Graded-index Rod Lens Research Articles

110 μm thin endo-microscope for deep-brain in vivo observations of neuronal connectivity, activity and blood flow dynamics

Light-based in-vivo brain imaging relies on light transport over large distances of highly scattering tissues. Scattering gradually reduces imaging contrast and resolution, making it difficult to reach structures at greater depths even with the use of multiphoton techniques. To reach deeper, minimally invasive endo-microscopy techniques have been established. These most commonly exploit graded-index rod lenses and enable a variety of modalities in head-fixed and freely moving animals. A recently proposed alternative is the use of holographic control of light transport through multimode optical fibres promising much less traumatic application and superior imaging performance. We present a 110 μm thin laser-scanning endo-microscope based on this prospect, enabling in-vivo volumetric imaging throughout the whole depth of the mouse brain. The instrument is equipped with multi-wavelength detection and three-dimensional random access options, and it performs at lateral resolution below 1 μm. We showcase various modes of its application through the observations of fluorescently labelled neurones, their processes and blood vessels. Finally, we demonstrate how to exploit the instrument to monitor calcium signalling of neurones and to measure blood flow velocity in individual vessels at high speeds.

Single-mode fiber-to-single-mode fiber coupling efficiency and tolerance analysis: comparative study for ball, conic and GRIN rod lens coupling schemes using Zemax Huygen's integration and physical optics calculations

In this work, numerical coupling efficiency calculations comparing single-mode fiber (SMF) to SMF coupling schemes using uncoated single ball, conic and graded-index (GRIN) rod lenses are discussed. The reported fiber coupling efficiency (FCE) calculations were performed using Huygens integral and Gaussian beam physical optics propagation (GBPOP) features in Zemax®. The Huygens integral method results indicate that the FCE for ball, conic and GRIN rod single uncoated lenses (without accounting for Fresnel reflection and bulk absorption effects) can reach with the optimal lens and fiber parameters 91.11% (N-BK7 glass), 99.68% (N-BK7 glass) and 96.58%, respectively. In comparison, the calculated FCE for uncoated N-BK7 glass ball lens using the GBPOP method was 87.22% (without accounting for Fresnel reflections and bulk absorption effects). Furthermore, FCE calculations for ball lenses made out of sapphire, fused silica, S-LAH79 and N-LASF9 glass are given. The calculated deviation between the GBPOP and Huygens integral methods is <0.5%. Finally, tolerance analysis for each lens coupling scheme relating FCE to the tilts and the decentering of the lens and the two fibers is provided. The tolerance analysis calculations indicate that decentering of fibers and the single lens has the highest impact on the FCE values. Finally, FCE results suggest that the GRIN lens coupling scheme is the most sensitive scheme to misalignment and the ball lens scheme is the least sensitive to misalignment.

Polarization entanglement with graded-index lenses

By using an optical device based on the integration of a graded-index (GRIN) rod lens and a single-mode optical fiber we efficiently collected photon pairs generated by spontaneous parametric down-conversion. We show that this system preserves the polarization entanglement of the two-photon states. Hence this device, characterized by a remarkable easiness of alignment and allowing for high coupling efficiency of single-mode radiation, can be used with photons entangled in various degrees of freedom, such as polarization and spatial momentum and to interconnect different sides of complex optical circuits.

Phase-shifting VOA with polymer dispersed liquid crystal

A polymer containing fine droplets of liquid crystal (LC) is investigated for obtaining an optical phase-shifting attenuator at 1550-nm wavelength. Two mixtures of liquid crystals and monomers are compared for a cell thickness of 15 μm. The first method uses nanosized LC droplets to achieve 2.29-rad phase shifting for an applied voltage of 230 Vrms. The second method uses microsized LC droplets to achieve 2.35-rad phase shifting for an applied voltage of 15 Vrms. Theoretical analysis of the phase shifting is developed. This optical property is used to achieve a variable optical attenuator (VOA) between two single-mode fibers. An optical architecture using graded index rod lenses and a pattern of photoresist polymer is presented. Typical characteristics of such VOA are: 12-dB range of attenuation, a maximum polarization dependence loss of 0.5 dB, 1.1-dB insertion loss, and a saturation voltage of 20 Vrms.

Propagation and transformation properties of an elliptic Gaussian optical beam with a Kerr-law nonlinear graded-index rod lens

An elliptic Gaussian optical beam (EGB) in a Kerr-law nonlinear graded-index rod lens is treated as two dependent optical beams. Two coupled differential equations of the dimensionless beam-width parameters of two beams in the rod lens are derived by a variational approach and then solved for what is to my knowledge the first time. Investigations of the propagation and the collapse of the EGB in the rod lens and the transformation of the EGB by the rod lens are presented. It is concluded that the properties of propagation, collapse, and transformation are largely determined by the power and initial ellipticity of the incident EGB. The field derived also applies to the EGB propagating in a nonlinear graded-index fiber.

Enhancement of collapse threshold of two Gaussian beams of light with orthogonal polarization in a nonlinear defocusing shifted parabolic graded-index rod lens

A semi-analytical treatment of propagation and object–image transformation of two orthogonally polarized Gaussian beams of light passing through a nonlinear defocusing shifted parabolic graded-index rod lens is presented. Fields in the rod lens and imaging formulas through the rod lens are derived in terms of the parameters of two incident beams of light and the rod lens. The investigations show that there are two regimes of propagation in the rod, and collapse powers of two beams in a nonlinear defocusing shifted parabolic graded-index rod lens are much larger than those in a nonlinear shifted parabolic graded-index rod lens. PACS: 42.20; 42.30; 42.65 Erbium-doped fibers whose nonlinear coefficients reach 10−14 m2/W [1] are extensively used in fiber amplifiers and fiber lasers [2]. Intensity-dependent refractive-index properties of nonlinear optical guided-wave materials have many potential applications in all-optical signal-processing devices [3]. We have investigated the field and propagation of two orthogonally polarized Gaussian beams of light passing through a nonlinear shifted parabolic graded-index (GRIN) rod lens [4] and a nonlinear parabolic GRIN rod lens [5]. When the power of one beam of light is changed, the refractive-index profile of the nonlinear rod lens will be changed. The field and propagation of the other beam of light will also be affected because of the variations in the index profile. Therefore one beam of light can affect and control the field and propagation of the other beam of light in the nonlinear rod lens [4, 5]. These properties have many potential applications in the control of light by light. In this paper, we study the field, propagation, and imaging of two orthogonally polarized Gaussian beams of light passing through a nonlinear defocusing shifted parabolic GRIN rod lens. 1 Beam-width and inverse of radius of curvature of the wave front As shown in Figs. 1 and 2, a x-polarized Gaussian beam of light, with an electric field E1 and a waist radius ω01 located at a distance L01 (object distance) from the input plane Fig. 1. The x-polarized beam of two orthogonally polarized Gaussian beams is transformed to a new beam by a nonlinear defocusing shifted parabolic GRIN rod lens whose length is Z. The surfaces of constant index are for A1 > 0 (z = 0) of the rod lens, is transformed to a new Gaussian beam of light with a new waist radius ω31 located at a distance L1 (imaging distance) from the output plane (z = Z) of the rod lens. A y-polarized Gaussian beam of light with an electric field E2 and a waist radius ω02, located at a distance L02 (object distance) from the input plane of the rod lens, is transformed to a new Gaussian beam of light with a new waist radius ω32 located at a distance L2 (imaging distance) from the output plane of the rod lens. According to the ABCD law of Gaussian-beam propagation, at the input plane of the rod, the beam-width radii are given by [6] ω11 = ω01 [ 1 + ( L01 Z01 )2]1/2 ,

Propagation and imaging of two orthogonally polarised optical beams in a nonlinear graded-index rod lens

The propagation and imaging of two orthogonally polarised Gaussian optical beams passing through a nonlinear graded-index rod lens are analysed using a variational approach, and it is concluded that there are two regimes of propagation, collapse and oscillation. The results show that the nonlinear interaction of two optical beams has great effects on the propagation and imaging characteristics of optical beams, and that one beam can control the propagation and imaging of the other beam.

Single‐mode fiber‐compatible plastic‐molded surface‐contact receptacles

A single-mode fiber-compatible surface-contact (SC) receptacle is fabricated by insert-molding technology with a zirconia sleeve in the mold patterns. The zirconia sleeve, lens holder, and a plastic case consist of the same mold pattern for precise coincidence of the optical axes. Almost all of the case structures are fundamentally cylindrical to disable temperature modifications due to mechanical expansion or deformation. For the same reason, the grade of liquid crystalline polymer is selected carefully. Furthermore, the roof mirror array lens used in the facsimile machine is selected as a graded-index (GRIN) rod lens to reduce costs. The fabrication results show that in this structure, the mechanical removal strength in the zirconia sleeve attained over 50 kg f, and mechanical tolerance is also maintained after more than 1000 plug coupling tests. The fabrication methods are successively suitable for mass production and contributed to the cost effective SC receptacle. This receptacle is compatible not only with multimode fiber but also with single-mode fiber. The total coupling loss in this receptacle equipped with a 1.3-µm multi-quantum-well laser diode is —6 dB with the singlemode fiber. The contribution due to the GRIN rod lens is —5.5 dB and the excess coupling loss due to the assembly is within —0.5 dB.

Effects of nonlinear interaction on field and imaging properties of two orthogonally polarized beams with a nonlinear defocusing graded index rod lens

Effects of nonlinear interaction on field and imaging properties of two orthogonally polarized beams with a nonlinear defocusing graded index rod lens

Effects of nonlinear interaction on field and imaging properties of two orthogonally polarized beams with a nonlinear defocusing graded-index rod lens

Abstract The field and imaging properties of two orthogonally polarized Gaussian optical beams through a nonlinear defocusing graded-index rod lens are studied for the first time to our knowledge. The beam width parameters, inverses of the radii of curvature of the wavefront, imaging distances, and linear magnifications respectively in terms of the power of beams, waist radii of incident beams, and rod dimensions are derived by using a variational approach. It is concluded that there are two regimes of propagation, divergence and collapse. A comparison of these results with linear cases shows that the power of beams and the nonlinear interaction of two beams have great effects on the field, propagation and imaging properties of two beams.

Two orthogonally polarized optical beams in a family of Kerr-law nonlinear shifted parabolic graded-index rod lenses

The field, the propagation and the imaging characteristics of two Gaussian optical beams with orthogonal polarization passing through a family of Kerr-law nonlinear shifted parabolic graded-index rod lenses are investigated. The coupled differential equations of the dimensionless beam-width parameters of two Gaussian optical beams are derived by using a variational approach and then solved. It is concluded that there are two regimes of propagation and that the power, the incident waist radius and the position of one beam have large effects on the field, the propagation and the imaging characteristics of the other beam.

Field and imaging properties of two orthogonally polarized Gaussian optical beams with a nonlinear parabolic graded-index rod lens

The field and imaging formulas of two orthogonally polarized Gaussian light beams through a nonlinear parabolic graded-index rod lens are derived by use of a variational approach and the ABCD law of Gaussian beam propagation. The effects of power and position of one optical beam on the field and propagation and imaging properties of the other optical beam are analyzed.

Single-mode fiber coupling efficiency with graded-index rod lenses

Losses are calculated for the single-mode graded-index- (GRIN-) lens coupler. The main advantage of this coupling system is large separation between fibers with small power loss. The excess loss of the GRIN-lens coupler is due primarily to the misalignments of the GRIN lenses and is most sensitive to angular tilt rather than lateral offset or end separation. The excess loss is calculated from the overlap of two differently sized or misaligned Gaussian beams. Experimental results show that this method is adequate for predicting losses that are due to misalignments of the GRIN lenses.

Imaging properties of Gaussian beams with a nonlinear graded-index rod lens

The imaging properties of Gaussian beams of light passing through a nonlinear graded-index rod are studied for the first time to our knowledge. The beam-width parameter, the distance of the focal plane, and the linear magnification in terms of the beam power, diffraction, and the rod dimensions are derived by using the variational approach and the ABCD law of Gaussian beam propagation. A comparison of these results with those derived from the ray equation and the linear case shows that the effects of the beam power on the imaging characteristics are significant.

Efficient highly stable laser diode module for single-mode fiber employing a combination of hemispherical ended GRIN rod lens and virtual fiber

An efficient and practical laser diode module is demonstrated for single-mode fiber applications. The module is developed through use of an earlier proposed combination lens method, where a hemispherical ended graded index rod lens and virtual fiber are employed. Since lens and virtual fiber misalignment tolerances are large in this coupling method, the YAG laser welding technique is easily applicable. This laser diode module has not only a simple structure but also high coupling efficiency, excellent reproducibility, and extremely high reliability.

Alignment-insensitive technique for wideband tuning of an unmodified semiconductor laser

Using simple optical components and an unmodified commercial semiconductor laser, a frequency-selective self-aligning optical-feedback technique has been devised that allows a semiconductor laser to be tuned to and scanned about any optical frequency within the laser gain curve. This technique employs a graded-index rod lens cat's eye and an intracavity étalon.

Aperture shared laser diode array beam combiner

An array of discrete semiconductor lasers utilizing graded-index rod lenses as collimators were fabricated to form a noncoherent laser beam combiner. Continuous wave output power of 600 mW and 5.25% total efficiency were achieved in a 5-mrad beam from a ten-diode laser array. A technique of dichroically combining five arrays is also described.

Optical fiber heterodyne interferometer probe free from external disturbance

A fiber heterodyne interferometer probe free from external disturbance, which can measure small displacement of an object as a pressure transducer or a vibrational object, is described. The phase fluctuation in the fiber due to external disturbance is excluded using a reference beat signal of light beams from a reflection mirror on a graded index rod lens. A graded index-type multimode fiber connected to one end of a single-mode fiber by arc fusion splicing is used to improve acceptance of the light. The characteristics of the fiber probe are also described.

Beam transformers for obtaining low-loss splices between dissimilar single-mode fibers

By introducing quantitative measures for the three effects of diffraction, focusing, and defocusing, physical-engineering insight is brought into the complex problem of Gaussian-beam propagation in graded-index media. Beam propagation in single-mode optical waveguides can be studied approximately by replacing them by equivalent focusing quadratic-index media. An “antiguiding” fiber is introduced for which the core index is smaller than the cladding index. Short sections of conventional and antiguiding fibers function similarly to positive and negative graded-index rod lenses. These fiber lenses are used to obtain low-loss connections between single-mode fibers with different spot sizes.

Design and characteristics of a branching component for bunched optical fiber using two graded-index rod lenses

An optical branching component is proposed for coupling bunched optical fiber to mono-core optical fibers and the component loss and crosstalk characteristics are investigated. The component is constructed with two graded-index (GRIN) rod lenses for matching different parameters between bunched and mono-core optical fibers. The method of analyzing mismatching and misalignment losses is based on geometrical optics. Measured losses are found to be in agreement with the calculated results and demonstrate that bunched optical fibers can be branched with low loss. Crosstalk measurements show that crosstalk attenuation greater than 30 dB can be easily maintained in the component.