Skew Rays Research Articles

Measuring the Radial Position of Defects within Optical Fibers Using Skew Rays

Defects within optical fibers can cause premature failure in fiber-based systems and must be detected early to avoid performance degradation. Addressing this need can ensure that no defective optical fibers are being used by end users and improve processes to reduce the number of defects during manufacturing. The main challenge to date has been developing a technique that can measure defects along long lengths of fiber, within opaque packaging, and with position information. We demonstrate a simple and novel technique for detecting and radially resolving microscopic defects in packaged/buried fibers using an angle-resolved interrogator that analyzes the transmission of different ray groups. We have measured the accuracy to be as low as ±2 μm, which is sufficient for most fibers that have diameters in the order of ~100 μm.

Enhanced Pump Absorption of Active Fiber Components With Skew Rays

We propose a model and then demonstrate a technique that can be used to optimize pump absorption in active multimode fibers with different cladding geometries, by varying the angle of pump light excitation. The analysis of the contribution of different ray groups at different wavelengths enables the design optimization of active and passive fiber components in fiber lasers.

Enhanced responsivity with skew ray excitation of reflection- and transmission-type refractometric sensors.

The responsivity of optical fibers to refractive index can be enhanced using high-order skew rays compared with using meridional rays. Skew rays can have a much higher number of reflections with increased interaction length along the core-cladding interface, which gives rise to stronger interactions with the external medium. Reflection/transmission-type refractometric sensors based on twin-coupled-core and multimode fibers showed one/two orders of magnitude increase in responsivity with skew ray excitation. The responsivity and sensitivity for the two types are ~2000%/RIU, ~1400%/RIU, and 4.9×10⁻⁵ RIU, 7.0×10⁻⁵ RIU, respectively.

Skew ray tracing and sensitivity analysis of hyperboloid optical boundary surfaces

One of the most popular mathematical tools in fields of robotics, mechanisms and computer graphics is the 4×4 homogeneous transformation matrix. Our group's previous application of the homogeneous transformation matrix to flat and spherical optical boundaries has been extended to hyperboloid surfaces for: (1) skew ray tracing to determine the paths of reflected/refracted skew rays; (2) sensitivity analysis for direct mathematical expression of differential changes of incident points and reflected/refracted vectors with respect to changes in incident light sources and boundary geometric parameters; (3) a sensitivity analysis-based merit function derived directly from mathematical expression of catadioptric imaging system components. The presented methodology is highly suited to digital implementation and offers direct and rapid analytical statement of ray path, chief ray, marginal rays and merit functions of optical systems.

The Role of Skew Rays in Biomedical Sensing

Hollow core waveguides are useful tools in biomedical optics both for transmission of radiation to the tissue to perform intervention and to sensing tissue optical parameters for diagnostics. These waveguides can also be used as an interaction chamber for sensing the presence and concentration of different aerosols and gases. To support the design and analyzing of such a device, we developed a computerized, ray tracing simulation. As aerosol particles tend to aggregate near the waveguide's wall, the role of skew rays (i.e., rays that follow a helical path inside the waveguide) is investigated here and compared with merdional rays, which “zig-zag” through the optical axis. To test quantitatively the sensing quality of different types of beam, a measure for the beam-sensing quality is developed. As first step, the validation of the simulation results is presented. Then, a compression between the sensing quality of Guassian, ring-like, and Bessel beam is made. These results allow the optimization of ray coupling to a hollow core waveguide-based, aerosol-sensing devices.

Skew ray tracing and sensitivity analysis of ellipsoidal optical boundary surfaces

The 4 × 4 homogeneous transformation matrix is one of the most commonly applied mathematical tools in the fields of robotics, mechanisms and computer graphics. Here we extend further this mathematical tool to geometrical optics by addressing the following two topics: (1) skew ray tracing to determine the paths of reflected/refracted skew rays crossing ellipsoidal boundary surfaces; and (2) sensitivity analysis to determine via direct mathematical analysis the differential changes of the incident point and the reflected/refracted vector with respect to changes in the incident light source. The proposed ray tracing and sensitivity analysis are projected as the nucleus of other geometrical optical computations.

Skew Ray Tracing and Sensitivity Analysis of Paraboloidal Optical Boundary Surfaces

One of the most popular mathematical tools in fields of robotics, mechanisms and computer graphics is the 4x4 homogeneous transformation matrix. In previous work we applied this matrix to the optical domains of flat and spherical surfaces for: (1) skew ray tracing to determine the paths of skew rays being reflected/refracted; (2) sensitivity analysis to determine by direct mathematical analysis the differential change of incident point and reflected/refracted vector with respect to change in incident light source. The present work extends our previous work to include the case of parabaloidal boundary surfaces.

9.2: Skew Ray Compensated Color Separation Prism for Projection Display Applications

AbstractProjection display systems that use polarization as a means for image recovery require phase compensation of skew rays to achieve high contrast. This paper describes a new color separation prism design that compensates skew ray phase errors using only thin film coatings. The new prism maintains high contrast for systems as fast as f/2.5.

Analytic Solutions of the Eikonal Equation for a GRIN-rod Lens 2. Skew Rays

Abstract Analytic solutions of the eikonal equation for a skew ray in a GRIN-rod lens are derived together with those of the ray equation by the perturbation method. It is algebraically shown that the derived solutions agree with the exact ones for a meridional ray in the sech profile and for a helical ray in the helical exact profile. The numerical accuracy is also examined by the Runge-Kutta-Gill method for the sech profile.

Skew rays in optical fibers

In order to justify the use of meridional analysis, the authors solve the Eikonal equation without approximationin two cases of index profile. Limit conditions are studied and attention is given to skew rays with inclination over the fiber axis greater than the critical angle of the meridional case. It is shown that skew rays introduce a queue in the impulse response of a fiber. In the case of solid state laser sources, they do not carry significant energy, and then can be neglected.

Analytic Solution of Ray Equations in Cylindrically Inhomogeneous Guiding Media Part 2: Skew Rays

Analytic solutions are found for skew ray paths in inhomogeneous cylindrical systems such as GRIN rods and gas lenses, which focus rays by virtue of a gradual radial decrease in refractive index. The solutions are obtained by employing digital computers to carry out analytic, as opposed to numerical, calculations.

Tracing Skew Rays through Concave Diffraction Gratings

A method for tracing exact skew rays through spherical concave reflecting gratings is developed; modifications for plane gratings and for gratings ruled on toric and ellipsoidal blanks are indicated.

The Wave Aberration Associated with Skew Rays

It is shown that invariant foci exist for skew rays, and simple formulae are obtained for the change in aberration relative to those foci due to refraction or reflection at an interface. The formulae are valid for any form of interface Expressions for focal shifts are obtained together with check formulae The method makes possible the analysis of the aberrations along skew rays as they arise at individual surfaces.

Vectorial Treatment of Refraction of Skew Rays By a Prism

Vectorial Treatment of Refraction of Skew Rays By a Prism