Abstract
If the medium is homogeneous, linear, isotropic, and non-dispersive, any electromagnetic wave can, in principle, be decomposed into plane waves, which are a simple and effective basis for complex wave equation solutions (1.4.12). But, in real cases, we have to deal with electromagnetic beams of limited size, and the decomposition in plane waves is not always the most appropriate. Consider, for example, the case of a monochromatic, and therefore continuous (CW, that is, continuous wave, single-frequency) laser beam; at every point in the space, its electric field oscillates sinusoidally over time. The spatial trend in this field is not equally simple: at first sight, a collimated laser beam is a genuinely good representation of a pencil of parallel geometric rays between them, but, with more careful observation, we find that the beam tends to expand due to the diffraction.
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Bibliographical references
Abramowitz M. and Stegun I.A., Handbook of Mathematical Functions, Dover Publications Inc., New York (1972).
Allen L. M., Beijersbergen W., Spreeuw R.J.C., and Woerdman J.P., Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev A 45, 8185-8189 (1992).
Anan’ev Y.A., Laser resonator and the beam resonance problem, Hadam Hilger, Bristol, IOP publishing Ltd (1992).
Arlt J. and Dholakia K., Generation of high-order Bessel beam by use of an axicon, Opt. Comm. 177, 297-301 (2000).
Arnaud J.A., Nonorthogonal Optical Waveguides and Resonators, The Bell System Technical Journal 49, 2311-2348 (November 1970).
Arnaud J.A. and Kogelnik H., Gaussian Light Beams with General Astigmatism, Appl. Optics 8, 1687-1693 (1969).
Bagini V., Frezza F., Santarsiero M., Schettini G., and Schirripa Spagnolo G., Generalized Bessel-Gauss Beams, J. of Mod. Optics 43, 1155-1166 (1996).
Boyd G.D. and Gordon J.P., Confocal Multimode Resonator for Millimeter Through Optical Wavelength Masers, Bell. Syst. Tech. J. 40, 489-508 (1961).
Boyd G.D. and Kogelnik H., Generalized Confocal Resonator Theory, Bell. Syst. Tech. J. 41, 1347-1369 (1962).
Bradley D.J. and Mitchell C.J., Characteristics of the defocused spherical Fabry-Perot interferometer as a quasi-linear dispersion instrument for high resolution spectroscopy of pulsed laser sources, Phil. Trans. R. Soc. A 263, 209-223 (1968).
Collins Stuart A. Jr., Analysis of Optical Resonators Involving Focusing Elements, Appl. Opt. 3, 1263-1275 (1964). Lens-System Diffraction Integral Written in Terms of Matrix Optics, J. Opt. Soc. Am. 60, 1168-1177 (1970).
Collins R.J., Nelson D.F., Schawlow A.L., Bond W., Garrett C.G.B., and Kaiser W., Coherence, Narrowing, Directionality, and Relaxation Oscillations in the Light Emission from Ruby, Phys. Rev. Lett. 5, 303-305 (1960).
Connes P., Augmentation du produit luminosité × résolution des interféromètres par l’emploi d’une différence de marche indépendante de l’incidence, Revue Opt. 35, 37- 43 (1956). L’étalon Fabry-Perot sphérique, J. Phys. Radium 19, 262-269 (1958).
Dingjan J., Multi-mode optical resonators and wave chaos, Thesis, Leiden University (2003), accessibile da http://iop.hqu.edu.cn/uploadfile/20111229162543941.pdf.
Durnin J., Exact solution for nondiffracting beams. I. The scalar theory, J. Opt. Soc. Am. A 4, 651-654 (1987).
Durnin J., Miceli J.J. Jr, and Eberly J.H., Diffraction-Free Beams, Phys. Rev. Lett. 58, 1499-1451 (1987).
Fox A.G. and Li T., Resonant Modes in a Maser Interferometer, Bell. Syst. Tech. J. 40, 453-488 (1961).
Gori F., Guattari G. and Padovani C., Bessel-Gauss Beams, Opt. Comm. 64, 491-495 (1987).
Guenther R., Modern Optics, John Wiley & Sons, New York (1990).
Herriott D., Kogelnik H., and Kompfner R., Off-axis paths in spherical mirror interferometers, Applied Optics 3, 523-526 (1964).
Iizuka K., Engineering Optics, Springer-Verlag, Berlino (1987).
Kogelnik H., On the Propagation of Gaussian Beams of Light Through Lenslike Media Including those with a Loss or Gain Variation, Appl. Optics 4, 1562-1569 (1965a). Imaging of Optical Modes - Resonators with Internal Lenses, Bell. Syst. Tech. J. 44, 455-494 (1965b).
Kogelnik H. and Li T., Laser Beams and Resonators, Appl. Opt. 5, 1550-1567 (1966a). Proc. IEEE 54, 1312-1320 (1966b).
Maiman T.H., Stimulated optical radiation in ruby, Nature 187, 493-494 (1960a). Optical and microwave-optical experiments in ruby, Phys. Rev. Lett. 4, 564-566 (1960b).
McLeod J.H., The axicon: a new type of optical element, J. Opt. Soc. Am. 44, 592-597 (1953).
Piccirillo B., Slussarenko S., Marrucci L., and Santamato E., The orbital angular momentum of light: genesis and evolution of the concept and of the associated photonic technology. Rivista del Nuovo Cimento 36, 501-554 (2013).
Popov M.M., Resonators for lasers with unfolded directions of principal curvatures, Opt. Spectrosc. 25, 231-217 (1968); Resonators for lasers with rotated directions of principal curvatures, Opt. Spectrosc. 25, 170-171 (1968).
Prokhorov A.M., Molecular amplifier and generator for submillimeter waves, Sov. Phys. JETP 7, 1140-1141 (1958).
Santarsiero M., Propagation of generalized Bessel-Gauss beams through ABCD optical Systems, Opt. Comm. 132, 1-7 (1996).
Schawlow A.L. and Townes C.H., Infrared and optical maser, Phys. Rev. 112, 1940-1949 (1958).
Scott G. and McArdle N., Efficient generation of nearly diffraction-free beams using an axicon, Opt. Engineering 31, 2640-2643 (1992).
Siegman A.E., Unstable optical resonator for laser application, Proc. IEEE 53, 277-287 (1965). Lasers, University Science Books, Mill Valley, California (1986).
Solimeno S., Crosignani B., Di Porto P., Guiding, Diffraction, and Confinement of Optical Radiation, Academic Press, inc., Orlando (1986).
Suematsu Y. and Fukinuki H., Matrix theory of light beam waveguides, Bull. Tokyo Inst. Technol. 88, 33-47 (1968).
Vasara A., Turunen J., and Friberg A.T., Realization of general nondiffracting beams with computer-generated holograms, J. Opt. Soc. Am. A 6, 1748-1754 (1989).
Vaughan J.M., The Fabry-Perot Interferometer, A. Hilger, Bristol (1989).
Weinstein L.A., Otkrytyye Rezonatory i otkrytyye volnovody (Moskow: Sovetskoye Radio, 1966); Open resonators and open waveguide, Golem Press (1969).
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Giusfredi, G. (2019). Propagation of Laser Beams in Linear Media. In: Physical Optics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-25279-3_6
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