There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation, photonic crystal fiber

We report the coherent mid-infrared supercontinuum generation in an all-solid chalcogenide microstructured fiber with all-normal dispersion. The chalcogenide microstructured fiber is a four-hole structure with core material of AsSe2 and air holes that are replaced by As2S5 glass rods. Coherent mid-infrared supercontinuum light extended to 3.3 μm is generated in a 2 cm long chalcogenide microstructured fiber pumped by a 2.7 μm laser.

Coherent mid-infrared supercontinuum generation in all-solid chalcogenide microstructured fibers with all-normal dispersion.

Several modern optical coating designs tools are discussed in the frame of a new design paradigm proposing the search not for a formally optimal solution with the lowest possible merit function value but for the most practical solution that takes into account additional feasibility demands. Considered design tools include a stochastic optimization procedure that takes into account upper and lower constraints for layer optical thicknesses. This procedure allows one to obtain multiple solutions to a design problem, which presents additional opportunities for choosing a practically optimal design. Two special design techniques involving integer optimization also take into account additional demands. The first one is aimed at designing multicavity narrow bandpass filters with quarter wave or multiple quarter wave layer optical thicknesses. It enables obtaining bandpass filters with extremely steep transmittance slopes, bandwidths of several tens of nanometers, and very small ripples in transmission zones. The second technique is aimed at covering design problems that have been traditionally solved using the theory of equivalent layers. One more technique considered in this paper is aimed at reducing the influence of noncorrelated thickness errors on design spectral characteristics.

Modern design tools and a new paradigm in optical coating design

We report the first chalcogenide microwire designed with all-normal dispersion to generate supercontinuum by optical wave breaking, a low-noise nonlinear process. The chalcogenide (As2S3) microwire is coated with PMMA and tapered to a diameter of 0.58 μm to achieve the all-normal dispersion regime. The generated supercontinuum spectrum spans over an octave from 960 to >2500  nm using a microwire length of only 3 mm and a low pulse energy of 150 pJ.

Broadband supercontinuum generation in all-normal dispersion chalcogenide microwires.

We have numerically investigated the supercontinuum generation and pulse compression in a specially designed all-normal dispersion photonic crystal fiber with a flat-top dispersion curve, pumped by typical pulses from state of the art Ti:Sapphire lasers at 800 nm. The optimal combination of pump pulse parameters for a given fiber was found, which provides a wide octave-spanning spectrum with superb spectral flatness (a drop in spectral intensity of ~1.7 dB). With regard to the pulse compression for these spectra, multiple-cycle pulses (~8 fs) can be obtained with the use of a simple quadratic compressor and nearly single-cycle pulses (3.3 fs) can be obtained with the application of full phase compensation. The impact of pump pulse wavelength-shifting relative to the top of the dispersion curve on the generated SC and pulse compression was also investigated. The optimal pump pulse wavelength range was found to be 750nm<λp<850nm, where the distortions of pulse shape are quite small (< −3.3 dB). The influences of realistic fiber fabrication errors on the SC generation and pulse compression were investigated systematically. We propose that the spectral shape distortions generated by fiber fabrication errors can be significantly attenuated by properly manipulating the pump.

Supercontinuum generation at 800 nm in all-normal dispersion photonic crystal fiber

Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers

Formation of parabolic pulses at femtosecond time scale by means of passive nonlinear reshaping in normally dispersive optical fibers is analyzed. Two approaches are examined and compared: the parabolic waveform formation in transient propagation regime and parabolic waveform formation in the steady-state propagation regime. It is found that both approaches could produce parabolic pulses as short as few hundred femtoseconds applying commercially available fibers, specially designed all-normal dispersion photonic crystal fiber and modern femtosecond lasers for pumping. The ranges of parameters providing parabolic pulse formation at the femtosecond time scale are found depending on the initial pulse duration, chirp and energy. Applicability of different fibers for femtosecond pulse shaping is analyzed. Recommendation for shortest parabolic pulse formation is made based on the analysis presented.

Femtosecond parabolic pulse shaping in normally dispersive optical fibers

Specialty shape ultrashort optical pulses, and triangular pulses in particular, are of great interest in optical signal processing. Compact fiber-based techniques for producing the special pulse waveforms from Gaussian or secant pulses delivered by modern ultrafast lasers are in demand in telecommunications. Using the nonlinear Schrodinger equation in an extended form the transformation of ultrashort pulses in a fiber towards triangular shape is characterized by the misfit parameter under variety of incident pulse shapes, energies, and chirps. It is shown that short (1–2 m) conventional single mode fiber can be used for triangular pulse formation in the steady-state regime without any pre-chirping if femtosecond pulses are used for pumping. The pulses obtained are stable and demonstrate linear chirp. The ranges and combinations of the pulse parameters found here will serve as a guide for scheduling the experiments and implementation of various all-fiber schemes for optical signal processing.

Formation of ultrashort triangular pulses in optical fibers

We investigated numerically the possibility of all normal dispersion fiber design for near-infrared supercontinuum generation based on a standard air-silica microstructure. The design procedure includes finding of target dispersion profile and subsequent finding of appropriate geometrical fiber design by inverse dispersion engineering. It was shown that the tailoring of dispersion profile could increase the spectral width of generated supercontinuum while maintaining perfect spectral flatness. Conditions necessary for wide and flat supercontinuum generation as well as restrictions imposed by chosen materials were discussed. As a result of design and optimization procedure, an air-silica design was found providing normal dispersion up to $\text{3}\;\mu {\text{m}}$ . Simulation results with 10 nJ, 100 fs pulses demonstrate supercontinuum generation up to 1.3 octave; whereas pumping with 30 nJ, 100 fs pulses could provide 1.8 octavse supercontinuum.

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Design of All-Normal Dispersion Microstructured Optical Fiber on Silica Platform for Generation of Pulse-Preserving Supercontinuum Under Excitation at 1550 nm

Sergii O. Iakushev

Papers

Supercontinuum generation at 800 nm in all-normal dispersion photonic crystal fiber

Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers

Femtosecond parabolic pulse shaping in normally dispersive optical fibers

Formation of ultrashort triangular pulses in optical fibers

Design of All-Normal Dispersion Microstructured Optical Fiber on Silica Platform for Generation of Pulse-Preserving Supercontinuum Under Excitation at 1550 nm