www.magiqtech.com/MagiQ/Products_files/8505_Data_Sheet.pdf

8.

Data sheet of SQBox Defender, http://www.smartquantum.com/IMG/pdf/SQBox_Defender_Datasheet-3.pdf

9.

M. E. Peck, “Geneva Vote Will Use Quantum Cryptography,” http://spectrum.ieee.org/oct07/5634

10.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” N. J. Phys. 4, 43 ( 2002). [CrossRef]

11.

J. W. Strohbehn and S. F. Clifford, “Polarization and Angle-of -Arrival Fluctuatifoonr sa Plane Wave Propagated Through a Turbulent Medium,” IEEE Trans. on Antennas and Propagation, AP 15(3), 416–421 ( 1967). [CrossRef]

12.

E. Collett and R. Alferness, “Depolarization of a Laser Beam in a Turbulent Medium,” J. Opt. Soc. Am. 62(4), 529–533 ( 1972). [CrossRef]

13.

D. Höhn, “Depolarization of a Laser Beam at 6328 Ǻ due to Atmospheric Transmission,” Appl. Opt. 8(2), 367–369 ( 1969). [CrossRef] [PubMed]

14.

J. N. Bradford and J. W. Tucker, “A Sensitive System for Measuring Atmospheric Depolarization of Light,” Appl. Opt. 8(3), 645–647 ( 1969). [CrossRef]

15.

M. Breger and J. C. Hsu, “On standard polarized stars,” Astrophys. J. 262, 732–738 ( 1982). [CrossRef]

16.

Interstellar-polarized standard stars, University of Arizona, http://chinadoll.as.arizona.edu/~schmidt/spol/polstds.html

17.

D. Batcheldor, A. Robinson, D. Axon, D. C. Hines, W. Sparks, and C. Tadhunter, “The NICMOS polarimetric calibration,” Publ. Astron. Soc. Pac. 118(842), 642–650 ( 2006). [CrossRef]

18.

G. D. Schmidt, R. Elston, and O. L. Lupie, “The Hubble Space Telescope northern-hemisphere grid of stellar polarimetric standards,” Astron. J. 104(4), 1563–1567 ( 1992). [CrossRef]

19.

J. Grosinger, “Investigation of Polarization Modulation in Optical Free Space Communications through the Atmosphere,” Master Thesis, Technical University of Vienna, February, (2008).

20.

S. R. Pal and A. I. Carswell, “The Polarization Characteristics of Lidar Scattering from Snow and Ice Crystals in the Atmosphere,” J. Appl. Meteorol. 16(1), 70–80 ( 1977). [CrossRef]

21.

Y. A. Kravtsov, “New effects in wave propagation and scattering in random media (a mini review),” Appl. Opt. 32(15), 2681–2691 ( 1993). [CrossRef] [PubMed]

22.

M. I. Mishchenko and L. D. Travis, “Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight,” J. Geophys. Res. 102(D14D14), 16989–17013 ( 1997). [CrossRef]

23.

Y. Jiang, Y. L. Yung, S. P. Stander, and L. D. Travis, “Modeling of atmospheric radiative transfer with polarization and its application to the remote sensing of tropospheric ozone,” J. Quant. Spectrosc. Radiat. Transf. 84(2), 169–179 ( 2004). [CrossRef]

24.

X. Guo, V. Natraj, D. R. Feldman, F. J. D. Spur, R.-L. Shia, S. P. Sander, and Y. L. Yung, “Retrieval of ozone profile from ground-based measurements with polarization: A synthetic study,” J. Quant. Spectrosc. Radiat. Transf. 103(1), 175–192 ( 2007). [CrossRef]

25.

M. Toyoshima, T. Takahashi, K. Suzuki, S. Kimura, K. Takizawa, T. Kuri, W. Klaus, M. Toyoda, H. Kunimori, T. Jono, Y. Takayama, and K. Arai, “Ground-to-satellite laser communication experiments,” IEEE AES Magazine 23, 10–18 ( 2008). [CrossRef]

26.

M. Toyoshima, T. Yamakawa, K. Yamawaki, and Arai, “Reconfirmation of the optical performances of the laser communications terminal onboard the OICETS satellite,” Acta Astronaut. 55(3-9), 261–269 ( 2004). [CrossRef]

27.

M. Born, and E. Wolf, Principles of Optics–7th ed. (Cambridge University Press, London, 1999).

28.

D. Roddy, Satellite communications–2nd ed. (McGraw-Hill, New York, 1989).

29.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement based quantum communication over 144 km,” Nat. Phys. 3(7), 481–486 ( 2007). [CrossRef]

30.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of Quantum Key Distribution Using d-Level Systems,” Phys. Rev. Lett. 88(127902), 1–4 ( 2002). [CrossRef]

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.3310) Atmospheric and oceanic optics : Laser beam transmission
(260.5430) Physical optics : Polarization
(060.2605) Fiber optics and optical communications : Free-space optical communication
(270.5568) Quantum optics : Quantum cryptography

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: September 2, 2009
Revised Manuscript: November 9, 2009
Manuscript Accepted: November 11, 2009
Published: November 23, 2009

Citation
Morio Toyoshima, Hideki Takenaka, Yozo Shoji, Yoshihisa Takayama, Yoshisada Koyama, and Hiroo Kunimori, "Polarization measurements through space-to-ground atmospheric propagation paths by using a highly polarized laser source in space," Opt. Express 17, 22333-22340 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-22333


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References

  1. Ministry of Education, Culture, Sports, Science and Technology (MEXT) “Report on science and technology policy on contributing the secure and safety society,” http://www.mext.go.jp/a_menu/kagaku/anzen/houkoku/04042302/all.pdf (in Japanese, 2004)
  2. C. H. Bennett, and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” Proc. International Conference on Computers, Systems & Signal Processing, Bangalore, India, (1984).
  3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
  4. D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information, (Springer, New York, 2000).
  5. M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90(16), 167906 (2003). [CrossRef] [PubMed]
  6. Specification sheet of Cerberis, http://www.idquantique.com/products/files/Cerberis-specs.pdf
  7. Data sheet of MAGIQ QPN 8505, http://www.magiqtech.com/MagiQ/Products_files/8505_Data_Sheet.pdf
  8. Data sheet of SQBox Defender, http://www.smartquantum.com/IMG/pdf/SQBox_Defender_Datasheet-3.pdf
  9. M. E. Peck, “Geneva Vote Will Use Quantum Cryptography,” http://spectrum.ieee.org/oct07/5634
  10. R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” N. J. Phys. 4, 43 (2002). [CrossRef]
  11. J. W. Strohbehn and S. F. Clifford, “Polarization and Angle-of -Arrival Fluctuatifoonr sa Plane Wave Propagated Through a Turbulent Medium,” IEEE Trans. on Antennas and Propagation, AP 15(3), 416–421 (1967). [CrossRef]
  12. E. Collett and R. Alferness, “Depolarization of a Laser Beam in a Turbulent Medium,” J. Opt. Soc. Am. 62(4), 529–533 (1972). [CrossRef]
  13. D. Höhn, “Depolarization of a Laser Beam at 6328 Ǻ due to Atmospheric Transmission,” Appl. Opt. 8(2), 367–369 (1969). [CrossRef] [PubMed]
  14. J. N. Bradford and J. W. Tucker, “A Sensitive System for Measuring Atmospheric Depolarization of Light,” Appl. Opt. 8(3), 645–647 (1969). [CrossRef]
  15. M. Breger and J. C. Hsu, “On standard polarized stars,” Astrophys. J. 262, 732–738 (1982). [CrossRef]
  16. Interstellar-polarized standard stars, University of Arizona, http://chinadoll.as.arizona.edu/~schmidt/spol/polstds.html
  17. D. Batcheldor, A. Robinson, D. Axon, D. C. Hines, W. Sparks, and C. Tadhunter, “The NICMOS polarimetric calibration,” Publ. Astron. Soc. Pac. 118(842), 642–650 (2006). [CrossRef]
  18. G. D. Schmidt, R. Elston, and O. L. Lupie, “The Hubble Space Telescope northern-hemisphere grid of stellar polarimetric standards,” Astron. J. 104(4), 1563–1567 (1992). [CrossRef]
  19. J. Grosinger, “Investigation of Polarization Modulation in Optical Free Space Communications through the Atmosphere,” Master Thesis, Technical University of Vienna, February, (2008).
  20. S. R. Pal and A. I. Carswell, “The Polarization Characteristics of Lidar Scattering from Snow and Ice Crystals in the Atmosphere,” J. Appl. Meteorol. 16(1), 70–80 (1977). [CrossRef]
  21. Y. A. Kravtsov, “New effects in wave propagation and scattering in random media (a mini review),” Appl. Opt. 32(15), 2681–2691 (1993). [CrossRef] [PubMed]
  22. M. I. Mishchenko and L. D. Travis, “Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight,” J. Geophys. Res. 102(D14D14), 16989–17013 (1997). [CrossRef]
  23. Y. Jiang, Y. L. Yung, S. P. Stander, and L. D. Travis, “Modeling of atmospheric radiative transfer with polarization and its application to the remote sensing of tropospheric ozone,” J. Quant. Spectrosc. Radiat. Transf. 84(2), 169–179 (2004). [CrossRef]
  24. X. Guo, V. Natraj, D. R. Feldman, F. J. D. Spur, R.-L. Shia, S. P. Sander, and Y. L. Yung, “Retrieval of ozone profile from ground-based measurements with polarization: A synthetic study,” J. Quant. Spectrosc. Radiat. Transf. 103(1), 175–192 (2007). [CrossRef]
  25. M. Toyoshima, T. Takahashi, K. Suzuki, S. Kimura, K. Takizawa, T. Kuri, W. Klaus, M. Toyoda, H. Kunimori, T. Jono, Y. Takayama, and K. Arai, “Ground-to-satellite laser communication experiments,” IEEE AES Magazine 23, 10–18 (2008). [CrossRef]
  26. M. Toyoshima, T. Yamakawa, K. Yamawaki, and Arai, “Reconfirmation of the optical performances of the laser communications terminal onboard the OICETS satellite,” Acta Astronaut. 55(3-9), 261–269 (2004). [CrossRef]
  27. M. Born, and E. Wolf, Principles of Optics–7th ed. (Cambridge University Press, London, 1999).
  28. D. Roddy, Satellite communications–2nd ed. (McGraw-Hill, New York, 1989).
  29. R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement based quantum communication over 144 km,” Nat. Phys. 3(7), 481–486 (2007). [CrossRef]
  30. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of Quantum Key Distribution Using d-Level Systems,” Phys. Rev. Lett. 88(127902), 1–4 (2002). [CrossRef]

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