We derive general analytic expressions for the chromatic dispersion orders valid to infinity, due to the k vector or phase ϕ dependence on the wavelength. Additionally, we identify polynomials and recursion relations associated with the chromatic dispersion orders and draw analogy to the generalized Lah and Laguerre transformations. Further, we give explicitly the dispersion terms to the 10th order and visualize the chromatic dispersion for material, grating and prism-pair compressors and hollow-core photonic anti-resonant fiber. These simple formulas are applicable for material dispersion, compressors, stretchers, waveguides, and any other type of known frequency-dependent phase.
We consider chromatic dispersion of capillary tubes and photonic crystal fibers infiltrated with liquid crystals. A perturbative scheme for inclusion of material dispersion of both liquid crystal and the surrounding waveguide material is derived. The method is used to calculate the chromatic dispersion at different temperatures.
The use of quantum correlations between photons to measure polarization mode dispersion (PMD) and chromatic dispersion is investigated. Two types of apparatus are discussed which use coincidence counting of entangled photon pairs to allow sub-femtosecond resolution for measurement of both PMD and chromatic dispersion, as well as separation of even-order and odd-order chromatic effects in the PMD. Group delays can be measured with a resolution of order 0.1 fs, whereas attosecond resolution can be achieved for phase delays.
The chromatic dispersion curve of the fundamental mode in small core microstructured fibres (SCMF) is both calculated using a Finite Element Method (FEM) and measured with a low coherence interferometric method. The great sensitivity of the chromatic dispersion to variations of the geometrical parameters of SCMFs (the pitch and the diameter) is pointed out. An excellent agreement is obtained between the numerical and the experimental results over a half micrometer spectral bandwidth [1.1 $μ$m-1.6 $μ$m].
In this letter, we experimentally report an achromatic metalens (AML) operating over a continuous bandwidth in the visible. This is accomplished via dispersion engineering of dielectric phase shifters: titanium dioxide nanopillars tiled on a dielectric spacer layer above a metallic mirror. The AML works in reflection mode with a focal length independent of wavelength from wavelength of 490 nm to 550 nm. We also design a metalens with reverse chromatic dispersion, where the focal length increases as the wavelength increases, contrary to conventional diffractive lenses. The ability to engineer t…
We propose and study an efficient photonic CDE method using MZI-based coherent optical matrix multiplication. It improves the compensation performance by about 60% when the tap-length is limited, and only 50% taps of the theoretical value is needed for photonic CDE with 1-dB penalty.
Using numerical simulations of an extended Lugiato-Lefever equation, we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion,…
Diffraction gratings disperse light in a rainbow of colors with the opposite order than refractive prisms, a phenomenon known as negative dispersion. While refractive dispersion can be controlled via material refractive index, diffractive dispersion is fundamentally an interference effect dictated by geometry. Here we show that this fundamental property can be altered using dielectric metasurfaces, and we experimentally demonstrate diffractive gratings and focusing mirrors with positive, zero, and hyper negative dispersion. These optical elements are implemented using a reflective metasurface …
In this paper we present a comparative study in order to specify the influence of equalization enhanced phase noise (EEPN) for pre- and post-compensation of chromatic dispersion in high capacity and high constellation systems. This is - to our knowledge - the first detailed study in this area for pre-compensation systems. Our main results show that the local oscillator phase noise determines the EEPN influence in post-compensation implementations whereas the transmitter laser determines the EEPN in pre-compensation implementations. As a result of significance for the implementation of practica…
The frequency domain equalizers (FDEs) employing two types of overlap-add zero-padding (OLA-ZP) methods are applied to compensate the chromatic dispersion in a 112-Gbit/s non-return-to-zero polarization division multiplexed quadrature phase shift keying (NRZ-PDM-QPSK) coherent optical transmission system. Simulation results demonstrate that the OLA-ZP methods can achieve the same acceptable performance as the overlap-save method. The required minimum overlap (or zero-padding) in the FDE is derived, and the optimum fast Fourier transform length to minimize the computational complexity is also a…
The performance of long-haul coherent optical fiber transmission system is significantly affected by the equalization enhanced phase noise (EEPN), due to the interaction between the electronic dispersion compensation (EDC) and the laser phase noise. In this paper, we present a comprehensive study on different chromatic dispersion (CD) compensation and carrier phase recovery (CPR) approaches, in the n-level phase shift keying (n-PSK) and the n-level quadrature amplitude modulation (n-QAM) coherent optical transmission systems, considering the impacts of EEPN. Four CD compensation methods are co…
Broadband Chromatic Dispersion of Thermo-refractive Coefficients and its Impact in Silicon Nitride Nonlinear Photonics
Joint Quantum Institute, NIST/University of Maryland（联合量子研究所，美国国家标准与技术研究院/马里兰大学）；Microsystems and Nanotechnology Division, National Institute of Standards and Technology（微系统与纳米技术部，美国国家标准与技术研究院）
We describe the formation, characterization and theoretical understanding of microlenses comprised of alternating polystyrene and polymethylmethacrylate layers produced by multilayer coextrusion. These lenses are fabricated by photolithography, using a grayscale mask followed by plasma etching, so that the refractive index alternation of the bilayer stack appears across the radius of the microlens. The alternating quarter-wave thick layers form a one-dimensional photonic crystal whose dispersion augments the material dispersion, allowing one to sculpt the chromatic dispersion of the lens by ad…
The replacement of bulk refractive optical elements with diffractive planar components enables the miniaturization of optical systems. However, diffractive optics suffers from large chromatic aberrations due to the dispersion of the phase accumulated by light during propagation. We show that this limitation can be overcome with an engineered wavelength-dependent phase shift imparted by a metasurface and demonstrate a design that deflects three wavelengths without dispersion. A planar lens without chromatic aberrations at three wavelengths is also presented. Our design is based on low-loss diel…
Refractive Index, Its Chromatic Dispersion, and Thermal Coefficients of Four Less Common Glycols
Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Laser and Fibre Optics Centre, Department of Physics, School of Physical Sciences, College of Agriculture and Natural Sciences, University of Cape Coast（开普海岸大学农业与科学学院物理学院激光与光纤中心）
The variance of nonlinear phase noise is analyzed by including the effect of intrachannel cross-phase modulation (IXPM)-induced nonlinear phase noise. Consistent with Ho and Wang [1] but in contrary to the conclusion of both Kumar [2] and Green et al. [3], the variance of nonlinear phase noise does not decrease much with the increase of chromatic dispersion. The results are consistent with a careful reexamination of both Kumar [2] and Green et al. [3].
Using the Lugiato-Lefever model, we analyze the effects of third order chromatic dispersion on the existence and stability of dark and bright soliton Kerr frequency combs in the normal dispersion regime. While in the absence of third order dispersion only dark solitons exist over an extended parameter range, we find that third order dispersion allows for stable dark and bright solitons to coexist. Reversibility is broken and the shape of the switching waves connecting the top and bottom homogeneous solutions is modified. Bright solitons come into existence thanks to the generation of oscillati…
Metasurface optics have demonstrated vast potential for implementing traditional optical components in an ultra-compact and lightweight form factor. Metasurface lenses, also called metalenses, however, suffer from severe chromatic aberrations, posing serious limitations on their practical use. Existing approaches for circumventing such aberrations via dispersion engineering are limited to small apertures and often entails multiple scatterers per unit cell with small feature sizes. Here, we present an alternative technique to mitigate chromatic aberration and demonstrate high-quality, full-colo…
The generation of optical frequency combs via direct electrical pumping of semiconductor lasers is an attractive alternative to the well-established mode-locked laser sources in terms of compactness, robustness and integrability. However, the high chromatic dispersion of bulk semiconductor materials can prevent the generation of frequency combs or lead to undesired pulse lengthening. In this letter, we present a novel dual waveguide for intracavity dispersion compensation in semiconductor lasers. We apply the concept to a short mid-infrared wavelength quantum cascade laser operating in the fir…
The waveguiding properties of two silica-based airguiding photonic bandgap fiber designs are investigated with special emphasis on material effects. The nonlinear coefficients are found to be 1-2 orders of magnitude smaller than those obtained in index-guiding microstructured fibers with large mode areas. The material dispersion of silica makes a significant contribution to the total chromatic dispersion although less than 10% of the field energy is located in the silica regions of the fibers. These findings suggest that dispersion engineering through the choice of base material may be a possi…
Measuring the dispersion of photonic devices with small dispersion-length products is challenging due to the phase-sensitive, and alignment-intensive nature of conventional methods. In this letter, we demonstrate a quantum technique to extract the second-, and third-order chromatic dispersion of a short single-mode fiber using a fiber-based quantum nonlinear interferometer. The interferometer consists of two cascaded fiber-based biphoton sources, with each source acting as a nonlinear beamsplitter. A fiber under test is placed in between these two sources, and introduces a frequency-dependent …
Dissipative soliton resonance (DSR) is a promising way for high-energy pulse generation typically having a symmetrical square pulse profile. While this method is well known, the impact of third order dispersion (TOD) on DSR is yet to be fully addressed in the literature. In this article, the impact of TOD on DSR is numerically investigated under the frame of the complex cubic-quintic Ginzburg-Landau equation (CQGLE). Our numerical investigations indicate that DSR can stably exist under TOD with nearly the same pulse amplitude, but with a (significantly) different pulse duration. Depending on t…
