## Powers of transfer matrices determined by means of eigenfunctions

JOSA A, Vol. 16, Issue 10, pp. 2413-2418 (1999)

http://dx.doi.org/10.1364/JOSAA.16.002413

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### Abstract

The parameters of the transfer matrix describing a first-order optical system that is a cascade of <i>k</i> identical subsystems defined by the transfer matrix <i>M</i> are determined from consideration of the subsystem’s eigenfunctions. A condition for the cascade to be cyclic is derived. Particular examples of cyclic first-order optical systems are presented. Structure and properties of eigenfunctions of cyclic transforms are considered. A method of optical signal encryption by use of cyclic first-order systems is proposed.

© 1999 Optical Society of America

**OCIS Codes**

(070.1170) Fourier optics and signal processing : Analog optical signal processing

(110.1650) Imaging systems : Coherence imaging

(110.6980) Imaging systems : Transforms

**Citation**

Tatiana Alieva and Martin J. Bastiaans, "Powers of transfer matrices determined by means of eigenfunctions," J. Opt. Soc. Am. A **16**, 2413-2418 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-10-2413

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### References

- R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, Berkeley, Calif., 1966).
- M. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
- T. Alieva and F. Agullo-Lopez, “Optical wave propagation of fractal fields,” Opt. Commun. 125, 267–274 (1996).
- T. Alieva and F. Agullo-Lopez, “Diffraction analysis of random fractal fields,” J. Opt. Soc. Am. A 15, 669–674 (1998).
- T. Alieva and M. J. Bastiaans, “Radon–Wigner transform for optical field analysis,” in Optics and Optoelectronics, Theory, Devices and Applications, O. P. Nijhawan, A. K. Gupta, A. K. Musla, and Kehar Singh, eds. (Narosa, New Delhi, 1998), Vol. 1, 132–135.
- D. F. V. James and G. S. Agarwal, “The generalized Fresnel transform and its application to optics,” Opt. Commun. 126, 207–212 (1996).
- D. Stolen, “Operator methods in physical optics,” J. Opt. Soc. Am. 71, 334–341 (1981).
- M. Nazarathy and J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982).
- C. Gomez-Reino, “GRIN optics and its application in optical connections,” Int. J. Optoelectron. 7, 607–680 (1992).
- T. Alieva and F. Agullo-Lopez, “Reconstruction of the optical correlation function in a quadratic refractive index medium,” Opt. Commun. 114, 161–169 (1995).
- V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).
- L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42, 3084–3091 (1994).
- D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transform and their optical implementation,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).
- A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
- J. Shamir and N. Cohen, “Root and power transformations in optics,” J. Opt. Soc. Am. A 12, 2415–2423 (1995).
- M. J. Caola, “Self-Fourier functions,” J. Phys. A 24, L1143–L1144 (1991).
- G. Cincotti, F. Gori, and M. Santarsiero, “Generalized self-Fourier functions,” J. Phys. A 25, L1191–L1194 (1992).
- A. W. Lohmann and D. Mendlovic, “Self-Fourier objects and other self-transform objects,” J. Opt. Soc. Am. A 9, 2009–2012 (1992).
- D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Self-Fourier functions and fractional Fourier transforms,” Opt. Commun. 105, 36–38 (1994).
- T. Alieva, “On the self-fractional Fourier functions,” J. Phys. A 29, L377–L379 (1996).
- T. Alieva and A. Barbé, “Self-fractional Fourier functions and selection of modes,” J. Phys. A 30, L211–L215 (1997).
- T. Alieva and A. Barbé, “Self-imaging in fractional Fourier transform systems,” Opt. Commun. 152, 11–15 (1998).
- D. Choudhury, P. N. Puntambekar, and A. K. Chakraborty, “Optical synthesis of self-Fourier functions,” Opt. Commun. 119, 279–282 (1995).
- B. Javidi, “Securing information with optical technologies,” Phys. Today 50, No. 3, 27–32 (1997).

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