-
1
-
-
0027652515
-
Fractional Fourier transforms and their implementations. I
-
D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their implementations. I,” J. Opt. Soc. Am. A 10 1875–1881 (1993)
-
(1993)
J. Opt. Soc. Am. A
, vol.10
, pp. 1875-1881
-
-
Mendlovic, D.1
Ozaktas, H.M.2
-
2
-
-
0027740848
-
Mendlovic, “Fractional Fourier transforms and their implementations. 11,”J
-
H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their implementations. 11,”J. Opt. Soc. Am. A 10, 2522–2531 (1993)
-
(1993)
Opt. Soc. Am. A
, vol.10
, pp. 2522-2531
-
-
Ozaktas, H.M.1
-
3
-
-
0027641018
-
Fractional Fourier transforms of fractional order and their optical interpretation
-
H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163–169 (1993)
-
(1993)
Opt. Commun.
, vol.101
, pp. 163-169
-
-
Ozaktas, H.M.1
Mendlovic, D.2
-
4
-
-
21344493264
-
Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: An operator approach
-
S. Abe and J. T. Sheridan, “Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: an operator approach,” J. Phys. A 27, 4179–4187 (1994)
-
(1994)
J. Phys. A
, vol.27
, pp. 4179-4187
-
-
Abe, S.1
Sheridan, J.T.2
-
6
-
-
77957697766
-
Optical fractional correlation: Experimental results
-
D. Mendlovic, Y. Bitran, R. G. Dorsch, and A. W. Lohmann, “Optical fractional correlation: experimental results,” J. Opt. Soc. Am. A 12, 1665–1670 (1995).
-
(1995)
J. Opt. Soc. Am. A
, vol.12
, pp. 1665-1670
-
-
Mendlovic, D.1
Bitran, Y.2
Dorsch, R.G.3
Lohmann, A.W.4
-
7
-
-
0006053360
-
Significance of phase and amplitude in the Fourier domain
-
A. W. Lohmann, D. Mendlovic, and G. Shabtay, “Significance of phase and amplitude in the Fourier domain,” J. Opt. Soc. Am. A 14, 2901–2904 (1997)
-
(1997)
J. Opt. Soc. Am. A
, vol.14
, pp. 2901-2904
-
-
Lohmann, A.W.1
Mendlovic, D.2
Shabtay, G.3
-
8
-
-
77957719167
-
Introduction to the fractional Fourier transform and its applications
-
H. M. Ozaktas, M. Alper Kutay, and D. Mendlovic, “Introduction to the fractional Fourier transform and its applications,” Adv. Imaging Electron Phys. 106, 239–291 (1999).
-
(1999)
Adv. Imaging Electron Phys.
, vol.106
, pp. 239-291
-
-
Ozaktas, H.M.1
Alper Kutay, M.2
Mendlovic, D.3
-
9
-
-
0029716077
-
Discrete fractional Fourier transform
-
Institute of Electrical and Electronics Engineers, Piscataway, N.J
-
S. C. Pei and M. H. Yeh, “Discrete fractional Fourier transform,” in Proceedings of IEEE International Symposium on Circuits Systems (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 536–539
-
(1996)
Proceedings of IEEE International Symposium on Circuits Systems
, pp. 536-539
-
-
Pei, S.C.1
Yeh, M.H.2
-
10
-
-
0031190361
-
Improved discrete fractional Fourier transform
-
S. C. Pei and M. H. Yeh, “Improved discrete fractional Fourier transform,” Opt. Lett. 22, 1047–1049 (1997)
-
(1997)
Opt. Lett.
, vol.22
, pp. 1047-1049
-
-
Pei, S.C.1
Yeh, M.H.2
-
11
-
-
0032072124
-
Two dimensional discrete fractional Fourier transform
-
S. C. Pei and M. H. Yeh, “Two dimensional discrete fractional Fourier transform,” Signal Process. 67, 99–108 (1998)
-
(1998)
Signal Process
, vol.67
, pp. 99-108
-
-
Pei, S.C.1
Yeh, M.H.2
-
12
-
-
0032669485
-
Discrete fractional Fourier transform based on orthogonal projections
-
S.-C. Pei, M.-H. Yeh, and C.-C. Tseng, “Discrete fractional Fourier transform based on orthogonal projections,” IEEE Trans. Signal Process. 47, 1335–1347 (1999).
-
(1999)
IEEE Trans. Signal Process.
, vol.47
, pp. 1335-1347
-
-
Pei, S.-C.1
Yeh, M.-H.2
Tseng, C.-C.3
-
13
-
-
0028483920
-
A simple realization of fractional Fourier transform and relation to harmonic oscillator Greens function
-
G. S. Agarwal and R. Simon, “A simple realization of fractional Fourier transform and relation to harmonic oscillator Green’s function,” Opt. Commun. 110, 23–26 (1994).
-
(1994)
Opt. Commun.
, vol.110
, pp. 23-26
-
-
Agarwal, G.S.1
Simon, R.2
-
15
-
-
0034132255
-
Structure of the set of paraxial optical systems
-
R. Simon and K. B. Wolf, “Structure of the set of paraxial optical systems,” J. Opt. Soc. Am. A 17, 342–355 (2000).
-
(2000)
J. Opt. Soc. Am. A
, vol.17
, pp. 342-355
-
-
Simon, R.1
Wolf, K.B.2
-
16
-
-
0020102107
-
First-order optics—a canonical operator representation: Lossless systems
-
M. Nazarathy and J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982).
-
(1982)
J. Opt. Soc. Am.
, vol.72
, pp. 356-364
-
-
Nazarathy, M.1
Shamir, J.2
-
17
-
-
0001332130
-
Realisation of first order optical systems using thin lenses
-
E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realisation of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985)
-
(1985)
Opt. Acta
, vol.32
, pp. 855-872
-
-
Sudarshan, E.C.G.1
Mukunda, N.2
Simon, R.3
-
18
-
-
0003429075
-
-
(Wiley, New York, Chap. 4
-
R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications (Wiley, New York, 1974), Chap. 4.
-
(1974)
Lie Groups, Lie Algebras, and Some of Their Applications
-
-
Gilmore, R.1
-
20
-
-
25344431927
-
Gaussian pure states in quantum mechanics and the symplectic group
-
R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Gaussian pure states in quantum mechanics and the symplectic group,” Phys. Rev. A 37, 2028–2038 (1988).
-
(1988)
Phys. Rev. A
, vol.37
, pp. 2028-2038
-
-
Simon, R.1
Sudarshan, E.C.G.2
Mukunda, N.3
-
22
-
-
36849112629
-
Linear canonical transformations and their unitary representation
-
M. Moshinsky and C. Quesne, “Linear canonical transformations and their unitary representation,” J. Math. Phys. 12, 1772–1780 (1971)
-
(1971)
J. Math. Phys.
, vol.12
, pp. 1772-1780
-
-
Moshinsky, M.1
Quesne, C.2
-
23
-
-
36849112326
-
Canonical transformations and matrix elements
-
M. Moshinsky and C. Quesne, “Canonical transformations and matrix elements,” J. Math. Phys. 12, 1780–1783 (1971)
-
(1971)
J. Math. Phys.
, vol.12
, pp. 1780-1783
-
-
Moshinsky, M.1
Quesne, C.2
-
25
-
-
27644491636
-
Root and power transformations in optics
-
J. Shamir and N. Cohen, “Root and power transformations in optics,” J. Opt. Soc. Am. A 12, 2415–2423 (1995).
-
(1995)
J. Opt. Soc. Am. A
, vol.12
, pp. 2415-2423
-
-
Shamir, J.1
Cohen, N.2
-
27
-
-
0000750528
-
Anisotropic Gaussian Schell-model beams: Passage through first order systems and associated invariants
-
R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through first order systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
-
(1985)
Phys. Rev. A
, vol.31
, pp. 2419-2434
-
-
Simon, R.1
Sudarshan, E.C.G.2
Mukunda, N.3
-
28
-
-
0001679261
-
Quantum noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms
-
R. Simon, N. Mukunda, and B. Dutta, “Quantum noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms,” Phys. Rev. A 49, 1567–1583 (1994).
-
(1994)
Phys. Rev. A
, vol.49
, pp. 1567-1583
-
-
Simon, R.1
Mukunda, N.2
Dutta, B.3
-
29
-
-
0037545183
-
Optical systems for rotating a beam
-
P. M. Mejías, H. Weber, R. Martínez-Herrero, and A. González-Urena, eds. (Sociedad Españila de Optica, Madrid
-
G. Nemes and A. G. Kostenbauder, “Optical systems for rotating a beam,” in Laser Beam Characterization, P. M. Mejías, H. Weber, R. Martínez-Herrero, and A. González-Urena, eds. (Sociedad Españila de Optica, Madrid, 1993), pp. 99–109.
-
(1993)
Laser Beam Characterization
, pp. 99-109
-
-
Nemes, G.1
Kostenbauder, A.G.2
-
30
-
-
0001515953
-
Immersion of the Fourier transform in a continuous group of functional transformations
-
E. U. Condon, “Immersion of the Fourier transform in a continuous group of functional transformations,” Proc. Natl. Acad. Sci. USA 23, 158–164 (1937).
-
(1937)
Proc. Natl. Acad. Sci. USA
, vol.23
, pp. 158-164
-
-
Condon, E.U.1
-
31
-
-
0010869715
-
Hamiltons theory of turns and a new geometrical representation for polarization optics,” Pramana
-
R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Hamilton’s theory of turns and a new geometrical representation for polarization optics,” Pramana J. Phys. 32, 769–792 (1989).
-
(1989)
J. Phys.
, vol.32
, pp. 769-792
-
-
Simon, R.1
Mukunda, N.2
Sudarshan, E.C.G.3
-
32
-
-
0001543889
-
Minimal three component SU(2) gadget for polarization optics
-
R. Simon and N. Mukunda, “Minimal three component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990)
-
(1990)
Phys. Lett. A
, vol.143
, pp. 165-169
-
-
Simon, R.1
Mukunda, N.2
-
33
-
-
0037570553
-
The Simon-Mukunda polarization gadget
-
V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon-Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
-
(1996)
Eur. J. Phys.
, vol.17
, pp. 279-284
-
-
Bagini, V.1
Borghi, R.2
Gori, F.3
Santarsiero, M.4
Frezza, F.5
Schettini, G.6
Spagnolo, G.S.7
-
36
-
-
0000236590
-
Nonseparable two-dimensional fractional Fourier transform
-
A. Sahin, M. Alper Kutay, and H. M. Ozaktas, “Nonseparable two-dimensional fractional Fourier transform,” Appl. Opt. 37, 5444–5453 (1998).
-
(1998)
Appl. Opt.
, vol.37
, pp. 5444-5453
-
-
Sahin, A.1
Alper Kutay, M.2
Ozaktas, H.M.3
-
37
-
-
0000881252
-
Jones-matrix formalism As a representation of the Lorentz group
-
D. Han, Y. S. Kim, and M. E. Noz, “Jones-matrix formalism As a representation of the Lorentz group,” J. Opt. Soc. Am. A 14, 2290–2298 (1997).
-
(1997)
J. Opt. Soc. Am. A
, vol.14
, pp. 2290-2298
-
-
Han, D.1
Kim, Y.S.2
Noz, M.E.3
-
38
-
-
0037570555
-
The SO(N, 1) Wigner rotation as an SL(2, R) problem
-
R. Simon and N. Mukunda, “The SO(n, 1) Wigner rotation as an SL(2, R) problem,” Found. Phys. Lett. 3, 425–434 (1990).
-
(1990)
Found. Phys. Lett.
, vol.3
, pp. 425-434
-
-
Simon, R.1
Mukunda, N.2
-
39
-
-
0029277263
-
Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams
-
K. Sundar, N. Mukunda, and R. Simon, “Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams,” J. Opt. Soc. Am. A 12, 560–569 (1995).
-
(1995)
J. Opt. Soc. Am. A
, vol.12
, pp. 560-569
-
-
Sundar, K.1
Mukunda, N.2
Simon, R.3
-
40
-
-
0027652533
-
Twisted Gaussian Schell-model beams: I. Symmetry structure and normalmode spectrum
-
R. Simon, K. Sundar, and N. Mukunda, “Twisted Gaussian Schell-model beams: I. Symmetry structure and normalmode spectrum,” J. Opt. Soc. Am. A 10, 2008–2016 (1993).
-
(1993)
J. Opt. Soc. Am. A
, vol.10
, pp. 2008-2016
-
-
Simon, R.1
Sundar, K.2
Mukunda, N.3
-
41
-
-
0028444203
-
Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters
-
M. Selvadoray, M. Sanjay Kumar, and R. Simon, “Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters,” Phys. Rev. A 49, 4957–4967 (1994).
-
(1994)
Phys. Rev. A
, vol.49
, pp. 4957-4967
-
-
Selvadoray, M.1
Sanjay Kumar, M.2
Simon, R.3
-
42
-
-
77958407025
-
The fractional order Fourier transform and its application to quantum mechanics
-
V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Its Appl. 25, 241–265 (1980)
-
(1980)
J. Inst. Math. Its Appl.
, vol.25
, pp. 241-265
-
-
Namias, V.1
-
43
-
-
84894009925
-
General thin-lens action on spatial intensity distribution behaves as non-integer powers of Fourier transform
-
of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C
-
L. F. Ludwig, “General thin-lens action on spatial intensity distribution behaves as non-integer powers of Fourier transform,” in Spatial Light Modulators and Applications, Vol. 8 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 173–176.
-
(1988)
Spatial Light Modulators and Applications
, vol.8
, pp. 173-176
-
-
Ludwig, L.F.1
-
44
-
-
0002839282
-
On angular momentum
-
L. C. Biedenharn and H. van Dam, eds. (Academic, New York
-
See, e.g., J. Schwinger, “On angular momentum,” in Quantum Theory of Angular Momentum, L. C. Biedenharn and H. van Dam, eds. (Academic, New York, 1965), pp. 229–279.
-
(1965)
Quantum Theory of Angular Momentum
, pp. 229-279
-
-
See, E.G.1
Schwinger, J.2
-
46
-
-
0000328798
-
Analogies between two optical systems (Photon beam splitters and laser beams) and two quantum systems (the two-dimensional oscillator and the two-dimensional hydrogen atom)
-
S. Danakas and P. K. Aravind, “Analogies between two optical systems (photon beam splitters and laser beams) and two quantum systems (the two-dimensional oscillator and the two-dimensional hydrogen atom),” Phys. Rev. A 45, 1973–1977 (1992).
-
(1992)
Phys. Rev. A
, vol.45
, pp. 1973-1977
-
-
Danakas, S.1
Aravind, P.K.2
-
47
-
-
0032184596
-
Free-space diffraction and the fractional Fourier transform
-
C. J. R. Sheppard, “Free-space diffraction and the fractional Fourier transform,” J. Mod. Opt. 45, 2097–2103 (1998).
-
(1998)
J. Mod. Opt.
, vol.45
, pp. 2097-2103
-
-
Sheppard, C.J.R.1
-
48
-
-
0038450087
-
Canonical transforms for paraxial wave optics
-
J. Sánchez-Mondragón and K. B. Wolf, eds., Vol. 250 of Lecture Notes in Physics (Springer-Verlag, Heidelberg
-
O. Castanos, E. Lopez-Moreno, and K. B. Wolf, “Canonical transforms for paraxial wave optics,” in Lie Methods in Optics, J. Sánchez-Mondragón and K. B. Wolf, eds., Vol. 250 of Lecture Notes in Physics (Springer-Verlag, Heidelberg, 1986), pp. 159–182
-
(1986)
Lie Methods in Optics
, pp. 159-182
-
-
Castanos, O.1
Lopez-Moreno, E.2
Wolf, K.B.3
-
49
-
-
0037570557
-
The symplectic groups, their parameterization and cover
-
J. Sánchez-Mondragón and K. B. Wolf, eds., Vol. 250 of Lecture Notes in Physics, Springer-Verlag, Heidelberg
-
K. B. Wolf, “The symplectic groups, their parameterization and cover,” in Lie Methods in Optics, J. Sánchez-Mondragón and K. B. Wolf, eds., Vol. 250 of Lecture Notes in Physics (Springer-Verlag, Heidelberg, 1986), pp. 227–238.
-
(1986)
Lie Methods in Optics
, pp. 227-238
-
-
Wolf, K.B.1
-
50
-
-
0038246169
-
The two-dimensional symplectic and metaplectic groups and their universal cover
-
B. Gruber, L. C. Biedenharn, and H. D. Doebner, eds. (Plenum, New York
-
R. Simon and N. Mukunda, “The two-dimensional symplectic and metaplectic groups and their universal cover,” in Symmetries in Science V: Algebraic Systems, Their Representation, Realizations, and Physical Applications, B. Gruber, L. C. Biedenharn, and H. D. Doebner, eds. (Plenum, New York, 1991), pp. 659–689.
-
(1991)
Symmetries in Science V: Algebraic Systems, Their Representation, Realizations, and Physical Applications
, pp. 659-689
-
-
Simon, R.1
Mukunda, N.2
-
51
-
-
0000136245
-
Poincaré-sphere equivalent for light beams containing orbital angular momentum
-
M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
-
(1999)
Opt. Lett.
, vol.24
, pp. 430-432
-
-
Padgett, M.J.1
Courtial, J.2
-
52
-
-
0008913550
-
SU(2) structure of the Poincaré sphere for light beams with orbital angular momentum
-
G. S. Agarwal, “SU(2) structure of the Poincaré sphere for light beams with orbital angular momentum,” J. Opt. Soc. Am. A 16, 2914–2916 (1999).
-
(1999)
J. Opt. Soc. Am. A
, vol.16
, pp. 2914-2916
-
-
Agarwal, G.S.1
|