{"title":"Photon Localization inside a Waveguide Modeled by Uncertainty Principle","authors":"Shilpa N. Kulkarni, Sujata R. Patrikar","volume":63,"journal":"International Journal of Nuclear and Quantum Engineering","pagesStart":272,"pagesEnd":275,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/2418","abstract":"In the present work, an attempt is made to understand\r\nelectromagnetic field confinement in a subwavelength waveguide\r\nstructure using concepts of quantum mechanics. Evanescent field in\r\nthe waveguide is looked as inability of the photon to get confined in\r\nthe waveguide core and uncertainty of position is assigned to it. The\r\nmomentum uncertainty is calculated from position uncertainty.\r\nSchr\u00f6dinger wave equation for the photon is written by incorporating\r\nposition-momentum uncertainty. The equation is solved and field\r\ndistribution in the waveguide is obtained. The field distribution and\r\npower confinement is compared with conventional waveguide theory.\r\nThey were found in good agreement with each other.","references":"[1] C. Adlard, E. Pike, S. Sarkar, \"On the Localization of One-Photon\r\nStates\", Phys.Rev.Lett. vol. 79, pp. 1585-1587, 1997.\r\n[2] I. Bialynicki-Birula, \"Exponential Localization of Photons\", Phys. Rev.\r\nLett, vol 80, pp. 5247- 5250, 1998.\r\n[3] K. W. Chan, C. K. Law, and J. H. Eberly, \"Localized Single-Photon\r\nWave Functions in Free Space\", Phys. Rev. Lett, vol 88, 100402 (4)\r\nFeb. 2002\r\n[4] O. Keller, \"On the theory of spatial localization of photons\", Physics\r\nReports, Volume 411, Issues 1-3, pp. 1-232, May 2005.\r\n[5] I. Bialynicki-Birula, \"Photon Wave Function\", Progress in Optics\", Vol.\r\nXXXVI, Ed. E. Wolf Elsevier, Amsterdam, 1996.\r\n[6] R.E Nistor, \"Quantum aspects of photon propagation in transparent\r\ninfinite homogeneous media\", Romanian Reports in Physics, Vol. 60,\r\nNo. 3, pp. 471-491, 2008\r\n[7] J E Sipe, \"Photon wave functions\", Physica review A, vol. 52, pp 1875-\r\n1883 September 1995\r\n[8] D.L. Khokhlov, \"Spatial and Temporal Wave Functions\" , Applied\r\nPhysics Research vol. 2, No. 2; pp. 49-54, November 2010.\r\n[9] M. G. Raymer and Brian J. Smith, \"The Maxwell wave function of the\r\nphoton\" in Proc. SPIE conference Optics and Photonics, number 5866,\r\nThe Nature of Light: What is a Photon?\" San Diego, Aug. 2005\r\n[10] I. Bialynicki-Birula, \"On the Wave Function of the Photon\", Acta\r\nPhysica Polonica, vol. 86 , pp. 97-116 1994.\r\n[11] J. J. Sakurai, \"Advanced Quantum Mechanics\", Addison-Wesley\r\nPublishing Company, 1967, pp.34-35.\r\n[12] Z.Y. Wang1, C. D.Xiong, O. Keller, \"Photon Position Operator and\r\nLocalization of Photons inside a Waveguide\" pp 9-10.\r\nhttp:\/\/arxiv.org\/ftp\/quant-ph\/papers\/0511\/0511270.pdf\r\n[13] Z.-Y. Wang, C.-D. Xion, B. He, \"Superluminal propagation of\r\nevanescent modes as a quantum effect\" Volume 17, Issue 5, pages 319-\r\n325, May 2008\r\n[14] P.N Prasad, \"Nanophotonics\", John Wiley &Sons Inc.,2004, pp.10-19.\r\n[15] A. Sarkar, T .K .Bhattacharyya, \"Interpretation of Electron Tunneling\r\nfrom Uncertainty Principle\", DOI: http:\/\/arXiv.org\/abs\/quantph\/\r\n0507239v1\r\n[16] C.R. Pollock, \"Fundamnetal of optoelectonics\", Richard D. Irwin Inc.\r\n1995, USA.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 63, 2012"}