Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

Design and fabrication of a nonlinear micro impact oscillator

In this paper we describe the design and fabrication of a mechanical autonomous impact oscillator with a MEMS resonator as the frequency control element. The design has been developed with scalability to large 2-D arrays of coupled oscillators in mind. The dynamic behaviour of the impact oscillator was numerically studied and it was found that the geometry nonlinearity has an effect on the static pull-in voltage and equilibrium position. The external driving power can alter the frequency of the impact oscillator. The autonomous nature of the oscillator simplifies the complexity of the drive circuitry and is essential for large 2-D arrays.

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.

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.