Electromagnetic Approach in Design of the Fiber-Based Evanescent Wave Sensors for the Mid-Infrared Spectroscopy

Abstract

In [1,2] we have proposed to use electromagnetic theory for analysis of radiation propagation in optical fibers immersed into an absorbing medium and applied this approach in design of chalcogenide sensing elements of the fiber-based evanescent wave sensors for the mid-IR spectroscopy of liquids. In theoretical treatment of the sensing elements made of unclad multimode fibers, ray optics was previously used. We have demonstrated that consideration of electromagnetic radiation propagating in a multimode fiber as a set of evanescent modes is efficient for revealing peculiarities of the evanescent wave sensing. For an unclad fiber, complex-valued propagation constants β=Re|β| + i· Im|β| of the evanescent modes can be found by solution of a characteristic equation [3], In fact, attenuation coefficients of the modes grow with increase of their radial m and azimuthal v orders (Fig. 1a) as well as with increase of wavelength (Fig. 1b). For selective excitation of evanescent modes with large attenuation coefficients 2· Im|β| in a sensing element, a source of coherent radiation is to be used. However a hybrid fiber-based element combining functions of sensing and supercontinuum generation can be designed because the group velocity dispersion (GVD) of the higher-order modes can be used to decrease the zero-GVD wavelength of chalcogenide glass (Fig. 1b inset). Besides the selective exciting of the evanescent modes, enhancing of attenuation coefficients in specially designed sensing elements can be applied. For a fiber with a multilayered cladding, a generalization of the exact finite difference method [4] based on solution of a linear system of equations written for longitudinal components of the electromagnetic field at the boundaries of the dielectric layers lias been used. For analysis of evanescent modes transformation at a fiber bend, the Wave Optics Module of Cortisol Multiphysics based on numerical solution of Maxwell's equations by using the finite-element method lias been applied. In this method, modes of a fiber bend are considered as modes of a straight fiber with a refractive index profile modified by using a conformai transformation. Attenuation coefficients of the modes grow with decrease of a bend radius (Fig.lc). Doubly degenerate modes are transformed at a bend at two modes having different polarizations and attenuation coefficients. We have revealed that in a bent fiber cross-section, there are energy flows oppositely propagating along the fiber axis (Fig. 1c, inset).