Mask-less lithography for fabrication of optical waveguides

A flexible method for fabricating shallow optical waveguides by using femtosecond laser writing of patterns on a metal coated glass substrate followed by ion-exchange is described. This overcomes the drawbacks of low index contrast and high induced stress in waveguides directly written using low-repetition rate ultrafast laser systems. When compared to conventional lithography, the technique is simpler and has advantages in terms of flexibility in the types of structures which can be fabricated.

Low-loss waveguides fabricated by femtosecond chirped-pulse oscillator

Recent results on direct femtosecond inscription of straight low-loss waveguides in borosilicate glass are presented. We also demonstrate lowest ever losses in curvilinear waveguides, which we use as main building blocks for integrated photonics circuits. Low-loss waveguides are of great importance to a variety of applications of integrated optics. We report on recent results of direct femtosecond fabrication of smooth low-loss waveguides in standard optical glass by means of femtosecond chirped-pulse oscillator only (Scientific XL, Femtolasers), operating at the repetition rate of 11 MHz, at the wavelength of 800 nm, with FWHM pulse duration of about 50 fs, and a spectral widths of 30 nm. The pulse energy on target was up to 70 nJ. In transverse inscription geometry, we inscribed waveguides at the depth from 10 to 300 micrometers beneath the surface in the samples of 50 x 50 x 1 mm dimensions made of pure BK7 borosilicate glass. The translation of the samples accomplished by 2D air-bearing stage (Aerotech) with sub-micrometer precision at a speed of up to 100 mm per second (hardware limit). Third direction of translation (Z-, along the inscribing beam or perpendicular to sample plane) allows truly 3D structures to be fabricated. The waveguides were characterized in terms of induced refractive index contrast, their dimensions and cross-sections, mode-field profiles, total insertion losses at both 633 nm and 1550 nm. There was almost no dependence on polarization for the laser inscription. The experimental conditions – depth, laser polarization, pulse energy, translation speed and others, were optimized for minimum insertion losses when coupled to a standard optical fibre SMF-28. We found coincidence of our optimal inscription conditions with recently published by other groups [1, 3] despite significant difference in practically all experimental parameters. Using optimum regime for straight waveguides fabrication, we inscribed a set of curvilinear tracks, which were arranged in a way to ensure the same propagation length (and thus losses) and coupling conditions, while radii of curvature varied from 3 to 10 mm. This allowed us to measure bend-losses – they less than or about 1 dB/cm at R=10 mm radius of curvature. We also demonstrate a possibility to fabricate periodical perturbations of the refractive index in such waveguides with the periods using the same set-up. We demonstrated periods of about 520 nm, which allowed us to fabricate wavelength-selective devices using the same set-up. This diversity as well as very short time for inscription (the optimum translation speed was found to be 40 mm/sec) makes our approach attractive for industrial applications, for example, in next generation high-speed telecom networks.

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.

Bragg Gratings, Photosensitivity and Poling in Glass Waveguides (BGPP

Polymer optical fibre Bragg gratings are useful for strain sensor applications for large dynamic range. We report recent progress in developing polymer optical fibres with higher photosensitivity and fabricating POF gratings at alternative wavelength.

Determining planar multiple sound-soft obstacles from scattered acoustic fields

An inverse problem is considered where the structure of multiple sound-soft planar obstacles is to be determined given the direction of the incoming acoustic field and knowledge of the corresponding total field on a curve located outside the obstacles. A local uniqueness result is given for this inverse problem suggesting that the reconstruction can be achieved by a single incident wave. A numerical procedure based on the concept of the topological derivative of an associated cost functional is used to produce images of the obstacles. No a priori assumption about the number of obstacles present is needed. Numerical results are included showing that accurate reconstructions can be obtained and that the proposed method is capable of finding both the shapes and the number of obstacles with one or a few incident waves.

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.

Low-loss waveguides fabricated by femtosecond chirped-pulse oscillator

Recent results on direct femtosecond inscription of straight low-loss waveguides in borosilicate glass are presented. We also demonstrate lowest ever losses in curvilinear waveguides, which we use as main building blocks for integrated photonics circuits. Low-loss waveguides are of great importance to a variety of applications of integrated optics. We report on recent results of direct femtosecond fabrication of smooth low-loss waveguides in standard optical glass by means of femtosecond chirped-pulse oscillator only (Scientific XL, Femtolasers), operating at the repetition rate of 11 MHz, at the wavelength of 800 nm, with FWHM pulse duration of about 50 fs, and a spectral widths of 30 nm. The pulse energy on target was up to 70 nJ. In transverse inscription geometry, we inscribed waveguides at the depth from 10 to 300 micrometers beneath the surface in the samples of 50 x 50 x 1 mm dimensions made of pure BK7 borosilicate glass. The translation of the samples accomplished by 2D air-bearing stage (Aerotech) with sub-micrometer precision at a speed of up to 100 mm per second (hardware limit). Third direction of translation (Z-, along the inscribing beam or perpendicular to sample plane) allows truly 3D structures to be fabricated. The waveguides were characterized in terms of induced refractive index contrast, their dimensions and cross-sections, mode-field profiles, total insertion losses at both 633 nm and 1550 nm. There was almost no dependence on polarization for the laser inscription. The experimental conditions – depth, laser polarization, pulse energy, translation speed and others, were optimized for minimum insertion losses when coupled to a standard optical fibre SMF-28. We found coincidence of our optimal inscription conditions with recently published by other groups [1, 3] despite significant difference in practically all experimental parameters. Using optimum regime for straight waveguides fabrication, we inscribed a set of curvilinear tracks, which were arranged in a way to ensure the same propagation length (and thus losses) and coupling conditions, while radii of curvature varied from 3 to 10 mm. This allowed us to measure bend-losses – they less than or about 1 dB/cm at R=10 mm radius of curvature. We also demonstrate a possibility to fabricate periodical perturbations of the refractive index in such waveguides with the periods using the same set-up. We demonstrated periods of about 520 nm, which allowed us to fabricate wavelength-selective devices using the same set-up. This diversity as well as very short time for inscription (the optimum translation speed was found to be 40 mm/sec) makes our approach attractive for industrial applications, for example, in next generation high-speed telecom networks.

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.

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.

Mask-less lithography for fabrication of optical waveguides

A flexible method for fabricating shallow optical waveguides by using femtosecond laser writing of patterns on a metal coated glass substrate followed by ion-exchange is described. This overcomes the drawbacks of low index contrast and high induced stress in waveguides directly written using low-repetition rate ultrafast laser systems. When compared to conventional lithography, the technique is simpler and has advantages in terms of flexibility in the types of structures which can be fabricated.

Planar variations in normal anisotropy in mild steel strip

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Low-loss waveguides in borosilicate glass fabricated by high-repetition-Rate femtosecond chirp-pulsed oscillator

We describe fabrication and characterisation of smooth low-loss waveguides in BK7 optical glass bymeans of direct femtosecond inscription with chirp-pulse oscillator, operating at 800 nm and 11 MHz repetition rate.

Method for characterisation of weakly guiding waveguides by measuring mode field diameter

In this paper, we described an efficient theoretical approach to determine the integral characteristics such as Mode Field Diameter (MFD) and V-parameter of the Weakly guiding waveguides. To test the described method we measured MFD for the commercially available step index single mode fibre with known parameters. The results of these measurements are presented for two different wavelengths. It is worth noting that the developed approach implies infinite cladding, thus care should be taken to avoid influence of finiteness of cladding when MFD compares to cladding diamete.

Femtosecond laser writing of buried waveguides in erbium III-Doped oxyfluoride glasses and nano-glass-ceramics

Femtosecond-pulsed laser writing of waveguides, a few mm long, is demonstrated; waveguides were written orthogonally to the writing beam inside the bulk of ErIII-doped oxyfluoride glasses at a depth of 160 mum. The writing beam was 795 nm wavelength, 54 fs pulse duration and 11 MHz repetition rate. Tracks were written at pulse energies of 13.1 nJ to 26.1 nJ and sample translational velocity of 10 mmmiddot.s-1 to 28 mmmiddots-1. The influence of translational velocity and pulse energy on the cross-sectional shape and integrity of the written tracks is reported. Tracks tend to be narrower as the pulse energy is lowered or translational velocity decreased. Above 22.9 nJ, pulse energy, tracks tend to crack. The estimated refractive index profile of one track has a maximum increase of refractive index of 0.003 at the centre. These glasses normally form nano-glass-ceramics on heat treatment just above the glass transformation temperature (Tg). Here, a post-fs-writing heat-treatment just above Tg causes nano-ceramming of the glass sample and removes a light-guiding peripheral region of the fs-written tracks suggesting that this region may have been fs-modified by stress alone. Waveguiding at 651 nm and 973 nm wavelengths, and upconversion, are demonstrated in optimally written tracks.