An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Transition of planar Couette flow at infinite Reynolds numbers

An outline of the state space of planar Couette flow at high Reynolds numbers (Re<105) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit. © 2013 American Physical Society.

In-fiber polymer–glass hybrid waveguide Bragg grating

A 1.2 µm (height) × 125 µm (depth) × 500 µm (length) microslot along a fiber Bragg grating was engraved across the optical fiber by femtosecond laser patterning and chemical etching. By filling epoxy in the slot and subsequent UV curing, a hybrid waveguide grating structure with a polymer core and glass cladding was fabricated. The obtained device is highly thermally responsive with linear coefficient of 211 pm/°C.

Micro-fabrication of advanced photonic devices by means of direct point-by-point femtosecond inscription in silica

We present recent results on experimental micro-fabrication and numerical modeling of advanced photonic devices by means of direct writing by femtosecond laser. Transverse inscription geometry was routinely used to inscribe and modify photonic devices based on waveguiding structures. Typically, standard commercially available fibers were used as a template with a pre-fabricated waveguide. Using a direct, point-by-point inscription by infrared femtosecond laser, a range of fiber-based photonic devices was fabricated including Fiber Bragg Gratings (FBG) and Long Period Gratings (LPG). Waveguides with a core of a couple of microns, periodic structures, and couplers have been also fabricated in planar geometry using the same method.

Planar variations in normal anisotropy in mild steel strip

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Highly thermally responsive hybrid in-fiber slab waveguide grating structure with a plastic core and a silica cladding

A 1.2(height)×125(depth)×500(length) micro-slot was engraved along a fiber Bragg grating by chemically assisted femtosecond laser processing. By filling epoxy and UV-curing, waveguide with plastic-core and silica-cladding was created, presenting high thermal responding coefficient of 211pm/°C.

Extended range interrogation of wavelength division multiplexed fibre Bragg grating sensors using arrayed waveguide grating

A technique for interrogating multiplexed fibre Bragg grating (FBG) sensors using an arrayed waveguide grating (AWG) is described. The approach considerably extends the sensing range from that achieved previously, while providing a strain resolution of 17nε/√Hz at 30 Hz.

Interferometric sensor interrogation using an arrayed waveguide grating

We experimentally investigate the use of an arrayed waveguide grating (AWG) to interrogate interferometric sensors. A single broad-band light source is used to illuminate the system. Reflected spectral information is directed to an AWG with integral photodetectors providing 40 electrical outputs. We show that using the dual-wavelength technique we can measure the length of a Fabry-Pérot cavity by determining the optical phase changes of the scanned interferometric pattern, which produced a maximum unambiguous range of 1440 μm with an active sensor and a maximum unambiguous range of 300 μm with the introduction of a second processing interferometer, which allows the sensor to be passive. © 2005 IEEE.

Highly thermally responsive hybrid in-fiber sSlab waveguide grating structure with a plastic core and a silica cladding

A 1.2(height)×125(depth)×500(length) micro-slot was engraved along a fiber Bragg grating by chemically assisted femtosecond laser processing. By filling epoxy and UV-curing, waveguide with plastic-core and silica-cladding was created, presenting high thermal responding coefficient of 211pm/°C.

Interrogation of fibre Bragg grating sensors using an arrayed waveguide grating

We experimentally investigate the use of an arrayed waveguide grating (AWG) to interrogate fibre Bragg grating (FBG) sensors. A broadband light source is used to illuminate the FBG sensors. Reflected spectral information is directed to the AWG containing integral photodetectors providing 40 electrical outputs. Three methods are described to interrogate FBG sensors. The first technique makes use of the wavelength-dependent transmission profile of an AWG channel passband, giving a usable range of 500 με and a dynamic strain resolution of 96 nε Hz-1/2 at 13 Hz. The second approach utilizes wide gratings larger than the channel spacing of the AWG; by monitoring the intensity present in several neighbouring AWG channels an improved range of 1890 με was achieved. The third method improves the dynamic range by utilizing a heterodyne approach based on interferometric wavelength shift detection, providing an improved dynamic strain resolution of 17 nε Hz -1/2 at 30 Hz. © 2005 IOP Publishing Ltd.

Waveguide fabrication in lithium-niobo-phosphate glasses by high repetition rate femtosecond laser:route to non-equilibrium material’s states

We study waveguide fabrication in lithium-niobo-phosphate glass, aiming at a practical method of single-stage fabrication of nonlinear integrated-optics devices. We observed chemical transformations or material redistribution during the course of high repetition rate femtosecond laser inscription. We believe that the laser-induced ultrafast heating and cooling followed by elements diffusion on a microscopic scale opens the way toward the engineering non-equilibrium sates of matter and thus can further enhance Refractive Index (RI) contrasts by virtue of changing glass composition in and around the fs tracks. © 2014 Optical Society of America.

Blue-to-red tunable SHG from a diode-pumped PPKTP waveguide

Summary form only given. Broadly tunable compact visible laser sources in the spectral region of 500-650 nm are valuable in biophotonics, photomedicine and for many applications including spectroscopy, laser projection and confocal microscopy. Unfortunately, commercially available lasers of this spectral range are in practice bulky and inconvenient in use. An attractive method for the realization of portable visible laser sources is the frequency-doubling of the infrared laser diodes in a nonlinear crystal containing a waveguide [1]. Nonlinear crystal waveguides that offer an order-of-magnitude increase in the IR-to-visible conversion efficiency also enable a very different approach to second-harmonic generation (SHG) tunability in periodically-poled crystals, promising order-of-magnitude increase of wavelength range for SHG conversion. This is possible by utilization of a significant difference in the effective refractive indices of the high-order and low-order modes in multimode waveguides [2]. The recent availability of low-cost, good quality semiconductor diode lasers, offering the coverage of a broad spectral range between 1 µ?? and 1.3 µp? [3,4], in combination with well-established techniques to fabricate good quality waveguides in nonlinear crystals, allows compact tunable CW laser sources in the visible spectral region to be realized [2].

Broadly tunable CW green-to-red laser source based on frequency doubling of a quantum-dot external cavity diode laser in a PPKTP waveguide

Here we present a compact tunable all-room-temperature frequency-doubling scheme, using a periodically poled potassium titanyl phosphate (PPKTP) waveguide and a QD-ECDL. A broad wavelength tunability of the second harmonic generated light (SHG) in the spectral region between 567.7 and 629.1 nm was achieved, with maximum conversion efficiencies in range of 0.34%-7.9%. The maximum output power for the SHG light was 4.11 mW at 591.5 nm, achieved for 52 mW of launched pump power at 1183 nm, resulting in a conversion efficiency of 7.9%.

Generation of CW tunable visible light by SHG of QD laser in a PPKTP waveguide

We demonstrate a CW tunable compact all-room-temperature laser system in the visible spectral region from 567.7 nm to 629.1 nm, by frequency doubling in a periodically-poled KTP waveguide crystal using a tunable quantum-dot external-cavity diode laser.