Equivalence Between K-functionals Based on Continuous Linear Transforms

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.

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.

Numerical analysis of artificial neural network and volterra-based nonlinear equalizers for coherent optical OFDM

One major drawback of coherent optical orthogonal frequency-division multiplexing (CO-OFDM) that hitherto remains unsolved is its vulnerability to nonlinear fiber effects due to its high peak-to-average power ratio. Several digital signal processing techniques have been investigated for the compensation of fiber nonlinearities, e.g., digital back-propagation, nonlinear pre- and post-compensation and nonlinear equalizers (NLEs) based on the inverse Volterra-series transfer function (IVSTF). Alternatively, nonlinearities can be mitigated using nonlinear decision classifiers such as artificial neural networks (ANNs) based on a multilayer perceptron. In this paper, ANN-NLE is presented for a 16QAM CO-OFDM system. The capability of the proposed approach to compensate the fiber nonlinearities is numerically demonstrated for up to 100-Gb/s and over 1000km and compared to the benchmark IVSTF-NLE. Results show that in terms of Q-factor, for 100-Gb/s at 1000km of transmission, ANN-NLE outperforms linear equalization and IVSTF-NLE by 3.2dB and 1dB, respectively.

Nanophotonics of optical fibers

This review is concerned with nanoscale effects in highly transparent dielectric photonic structures fabricated from optical fibers. In contrast to those in plasmonics, these structures do not contain metal particles, wires, or films with nanoscale dimensions. Nevertheless, a nanoscale perturbation of the fiber radius can significantly alter their performance. This paper consists of three parts. The first part considers propagation of light in thin optical fibers (microfibers) having the radius of the order of 100 nanometers to 1 micron. The fundamental mode propagating along a microfiber has an evanescent field which may be strongly expanded into the external area. Then, the cross-sectional dimensions of the mode and transmission losses are very sensitive to small variations of the microfiber radius. Under certain conditions, a change of just a few nanometers in the microfiber radius can significantly affect its transmission characteristics and, in particular, lead to the transition from the waveguiding to non-waveguiding regime. The second part of the review considers slow propagation of whispering gallery modes in fibers having the radius of the order of 10–100 microns. The propagation of these modes along the fiber axis is so slow that they can be governed by extremely small nanoscale changes of the optical fiber radius. This phenomenon is exploited in SNAP (surface nanoscale axial photonics), a new platform for fabrication of miniature super-low-loss photonic integrated circuits with unprecedented sub-angstrom precision. The SNAP theory and applications are overviewed. The third part of this review describes methods of characterization of the radius variation of microfibers and regular optical fibers with sub-nanometer precision.

Optical RI sensor based on an in-fiber bragg grating fabry-perot cavity embedded with a micro-channel

We report a linear response optical refractive index (RI) sensor, which is fabricated based on a micro-channel created within a Fabry Perot (F-P) cavity by chemical etching assisted by femtosecond laser inscription. The experimental results show the F-P resonance peak has a linear response with the RI of medium and the measuring sensitivity is proportion to the length of micro-channel. The sensor with 5 μm -long micro-channel exhibited an RI sensitivity of 1.15nm/RIU and this sensitivity increased to 9.08nm/RIU when widening the micro-channel to 35μm. Furthermore, such micro-channel FP sensors show a much broader RI sensing dynamic range (from 1.3 to 1.7) than other reported optical fiber sensors. © 2012 SPIE.

Femtosecond and UV inscribed grating characterization in photonic crystal fibres:optimization for sensing applications

Photonic crystal fibres (PCF) and more commonly microstructure fibres, remain interesting and novel fibre types and when suitably designed can prove to be "ideal" for sensing applications, as the different geometrical arrangement of the air holes alters their optical wave-guiding properties, whilst also providing tailored dispersion characteristics. This impacts the performance of grating structures, which offer wavelength encoded sensing information. We undertake a study on different air hole geometries and proceed with characterization of fibre Bragg and long period gratings, FBG and LPG, respectively that have been inscribed (using either a femtosecond or ultraviolet laser system) within different designs of microstructured fibre that are of interest for sensing applications. © 2012 SPIE.

Evaluation on a 60 GHz radio over fiber system employing photonic up conversion and optically beam formed linear array antenna for broadband indoor access

In this study, two linear coplanar array antennas based on Indium Phosphide (InP) substrate are designed, presented and compared in terms of bandwidth and gain. Slot introduction in combination with coplanar structure is investigated, providing enhanced antenna gain and bandwidth at the 60 GHz frequency band. In addition the proposed array antennas are evaluated in terms of integration with a high-speed photodiode and investigated in terms of matching, providing a bandwidth that reaches 2 GHz. Moreover a potential beam forming scenario combined with photonic up-conversion scheme has been proposed. © 2013 IEEE.

Optical fibre limits:an approach using ASE channel estimation

In this talk we investigate the usage of spectrally shaped amplified spontaneous emission (ASE) in order to emulate highly dispersed wavelength division multiplexed (WDM) signals in an optical transmission system. Such a technique offers various simplifications to large scale WDM experiments. Not only does it offer a reduction in transmitter complexity, removing the need for multiple source lasers, it potentially reduces the test and measurement complexity by requiring only the centre channel of a WDM system to be measured in order to estimate WDM worst case performance. The use of ASE as a test and measurement tool is well established in optical communication systems and several measurement techniques will be discussed [1, 2]. One of the most prevalent uses of ASE is in the measurement of receiver sensitivity where ASE is introduced in order to degrade the optical signal to noise ratio (OSNR) and measure the resulting bit error rate (BER) at the receiver. From an analytical point of view noise has been used to emulate system performance, the Gaussian Noise model is used as an estimate of highly dispersed signals and has had consider- able interest [3]. The work to be presented here extends the use of ASE by using it as a metric to emulate highly dispersed WDM signals and in the process reduce WDM transmitter complexity and receiver measurement time in a lab environment. Results thus far have indicated [2] that such a transmitter configuration is consistent with an AWGN model for transmission, with modulation format complexity and nonlinearities playing a key role in estimating the performance of systems utilising the ASE channel emulation technique. We conclude this work by investigating techniques capable of characterising the nonlinear and damage limits of optical fibres and the resultant information capacity limits. REFERENCES McCarthy, M. E., N. Mac Suibhne, S. T. Le, P. Harper, and A. D. Ellis, “High spectral efficiency transmission emulation for non-linear transmission performance estimation for high order modulation formats," 2014 European Conference on IEEE Optical Communication (ECOC), 2014. 2. Ellis, A., N. Mac Suibhne, F. Gunning, and S. Sygletos, “Expressions for the nonlinear trans- mission performance of multi-mode optical fiber," Opt. Express, Vol. 21, 22834{22846, 2013. Vacondio, F., O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems," Opt. Express, Vol. 20, 1022-1032, 2012.

Optical rogue waves in telecommunication data streams

Large broadening of short optical pulses due to fiber dispersion leads to a strong overlap in information data streams resulting in statistical deviations of the local power from its average. We present a theoretical analysis of rare events of high-intensity fluctuations-optical freak waves-that occur in fiber communication links using bit-overlapping transmission. Although the nature of the large fluctuations examined here is completely linear, as compared to commonly studied freak waves generated by nonlinear effects, the considered deviations inherit from rogue waves the key features of practical interest-random appearance of localized high-intensity pulses. We use the term "rogue wave" in an unusual context mostly to attract attention to both the possibility of purely linear statistical generation of huge amplitude waves and to the fact that in optics the occurrence of such pulses might be observable even with the standard Gaussian or even rarer-than-Gaussian statistics, without imposing the condition of an increased probability of extreme value events. © 2011 American Physical Society.

Reply to "comment on 'Optical rogue waves in telecommunication data streams'"

We feel that the main claim made in the abstract of the preceding Comment is wrong. Using results obtained in our paper, we prove that rogue waves with amplitudes much larger than the average level can be observed during a short period of time in purely linear propagation regimes in optical fiber systems. © 2011 American Physical Society.

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

Aviation fuel gauging sensor utilizing multiple diaphragm sensors incorporating polymer optical fiber Bragg gratings

A high-performance fuel gauging sensor is described that uses five diaphragm-based pressure sensors, which are monitored using a linear array of polymer optical fiber Bragg gratings. The sensors were initially characterized using water, revealing a sensitivity of 98 pm/cm for four of the sensors and 86 pm/cm for the fifth. The discrepancy in the sensitivity of the fifth sensor has been explained as being a result of the annealing of the other four sensors. Initial testing in JET A-1 aviation fuel revealed the unsuitability of silicone rubber diaphragms for prolonged usage in fuel. A second set of sensors manufactured with a polyurethane-based diaphragm showed no measurable deterioration over a three month period immersed in fuel. These sensors exhibited a sensitivity of 39 pm/cm, which is less than the silicone rubber devices due to the stiffer nature of the polyurethane material used.

Advanced digital signal processing for coherent optical OFDM transmissions

Coherent optical orthogonal frequency division multiplexing (CO-OFDM) has been actively considered as a potential candidate for long-haul transmission and 400 Gb/s to 1 Tb/s Ethernet transport because of its high spectral efficiency, efficient implementation, flexibility and robustness against linear impairments such as chromatic dispersion and polarization mode dispersion. However, due to the long symbol duration and narrow subcarrier spacing, CO-OFDM systems are sensitive to laser phase noise and fibre nonlinearity induced penalties. As a result, the development of CO-OFDM transmission technology crucially relies on efficient techniques to compensate for the laser phase noise and fibre nonlinearity impairments. In this thesis, high performance and low complexity digital signal processing techniques for laser phase noise and fibre nonlinearity compensation in CO-OFDM transmissions are demonstrated. For laser phase noise compensation, three novel techniques, namely quasipilot-aided, decision-directed-free blind and multiplier-free blind are introduced. For fibre nonlinear compensation, two novel techniques which are referred to as phase conjugated pilots and phase conjugated subcarrier coding, are proposed. All these abovementioned digital signal processing techniques offer high performances and flexibilities while requiring relatively low complexities in comparison with other existing phase noise and nonlinear compensation techniques. As a result of the developments of these digital signal processing techniques, CO-OFDM technology is expected to play a significant role in future ultra-high capacity optical network. In addition, this thesis also presents preliminary study on nonlinear Fourier transform based transmission schemes in which OFDM is a highly suitable modulation format. The obtained result paves the way towards a truly flexible nonlinear wave-division multiplexing system that allows the current nonlinear transmission limitations to be exceeded.

Characterization of ultra wideband antennas for personal communication devices using finite difference time domain technique

The current mobile networks don't offer sufficient data rates to support multimedia intensive applications in development for multifunctional mobile devices. Ultra wideband (UWB) wireless technology is being considered as the solution to overcome data rate bottlenecks in the current mobile networks. UWB is able to achieve such high data transmission rates because it transmits data over a very large chunk of the frequency spectrum. As currently approved by the U.S. Federal Communication Commission it utilizes 7.5 GHz of spectrum between 3.1 GHz and 10.6 GHz. ^ Successful transmission and reception of information data using UWB wireless technology in mobile devices, requires an antenna that has linear phase, low dispersion and a voltage standing wave ratio (VSWR) ≤ 2 throughout the entire frequency band. Compatibility with an integrated circuit requires an unobtrusive and electrically small design. The previous techniques that have been used to optimize the performance of UWB wireless systems, involve proper design of source pulses for optimal UWB performance. The goal of this work is directed towards the designing of antennas for personal communication devices, with optimal UWB bandwidth performance. Several techniques are proposed for optimal UWB bandwidth performance of the UWB antenna designs in this Ph.D. dissertation. ^ This Ph.D. dissertation presents novel UWB antenna designs for personal communication devices that have been characterized and optimized using the finite difference time domain (FDTD) technique. The antenna designs reported in this research are physically compact, planar for low profile use, with sufficient impedance bandwidth (>20%), antenna input impedance of 50-Ω, and an omni-directional (±1.5 dB) radiation pattern in the operating bandwidth. ^