Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism

Abstract

A fiber-optic collimator that emits a Gaussian beam with its beam waist at a certain distance after the exit face of the lens is labeled a self-imaging collimator. For such a collimator, the waist of the emitted Gaussian beam and its location are partly dependent on the properties of the gradient-index (GRIN) lens. Parameters for the self-imaging collimator are formulated in terms of the parameters of a GRIN lens (e.g., pitch, core refractive index, gradient index, length) and the optical wavelength. Next, by use of the Gaussian beam approximation, a general expression for the coupling power loss between two self-imaging-type single-mode fiber (SMF) collimators is, for the first time to our knowledge, derived as a function of three types of misalignment, namely, separation, lateral offset, and angular tilt misalignment. A coupling experiment between two self-imaging collimators with changing separation distance is successfully performed and matches the proposed self-imaging mechanism coupling loss theory. In addition, using a prism, lateral offset, as well as angular tilt, misalignments are experimentally simulated for a two self-imaging collimator coupling condition by a single collimator reflective test geometry. Experimental results agree well with the proposed loss formulas for self-imaging GRIN lenses. Hence, for the first time to our knowledge, the mathematical foundations are laid for employing self-imaging-type fiber collimators in SMF-based free-space systems allowing optimal design for ultra-low-loss coupling.

Single-lens equivalent systems for Grin lenses

“…(11) proves that at this pitch length the Grin lens is equal to the combination of one optical inverter and one single lens system. In other words, this Grin lens at first inverts the object, and then act as a single lens system to form the images of objects, as shown in Fig.…”

“…Particularly, the recent development of medical endoscope system employing Grin lens [8][9][10] and many other applications [11] have created urgency for one simple optical equivalent system to substitute for complex Grin lens, facilitating its optical analysis, especially the objectimaging relation. In this paper, one simple single-lens equivalent system for Grin lens in homogeneous medium, which is based on matrix optics, is proposed.…”

Ultra-High Temperature Sensors Based on Optical Property

“…The computer also stores the received optical power readings for the given wavelength as well as the received Infrared (IR) beam video images from the alignment camera. To measure the gas temperature, the computer instructs the laser to provide optical power of a given infrared wavelength (e.g., 1550 nm) and amount (e.g., 10 dBm) to the SMF that in-turn feeds the FL operated in the low freespace-SMF coupling loss self-imaging condition between SiC chip plane and FL [36]. This light is launched towards the SiC chip sitting at the tip of the probe.…”

Numerical analysis of gradient index lens–based optical coherence tomography imaging probes

“…However, the theory of GRIN lens-based probes has either been largely overlooked or only simplified configurations of probe designs have been considered. [7][8][9][10][11] In this paper, we numerically analyze the performance of various GRIN lens-based OCT probes constructed from commercially available components. A theoretical model is formulated by analyzing the propagation of a single-mode (TEM 00 ) Gaussian beam, within the paraxial approximation.…”