Reconstruction of 3D refractive index distribution across the graded index optical fibre using digital holographic interferometry

Digital holographic interferometric phase shifting method is used to calculate the refractive index profile of graded index (GRIN) optical fibre and the 3D refractive index distribution across the GRIN fibre. GRIN optical fibre sample is immersed in a suitable liquid and then Mach-Zehnder-like arrangement phase shifting digital holographic system is used. The optical phase difference due to the graded index optical fibre can be extracted by digital holographic interferometric phase shifting technique. The problem of the tilted GRIN optical fibre with respect to the reference axis is solved, since the fibre must be perpendicular to the reference axis according to symmetry considerations. The optical phase difference map along the GRIN optical fibre is used to calculate the mean values of the optical phase difference across the fibre. The refractive index profile of GRIN optical fibre is calculated using the multilayer mathematical model, where the refraction of the incident rays through the fibre layers is considered. The shape parameter of the investigated optical fibre is determined. The mode field distributions can be analyzed for the used GRIN optical fibre. The calculated refractive index profile is used to reconstruct the 3D refractive index distribution across the fibre sample.

[1]  R. M. Derosier,et al.  Refractive index profiling of graded index optical fibers , 1976 .

[2]  E. M. Lifshitz,et al.  Electrodynamics of continuous media , 1961 .

[3]  U. Schnars.  Direct phase determination in hologram interferometry with use of digitally recorded holograms , 1994 .

[4]  D. Gabor.  Microscopy by reconstructed wave-fronts , 1949, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[5]  Mostafa Agour,et al.  On the digital holographic interferometry of fibrous material, I: Optical properties of polymer and optical fibers , 2010 .

[6]  P. Mathey,et al.  Numerical analysis of a WKB inverse method in view of index profile reconstruction in diffused waveguides , 1996 .

[7]  T. Kreis.  Holographic Interferometry: Principles and Methods , 1996 .

[8]  Dietrich Marcuse,et al.  TE modes of graded-index slab waveguides , 1973 .

[9]  T. Kreis.  Handbook of Holographic Interferometry: Optical and Digital Methods , 2004 .

[10]  A. Roberts,et al.  Three‐dimensional refractive index reconstruction with quantitative phase tomography , 2008, Microscopy research and technique.

[11]  E. Cuche,et al.  Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy. , 2005, Optics express.

[12]  J. Kahn,et al.  Principal Modes in Graded-Index Multimode Fiber in Presence of Spatial- and Polarization-Mode Coupling , 2009, Journal of Lightwave Technology.

[13]  W. A. Ramadan,et al.  On the determination of the refractive index of a fibre. II. Graded index fibre , 1995 .

[14]  D. Gabor.  A New Microscopic Principle , 1948, Nature.

[15]  W. A. Ramadan,et al.  On the determination of the refractive index of a fibre: I. Skin-core fibre , 1994 .

[16]  E. M. Lifshitz,et al.  Electrodynamics of continuous media (in Russian) , 1982 .

[17]  A. A. Hamza,et al.  Interferometric studies on the influence of temperature on the optical and dispersion parameters of GRIN optical fibre , 2007 .

[18]  Thomas Kreis,et al.  Digital holographic interferometric characterization of bent optical fibers , 2009 .

[19]  Toyohiko Yatagai,et al.  Multiple‐beam Fizeau fringe‐pattern analysis using Fourier transform method for accurate measurement of fiber refractive index profile of polymer fiber , 2002 .

[20]  Kin Seng Chiang,et al.  Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes , 1985 .

[21]  Hatem El-Ghandoor,et al.  Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes , 2001 .

[22]  Thomas Kreis,et al.  Characterization of graded index optical fibers by digital holographic interferometry. , 2009, Applied optics.

[23]  G. W. Stroke,et al.  Reconstruction of Phase Objects by Holography , 1965, Nature.

[24]  H. H. Wahba,et al.  Automatic fringe analysis of the induced anisotropy of bent optical fibres , 2008 .

[25]  M. Eguchi,et al.  Finite-element modal analysis of large-core multimode optical fibers. , 2004, Applied optics.

[26]  Toyohiko Yatagai,et al.  A subfringe integration method for multiple-beam Fizeau fringe analysis , 2003 .

[27]  A. A. Hamza,et al.  Refractive index profile of polyethylene fiber using interactive multiple‐beam fizeau fringe analysis , 2000 .

[28]  J. A. Buck,et al.  Fundamentals of optical fibers , 1995 .

[29]  W. A. Ramadan,et al.  Core-index determination of a thick fibre using lens-fibre interference (LFI) technique , 2004 .

[30]  W. A. Ramadan,et al.  Determination of GR-IN optical fibre parameters from transverse interferograms considering the refraction of the incident ray by the fibre , 2001 .

[31]  Thomas S. Huang,et al.  Digital Holography , 2003 .

[32]  Thomas Kreis,et al.  Characterization of optical fibers by digital holographic interferometry , 2009, Optical Metrology.

[33]  P. F. Heidrich,et al.  Optical waveguide refractive index profiles determined from measurement of mode indices: a simple analysis. , 1976, Applied optics.

[34]  J. Kahn,et al.  Higher-Order Modal Dispersion in Graded-Index Multimode Fiber , 2009, Journal of Lightwave Technology.