Mode Photonic Crystal Fiber Research Articles

A simple and intuitive procedure for evaluating mode degeneracy in photonic crystal fibers

A simple and intuitive procedure for evaluating the degeneracy of the modes of photonic crystal fibers is presented. The procedure requires only a visual inspection of the vector plots of the transverse modal field profiles and can be applied without knowing group theory and without doing extra computations. Several examples are given.

Toward all-fiber coherent anti-Stokes Raman scattering in the gas phase

The available fiber lasers, photonic-crystal fiber (PCF) frequency converters, and hollow-core PCFs are shown to offer realistic practical solutions for an all-fiber format of coherent anti-Stokes Raman scattering (CARS) in the gas phase. In view of the substantial enhancement of CARS in the guided modes of hollow-core PCFs, a broad class of compact ytterbium and erbium fiber laser sources become suitable for the CARS analysis of gas media. The quantum limit of the signal-to-noise ratio, S/N, in all-fiber CARS is shown to scale as λα-1a-2 with radiation wavelength λ, fiber loss α, and the fiber core radius,aleading, in the case of a hollow-PCF gas cell, to a dramatic improvement of S/N relative to CARS in the regime of tight focusing.

Mode-selective mapping and control of vectorial nonlinear-optical processes in multimode photonic-crystal fibers

We demonstrate an experimental technique that allows a mapping of vectorial nonlinear-optical processes in multimode photonic-crystal fibers (PCFs). Spatial and polarization modes of PCFs are selectively excited in this technique by varying the tilt angle of the input beam and rotating the polarization of the input field. Intensity spectra of the PCF output plotted as a function of the input field power and polarization then yield mode-resolved maps of nonlinear-optical interactions in multimode PCFs, facilitating the analysis and control of nonlinear-optical transformations of ultrashort laser pulses in such fibers.

Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area

We propose a novel type of photonic crystal fiber (PCF), including an elliptical hole in its solid core. We prove the feasibility of such a fiber and investigate both experimentally and theoretically the dependence of its group birefringence on the geometric hole parameters. We show, for the first time, that form-induced birefringence can be achieved in single mode PCFs with large mode area and suggest it as a possible route for the development of polarization maintaining PCF-based LMA fiber devices.

Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fibre

Reported are experimental results from investigations of the sensing properties of long-period gratings (LPGs) recorded in two different geometries of photonic crystal fibre (PCF): a large-mode area PCF and an endlessly single mode PCF. The LPGs have been characterised for their sensitivity to temperature, bending, surrounding index and strain. The LPGs in both fibres have been found to have negligible temperature sensitivity whilst exhibiting useful strain sensitivities. Strong directional bend sensitivity is shown by one PCF whilst the other shows good non-directional bend sensitivity. The fibres exhibit differing sensitivities to surrounding refractive index.

Analytical solution of the fundamental space filling mode of photonic crystal fibers

Analytical solution of the fundamental space filling mode of photonic crystal fibers is revisited based on previous results by Midrio et al. [J Lightwave Technol 2000;18(7):1031–7]. The fundamental space filling mode is designated HE 11 mode following the conventional mode classification. A comparison is made between the vectorial method and the scalar method when identical parameters are used in the analytical solution. A more accurate radius of the equivalent circular unit cell is determined.

Effective index model and guided modes in a photonic crystal fiber

AbstractWe analyze the guided modes of photonic crystal fibers. We compare the values of the V‐parameter obtained using the effective index for the fundamental space‐filling mode with those values obtained by using the effective index of the modes propagating in the photonic crystal fiber. We obtain the condition for single‐mode operation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fundamental Characteristics of Localized Acoustic Modes in Photonic Crystal Fibers

Propagation characteristics of acoustic waves in photonic crystal fibers (PCFs) have been theoretically investigated in details. In order to evaluate acoustic band structures and guided modes for out-of-plane propagation in PCFs, analysis methods based on the finite element method are newly formulated. It is shown through numerical results that complete acoustic band-gaps (ABGs) exist in the cladding region of PCFs and that acoustic guided modes could be localized in the defect region of PCFs by the ABG effect. Furthermore, it is shown that acoustic guided modes could also be localized in the defect region of PCFs by the total internal reflection. These confinement mechanisms of acoustic waves propagating along the fiber length are completely different to those of lightwaves.

Switching intense laser pulses guided by Kerr-effect-modified modes of a hollow-core photonic-crystal fiber

A Kerr-nonlinearity-induced profile of the refractive index in the hollow core of a photonic-crystal fiber (PCF) changes the spectrum of propagation constants of air-guided modes, effectively shifting the passbands in fiber transmission, controlled by the photonic band gaps (PBGs) of the cladding. This effect is shown to allow the creation of fiber switches for high-intensity laser pulses. The Kerr-nonlinearity control of air-guided modes in PCFs and the performance of a PCF switch are quantified by solving the propagation equation for the slowly varying envelope of a laser pulse guided in Kerr-effect-modified PCF modes. The spatial dynamics of the light field in a PBG waveguide switch is analyzed with the use of the slowly varying envelope approximation, demonstrating high contrasts of optical switching with PBG waveguides and hollow PCFs.

Phononic band-gap guidance of acoustic modes in photonic crystal fibers

The elastic modes guided along the axis of an optical fiber are obtained for an arbitrary finite cross section using waveguide finite element analysis. The band structure of acoustic phonons is obtained from this full-vector computation. The analysis is applied to the case of a photonic crystal fiber possessing a honeycomb lattice. It is shown that this fiber exhibits band gaps for elastic modes propagating along the longitudinal fiber axis. For frequencies within a band gap, the external boundary of the fiber becomes a defect of the phononic crystal that supports the propagation of guided elastic modes. Such boundary modes are very sensitive to the boundary conditions. The further introduction of a defect within the two-dimensional phononic crystal leads to the formation of highly confined elastic waveguide modes that copropagate in the same core volume as the guided optical mode. We consider the application of these properties to the suppression of stimulated Brillouin scattering and to enhanced collinear acousto-optical interactions. In particular, we obtain the optimum elastic modal shape that maximizes the acousto-optical scattering coefficient for given optical modes.

The radiated fields of the fundamental mode of photonic crystal fibers

The six-fold rotational symmetry of photonic crystal fibers has important manifestations in the radiated fields in terms of i) a focusing phenomena at a finite distance from the end-facet and ii) the formation of low-intensity satellite peaks in the asymptotic far field. For our study, we employ a surface equivalence principle which allows us to rigorously calculate radiated fields starting from fully-vectorial simulations of the near field. Our simulations show that the focusing is maximal at a characteristic distance from the end-facet. For large-mode area fibers the typical distance is of the order 10xLambda with Lambda being the pitch of the triangular air-hole lattice of the photonic crystal fiber.

A New Design for Terahertz Photonic Crystal Fiber Using the Finite-Difference Time-Domain Method

With unsplit anisotropic perfectly matched layer (APML) for the boundary treatment, a new design for terahertz photonic crystal fiber (PCF) by using the finite-difference time-domain (FDTD) method is present. Electromagnetic fields of guided mode and transmission spectrum in PCFs are computed.

Stress-induced single-polarization single-transverse mode photonic crystal fiber with low nonlinearity

We report on the design of a single-polarization single-transverse mode large mode area photonic crystal fiber. By including index-matched stress applying elements in the photonic cladding an ultra-broadband single polarization window is obtained while a large mode field area of ~700 microm(2) is maintained. Based on that design, an Yb-doped double-clad photonic crystal fiber is realized that combines low nonlinearity and single polarization properties. A first result of the high power operation using this fiber is demonstrated.

Analysis of strictly bound modes in photonic crystal fibers by use of a source-model technique.

We describe a source-model technique for the analysis of the strictly bound modes propagating in photonic crystal fibers that have a finite photonic bandgap crystal cladding and are surrounded by an air jacket. In this model the field is simulated by a superposition of fields of fictitious electric and magnetic current filaments, suitably placed near the media interfaces of the fiber. A simple point-matching procedure is subsequently used to enforce the continuity conditions across the interfaces, leading to a homogeneous matrix equation. Nontrivial solutions to this equation yield the mode field patterns and propagation constants. As an example, we analyze a hollow-core photonic crystal fiber. Symmetry characteristics of the modes are discussed and exploited to reduce the computational burden.

Study on mode degeneracy in photonic crystal fibers

A novel full vector model is applied to analyze the photonic crystal fibers (PCF). From symmetry analysis of modes of a waveguide, we classify the modes of PCF into nondegenerate or degenerate pairs according to the minimum waveguide sectors and its appropriate boundary conditions. We present the modes of PCF that can be labeled by its step index fiber analogs. It is shown that these modes either exhibit the full waveguide symmetry and nondegenerate or occur in degenerate pairs that support this symmetry only in combination. The doublet of the degenerate pairs in which both have the same symmetry as PCF will be split into two nondegenerate modes.

Fast, accurate integral equation methods for the analysis of photonic crystal fibers I: Theory

We present a new integral equation method for calculating the electromagnetic modes of photonic crystal fiber (PCF) waveguides. Our formulation can easily handle PCFs with arbitrary hole geometries and irregular hole distributions, enabling optical component manufacturers to optimize hole designs as well as assess the effect of manufacturing defects. The method produces accurate results for both the real and imaginary parts of the propagation constants, which we validated through extensive convergence analysis and by comparison with previously published results.

Modal interference in dual-core photonic crystal fibers

The modal characteristics of dual-core photonic crystal fibers(PCFs) are analyzed by a full vector supercell lattice overlapping model. The fundamental and second-order modes of dual-core PCFs consist of a pair of even and odd modes with different polarization. The parity properties of the modal electric field for the fundamental and second-order modes are discussed. Based on the analysis of parity of the modal electric fields, we investigated the vector modal interference in dual-core PCFs.It is the interference between two same polarized modes that conributes to the inter-core coupling of power. It is shown that the optical power will oscillate from one core to the other and the phase difference between both cores is about π/2. The dependence of coupling coefficients for different polarization on wavelength is discussed.

Continuous-wave wavelength conversion in a photonic crystal fiber with two zero-dispersion wavelengths

We demonstrate continuous-wave wavelength conversion through four-wave mixing in an endlessly single mode photonic crystal fiber. Phasematching is possible at vanishing pump power in the anomalous dispersion regime between the two zero-dispersion wavelengths. By mixing appropriate pump and idler sources, signals in the range 500-650 nm are obtained in good accordance with calculated phasematching curves. The conversion efficiency from idler to signal power is currently limited to 0.3% by the low spectral density of the pump and idler sources at hand, but can be greatly enhanced by applying narrow line width lasers.

Temperature-insensitive long period grating sensors in photonic crystal fibre

Presented are long-period gratings (LPGs) fabricated in pure silica photonic crystal fibre (PCF) using an electric arc. Two different varieties of PCF have been investigated, an endlessly single mode PCF and a large-mode area PCF. The LPGs have been characterised for their sensitivity to a variety of external measurands. The LPGs in both fibres have been found to have negligible temperature sensitivity whilst exhibiting good sensitivity to bending and strain.

Loss analysis of air-core photonic crystal fibers.

By using a multipole moment approach, we analyze the loss of an air-core photonic crystal fiber and demonstrate that it is possible reduce the transmission loss that is due to photon radiation leakage through the photonic crystal cladding to a level below 0.01 dB/km, with eight rings of air holes. An analogy is drawn between air-core photonic crystal fiber modes and Bragg fiber modes. The influence of material absorption in the silica glass is discussed.