On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS VIA CONLEY INDEX THEORY

In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.

Simultaneous measurement of refractive index and temperature using multimode microfiber-based dual Mach-Zehnder interferometer

A multimode microfiber (MMMF)-based dual Mach-Zehnder interferometer (MZI) is proposed and demonstrated for simultaneous measurement of refractive index (RI) and temperature. By inserting a section of MMMFsupporting a few modes in the sensing arm of the MZI setup, an inline interference between the fundamental mode and the high-order mode of MMMF, as well as the interference between the high-order mode of MMMF and the reference arm, i.e., the dual MZI, is realized. Due to different interference mechanisms, the former interferometer achieves RI sensitivity of 2576.584 nm/RIU and temperature sensitivity of 0.193 nm/°C, while the latter one achieves RI sensitivity of 1001.864 nm/RIU and temperature sensitivity of 0.239 nm/°C, demonstrating the ability to attain highly accurate multiparameter measurements. © 2014 Optical Society of America.

Single-Mode Fiber Refractive Index Sensor Based on Core-Offset Attenuators

Mach-Zehnder and Michelson interferometers using core-offset attenuators were demonstrated. As the relative offset direction of the two attenuators in the Mach-Zehnder interferometer can significantly affect the extinction ratio of the interference pattern, single core-offset attenuator-based sensors appear more robust and repeatable. A novel fiber Michelson interferometer refractive index (RI) sensor was subsequently realized by a single core-offset attenuator and a layer of ~ 500-nm gold coating. The device had a minimum insertion loss of 0.01 dB and maximum extinction ratio over 9 dB. The sensitivity (0.333 nm) of the new sensor to its surrounding RI change (0.01) was found to be comparable to that (0.252 nm) of an identical long period gratings pair Mach-Zehnder interferometric sensor, and its ease of fabrication makes it a low-cost alternative to existing sensing applications.

A high sensitivity refractometer based upon a long period grating Mach-Zehnder interferometer

A low cost interrogation scheme is demonstrated for a refractometer based on an in-line fiber long period grating (LPG) Mach–Zehnder interferometer. Using this interrogation scheme the minimum detectable change in refractive index of ?n ~ 1.8×10-6 is obtained, which is the highest resolution achieved using a fiber LPG device, and is comparable to precision techniques used in the industry including high performance liquid chromatography and ultraviolet spectroscopy.

A high sensitivity long period grating Mach-Zehnder refractometer

A refractive index sensing system has been demonstrated, which is based upon an in-line fibre long period grating Mach-Zehnder interferometer with a heterodyne interrogation technique. This sensing system has comparable accuracy to laboratory-based techniques used in industry such as high performance liquid chromatography and UV spectroscopy. The advantage of this system is that measurements can be made in-situ for applications in continuous process control. Compared to other refractive index sensing schemes using LPGs, this approach has two main advantages. Firstly, the system relies on a simple optical interrogation system and therefore has the real potential for being low cost, and secondly, so far as we are aware it provides the highest refractive index resolution reported for any fibre LPG device.

Microfiber-based inline Mach-Zehnder interferometer for dual-parameter measurement

An approach to realizing simultaneous measurement of refractive index (RI) and temperature based on a microfiber-based dual inline Mach-Zehnder interferometer (MZI) is proposed and demonstrated. Due to different interference mechanisms, as one interference between the core mode and the lower order cladding mode in the sensing single-mode fiber and the other interference between the fundamental mode and the high-order mode in the multimode microfiber, the former interferometer achieves RI sensitivity of -23.67 nm/RIU and temperature sensitivity of 81.2 pm/oC, whereas those of the latter are 3820.23 nm/RIU, and -465.7 pm/oC, respectively. The large sensitivity differences can provide a more accurate demodulation of RI and temperature. The sensor is featured with multiparameters measurement, compact structure, high sensitivity, low cost, and easy fabrication.