H.H. Wahba

Two-dimensional refractive index and stresses profiles of a homogenous bent optical fiber

We present a significant contribution to the theory of determining the refractive index profile of a bent homogenous optical fiber. In this theory we consider two different processes controlling the index profile variations. The first is the linear index variation due to stress along the bent radius, and the second is the release of this stress on the fiber surface. This release process is considered to have radial dependence on the fiber radius. These considerations enable us to construct the index profile in two dimensions normal to the optical axis, considering the refraction of light rays traversing the fiber. This theory is applied to optical homogenous bent fiber with two bending radii when they are located orthogonal to the light path of the object arm in the holographic setup (like the Mach-Zehnder interferometer). Digital holographic phase shifting interferometry is employed in this study. The recorded phase shifted holograms have been combined, reconstructed, and processed to extract the phase map of the bent optical fiber. A comparison between the extracted optical phase differences and the calculated one indicates that the refractive index profile variation should include the above mentioned two processes, which are considered as a response for stress distribution across the fibers cross section. The experimentally obtained refractive index profiles provide the stress induced birefringence profile. Thus we are able to present a realistic induced stress profile due to bending.

Nonray‐tracing determination of the 3D refractive index profile of polymeric fibres using single‐frame computed tomography and digital holographic interferometric technique

In this paper, we present a nonray‐tracing technique for evaluating the three dimensional distribution of the refractive index values inside polymeric fibres. This technique, named ‘single‐frame computed‐tomography (SFCT)’, is applied to digital holography. A comparative study between the calculated optical phase values using ordinary tomography and SFCT is carried out, and a negligible deviation is detected. The proposed technique is used to determine the three‐dimensional refractive index profile of isotactic Polypropylene fibres, IPP. The variation of the optical properties is measured before, during and after the formation of the necking phenomenon. In addition, SFCT technique is applied to the online determination of the change of the optical properties of IPP fibres. Holograms are given for illustration.

Characterization of a waveguide written by a UV laser into a planar polymer chip by digital holographic interferometry

The optical- functional properties of an integrated-optical strip-waveguide in a planar polymer chip are presented in this article. The waveguide was directly written into the surface of a planar polymer chip by UV-laser irradiation. Digital holographic interferometric phase shifting method is used to calculate the refractive index profile of the waveguide. This profile contains one or two zones according to the parameters of UV-laser. The mode field distribution and the effective mode indices for each zone are obtained. The study shows that the optical-functional properties strongly depend on the UV-irradiation parameters. Several mostly independently occurring photochemical processes competing with one another are proposed to explain the formation and shape of the refractive index distribution.

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.

A novel method for identifying the order of interference using phase-shifting digital holography

In this paper, we introduced a mathematical method for measuring the optical path length differences (OPDs), which is suitable for large OPD values where the fringes connections are difficult to detect. The proposed method is based on varying the width of the fringes, without changing the wavelength of the used coherent source. Also, in this work, we discussed the need for such method in off‐axis phase‐shifting digital holography. Low‐resolution off‐axis holograms failed to detect the correct interference order. In general, off‐axis phase‐shifting digital holography is limited by the resolution of the captured holograms. The results obtained using our proposed technique were compared to the results obtained using off‐axis phase‐shifting digital holograms and conventional two‐beam interferometry. Holograms were given for illustration.