GRIN Rod Lens Research Articles

Coupling efficiency of single-mode fiber components using GRIN-rod lenses

Abstract This article analyzes the characteristics of single-mode fiber (SMF) components using graded-index-rod (GRIN-rod) lenses. The coupling efficiency of the SMF to GRIN-rod lens to SMF coupling system is derived in the general case. The problem is simplified by using the reciprocal field method. All solutions are in closed form. It is found that SMF position tolerance is about 3 μm; the angular tolerance is about 1°. The GRIN-rod lens position tolerance is much less critical while the angular tolerance is extremely small. These tolerances could be much less critical if the fiber is kept near the GRIN-rod lens axis.

Characteristic analysis of laser diode to multimode fiber coupling using a plano-convex GRIN lens

A ray model for a laser diode to analyze a multimode fiber coupling system is extended by taking the directivity into account. The validity is examined from the point of view of a far-field pattern. It is shown that the maximum coupling efficiency obtained at the best position of the fiber is strongly affected by the directivity, while the best position of the fiber existing between the paraxial image point and the best focus is almost independent of the directivity. The result of an extensive tolerance analysis of the longitudinal and lateral shifts of laser diode and optical fiber and of the curvature, the error in lens length, and the fourth-order index coefficient of the GRIN-rod lens is also shown as a contour map of coupling efficiency.

Narrow-linewidth laser with a prism grating/GRIN rod lens combination serving as external cavity

An external cavity laser transmitter module with only 20 mm cavity length is presented. A prism grating is used as a frequency-selective reflector. The coupling element between the laser diode and the prism grating is a permanently attached GRIN rod lens. Linewidths below 500 kHz at an output power of approximately 2mW have been reached with this compact set-up.

A reflective optical sensing technique employing a GRIN rod lens

A novel optical sensing technique is described, in which a mirror is displaced from a GRIN rod lens attached to two GRIN optical fibres. The reflected optical power is plotted as a function of mirror displacement and the displacement range is found to significantly exceed that available from a similar system employing fibres alone.

Design for SMF optical focusing‐beam system using GRIN rod lens

AbstractOptical communication systems using single mode fiber (SMF) with a low loss and a broad band are promising for a long distance large capacity transmission. In this paper, we found a design guideline for the actual accuracy required in the fabrication and for realizing a low insertion loss LD module essential for the system realization. A modal expansion method has been used for analysis of the coupling system with a GRIN rod lens created on one end of the fiber for an efficient coupling. Next, coupling experiments have been carried out to confirm the validity of the theoretical analysis. In addition, a low loss coupling system with a coupling loss of about 2.8 dB has been realized. Allowable displacements have been studied which determine the practical accuracy in the fabrication of the LD module. It is found that a coupling system with a large tolerance in displacement allowance can be realized with a focusing rod lens.

Characteristics of a compact three cavity laser configuration

Experimental and theoretical results on the characteristics of a compact three cavity transmitter configuration are presented. The configuration consists of a 1.3-μm semiconductor laser with external resonators on each side. One resonator is a spherical reflector positioned at the rear facet for sidemode suppression to about 30 dB. The other resonator at the front facet is a semitransparently gold coated grin-rod lens for linewidth reduction to about 1 MHz. The whole configuration has a length of less than 2 cm.

Aberration of GRIN-rod lenses in single-mode optical devices

Aberration of GRIN-rod lenses used in single-mode optical devices is analysed to the degree of third-order aberration. A valuable relationship is derived between the lens parameters and coupling efficiency of the devices. This relationship is very useful to evaluate and optimise optical device design.

Aberrations of Wood and GRIN rod lenses

Previously, fifth-order algebraic raytracing formulas for radial gradients have been derived by a method of successive approximations. These formulas are here extended to the trace of optical path lengths in radial gradients. Also, the formulas are exploited to obtain algebraic formulas for third- and fifth-order aberrations of Wood and GRIN rod lenses.

Accurate reconstruction of the refractive-index profile of fibers and preform rods from transverse interferometric data

A closed-form strict correlation between the interference fringe shift and the ray deflection function is derived which enables an accurate determination of the refractive-index distribution in fibers, preform rods, and GRIN-rod lenses to be performed by transverse interferometric methods. The refraction of the probing rays as well as the defocusing effect are entirely compensated and the immersion-object index mismatch is also taken into account. The comprehensive analysis presented proves that nondestructive transverse interferometry can be utilized as a reliable tool in the examination of both GRIN and step-index fibers and rods with low as well as with high numerical apertures.

Coupling loss analysis on a multimode fiber directional coupler using GRIN-rod lenses

For an efficient analysis of the coupling characteristic of a multimode fiber device using a GRIN-rod lens, a skew ray path in radial gradient suitable for an investigation of the third-order property of a GRIN-rod lens is derived by greatly modifying the first-order asymptotic solution found by Paxton and Streifer. Then, using the derived skew ray path, a coupling characteristic is analyzed on the multimode fiber directional coupler developed by Minemura et al. The result is shown as a contour map of coupling efficiency when the influences of defocus and the third-order aberrations of the GRIN-rod lens and of the lateral shifts of the optical fiber are taken into account. The validity of the ray trace analysis is also examined from the point of view of the far-field pattern of a multimode fiber.

Estimation of the fourth-order index coefficient of GRIN-rod lenses

The fourth-order index coefficients of GRIN-rod lenses are estimated using the magnitudes of the third-order wave-front spherical aberration reported by Cline and Jander and with the relationship between the third-order wave-front spherical aberration and the fourth-order index coefficient derived for the model of a near one-quarter pitch GRIN-rod lens in a double-pass configuration using the optical path length which is found analytically by algebraic manipulation of the asymptotic solution for the meridional ray equation derived by Streifer and Paxton.

Coupling characteristics of lens systems for laser diode modules using single-mode fiber

The characteristics of lens systems for coupling InGaAsP laser diodes to single-mode (SM) fibers are studied. Two groups of lens systems are investigated. One group employs a combination of lenses and a SM fiber in a conventional configuration. The other group utilizes a combination of lenses and a virtual fiber, where the virtual fiber is formed by attaching a GRIN rod lens to the input endface of the SM fiber. The maximum coupling efficiency and misalignment tolerances for the optical circuit components in these lens systems are compared from the viewpoint of fabricating laser diode modules. It is confirmed that lens systems using virtual fibers offer better coupling characteristics than does the conventional coupling method.

Reliable laboratory transmitter with submegahertz linewidth

An external-cavity transmitter configuration is introduced using a semiconductor laser at 1.3 μm wavelength, a spherical reflector for laser mode selection and a semitransparent Au-coated GRIN-rod lens for linewidth reduction. At 1.45 mW output power a linewidth of 700 kHz and a laser sidemode suppression of 30 dB is achieved.

Coupling characteristics of laser diode to multimode fiber using separate lens methods

This paper presents the characteristics of an InGaAsP laser diode to a multimode fiber coupling using four separate lens methods. The maximum coupling efficiencies and misalignment tolerances of optical circuit components are clarified for the specific methods: (1) using a relatively large spherical lens, (2) applying a hemispherical-ended GRIN rod lens, (3) using a combination of a relatively large spherical lens and a GRIN rod lens, and (4) employing a combination of two relatively large spherical lenses. The measured results are compared with those for a butt joint and tapered hemispherical-ended fiber methods. The coupling methods utilizing relatively large lenses are shown to have several features advantageous in the fabrication of practical laser diode modules.

Imaging and transforming capabilities of GRIN rods with noncylindrical surfaces of constant index: a family of exact solutions

Following the previously derived results a general condition is formulated which determines a family of the exact solutions for GRIN rod lenses with perfect (within the paraxial approximation) imaging and transforming capabilities. Using this condition a new index profile is closely evaluated, and the detailed analysis of this construction is presented.

A new confocal combination lens method for a laser-diode module using a single-mode fiber

A new confocal combination lens method is proposed, which can overcome severe misalignment tolerances for an InGaAsP laser diode to single-mode fiber coupling. Lens 2 in the confocal two-lens method is divided into two lenses, that is, lenses 21 and 22. The optimal distance between lenses 1 and 21 is found to be shorter than that for a confocal condition. Lens 22 is attached to the input endface of the single-mode fiber, thus forming a virtual fiber. Using 0.06- and 0.18-pitch GRIN rod lenses as lenses 21 and 22, the lateral and axial misalignment tolerances for the virtual fiber are improved by three and nine times, respectively, in comparison with those for the single-mode fiber. High-coupling efficiency of -3.0 dB of the laser diode to the single-mode fiber can be easily obtained including Fresnel reflections.

Combination lens method for coupling a laser diode to a single-mode fiber

A new combination lens method using a relatively large spherical lens and a virtual fiber is proposed for coupling an InGaAsP laser diode to a single-mode fiber. The virtual fiber is formed by attaching a GRIN rod lens to the input endface of the single-mode fiber. Coupling efficiency of from −3 to −4 dB is easily obtained. Alignment sensitivities of the proposed optical coupling circuit are investigated both theoretically and experimentally. The lateral and axial misalignment tolerances for the virtual fiber are improved three and nine times, respectively, in comparison with those for the single-mode fiber. The measured dependence of the coupling efficiency on the misalignments for the optical components agrees relatively well with the theoretical results through the ray matrix approach.

Misalignment losses at multimode graded-index fiber splices and GRIN rod lens couplers

A geometric optics model to describe transverse offset splice loss in multimode graded-index fiber, which has been adapted to evaluate misalignment losses at a graded-index rod (GRIN rod) lens-to-lens coupler, is reported. In both cases, the model gives close agreement with experimental measurements. Finally, in contrast with fiber splice losses, invariance of the lens coupler loss with the optical launch and receive conditions is shown.

Angular division multiplexer for fiber communication using graded-index rod lenses

An angular division multiplexer which uses graded-index (GRIN) rod lenses and a spatial modal filter (SMF) is described. Angular division multiplexing (ADM) uses selective excitation of mode groups " to multiplex signals in a transmission fiber. The GRIN-rod lenses collimate the input beams from two input fibers. The SMF selects particular mode groups from each input to be imaged on the transmission fiber. Design and construction of the device are described. Experimental results show that each signal is well confined to its designated mode groups. Crosstalk results are adequate for digital data transmission.

Focusing properties of gradient-index lens for laser-diode beam

Spot size and peak intensity of a light spot focused by a GRIN rod lens using a collimated laser-diode beam were measured as a function of the amount of defocus and of lens tilt. Assuming only primary spherical aberration, the wave aberration of the GRIN lens was estimated by diffraction theory taking the presence of aberrations into account. In a point-to-point imaging system, the spot size was measured as a function of the distance between lens and light source.