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Focusing of dark hollow Gaussian electromagnetic beams in a plasma

Published online by Cambridge University Press:  08 January 2009

M.S. Sodha*
Affiliation:
Disha Academy of Research and Education, Disha Crown, Katchna Road, Shankarnagar, Raipur, India
S.K. Mishra
Affiliation:
Ramanna Fellowship Program, Department of Education Building, Lucknow University, Lucknow, India
S. Misra
Affiliation:
Ramanna Fellowship Program, Department of Education Building, Lucknow University, Lucknow, India
*
Address correspondence and reprint requests to: M.S. Sodha, Disha Academy of Research and Education, Disha Crown, Katchna Road, Shankarnagar, Raipur - 492 007, India. E-mail: [email protected]

Abstract

This paper presents an investigation of the focusing of dark hollow Gaussian electromagnetic beams (HGB) in plasma, considering collisional, ponderomotive, and relativistic nonlinearities. A paraxial like approach, in which the parameters are expanded, in terms of radial distance from the maximum of irradiance rather than that from the axis, has been adopted. To highlight the nature of focusing, both critical curves and the divider curves have been obtained as a plot of dimensionless radius vs. power of the beam. The effect of the order of HGB (n), and nature of nonlinearity on self focusing of the beam has also been explored.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Akhmanov, S.A., Sukhorukov, A.P. & Khokhlov, R.V. (1968). Self focusing and diffraction of light in a nonlinear medium. Sov. Phys. Usp. 10, 609636.CrossRefGoogle Scholar
Amiranoff, F., Baton, S., Bernard, D., Cros, B., Descamps, D., Derchies, F., Jaquet, F., Malka, V., Marques, J.R., Matthieussent, G., Mine, P., Modena, A., Mora, P., Manillo, J. & Nazmudin, Z. (1998). Observation of laser wakefield acceleration of electrons. Phys. Rev. Lett. 81, 995998.CrossRefGoogle Scholar
Andreev, N.E., Gorbunov, L.M., Kirsanov, V.I., Nakajima, K. & Ogata, A. (1997). Structure of the wake field in plasma channels. Phys. Plasma 4, 11451153.CrossRefGoogle Scholar
Andreev, N.E., Gorbunov, L.M. & Frolov, A.A. (1998). On the laser wakefield acceleration in plasma channels. Fiz. Plasmy 24, 888.Google Scholar
Arlt, J. & Dholakia, K. (2000). Generation of high order Bessel beams by use of an axicon. Opt. Commun. 177, 297301.CrossRefGoogle Scholar
Berge, L. (1998). Wave collapse in physics: principles and applications in light and plasma waves. Phys. Rep. 303, 259370.CrossRefGoogle Scholar
Cai, Y. & Lin, Q. (2004). Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems. J. Opt. Soc. Am. A 21, 10581065.CrossRefGoogle ScholarPubMed
Cai, Y., Lu, X. & Lin, Q. (2003). Hollow Gaussian beam and their propagation properties. Opt. Lett. 28, 10841086.CrossRefGoogle ScholarPubMed
Cai, Y. & He, S. (2006). Propagation of hollow Gaussian beams through apertured paraxial optical systems. J. Opt. Soc. Am. A 23, 14101418.CrossRefGoogle ScholarPubMed
Cai, Y. & Zhang, L. (2006 a). Coherent and partially coherent dark hollow beams with rectangular symmetry and paraxial propagation properties. J. Opt. Soc. Am. B 23, 13981407.CrossRefGoogle Scholar
Cai, Y. & Zhang, L. (2006 b). Propagation of various dark hollow beams in a turbulent atmosphere. Opt. Express 14, 13531367.CrossRefGoogle Scholar
Chen, Z.L., Unick, C., Vafaei-Najafabadi, N., Tsui, Y.Y., Fedosejevs, R., Naseri, N., Masson-Laborde, P.E. & Rozmus, W. (2008). Quasi-monoenergetic electron beams generated from 7 TW laser pulses in N2 and He gas targets. Laser Part. Beams 26, 147155.CrossRefGoogle Scholar
Chioa, R.Y., Garmire, E. & Townes, C.H. (1964). Self-trapping of optical beams. Phys. Rev. Lett. 13, 479482.CrossRefGoogle Scholar
Deng, D., Fu, X., Wei, C., Shao, J. & Fan, Z. (2005). Far field intensity distribution and M2 factor of hollow Gaussian beams. Appl. Opt. 44, 71877190.CrossRefGoogle ScholarPubMed
Desaix, M., Anderson, D. & Lisak, M.J. (1991). Variational approach to collapse of optical pulses. J. Opt. Soc. Am. B. 8, 20822086.CrossRefGoogle Scholar
Deutsch, C., Furukaw, H., Mima, K., Murakami, M. & Nishihara, K. (1996). Interaction physics of fast ignitor concept. Phys. Rev. Lett. 77, 24832486.CrossRefGoogle ScholarPubMed
Eder, D.C., Amendt, P., DaSilva, L.B., London, R.A., MacGowan, B.J., Matthaws, D.L., Penetrante, B.M., Rosen, M.D., Wilks, S.C., Donnelly, T.D., Falcone, R.W. & Strobel, G.L. (1994). Tabletop X-ray lasers. Phys. Plasmas 1, 17441752.CrossRefGoogle Scholar
Esarey, E., Sprangle, P., Krall, J. & Ting, A. (1997). Self-Focusing and Guiding of Short Laser Pulses in Ionizing Gases and Plasmas. IEEE J. Quantum Electron. 33, 18791914.CrossRefGoogle Scholar
Feit, M.D. & Fleck, J.A. Jr. (1988). Beam non-paraxiality, filament formation and beam breakup in the self focusing of optical beams. Opt. Soc. Am. B 5, 633640.CrossRefGoogle Scholar
Fibich, G. (2007). Some Modern Aspects of Self-Focusing Theory, a chapter in Self-focusing: Past and Present (Boyd, R.W., Lukishova, S.G. & Shen, Y. R., eds.) New York: Springer Verlag.Google Scholar
Ganic, D., Gan, X. & Gu, M. (2003). Focusing of doughnut laser beams by high numerical aperture objective in free space. Opt. Express 11, 27472752.CrossRefGoogle ScholarPubMed
Gill, T.S. & Saini, N.S. (2007). Nonlinear interaction of a rippled laser beam with an electrostatic upper hybrid wave in collisional plasma. Laser Part. Beams 25, 283293.CrossRefGoogle Scholar
Gao, Z. & Lu, B. (2006). Non-paraxial dark hollow Gaussian beams. Chin. Phys. Lett. 23, 106109.Google Scholar
Grow, T.D., Ishaaya, A.A., Vuong, L.T., Gaeta, A.L., Gavish, N. & Fibich, G. (2006). Collapse dynamics of super-Gaussian Beams. Opt. Express, 14, 54685475.CrossRefGoogle ScholarPubMed
Hauser, T., Scheid, W. & Hora, H. (1992). Theory of ions emitted from a plasma by relativistic self focusing of laser beams. Phys. Rev. A 45, 12781281.CrossRefGoogle ScholarPubMed
Herman, R.M. & Wiggins, T.A. (1991). Production and uses of diffractionless beams. J. Opt. Soc. Am. A 8, 932942.CrossRefGoogle Scholar
Hora, H. (1969). Self focusing of laser beams in a plasma by Ponderomotive forces. Z. Phys. 226, 156159.CrossRefGoogle Scholar
Hora, H. (1975). Theory of relativistic self focusing of laser radiations in plasmas. J. Opt. Soc. Am. 65, 882886.CrossRefGoogle Scholar
Hora, H. (1991). Plasmas at High Temperature and Density, Heildelberg: Springer.Google Scholar
Johannisson, P., Anderson, D., Lisak, M. & Marklund, M. (2003). Nonlinear Bessel beams. Opt. Commun. 222, 107115.CrossRefGoogle Scholar
Johnston, T.W., Vidal, F. & Fre'chette, D. (1997). Laser plasma filamentation and spatially periodic nonlinear Schrödinger equation approximation. Phys. Plasmas 4, 15821588.CrossRefGoogle Scholar
Jones, D.A., Kane, E.L., Lalousis, P., Wiles, P. & Hora, H. (1982). Density modification and energetic ion production at relativistic self focusing of laser beams in plasmas. Phys. Fluids 25, 22952301.CrossRefGoogle Scholar
Kane, E.L. & Hora, H. (1977). Laser Interaction and Related Plasma Phenomena (Schwarz, H.J. & Hora, H., Eds.). New York: Plenum.Google Scholar
Karlsson, M. (1992). Optical beams in saturable self focusing media. Phys. Rev. A 46, 27262734.CrossRefGoogle ScholarPubMed
Karlsson, M. & Anderson, D.J. (1992). Super-Gaussian approximation of the fundamental radial mode in nonlinear parabolic-index optical fibers. Opt. Soc. Am. B 9, 15581562.CrossRefGoogle Scholar
Kelley, P.L. (1965). Self-focusing of laser beams and stimulated Raman gain in liquids. Phys. Rev. Lett. 15, 10101012.Google Scholar
Kothari, N.C. & Abbi, S.C. (1990). Instability growth and filamentation of very intense laser beams in self-focusing media. Progr. Theor. Phys. 83, 414442.CrossRefGoogle Scholar
Kuga, T., Torii, Y., Shiokawa, N., Hirano, T., Shimizu, Y. & Sasada, H. (1997). Novel optical trap of atoms with a doughnut beam. Phys. Rev. Lett. 78, 47134716.CrossRefGoogle Scholar
Lee, H.S., Atewart, B.W., Choi, K. & Fenichel, H. (1994). Holographic non-diverging hollow beams. Phys. Rev. A 49, 49224927.CrossRefGoogle Scholar
Mei, Z. & Zhao, D. (2005). Controllable dark hollow beams and their propagation characteristics. J. Opt. Soc. Am. A 22, 18981902.CrossRefGoogle ScholarPubMed
Mei, Z. & Zhao, D. (2006). Controllable elliptical dark hollow beams. J. Opt. Soc. Am. A 23, 919925.CrossRefGoogle ScholarPubMed
Milchberg, H.M., Durfee, C.G. III & Mcllrath, T.J. (1995). Highorder frequency conversion in the plasma waveguide. Phys. Rev. Lett. 75, 24942497.CrossRefGoogle ScholarPubMed
Mora, P. & Antonsen, T.M. (1996). Electron cavitation and acceleration in the wake of an ultraintense self focused laser pulse. Phys. Rev. E 53, R2068R2071.CrossRefGoogle ScholarPubMed
Nayyar, V.P. (1986). Non-linear propagation of a mixture of degenerate modes of a laser cavity. J. Opt. Soc. Am. B 3, 711714.CrossRefGoogle Scholar
Neff, S., Knobloch, R., Hoffmann, D.H.H., Tauschwitz, A. & Yu, S.S. (2006). Transport of heavy-ion beams in a 1 m free-standing plasma channel. Laser Part. Beams 24, 7180.CrossRefGoogle Scholar
Niu, H.Y., He, X.T., Qiao, B. & Zhou, C.T. (2008). Resonant acceleration of electrons by intense circularly polarized Gaussian laser pulses. Laser Part. Beams 26, 5159.CrossRefGoogle Scholar
Osman, F., Castillo, R. & Hora, H. (1999). Relativistic and ponderomotive self- focusing at laser plasma interaction. J. Plasma Phys. 61, 263273.CrossRefGoogle Scholar
Ovchinnikov, Yu.B., Manek, I. & Grimm, R. (1997). Surface trap for Cs. Atoms based on evanescent-wave cooling. Phys. Rev. Lett. 79, 2225.CrossRefGoogle Scholar
Prakash, G., Sharma, A., Verma, M.P. & Sodha, M.S. (2006). Proc. Nat. Acad. Sci. India 76, 257263.Google Scholar
Rasmussen, J.J. & Rypdal, K. (1986). Blow-up in NLSE: A General Review. Phys. Scripta 33, 481497.CrossRefGoogle Scholar
Saini, N.S. & Gill, T.S. (2006). Self-focusing and self-phase modulation of an elliptic Gaussian laser beam in collisionless magnetoplasma. Laser Part. Beams 24, 447453.CrossRefGoogle Scholar
Sari, A.H., Osman, F., Doolan, K.R., Ghoranneviss, M., Hora, H., Hopfl, R, Benstetter, G. & Hantehzadehi, M.H. (2005). Application of laser driven fast high density plasma blocks for ion implantation. Laser Part. Beams 23, 467473.CrossRefGoogle Scholar
Sharma, A., Prakash, G., Verma, M.P. & Sodha, M.S. (2003). Three regimes of intense laser propagation in plasmas. Phys. Plasmas 10, 40794084.CrossRefGoogle Scholar
Sharma, A., Verma, M.P. & Sodha, M.S. (2004). Self focusing of electromagnetic beams in a collisional plasmas with nonlinear absorption. Phys. Plasmas 11, 42754279.CrossRefGoogle Scholar
Sharma, A., Verma, M.P., Sodha, M.S. & Tripathi, V.K. (2005). Self focusing of TEM-10 mode laser beam in a plasma. Indian J. Phys. 79, 393399.Google Scholar
Silberbarg, Y. (1990). Collapse of optical pulses. Opt. Lett. 15, 12821284.CrossRefGoogle Scholar
Snyder, A.W., Chen, Y., Poladian, L. & Mitchell, D.J. (1990). Fundamental modes of highly nonlinear fibers. Electron. Lett. 26, 643644.CrossRefGoogle Scholar
Sodha, M.S., Ghatak, A.K. & Tripathi, V.K. (1974 a). Self Focusing of Laser Beams in Dielectrics, Semiconductors and Plasmas, Delhi: Tata-McGraw-Hill.Google Scholar
Sodha, M.S., Nayyar, V.P. & Tripathi, V.K. (1974 b). Asymmetric focusing of the laser beam in a TEM-01 doughnut mode in dielectrics. J. Opt. Soc. Am. 64, 941943.CrossRefGoogle Scholar
Sodha, M.S., Tripathi, V.K. & Ghatak, A.K. (1976). Seif focusing of laser beams in plasmas and semiconducters. Prog. Opt. 13, 169265.CrossRefGoogle Scholar
Soding, J., Grimm, R. & Ovchinnikov, Yu.B. (1995). Gravitational laser trap for atoms with evanescent-wave cooling. Opt. Commun. 119, 652662.CrossRefGoogle Scholar
Song, Y., Milam, D. & Hill, W.T. (1999). Long narrow all-light atom guide. Opt. Lett. 24, 18051807.CrossRefGoogle ScholarPubMed
Sprangle, P. & Esarey, E. (1991). Stimulated backscattered harmonic generation from intense laser interactions with beams and plasmas. Phys. Rev. Lett. 67, 20212024.CrossRefGoogle ScholarPubMed
Sprangle, P., Esarey, E., Ting, A. & Joyee, G. (1988). Laser wakefield acceleration and relativistic optical guiding. Appl. Phys. Lett. 53, 21462148.CrossRefGoogle Scholar
Tabak, M., Hammer, J., Glinisky, M.E., Kruer, W.L., Wilks, S.C., WoodWorth, J., Campbell, E.M., Perry, M.D. & Mason, R.J. (1994). Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 16261634.CrossRefGoogle Scholar
Umstadter, D., Chen, S.Y., Maksimchuk, A., Mourou, G. & Wagner, R. (1996). Nonlinear optics in relativistic plasmas and plasmas and laser wakefield acceleration of electrons. Science 273, 472475.CrossRefGoogle Scholar
Umstadter, D. (2001). Review of physics and applications of relativistic plasmas driven by ultra-intense lasers. Phys. Plasmas 8, 17741785.CrossRefGoogle Scholar
Upadhyaya, A., Tripathi, V.K., Sharma, A.K. & Pant, H.C. (2002). Asymmetric self-focusing of a laser pulse in plasma. J. Plasma Phys. 68, 7580.CrossRefGoogle Scholar
Vidal, F. & Johnston, T.W. (1996). Electromagnetic beam breakup: multi filaments, single beam equilbriya and radiation. Phys. Rev. Lett. 77, 12821285.CrossRefGoogle Scholar
Wang, X. & Littman, M.G. (1993). Laser cavity for generation of variable radius rings of light. Opt. Lett. 18, 767770.CrossRefGoogle ScholarPubMed
Xu, X., Wang, Y. & Jhe, W. (2002). Theory of atom guidance in a hollow laser beam: dressed atom approach. J. Opt. Soc. Am. B 17, 10391050.CrossRefGoogle Scholar
Yin, J., Gao, W. & Zhu, Y. (2003). Propagation of various dark hollow beams in a turbulent atmosphere. Prog. Opt. 44, 119204.CrossRefGoogle Scholar
Yin, J., Zhu, Y., Wang, W., Wang, Y. & Jhe, W. (1998). Optical potential for atom guidance in a hollow laser beam. J. Opt. Soc. Am. B 15, 2533.CrossRefGoogle Scholar
York, A.G., Milchberg, H.M., Palastro, J.P. & Antonsen, T.M. (2008). Direct Acceleration of Electrons in a Corrugated Plasma Waveguide. Phys. Rev. Lett. 100, 195001–7.CrossRefGoogle Scholar
Yu, W., Yu, M.Y., Xu, H., Tian, Y.W., Chen, J. & Wong, A.Y. (2007). Intense local plasma heating by stopping of ultrashort ultraintense laser pulse in dense plasma. Laser Part. Beams 25, 631638.CrossRefGoogle Scholar
Zhou, J., Peatross, J., Murnane, M.M., Kapteyn, H.C. & Christov, I.P. (1996). High-order frequency conversion in the plasma waveguide. Phys. Rev. Lett. 76, 752755.CrossRefGoogle Scholar
Zhou, C.T., Yu, M.Y. & He, X.T. (2007). Electron acceleration by high current-density relativistic electron bunch in plasmas. Laser Part. Beams 25, 313319.CrossRefGoogle Scholar
Zhu, K., Tang, H., Sun, X., Wang, X. & Liu, T. (2002). Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams. Opt. Commun. 207, 2934.CrossRefGoogle Scholar