The induced nonlinear electric dipole and higher moments in an atomic system, irradiated simultaneously by two or three light waves, are calculated by quantum-mechanical perturbation theory. Terms quadratic and cubic in the field amplitudes are included. An important permutation symmetry relation for the nonlinear polarizability is derived and its frequency dependence is discussed. The nonlinear microscopic properties are related to an effective macroscopic nonlinear polarization, which may be incorporated into Maxwell's equations for an infinite, homogeneous, anisotropic, nonlinear, dielectric medium. Energy and power relationships are derived for the nonlinear dielectric which correspond to the Manley-Rowe relations in the theory of parametric amplifiers. Explicit solutions are obtained for the coupled amplitude equations, which describe the interaction between a plane light wave and its second harmonic or the interaction between three plane electromagnetic waves, which satisfy the energy relationship ${\ensuremath{\omega}}_{3}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$, and the approximate momentum relationship ${\mathrm{k}}_{3}={\mathrm{k}}_{1}+{\mathrm{k}}_{2}+\ensuremath{\Delta}\mathrm{k}$. Third-harmonic generation and interaction between more waves is mentioned. Applications of the theory to the dc and microwave Kerr effect, light modulation, harmonic generation, and parametric conversion are discussed.

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Interactions between Light Waves in a Nonlinear Dielectric

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

The notorious implication of integrated optics in the nowadays communication systems makes more interesting the development of optical integrated devices and circuits. The evolution of the communication systems was sustained by the integrated optics and it is obvious that the actual interests in the optical communications are also transferred and adapted to integrated optics. The presentation of actual state-of-the-art in this field is a good opportunity both for an evaluation on the above mentioned evolution and for discerning the actual trends and their perspectives. These trends, guided by applicative goals, have to be discussed not only from the theoretical point of view but also from a practical one.

Optical integrated circuits

Surface plasmon resonance has established itself as an immensely acclaimed and influential optical sensing tool with quintessential applications in life sciences, environmental monitoring, clinical diagnostics, pharmaceutical developments and ensuring food safety. The implementation of sensing principle of surface plasmon resonance employing an optical fiber as a substrate has concomitantly resulted in the evolution of fiber optic surface plasmon resonance as an exceptionally lucrative scaffold for chemical and biosensing applications. This perspective article outlines the contemporary studies on fiber optic sensors founded on the sensing architecture of propagating as well as localized surface plasmon resonance. An in-depth review of the prevalent analytical and surface chemical tactics involved in configuring the sensing layer over an optical fiber for the detection of various chemical and biological entities is presented. The involvement of nanomaterials as a strategic approach to enhance the sensor sensitivity is furnished concurrently providing an insight into the diverse geometrical blueprints for designing fiber optic sensing probes. Representative examples from the literature are discussed to appreciate the latest advancements in this potentially valuable research avenue. The article concludes by identifying some of the key challenges and exploring the opportunities for expanding the scope and impact of surface plasmon resonance based fiber optic sensors.

[INVITED] Recent advances in surface plasmon resonance based fiber optic chemical and biosensors utilizing bulk and nanostructures

An overview of the progress on pulse-preserving, coherent, nonlinear fiber-based supercontinuum generation is presented. The context encompasses various wavelength ranges and pump sources, starting with silica photonic crystal fibers pumped with 1.0 μm femtosecond lasers up to chalcogenide step-index and microstructured fibers pumped from optical parametric amplifiers tuned to mid-infrared wavelengths. In particular, silica and silicate-based all-normal dispersion (ANDi) photonic crystal fibers have been demonstrated for pumping with femtosecond lasers operating at 1.56 μm with the recorded spectra covering 0.9–2.3 μm. This matches amplification bands of robust fiber amplifiers and femtosecond lasers. The review therefore focuses specifically on this wavelength range, discussing glass and nonlinear fiber designs, experimental results on supercontinuum generation up to the fundamental limit of oxide glass fiber transmission around 2.8 μm, and various limitations of supercontinuum bandwidth and coherence. Specifically, the role of nonlinear response against the role of dispersion profile shape is analyzed for two different soft glass ANDi fibers pumped at more than 2.0 μm. A spatio-temporal interaction of the fundamental fiber mode with modes propagating in the photonic lattice of the discussed ANDi fibers is shown to have positive effects on the coherence of the supercontinuum at pump pulse durations of 400 fs. Finally, the design and development of graded-index, nanostructured core optical fibers are discussed. In such structures the arbitrary shaping of the core refractive index profile could significantly improve the engineering flexibility of dispersion and effective mode area characteristics, and would be an interesting platform to further study the intermodal interaction mechanisms and their impact on supercontinuum coherence for sub-picosecond laser pumped setups.

Coherent supercontinuum generation in soft glass photonic crystal fibers

The purpose of this paper is to demonstrate the quasi-phase-matching of third harmonic generation process in optical fibers using refractive-index gratings. We compare conversion efficiency calculated with analytical coupled-modes theory and numerical approach employing a system of coupled generalized nonlinear Schrodinger equation. Moreover, we show that introducing the phase matching condition that takes into account the nonlinear contribution to propagation constants significantly increases the conversion efficiency by several orders of magnitude. Finally, we optimize the grating constant to maximize conversion efficiency.

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Quasi-Phase-Matched Third Harmonic Generation in Optical Fibers Using Refractive-Index Gratings

Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings

We analyzed the effect of resonant coupling between core and cladding modes in a helical core fiber with large core offset using the fully vectorial method based on the transformation optics formalism. Our study revealed that the resonant couplings to lower order cladding modes predicted by perturbative methods and observed experimentally in fibers with small core offsets are in fact prohibited for larger core offsets. This effect is related to the lack of phase matching caused by elongation of the optical path of the fundamental modes in the helical core. Moreover, strong couplings to the cladding modes of the azimuthal modal number much higher than predicted by perturbative methods may be observed for large core offsets, as the core offset introduces higher order angular harmonics in the field distribution of the fundamental modes. Finally, in contrast to previous studies, we demonstrate the existence of spectrally broad polarization sensitive couplings to the cladding modes suggesting that helical core fibers with large core offsets may be used as broadband circular polarizers.

http://iopscience.iop.org/article/10.1088/2040-8978/18/5/055601/pdf

Coupling between core and cladding modes in a helical core fiber with large core offset

A design of technologically feasible hole-assisted silica fibers with all-normal dispersion was proposed and optimized for maximum dispersion located, respectively, at 1.55 and 1.97 $\mu\text{m} $ . Such fibers allow for efficient supercontinuum generation using erbium- or thulium-doped fs fiber laser as a pump. Nonlinear simulations accounting for fiber loss were performed to find optimum pumping conditions. Our results point to the possibility of coherent supercontinuum generation in silica fibers with a long-wavelength limit reaching midinfrared.

All-Normal Dispersion Hole-Assisted Silica Fibers for Generation of Supercontinuum Reaching Midinfrared

Using a rigorous modeling method based on transformation optics formalism, we have studied, for the first time to our knowledge, the surface plasmon resonance (SPR) effect in helical core fibers with a cladding covered by a gold layer. The obtained results prove that by twisting the fiber one can tune several parameters of the SPR resonance which may be of importance in sensing applications. In particular, we have shown that circularly polarized fundamental modes propagating in the helical core fiber exhibit almost the same SPR loss. Moreover, the SPR loss can be amplified with a twist rate by more than two orders of magnitude due to twist-induced displacement of the core modes towards a metal layer. The fiber twist modifies the coupling conditions between the fundamental modes and plasmons, which results in the redshift and split of the resonance wavelengths for circularly polarized modes of opposite handedness. Analytical formulas were derived for the SPR peak loss, redshift and split, which are valid for small twist rates, in which the fundamental modes couple only with plasmons. For higher twist rates we observed the coupling between fundamental and cladding modes, which results in significant broadening of the SPR resonance peaks and emergence of additional maxima in the SPR loss curves.

https://iopscience.iop.org/article/10.1088/2040-8978/18/8/085001/pdf

W. Urbanczyk

Papers

Quasi-Phase-Matched Third Harmonic Generation in Optical Fibers Using Refractive-Index Gratings

Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings

Coupling between core and cladding modes in a helical core fiber with large core offset

All-Normal Dispersion Hole-Assisted Silica Fibers for Generation of Supercontinuum Reaching Midinfrared

Surface plasmon resonance effect in helical core fibers