Photon Localization inside a Waveguide Modeled by Uncertainty Principle
In the present work, an attempt is made to understand
electromagnetic field confinement in a subwavelength waveguide
structure using concepts of quantum mechanics. Evanescent field in
the waveguide is looked as inability of the photon to get confined in
the waveguide core and uncertainty of position is assigned to it. The
momentum uncertainty is calculated from position uncertainty.
Schrödinger wave equation for the photon is written by incorporating
position-momentum uncertainty. The equation is solved and field
distribution in the waveguide is obtained. The field distribution and
power confinement is compared with conventional waveguide theory.
They were found in good agreement with each other.
[1] C. Adlard, E. Pike, S. Sarkar, "On the Localization of One-Photon
States", Phys.Rev.Lett. vol. 79, pp. 1585-1587, 1997.
[2] I. Bialynicki-Birula, "Exponential Localization of Photons", Phys. Rev.
Lett, vol 80, pp. 5247- 5250, 1998.
[3] K. W. Chan, C. K. Law, and J. H. Eberly, "Localized Single-Photon
Wave Functions in Free Space", Phys. Rev. Lett, vol 88, 100402 (4)
Feb. 2002
[4] O. Keller, "On the theory of spatial localization of photons", Physics
Reports, Volume 411, Issues 1-3, pp. 1-232, May 2005.
[5] I. Bialynicki-Birula, "Photon Wave Function", Progress in Optics", Vol.
XXXVI, Ed. E. Wolf Elsevier, Amsterdam, 1996.
[6] R.E Nistor, "Quantum aspects of photon propagation in transparent
infinite homogeneous media", Romanian Reports in Physics, Vol. 60,
No. 3, pp. 471-491, 2008
[7] J E Sipe, "Photon wave functions", Physica review A, vol. 52, pp 1875-
1883 September 1995
[8] D.L. Khokhlov, "Spatial and Temporal Wave Functions" , Applied
Physics Research vol. 2, No. 2; pp. 49-54, November 2010.
[9] M. G. Raymer and Brian J. Smith, "The Maxwell wave function of the
photon" in Proc. SPIE conference Optics and Photonics, number 5866,
The Nature of Light: What is a Photon?" San Diego, Aug. 2005
[10] I. Bialynicki-Birula, "On the Wave Function of the Photon", Acta
Physica Polonica, vol. 86 , pp. 97-116 1994.
[11] J. J. Sakurai, "Advanced Quantum Mechanics", Addison-Wesley
Publishing Company, 1967, pp.34-35.
[12] Z.Y. Wang1, C. D.Xiong, O. Keller, "Photon Position Operator and
Localization of Photons inside a Waveguide" pp 9-10.
http://arxiv.org/ftp/quant-ph/papers/0511/0511270.pdf
[13] Z.-Y. Wang, C.-D. Xion, B. He, "Superluminal propagation of
evanescent modes as a quantum effect" Volume 17, Issue 5, pages 319-
325, May 2008
[14] P.N Prasad, "Nanophotonics", John Wiley &Sons Inc.,2004, pp.10-19.
[15] A. Sarkar, T .K .Bhattacharyya, "Interpretation of Electron Tunneling
from Uncertainty Principle", DOI: http://arXiv.org/abs/quantph/
0507239v1
[16] C.R. Pollock, "Fundamnetal of optoelectonics", Richard D. Irwin Inc.
1995, USA.
[1] C. Adlard, E. Pike, S. Sarkar, "On the Localization of One-Photon
States", Phys.Rev.Lett. vol. 79, pp. 1585-1587, 1997.
[2] I. Bialynicki-Birula, "Exponential Localization of Photons", Phys. Rev.
Lett, vol 80, pp. 5247- 5250, 1998.
[3] K. W. Chan, C. K. Law, and J. H. Eberly, "Localized Single-Photon
Wave Functions in Free Space", Phys. Rev. Lett, vol 88, 100402 (4)
Feb. 2002
[4] O. Keller, "On the theory of spatial localization of photons", Physics
Reports, Volume 411, Issues 1-3, pp. 1-232, May 2005.
[5] I. Bialynicki-Birula, "Photon Wave Function", Progress in Optics", Vol.
XXXVI, Ed. E. Wolf Elsevier, Amsterdam, 1996.
[6] R.E Nistor, "Quantum aspects of photon propagation in transparent
infinite homogeneous media", Romanian Reports in Physics, Vol. 60,
No. 3, pp. 471-491, 2008
[7] J E Sipe, "Photon wave functions", Physica review A, vol. 52, pp 1875-
1883 September 1995
[8] D.L. Khokhlov, "Spatial and Temporal Wave Functions" , Applied
Physics Research vol. 2, No. 2; pp. 49-54, November 2010.
[9] M. G. Raymer and Brian J. Smith, "The Maxwell wave function of the
photon" in Proc. SPIE conference Optics and Photonics, number 5866,
The Nature of Light: What is a Photon?" San Diego, Aug. 2005
[10] I. Bialynicki-Birula, "On the Wave Function of the Photon", Acta
Physica Polonica, vol. 86 , pp. 97-116 1994.
[11] J. J. Sakurai, "Advanced Quantum Mechanics", Addison-Wesley
Publishing Company, 1967, pp.34-35.
[12] Z.Y. Wang1, C. D.Xiong, O. Keller, "Photon Position Operator and
Localization of Photons inside a Waveguide" pp 9-10.
http://arxiv.org/ftp/quant-ph/papers/0511/0511270.pdf
[13] Z.-Y. Wang, C.-D. Xion, B. He, "Superluminal propagation of
evanescent modes as a quantum effect" Volume 17, Issue 5, pages 319-
325, May 2008
[14] P.N Prasad, "Nanophotonics", John Wiley &Sons Inc.,2004, pp.10-19.
[15] A. Sarkar, T .K .Bhattacharyya, "Interpretation of Electron Tunneling
from Uncertainty Principle", DOI: http://arXiv.org/abs/quantph/
0507239v1
[16] C.R. Pollock, "Fundamnetal of optoelectonics", Richard D. Irwin Inc.
1995, USA.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51550", author = "Shilpa N. Kulkarni and Sujata R. Patrikar", title = "Photon Localization inside a Waveguide Modeled by Uncertainty Principle", abstract = "In the present work, an attempt is made to understand
electromagnetic field confinement in a subwavelength waveguide
structure using concepts of quantum mechanics. Evanescent field in
the waveguide is looked as inability of the photon to get confined in
the waveguide core and uncertainty of position is assigned to it. The
momentum uncertainty is calculated from position uncertainty.
Schrödinger wave equation for the photon is written by incorporating
position-momentum uncertainty. The equation is solved and field
distribution in the waveguide is obtained. The field distribution and
power confinement is compared with conventional waveguide theory.
They were found in good agreement with each other.", keywords = "photon localization in waveguide, photon tunneling,
quantum confinement of light, Schrödinger wave equation,
uncertainty principle.", volume = "6", number = "3", pages = "227-3", }