Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems

We derive rigorously the Fokker-Planck equation that governs the statistics of soliton parameters in optical transmission lines in the presence of additive amplifier spontaneous emission. We demonstrate that these statistics are generally non-Gaussian. We present exact marginal probability-density functions for soliton parameters for some cases. A WKB approach is applied to describe the tails of the probability-density functions. © 2005 Optical Society of America.

Non-Gaussian error probability in optical soliton transmission

We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation. © 2004 Elsevier B.V. All rights reserved.

Reduction of the phase jitter in differential phase-shift-keying soliton transmission systems by in-line Butterworth filters

We examine reduction of phase jitter by use of in-line Butterworth filters in soliton systems in the context of differential phase-shift-keying coding. We also demonstrate numerically that the use of a Butterworth filter in a return-to-zero differential phase-shift-keying system can reduce continuum background radiation.

High-frequency conductivity of optically excited charge carriers in hydrogenated nanocrystalline silicon investigated by spectroscopic femtosecond pump-probe reflectivity measurements

We report an investigation into the high-frequency conductivity of optically excited charge carriers far from equilibrium with the lattice. The investigated samples consist of hydrogenated nanocrystalline silicon films grown on a thin film of silicon oxide on top of a silicon substrate. For the investigation, we used an optical femtosecond pump-probe setup to measure the reflectance change of a probe beam. The pump beam ranged between 580 and 820nm, whereas the probe wavelength spanned 770 to 810nm. The pump fluence was fixed at 0.6mJ/cm2. We show that at a fixed delay time of 300fs, the conductivity of the excited electron-hole plasma is described well by a classical conductivity model of a hot charge carrier gas found at Maxwell-Boltzmann distribution, while Fermi-Dirac statics is not suitable. This is corroborated by values retrieved from pump-probe reflectance measurements of the conductivity and its dependence on the excitation wavelength and carrier temperature. The conductivity decreases monotonically as a function of the excitation wavelength, as expected for a nondegenerate charge carrier gas.

Single process femtosecond microfabrication of key components for integrated optics

We present recent results on femtosecond microfabrication of key components for integrated optics such as highly curved low-loss waveguides in glasses, depressed cladding waveguides in crystals. Details of microfabrication and characterisation are discussed. © 2009 Optical Society of America.

Polarisation dynamics of vector soliton molecules in mode locked fibre laser

Two fundamental laser physics phenomena - dissipative soliton and polarisation of light are recently merged to the concept of vector dissipative soliton (VDS), viz. train of short pulses with specific state of polarisation (SOP) and shape defined by an interplay between anisotropy, gain/loss, dispersion, and nonlinearity. Emergence of VDSs is both of the fundamental scientific interest and is also a promising technique for control of dynamic SOPs important for numerous applications from nano-optics to high capacity fibre optic communications. Using specially designed and developed fast polarimeter, we present here the first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation switching with SOP precessing. The underlying physics presents an interplay between linear and circular birefringence of a laser cavity along with light induced anisotropy caused by polarisation hole burning.

Microstructured waveguides in z-cut LiNbO3 by high-repetition rate direct femtosecond laser inscription

We report on the operational parameters that are required to fabricate buried, microstructured waveguides in a z-cut lithium niobate crystal by the method of direct femtosecond laser inscription using a highrepetition-rate, chirped-pulse oscillator system. Refractive index contrasts as high as −0.0127 have been achieved for individual modification tracks. The results pave the way for developing microstructured WGs with low-loss operation across a wide spectral range, extending into the mid-infrared region up to the end of the transparency range of the host material.

Sensing properties of femtosecond laser-inscribed long period gratings in photonic crystal fiber

The use of near infrared, high intensity femtosecond laser pulses for the inscription of long period fiber gratings in photonic crystal fiber is reported. The formation of grating structures in photonic crystal fiber is complicated by the fiber structure that allows wave-guidance but that impairs and scatters the femtosecond inscription beam. The effects of symmetric and asymmetric femtosecond laser inscriptions are compared and the polarization characteristics of long period gratings and their responses to external perturbations are reported.

Optimization and characterization of femtosecond laser inscribed in-fiber microchannels for liquid sensing

In-fiber microchannels were fabricated directly in standard single mode fiber using the femtosecond laser inscribe and etch technique. This method of creating in-fiber microchannels offers great versatility since it allows complex three dimensional structures to be inscribed and then etched with hydrofluoric acid. Four in-fiber microchannel designs were experimentally investigated using this technique. Device characteristics were evaluated through monitoring the spectral change while inserting index matching oils into each microchannel - a R.I. sensitivity up to 1.55 dB/RIU was achieved. Furthermore, a simple Fabry-Pérot based refractometer with a R.I. sensitivity of 2.75 nm/RIU was also demonstrated. © 2014 SPIE.

Control of the properties of micro-structured waveguides in LiNbO3 fabricated by direct femtosecond laser inscription

This paper reports on buried waveguides fabricated in lithium niobate (LN) by the method of direct femtosecond (fs) laser inscription. 5% MgO doped LiNbO3 was chosen as the host material because of its high quality and damage threshold, as well as relatively low cost. Direct fs inscription by astigmatically shaped beam in crystals usually produces multiple 'smooth' tracks (with reduced refractive index), which encircle the light guiding 'core', thus creating a depressed cladding WG. A high-repetition rate fs laser system was used for inscription at a depth of approximately 500 μm. Using numerical modelling, it was demonstrated that the properties of fs-written WGs can be controlled by the WG geometry. Buried, depressed-cladding WGs in LN host with circular cross-section were also demonstrated. Combining control over the WG dispersion with quasi-phase matching will allow various ultralow-pump-power, highly-efficient, nonlinear light-guiding devices - all in an integrated optics format.

Parametric study of femtosecond inscription of microstructures for OCT artefact fabrication

As optical coherence tomography (OCT) becomes widespread, validation and characterization of systems becomes important. Reference standards are required to qualitatively and quantitatively measure the performance between difference systems. This would allow the performance degradation of the system over time to be monitored. In this report, the properties of the femtosecond inscribed structures from three different systems for making suitable OCT characterization artefacts (phantoms) are analyzed. The parameter test samples are directly inscribed inside transparent materials. The structures are characterized using an optical microscope and a swept-source OCT. The high reproducibility of the inscribed structures shows high potential for producing multi-modality OCT calibration and characterization phantoms. Such that a single artefact can be used to characterize multiple performance parameters such the resolution, linearity, distortion, and imaging depths. © 2012 SPIE.

Device fabrication by femtosecond laser inscription

Microfabrication of photonic devices by means of femtosecond (fs) laser pulses is reviewed. Adaptive modeling of fs laser pulse propagation was performed for detailed study of different regimes. Submicron structures are demonstrated in both infrared and UV ranges. Applications to fibre based devices and prototype integrated planar devices are discussed. © 2007 Optical Society of America.

Implications of high power losses in IR femtosecond laser inscribed fibre Bragg gratings

We report on high power issues related to the reliability of fibre Bragg gratings inscribed with an infrared femtosecond laser using the point-by-point writing method. Conventionally, fibre Bragg gratings have usually been written in fibres using ultraviolet light, either holographically or using a phase mask. Since the coating is highly absorbing in the UV, this process normally requires that the protective polymer coating is stripped prior to inscription, with the fibre then being recoated. This results in a time consuming fabrication process that, unless great care is taken, can lead to fibre strength degradation, due to the presence of surface damage. The recent development of FBG inscription using NIR femtosecond lasers has eliminated the requirement for the stripping of the coating. At the same time the ability to write gratings point-by-point offers the potential for great flexibility in the grating design. There is, however, a requirement for reliability testing of these gratings, particularly for use in telecommunications systems where high powers are increasingly being used in long-haul transmission systems making use of Raman amplification. We report on a study of such gratings which has revealed the presence of broad spectrum power losses. When high powers are used, even at wavelengths far removed from the Bragg condition, these losses produce an increase in the fibre temperature due to absorption in the coating. We have monitored this temperature rise using the wavelength shift in the grating itself. At power levels of a few watts, various temperature increases were experienced ranging from a few degrees up to the point where the buffer completely melts off the fibre at the grating site. Further investigations are currently under way to study the optical loss mechanisms in order to optimise the inscription mechanism and minimise such losses.

Highly birefringent long period gratings fabricated with femtosecond laser

Long Period Gratings (LPG) in standard fibre have been manufactured with a sharply focused near infrared (NIR) femtosecond laser beam. Polarization splitting of the attenuation bands is strongly dependent upon the inscription power.