Auto-solitons guided by in-line nonlinear optical loop mirrors in dispersion-managed communication systems

Summary form only given. Both dispersion management and the use of a nonlinear optical loop mirror (NOLM) as a saturable absorber can improve the performance of a soliton-based communication system. Dispersion management gives the benefits of low average dispersion while allowing pulses with higher powers to propagate, which helps to suppress Gordon-Haus timing jitter without sacrificing the signal-to-noise ratio. The NOLM suppresses the buildup of amplifier spontaneous emission noise and background dispersive radiation which, if allowed to interact with the soliton, can lead to its breakup. We examine optical pulse propagation in dispersion-managed (DM) transmission system with periodically inserted in-line NOLMs. To describe basic features of the signal transmission in such lines, we develop a simple theory based on a variational approach involving Gaussian trial functions. It, has already been proved that the variational method is an extremely effective tool for description of DM solitons. In the work we manage to include in the variational description the point action of the NOLM on pulse parameters, assuming that the Gaussian pulse shape is inherently preserved by propagation through the NOLM. The obtained results are verified by direct numerical simulations

Time-spatial drift of decelerating electromagnetic pulses

A time dependent electromagnetic pulse generated by a current running laterally to the direction of the pulse propagation is considered in paraxial approximation. It is shown that the pulse envelope moves in the time-spatial coordinates on the surface of a parabolic cylinder for the Airy pulse and a hyperbolic cylinder for the Gaussian. These pulses propagate in time with deceleration along the dominant propagation direction and drift uniformly in the lateral direction. The Airy pulse stops at infinity while the asymptotic velocity of the Gaussian is nonzero. © 2013 Optical Society of America.

Parabolic similaritons in optical fibres

Recent developments in nonlinear optics have brought to the fore of intensive research an interesting class of pulses with a parabolic intensity profile and a linear instantaneous frequency shift or chirp. Parabolic pulses propagate in optical fibres with normal group-velocity dispersion in a self-similar manner, holding certain relations (scaling) between pulse power, duration and chirp parameter, and can tolerate strong nonlinearity without distortion or wave breaking.  These solutions, which have been dubbed similaritons, were demonstrated theoretically and experimentally in fiber amplifiers in 2000. Similaritons in fiber amplifiers are, along with solitons in passive fibres, the most well-known classes of nonlinear attractors for pulse propagation in optical fibre, so they take on major fundamental importance. The unique properties of parabolic similaritons have stimulated numerous applications in nonlinear optics, ranging from ultrashort high-power pulse generation to highly coherent continuum sources and to optical nonlinear processing of telecommunication signals.

Parabolic similaritons in optical fibres

Recent developments in nonlinear optics have brought to the fore of intensive research an interesting class of pulses with a parabolic intensity profile and a linear instantaneous frequency shift or chirp. Parabolic pulses propagate in optical fibres with normal group-velocity dispersion in a self-similar manner, holding certain relations (scaling) between pulse power, duration and chirp parameter, and can tolerate strong nonlinearity without distortion or wave breaking. These solutions, which have been dubbed similaritons, were demonstrated theoretically and experimentally in fibre amplifiers in 2000. Similaritons in fibre amplifiers are, along with solitons in passive fibres, the most well-known classes of nonlinear attractors for pulse propagation in optical fibre, so they take on major fundamental importance. The unique properties of parabolic similaritons have stimulated numerous applications in nonlinear optics, ranging from ultrashort high-power pulse generation to highly coherent continuum sources and to optical nonlinear processing of telecommunication signals. In this work, we review the physics underlying the generation of parabolic similaritons as well as recent results obtained in a wide range of experimental configurations.

Design rules for nonlinear spectral compression in optical fibers

We present comprehensive design rules to optimize the process of spectral compression arising from nonlinear pulse propagation in an optical fiber. Extensive numerical simulations are used to predict the performance characteristics of the process as well as to identify the optimal operational conditions within the space of system parameters. It is shown that the group velocity dispersion of the fiber is not detrimental and, in fact, helps achieve optimum compression. We also demonstrate that near-transform-limited rectangular and parabolic pulses can be generated in the region of optimum compression.

Time-varying airy pulses

Pulses in the form of the Airy function as solutions to an equation similar to the Schrodinger equation but with opposite roles of the time and space variables are derived. The pulses are generated by an Airy time varying field at a source point and propagate in vacuum preserving their shape and magnitude. The pulse motion is decelerating according to a quadratic law. Its velocity changes from infinity at the source point to zero in infinity. These one dimensional results are extended to the 3D+time case for a similar Airy-Bessel pulse with the same behaviour, the non-diffractive preservation and the deceleration. This pulse is excited by the field at a plane aperture perpendicular to the direction of the pulse propagation. © 2011 IEEE.

Generation of decelerating Airy pulses

The explicit expression for spatial-temporal Airy pulse is derived from the Maxwell's equations in paraxial approximation. The trajectory of the pulse in the time-space coordinates is analysed. The existence of a bifurcation point that separates regions with qualitatively different features of the pulse propagation is demonstrated. At this point the velocity of the pulse becomes infinite and the orientation of it changes to the opposite. © 2011 IEEE.

Enhanced spectral compression in nonlinear optical fibres

We propose two new approaches to enhance the spectral compression process arising from nonlinear pulse propagation in an optical fibre. We numerically show that an additional sinusoidal temporal phase modulation of the pulse enables efficient reduction of the intensity level of side lobes in the spectrum. Another strategy is to select a regime of propagation in which normal group-velocity dispersion reshapes the initial stretched pulse to a near-Fourier-transform-limited rectangular waveform.

Enhanced nonlinear spectral compression in fiber by external sinusoidal phase modulation

We propose a new, simple approach to enhance the spectral compression process arising from nonlinear pulse propagation in an optical fiber. We numerically show that an additional sinusoidal temporal phase modulation of the pulse enables efficient reduction of the intensity level of the side lobes in the spectrum that are produced by the mismatch between the initial linear negative chirp of the pulse and the self-phase modulation-induced nonlinear positive chirp. Remarkable increase of both the extent of spectrum narrowing and the quality of the compressed spectrum is afforded by the proposed approach across a wide range of experimentally accessible parameters.

Enhanced nonlinear spectral compression in fibre by sinusoidal phase modulation

We propose a simple approach to enhance the spectral compression arising from nonlinear pulse propagation in a Kerr medium. We numerically show that an additional sinusoidal temporal phase modulation enables efficient reduction of the intensity level of spectral side lobes.

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.

Direct femtosecond laser inscription in transparent dielectrics

Since 1996 direct femtosecond inscription in transparent dielectrics has become the subject of intensive research. This enabling technology significantly expands the technological boundaries for direct fabrication of 3D structures in a wide variety of materials. It allows modification of non-photosensitive materials, which opens the door to numerous practical applications. In this work we explored the direct femtosecond inscription of waveguides and demonstrated at least one order of magnitude enhancement in the most critical parameter - the induced contrast of the refractive index in a standard borosilicate optical glass. A record high induced refractive contrast of 2.5×10-2 is demonstrated. The waveguides fabricated possess one of the lowest losses, approaching level of Fresnel reflection losses at the glassair interface. High refractive index contrast allows the fabrication of curvilinear waveguides with low bend losses. We also demonstrated the optimisation of the inscription regimes in BK7 glass over a broad range of experimental parameters and observed a counter-intuitive increase of the induced refractive index contrast with increasing translation speed of a sample. Examples of inscription in a number of transparent dielectrics hosts using high repetition rate fs laser system (both glasses and crystals) are also presented. Sub-wavelength scale periodic inscription inside any material often demands supercritical propagation regimes, when pulse peak power is more than the critical power for selffocusing, sometimes several times higher than the critical power. For a sub-critical regime, when the pulse peak power is less than the critical power for self-focusing, we derive analytic expressions for Gaussian beam focusing in the presence of Kerr non-linearity as well as for a number of other beam shapes commonly used in experiments, including astigmatic and ring-shaped ones. In the part devoted to the fabrication of periodic structures, we report on recent development of our point-by-point method, demonstrating the shortest periodic perturbation created in the bulk of a pure fused silica sample, by using third harmonics (? =267 nm) of fundamental laser frequency (? =800 nm) and 1 kHz femtosecond laser system. To overcome the fundamental limitations of the point-by-point method we suggested and experimentally demonstrated the micro-holographic inscription method, which is based on using the combination of a diffractive optical element and standard micro-objectives. Sub-500 nm periodic structures with a much higher aspect ratio were demonstrated. From the applications point of view, we demonstrate examples of photonics devices by direct femtosecond fabrication method, including various vectorial bend-sensors fabricated in standard optical fibres, as well as a highly birefringent long-period gratings by direct modulation method. To address the intrinsic limitations of femtosecond inscription at very shallow depths we suggested the hybrid mask-less lithography method. The method is based on precision ablation of a thin metal layer deposited on the surface of the sample to create a mask. After that an ion-exchange process in the melt of Ag-containing salts allows quick and low-cost fabrication of shallow waveguides and other components of integrated optics. This approach covers the gap in direct fs inscription of shallow waveguide. Perspectives and future developments of direct femtosecond micro-fabrication are also discussed.

Inscription and characterization of waveguides written into borosilicate glass by a high-repetition-rate femtosecond laser at 800 nm

A series of waveguides was inscribed in a borosilicate glass (BK7) by an 11 MHz repetition rate femtosecond laser operating with pulse energies from 16 to 30 nJ and focused at various depths within the bulk material. The index modification was measured using a quantitative phase microscopy technique that revealed central index changes ranging from 5×10-3 to 10-2, leading to waveguides that exhibited propagation losses of 0.2 dB/cm at a wavelength of 633 nm and 0.6 dB/cm at a wavelength of 1550 nm with efficient mode matching, less than 0.2 dB, to standard optical fibers. Analysis of the experimental data shows that, for a given inscription energy, the index modification has a strong dependence on inscription scanning velocity. At higher energies, the index modification increases with increasing inscription scanning velocity with other fabrication parameters constant.

Femtosecond laser microfabrication of subwavelength structures in photonics

This paper describes experimental and numerical results of the plasma-assisted microfabrication of subwavelength structures by means of point-by point femtosecond laser inscription. It is shown that the spatio-temporal evolution of light and plasma patterns critically depend on input power. Subwavelength inscription corresponds to the supercritical propagation regimes when pulse power is several times self-focusing threshold. Experimental and numerical profiles show quantitative agreement.