SLIDE 6 7/31/20 6
II: Myth: You can only use polarization encoding in free-space quantum communications
Breckinridge, Lam, Chipman, Publications of the Astronomical Society of the Pacific, Vol. 127, No. 951 (2015), pp. 445 2015 / Vol. 54, No. 3 / APPLIED OPTICS
Measurement error, induced by a Cassegrain telescope with an aluminum coating, changes with the parameter d ; c
Polarization effect of mirrors due to Fresnel-coefficients
Depolarization of a Laser Beam at 6328 A due to Atmospheric Transmission
The depolarization of a linearly polarized laser beam was investigated primarily with an optical path of 4.5 km. A He-Ne gas laser at 6328 A was used with an additional polarizer at the output and with a ro- tating polarization filter assembly in front of the receiver. Values of depolarization found ranged between 10-7 rad and about 5 X 10- rad. The lower limit was determined by the quality of the polarizer-ana- lyzer combination used. These experimental values of depolarization are very much higher than that pre- dicted by theories regarding turbulence-induced depolarization.
The results of an experimental study of the depolar- ization of a linearly polarized laser beam traversing the atmosphere near ground level are presented and dis- cussed in this paper. A theoretical prediction, probably the first one con- cerned with turbulence-induced polarization fluctua- tions, was published by Hodara, but his results were in error by some orders of magnitude,2 even if actual measurements2 seemed to confirm his theory. Fried and Mevers3 found very high degrees of polarization fluctuations experimentally but "now it seems that this rather large measured value was mainly due to a defect in the experiment." 4 Strohbehm and Clifford5 presented a new theory on turbulence-induced polarization fluctua- tions. A first order solution to the wave equation was found using spectral analysis techniques. Finally, Saleh4 published a theory on polarization fluctuations using the geometrical optics approximation and Chernov's three-dimensional ray statistical model, together with some experimental results. The sensitivity of his measurements was limited by the equipment used, to
- 42 dB in the daytime and -45 dB at night.
No depolarization-corresponding to time- or space-aver- aged fluctuations of the polarization angle of a linearly polarized laser beam-was found at a propagation range of 2.6 km. In agreement with his theory, it must be much smaller as long as turbulence is the only source
Because of the fact that the above-mentioned theoret- ical predictions are contradictory, which is shown in The author is with the Astronomisches Institut der Universitdt Tdbingen, Waldhauserstrasse 64, Ttibingen 74, Germany. Received 6 August 1968.
- Sec. II, the results of the measurements made near
Tilbingen should not be compared directly with any one theory, but should be discussed in light of the theoretical situation at present. In the Tubingen experiments, a range of 4.5 km was usually used. The experiments were conducted at night from the middle of 1966 until the middle of 1967. Using a rotating-filter method similar to that used by Saleh,4 depolarizations were found. The root-mean-square variation of the angle of polarization a,, used as a parameter for the depolariza- tion, is compared with the root-mean-square variation
- f the logarithm of intensity slog ,, from which the struc-
ture constant of the index of refraction C. can be de- duced; C. is a characteristic parameter of atmospheric turbulence.6
11.
Theoretical Results A. Polarization Fluctuations If the laser beam is polarized linearly at the trans- mitter output, the root-mean-square variation a-,, of the angle of polarization 0 induced by atmospheric turbu- lence is given by
1 (An2)'/2 l =
1'/2 (1)
if we follow the theory of Strohbehm and Clifford [Ref. 5, Eq. (9) ]. An is the deviation of the index of refrac- tion of the atmosphere from its mean, normalized to unity; is the scale factor of the gaussian approxima- tion of the three-dimensional spectral density of the index of refraction used, and may be considered to be the correlation length [Ref. 5, Eq. (31) ]; X is the wave- length; L is the range of propagation. Assuming An2 = 10-12 and = 10 cm, corresponding to strong tur- bulence near the ground, we find when X = 632.8 nm February 1969 / Vol. 8, No. 2 / APPLIED OPTICS 367
Depolarization of a Laser Beam at 6328 A due to Atmospheric Transmission
The depolarization of a linearly polarized laser beam was investigated primarily with an optical path of 4.5 km. A He-Ne gas laser at 6328 A was used with an additional polarizer at the output and with a ro- tating polarization filter assembly in front of the receiver. Values of depolarization found ranged between
10-7 rad and about 5 X 10- rad.
The lower limit was determined by the quality of the polarizer-ana- lyzer combination used. These experimental values of depolarization are very much higher than that pre- dicted by theories regarding turbulence-induced depolarization.
The results of an experimental study of the depolar- ization of a linearly polarized laser beam traversing the atmosphere near ground level are presented and dis- cussed in this paper. A theoretical prediction, probably the first one con- cerned with turbulence-induced polarization fluctua- tions, was published by Hodara, but his results were in error by some orders of magnitude,2 even if actual measurements2 seemed to confirm his theory. Fried and Mevers3 found very high degrees of polarization fluctuations experimentally but "now it seems that this rather large measured value was mainly due to a defect in the experiment." 4 Strohbehm and Clifford5 presented a new theory on turbulence-induced polarization fluctua- tions. A first order solution to the wave equation was found using spectral analysis techniques. Finally, Saleh4 published a theory on polarization fluctuations using the geometrical optics approximation and Chernov's three-dimensional ray statistical model, together with some experimental results. The sensitivity of his measurements was limited by the equipment used, to
- 42 dB in the daytime and -45 dB at night.
No depolarization-corresponding to time- or space-aver- aged fluctuations of the polarization angle of a linearly polarized laser beam-was found at a propagation range of 2.6 km. In agreement with his theory, it must be much smaller as long as turbulence is the only source
Because of the fact that the above-mentioned theoret- ical predictions are contradictory, which is shown in
The author is with the Astronomisches Institut der Universitdt Tdbingen, Waldhauserstrasse 64, Ttibingen 74, Germany. Received 6 August 1968.
- Sec. II, the results of the measurements made near
Tilbingen should not be compared directly with any one theory, but should be discussed in light of the theoretical situation at present. In the Tubingen experiments, a range of 4.5 km was usually used. The experiments were conducted at night from the middle of 1966 until the middle of 1967. Using a rotating-filter method similar to that used by Saleh,4 depolarizations were found. The root-mean-square variation of the angle of polarization a,, used as a parameter for the depolariza- tion, is compared with the root-mean-square variation
- f the logarithm of intensity slog ,, from which the struc-
ture constant of the index of refraction C. can be de- duced; C. is a characteristic parameter of atmospheric turbulence.6
11.
Theoretical Results A. Polarization Fluctuations If the laser beam is polarized linearly at the trans- mitter output, the root-mean-square variation a-,, of the angle of polarization 0 induced by atmospheric turbu- lence is given by
1 (An2)'/2
l
=
1'/2
(1)
if we follow the theory of Strohbehm and Clifford [Ref. 5, Eq. (9) ]. An is the deviation of the index of refrac- tion of the atmosphere from its mean, normalized to unity; is the scale factor of the gaussian approxima- tion of the three-dimensional spectral density of the index of refraction used, and may be considered to be the correlation length [Ref. 5, Eq. (31) ]; X is the wave- length; L is the range of propagation. Assuming An2 = 10-12 and = 10 cm, corresponding to strong tur- bulence near the ground, we find when X = 632.8 nm February 1969 / Vol. 8, No. 2 / APPLIED OPTICS 367
Dpolarization measured ca. 10-7 to 10-5 rad. Limited by apparatus and background light. What about Time- bin encoding in Free-Space?
44
The issue with asymmetric MZI and distorted modes
- Different incident angles and modal distortions experience different
Phase
- Tim—bin analyzer interferometer with ‘flat’ optics not suitable
- where δ(α) = l0 tan(α)/[1 + tan(α)] is
tween the two rays coming from each path
- [J. Jin, S. Agne, J.P. Bourgoin, Y. Zhang, N. Lutkenhaus, T. Jennewein, arXiv:1509.07490,
- Phys. Rev. A 97, 043847 (2018)]
45
Multi-mode Michelson Interferometers
Erskine, Holmes, Nature, Vol 377, p317 (1995)
US006115121A
United States Patent [19]
[11] Patent Number:
6,115,121 Erskine
[45] Date of Patent: *Sep. 5, 2000 [54] SINGLE AND DOUBLE SUPERIMPOSING
and
“Multiple—line laser Doppler veloci INTERFEROMETER SYSTEMS [75] Inventor: David
- J. Erskine, Oakland, Calif.
[73] Assignee: The Regents of the University of California, Oakland, Calif. [*] Notice: This patent is subject to a terminal dis claimer. [21] Appl. No.: 08/963,682 [22] Filed:
[51]
- Int. Cl.7 .....................................................
.. G01B 9/02 [52]
US.
- Cl. ........................
.. 356/345; 356/285; 356/352 [58] Field of Search ................................... .. 356/345, 346,
356/351, 352, 357, 359, 28.5 [56] References Cited U.S. PATENT DOCUMENTS 5,642,194 6/1997 Erskine .................................
.. 356/345
OTHER PUBLICATIONS Rernhard Beer, “Remote Sensing by Fourier Transform Spectrometry,” John Wiley & Sons, NeW York, 1992, QD96.F68B415,
“L’Etalon de Fabry—Perot Spherique,” Le Journal De Physique et le Radium, 19, pp. 262—269, 1958.
- R. L. Hilliard and G. G. Shepherd, “Wide
Angle Michelson Interferometer for Measuring Doppler Line Widths,”
- J. Opt.
- Soc. Am., vol. 56, No. 3, pp. 362—369, Mar. 1966.
SM.
88,57
\\\\
AM. 90
metry,” Applied Optics, vol. 27, No. 11, pp. 2315—2319, 1988. Pierre Connes, “DeuXieme Journee D’Etudes Sur Les Inter ferences,” Revue D’Optique Theorique Instrumentale, vol. 35, p. 37, Jun. 1956. Book by Eugene Hecht and Alfred Zaj ac, “Optics,” Addison Wesley, Reading Massachusetts, pp. 307—309, 1976. David
- J. Erskine and Neil C. Holmes, “White Light Veloc
ity,” Nature, vol. 377, pp. 317—320, Sep. 28, 1995. David
Neil
“Imaging White Light VISAR,” Proceedings of 22nd International Congress on High—speed Photography and Photonics, October 1996. Primary Examiner—Samuel
Attorney, Agent, or Firm—John P. Wooldridge; Alan H. Thompson [57] ABSTRACT Interferometers Which can imprint a coherent delay on a broadband uncollimated beam are described. The delay value can be independent of incident ray angle, alloWing interferometry using uncollimated beams from common extended sources such as lamps and ?ber bundles, and facilitating Fourier Transform spectroscopy of Wide angle
such interferometers matched in delay and dispersion can measure velocity and communicate using
- rdinary lamps, Wide diameter optical ?bers and arbitrary
non-imaging paths, and not requiring a laser. 32 Claims, 34 Drawing Sheets
Delaying Mirror Assembly
Erskine, US Patent 6,115,121 (2000)
Superimposing Interferometers Field-Widened Michelson Interferometers
Liu et al, Vol. 20, No. 2 / OPTICS EXPRESS 1406 (2012)
#156591 - $15.00 USD Received 17 Oct 2011; revised 28 Nov 2011; accepted 21 Dec 2011; published 9 Jan 2012
2 1 2 1 1 2 2 1 2 4 6 1 2 1 2 3 3 5 5 1 2 1 2
2( ) sin ( ) , sin sin ( ) ( ) 4 8 d d W n d n d n n d d d d n n n n θ θ θ = − − − − − − − ⋯⋯ ( − = θ λ
#156591 - $15.00 USD Received 17 Oct 2011; revised 28 Nov 2011; accepted 21 Dec 2011; published 9 Jan 2012
1 1 2 2
/ / 0. d n d n − = ependent of incident ang θ λ
#156591 - $15.00 USD Received 17 Oct 2011; revised 28 Nov 2011; accepted 21 Dec 2011; published 9 Jan 2012
4 6 1 2 1 2 1 1 2 2 3 3 5 5 1 2 1 2
sin sin 2( ) ( ) ( ) 4 8 d d d d W n d n d n n n n θ θ = − − − − − ⋯⋯ ( θ λ
#156591 - $15.00 USD Received 17 Oct 2011; revised 28 Nov 2011; accepted 21 Dec 2011; published 9 Jan 2012
θ
#156591 - $15.00 USD Received 17 Oct 2011; revised 28 Nov 2011; accepted 21 Dec 2011; published 9 Jan 2012
Used in applications for multi-mode images in Doppler-LIDAR Velocimetry with incoherent light sources, Astronomy, Narrowband Filters in LIDAR
- Appl. Opt. 24(11), 1571–1584 (1985)
- Appl. Opt. 11(3), 507–516 (1972).
46
mirror lens 50/50 beam splitter multimode fiber
(b)
Figure 2. Measured interference visibilities with multimode beam (inset) while varying incidence (a) and rotation (b) angles.
visibilities of >97 % in both
- utputs,
- Average visibility of 98.5 %
for the 4 QKD states.
multimode fiber of 80 %, from input to output!
New Configuration with Symmetric Imaging Paths
48
