Theoretical formulation and numerical simulation of 1D Fresnel diffraction from a phase step with two different kinds of material on sides of step in reflection mode

Authors

Abstract

    When a plane wavefront of a monochromatic and semi coherent is incident on a step, the reflected beam of light diffracted from the step because of the abrupt changes in the amplitude and phase of wave at the boundary of the step therefore fringes pattern is formed in perpendicular of propagation of light that can be described by Fresnel- Kirchhoff integrals. Recently numerous applications of this kind of Fresnel diffraction has been investigated involving measurement of thickness of thin films by accuracy of nanometers, accurate measurement of refractive index of solids and liquids, determination of dispersion relation of materials, measurement of nanometer displacement and measurement of wavelength by angstrom accuracy. In this report we will be shown that when two sides of a phase step which its boundary is perpendicular to the plane of incidence are two different materials, the intensity distribution in the fringes pattern of diffraction from a step is a function of optical constants of materials and height of the step. Numerical simulations of this case indicates that by having the intensity distribution of fringes pattern in several incident angels for polarized beam of light parallel or normal to the plane of incident we can determine optical constants of materials of both sides of step and its height. These simulations are performed for cases of one side dielectric and other side conductor, both side’s conductor and both side dielectric. Primary experimental results are in good agreement with theoretical and numerical results.

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References

[1]     J.J. Chieh, S.Y. Yang, H.E. Horng, C.Y. Hong, and H.C. Yang, "Measurements of the Complex Transmission/Reflection Coefficient of a Material Using Mixed-Type Common-Path Heterodyne Interferometry", IEEE Transactions on Instrumentation and Measurement 58, NO. 6 (2009) 1878 - 1885.
[2]     R.M.A. Azzam and N.M. Bashara, “Ellipsometery and Polaraized Light”, North-Holland Company publishing (1977).
[3]    J. Jung, J. Bork, T. Holmgaard, N.A. Kortbek, and K. Pedersen," Ellipsometery", Aalborg University, Institute of Physics and Nanotechno- logy (2004).
[4]   N. Farahi, A. Motazedi Fard, S. R. Hosseini and M. Taghi Tavassoly, "Fresnel diffraction by abrupt change of amplitude, phase, coherency and polarization", Winter College on Optics in Imaging Science, miramare- trieste-italy (2011).
[5]  M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.R. Moradi, "Optical diffractometry," J. Opt. Soc. Am. A 26 (2009) 540-547.
[6]   M. Amiri and M.T. Tavassoly, "Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes," Optics Communications 272 (2007) 349-361.
[7]  M. Taghi Tavassoly, I. Moaddel Haghighi, and K. Hassani, "Application of Fresnel diffraction from a phase step to the measurement of film thickness," Appl. Opt. 48 (2009) 5497-5501.
[8]   M. Taghi Tavassoly and A. Saber, “Optical Refractometry Based on Fresnel Diffraction from a Phase Wedge,” Opt. Lett. 35 (2010) 3679-3681.
[9]   M. Taghi Tavassoly, R. Rezvani Naraghi, A. Nahal and K. Hassani, “High precision refractometry based on Fresnel diffraction from phase plates”, Opt. Lett. 37, No. 9 (2012) 1493-1495. 
[11] M. Taghi Tavassoly, S.R. Hosseini, A. Motazedi Fard, and R. Rezvani Naraghi, “Applications of Fresnel diffraction from the edge of a transparent plate in transmission,” Appl. Opt. 51, No. 30 (2012) 7170–7175.319
[13]     M.T. Tavassoly, A. Darudi, H.R. Khalesifard, and S.M.R. Sadat Hosseini, "Applications of Fresnel diffraction from phase objects," SPIE the International Society for Optical Engineering 4399 (2001) 98-106.
[14]   M.T. Tavassoly, M. Amiri, E. Karimi, and H.R. Khalesifard, "Spectral modification by line singularity in Fresnel diffraction from 1D phase step," Optics Communications 255 (2005) 23-34.
[15]   R. Aalipour, M. Taghi Tavassoly, and A. Drrudi,"Superimposing the waves diffracted from two similar hot and cold wires provides the temperature profile around the hot one", Appl. Opt. 49 No. 22 (2010) 3768- 3773.
[16]   M. Born, E. Wolf, and A. B. Bhatia, “Principles of Optics”, Pergamon Press (1975).
[17]   T. C. Poon and T. Kim, “Engineering Optics with MATLAB”, World Scientific Publishing, (2006).
Iranian Journal of Applied Physics
Volume 2, Issue 2 - Serial Number 2
December 2012
Pages 5-29

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History

  • Receive Date: 03 December 2012
  • Revise Date: 02 January 2013
  • Accept Date: 28 January 2013

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