We numerically calculate the equivalent mode-field radius of the fundamental mode in a photonic crystal fiber (PCF) and show that this is a function of the V-parameter only and not the relative hole size. This dependency is similar to what is found for graded-index standard fibers and we furthermore show that the relation for the PCF can be excellently approximated with the same general mathematical expression. This is to our knowledge the first semi-analytical description of the mode-field radius of a PCF.
We introduce a small-core air-guiding photonic crystal fiber whose cladding is made of improved air-silica photonic crystal with non-circular air holes placed in triangular lattice. The fiber achieves un-disturbed bandgap guidance over 350nm wavelength range.
Optical waveguide segments based on geometrically unbound photonic crystal fibers (PCF) designs could be exploited as building blocks to realize miniaturized complex devices which implement advanced photonic operations. Here, we show how to fabricate optical waveguide segments with PCF designs by direct high-resolution 3D printing and how the combination of these segments can realise complex photonic devices. We demonstrate the unprecedented precision and flexibility of our method by fabricating the first-ever fiber polarising beam splitter based on PCFs. The device was directly printed in one…
We present a formal analogy between the eigenvalue problem for guided scalar modes in a low-contrast photonic bandgap fiber and quasi-stationary TM modes of a two-dimensional (2D) photonic structure. Using this analogy, we numerically study the confinement losses of disordered microstructured fibers through the leakage rate of an open 2D system with high refractive index inclusions. Our results show that for large values of the disorder, the confinement losses increase. However, they also suggest that losses might be improved in strongly disordered fibers by exploring ranges of physical parame…
The efficiency of evanescent coupling between a silica optical fiber taper and a silicon photonic crystal waveguide is studied. A high reflectivity mirror on the end of the photonic crystal waveguide is used to recollect, in the backwards propagating fiber mode, the optical power that is initially coupled into the photonic crystal waveguide. An outcoupled power in the backward propagating fiber mode of 88% of the input power is measured, corresponding to a lower bound on the coupler efficiency of 94%.
Photonic crystal fibers represent one of the most active research fields in modern fiber optics. The recent advancements of topological photonics have inspired new fiber concepts and designs. Here, we demonstrate a new type of topological photonic crystal fibers based on second order photonic corner modes from the Su-Schrieffer-Heeger model. Different from previous works where the in-plane properties at $k_z=0$ have been mainly studied, we find that in the fiber configuration of $k_z>0$, a topological bandgap only exists when the propagation constant $k_z$ along the fiber axis is larger than a…
A single-mode all-silica photonic crystal fiber with an effective area of 600 square-micron and low bending loss is demonstrated. The fiber is characterized in terms of attenuation, chromatic dispersion and modal properties.
We experimentally compare the optical bandwidth of a conventional single-mode fiber (SMF) with 3 different photonic crystal fibers (PCF) all optimized for visible applications. The spectral attenuation, single-turn bend loss, and mode-field diameters (MFD) are measured and the PCF is found to have a significantly larger bandwidth than the SMF for an identical MFD. It is shown how this advantage can be utilized for realizing a larger MFD for the PCF while maintaining a bending resistant fiber.
We report on a polarization maintaining large mode area photonic crystal fiber. Unlike, previous work on polarization maintaining photonic crystal fibers, birefringence is introduced using stress applying parts. This has allowed us to realize fibers, which are both single mode at any wavelength and have a practically constant birefringence for any wavelength. The fibers presented in this work have mode field diameters from about 4 to 6.5 micron, and exhibit a typical birefringence of 1.5e-4.
We report generation of broadband low divergent supercontinuum over the entire wavelength window of 1.5 to 3.5 μm from a 2.25 meter long effective single moded photonic bandgap fiber with mode area of 1100 μm2.
We demonstrate a simple and rapid epoxy-based method for transferring photonic crystal cavities to the facets of optical fibers. Passive Si cavities were measured via fiber taper coupling as well as direct transmission from the fiber facet. Active quantum dot containing GaAs cavities showed photoluminescence that was collected both in free space and back through the original fiber. Cavities maintain a high quality factor (2000-4000) in both material systems. This new design architecture provides a practical mechanically stable platform for the integration of photonic crystal cavities with macr…
We analyze the guiding problem in a realistic photonic crystal fiber using a novel full-vector modal technique, a biorthogonal modal method based on the nonselfadjoint character of the electromagnetic propagation in a fiber. Dispersion curves of guided modes for different fiber structural parameters are calculated along with the 2D transverse intensity distribution of the fundamental mode. Our results match those achieved in recent experiments, where the feasibility of this type of fiber was shown.
We study the class of endlessly single-mode all-silica photonic crystal fibers with a triangular air-hole cladding. We consider the sensibility to longitudinal nonuniformities and the consequences and limitations for realizing low-loss large-mode area photonic crystal fibers. We also discuss the dominating scattering mechanism and experimentally we confirm that both macro and micro-bending can be the limiting factor.
The field energy distributions and effective mode areas of silica-based photonic bandgap fibers with a honeycomb airhole structure in the cladding and an extra airhole defining the core are investigated. We present a generalization of the common effective area definition, suitable for the problem at hand, and compare the results for the photonic bandgap fibers with those of index-guiding microstructured fibers. While the majority of the field energy in the honeycomb photonic bandgap fibers is found to reside in the silica, a substantial fraction (up to ~30%) can be located in the airholes. Thi…
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.
Results from the calculation of the basic characteristics of the photonic crystal fiber with two rings of holes are presented by the approach which takes into account the exact distribution of the refractive index over the cross section of the photonic crystal fiber. Formulae are theoretically derived for the calculation of holes with arbitrary shapes by dividing the material within them into rotated at different angles rectangles. Keywords: photonic crystal fibre, Galerkin method, a set of sine functions, local coordinate systems.
In the paper, we propose the new technology for mass production of the photonic crystal devices and all-optical integrated circuits. We carry out the brief analysis of positive and negative sides paying attention to recent advances in silicon fibers fabrication which is crucial moment in the proposed technology.
Quasi error-free 10 Gbit/s data transmission is demonstrated over a novel type of 50 micron core diameter photonic crystal fiber with as much as 100 m length. Combined with 850$ nm VCSEL sources, this fiber is an attractive alternative to graded-index multi-mode fibers for datacom applications. A comparison to numerical simulations suggests that the high bit-rate may be partly explained by inter-modal diffusion.
For the first time, we demonstrated that a hyper-broadband from 2μm to 10μm can be generated with a high spectral flatness by using a ~4 um pump and an As2Se3 photonic crystal fiber. The broad and flat dispersion profile and the low guiding loss of the endlessly single-mode As2Se3 photonic crystal fibers combining with the high nonlinearity and wide mid-infrared transparent window of As2Se3 chalcogenide glass are essential for this high performance mid-infrared laser source.
We build ring resonators to assess the potentialities of Kagome Hollow-Core Photonic Crystal Fibers for future applications to resonant rotation sensing. The large mode diameter of Kagome fibers permits to reduce the free space fiber-to-fiber coupling losses, leading to cavities with finesses of about 30 for a diameter equal to 15 cm. Resonance linewidths of 3.2~MHz with contrasts as large as 89\% are obtained. Comparison with 7-cell photonic band gap (PBG) fiber leads to better finesse and contrast with Kagome fiber. Resonators based on such fibers are compatible with the angular random walk …
Structured light have made deep impacts on modern biotechnology and clinical practice, with numerous optical systems and lasers currently being used in medicine to treat disease. We demonstrate a new concept of fiber-based optical hook scalpel. The subwavelength photonic hook is obtained in the vicinity of a shaped fiber tip with asymmetric radiation. A 1550 nm continuous-wave source, commonly used for medical imaging, has been required. Photonic hook with a lateral feature size less than the half-wavelength is achieved using a hemispherical shaped fiber tip with metallic mask. This breakthrou…
Optical fiber tapers are used to collect photoluminescence emission at ~1.5 um from photonic crystal cavities fabricated in erbium doped silicon nitride on silicon. Photoluminescence collection via fiber taper is enhanced 2.5 times relative to free space, with a total taper collection efficiency of 53%. By varying the fiber taper offset from the cavity, a broad tuning range of coupling strength is obtained. This material system combined with fiber taper collection is promising for building on-chip optical amplifiers.
We demonstrate experimentally that the spectral broadening of CW supercontinuum can be controlled by using photonic crystal fibers with two zero-dispersion wavelengths pumped by an Yb fiber laser at 1064 nm. The spectrum is bounded by two dispersive waves whose spectral location depends on the two zero-dispersion wavelengths of the fiber. The bandwidth of the generated spectrum and the spectral power density may thus be tailored for particular applications, such as high-resolution optical coherence tomography or optical spectroscopy.
Transient fully reconfigurable photonic circuits can be introduced at the optical fiber surface with subangstrom precision. A building block of these circuits, a 0.7 angstrom-precise nano-bottle resonator, is experimentally created by local heating, translated, and annihilated.
We present highly sensitive refractometers based on a long-period grating in a large mode area PCF. The maximum sensitivity is 1500 nm/RIU at a refractive index of 1.33, the highest reported for any fiber grating. The minimal detectable index change is $2\times 10^{-5}$. The high sensitivity is obtained by infiltrating the sample into the holes of the photonic crystal fiber to give a strong interaction between the sample and the probing field.
The possibility of soliton self-compression of ultrashort laser pulses down to the few-cycle regime in photonic crystal fibers is numerically investigated. We show that efficient sub-two-cycle temporal compression of nanojoule-level 800 nm pulses can be achieved by employing short (typically 5-mm-long) commercially available photonic crystal fibers and pulse durations of around 100 fs, regardless of initial linear chirp, and without the need of additional dispersion compensation techniques. We envisage applications in a new generation of compact and efficient sub-two cycle laser pulse sources.
We propose a new method for mass production of the photonic crystal devices on the basis of widely-known and well-developed technology such as microstructured optical fibers. In this paper, we investigate the optical properties of side-excited microstructured optical fiber and discuss the conditions for utilization such a structure as a planar photonic crystal device, namely, the high-quality resonance filter.
In this paper we propose a new hypothesis of out of plane band gap formation in all solid photonic band gap (PBG) fibers. At first, one considers the process of the core modes formation as a result of excitation of continuous mode spectrum of single dielectric rod of the cladding. It is shown that the core modes can be considered as transverse resonance of a set of the radiation modes decoupled from the continuum provided that the phase matching condition for the propagation constants are fulfilled. An analogy between the core mode formation in all solid PBG fibers and formation of bound state…
In a recent paper, Subbaraman et al report a theoretical and numerical study of highly dispersive pure silica photonic crystal fiber supporting group-velocity dispersion exceeding -2*10^4 ps/nm/km. This comment argues that the authors only consider one out of the two sides of the same coin, by not taking the corresponding beating length into account.
Based on a recent formulation of the V-parameter of a photonic crystal fiber we provide numerically based empirical expressions for this quantity only dependent on the two structural parameters - the air hole diameter and the hole-to-hole center spacing. Based on the unique relation between the V-parameter and the equivalent mode field radius we identify how the parameter space for these fibers is restricted in order for the fibers to remain single mode while still having a guided mode confined to the core region.
We study photonic crystal fibers and ring resonators with topological features induced by Aubry- Andre-Harper modulations of the cladding. We find non trivial gaps and edge states at the interface between regions with different Chern numbers. We calculate the field profile and eigenvalue dispersion by an exact recursive approach. Compared with conventional circular resonators and fibers, the proposed structure features topological protection and hence robustness against symmetry-preserving local perturbations that do not close the gap. These topological photonic crystal fibers sustain strong f…
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…
Flying particle sensors in hollow-core photonic crystal fibers require accurate localization of the optically trapped microparticles. We report position measurement to micrometer-resolution, using optical frequency domain reflectometry, of two 1.65-$μ$m-diameter polystyrene particles.
We investigate resonant nonlinear optical interactions and demonstrate induced transparency in acetylene molecules in a hollow-core photonic band-gap fiber at 1.5$μ$m. The induced spectral transmission window is used to demonstrate slow-light effects, and we show that the observed broadening of the spectral features is due to collisions of the molecules with the inner walls of the fiber core. Our results illustrate that such fibers can be used to facilitate strong coherent light-matter interactions even when the optical response of the individual molecules is weak.
We propose an optical trapping technique in which a fundamental soliton traps an ultrashort small amplitude radiation in a symmetric hollow-core photonic crystal fiber filled with a noble gas, preventing its dispersion. The system is Raman- and plasma-free. Trapping is due to the cross phase modulation effect between the two pulses. The trapped radiation inside the soliton-induced potential will oscillate periodically due to the shock effect, similar to the motion of a mechanical pendulum.
We consider large-mode area photonic crystal fibers for visible applications where micro-deformation induced attenuation becomes a potential problem when the effective area A_eff is sufficiently large compared to lambda^2. We argue how a slight increase in fiber diameter D can be used in screening the high-frequency components of the micro-deformation spectrum mechanically and we confirm this experimentally for both 15 and 20 micron core fibers. For typical bending-radii (R~16 cm) the operating band-width increases by ~3-400 nm to the low-wavelength side.
We demonstrate an amplitude-based micro-displacement sensor that uses a plastic photonic bandgap Bragg fiber with one end coated with a silver layer. The reflection intensity of the Bragg fiber is characterized in response to different displacements (or bending curvatures). We note that the Bragg reflector of the fiber acts as an efficient mode stripper for the wavelengths near the edge of the fiber bandgap, which makes the sensor extremely sensitive to bending or displacements at these wavelengths. Besides, by comparison of the Bragg fiber sensor to a sensor based on a regular multimode fiber…
We demonstrate analytically and numerically that a subwavelength-core dielectric photonic nanowire embedded in a properly designed photonic crystal fiber cladding shows evidence of a previously unknown kind of nonlinearity (the magnitude of which is strongly dependent on the waveguide parameters) which acts on solitons so as to considerably reduce their Raman self-frequency shift. An explanation of the phenomenon in terms of indirect pulse negative chirping and broadening is given by using the moment method. Our conclusions are supported by detailed numerical simulations.
We address the long-standing unresolved problem concerning the V-parameter in a photonic crystal fiber (PCF). Formulate the parameter appropriate for a core-defect in a periodic structure we argue that the multi-mode cut-off occurs at a wavelength lambda* which satisfies V_PCF(lambda*)=pi. Comparing to numerics and recent cut-off calculations we confirm this result.
We have investigated the interaction between a strong soliton and a weak probe with certain configurations that allow optical trapping in gas-filled hollow-core photonic crystal fibers in the presence of the shock effect. We have shown theoretically and numerically that the shock term can lead to an unbroken parity-time $ \left(\mathcal{PT}\right) $ symmetry potential in these kinds of fibers. Reciprocity breaking, a remarkable feature of the $ \mathcal{PT} $ symmetry, is also demonstrated numerically. Our results will open different configurations and avenues for observing $ \mathcal{PT} $-sy…
We show that point defects in two-dimensional photonic crystals can support bound states in the continuum (BICs). The mechanism of confinement is a symmetry mismatch between the defect mode and the Bloch modes of the photonic crystal. These BICs occur in the absence of bandgaps and therefore provide an alternative mechanism to confine light. Furthermore, we show that such BICs can propagate in a fiber geometry and exhibit arbitrarily small group velocity which could serve as a platform for enhancing non-linear effects and light-matter interactions in structured 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 t…
In our work we focus on the accurate computation of light propagation in finite size photonic crystal structures with the finite element method (FEM). We discuss how we utilize numerical concepts like high-order finite elements, transparent boundary conditions and goal-oriented error estimators for adaptive grid refinement in order to compute radiation leakage in photonic crystal fibers and waveguides. Due to the fast convergence of our method we can use it e.g. to optimize the design of photonic crystal structures with respect to geometrical parameters, to minimize radiation losses and to com…
We experimentally and theoretically study self-phase modulation by Kerr effect in a liquid filled hollow core photonic crystal fiber. We perform a complete characterization of the linear optical properties of the hollow core photonic band gap fiber filled with deuterated acetone to determine all the characteristics of the propagation mode. The nonlinear coefficient of the fiber is determined by fitting the output spectra broadened by self-phase modulation with a new analytical expression giving the spectra of a secant hyperbolic pulse transmitted through a Kerr media. The experiment allows a p…
Photonic crystal fibers are used in fiber amplifiers and lasers because of the flexibility in the design of mode area and dispersion. However, these quantities depend strongly on the wavelength. The wavelength dependence of gain, nonlinearity and dispersion are investigated here by including the wavelength dependence explicitly in the nonlinear Schrödinger equation for photonic crystal fibers with varying periods and hole sizes. The effect of the wavelength dependence of each parameter is studied separately as well as combined. The wavelength dependence of the parameters is shown to create asy…
Motivated by recent experimental work by Folkenberg et al. we consider the effect of weak disorder in the air-hole lattice of small-core photonic crystal fibers. We find that the broken symmetry leads to higher-order modes which have generic intensity distributions resembling those found in standard fibers with elliptical cores. This explains why recently reported experimental higher-order mode profiles appear very different from those calculated numerically for ideal photonic crystal fibers with inversion and six-fold rotational symmetry. The splitting of the four higher-order modes into two …
We present the use of linearly down-tapered gas-filled hollow-core photonic crystal fiber in a single-stage, pumped with pulses from a compact infrared laser source, to generate a supercontinuum carrying significant spectral power in the deep ultraviolet (200 - 300 nm). The generated supercontinuum extends from the near infrared down to around 213 nm with up to 0.83 mW/nm in the deep ultraviolet.
We found the self-similar solitary solutions of a recently proposed model for propagation of pulses in gas filled hollow-core photonic crystal fibers that includes a plasma induced nonlinearity. As anticipated for a simpler model and using a perturbation analysis, there are indeed stationary solitary waves that accelerate and self-shift to higher frequencies. However, if the plasma nonlinearity strength is large or the pulse amplitudes are small, the solutions have distinguished long tails and decay as they propagate.
We report the generation of a purely vibrational Raman comb, extending from the vacuum ultraviolet (184 nm) to the visible (478 nm), in hydrogen-filled kagomé-style photonic crystal fiber pumped at 266 nm. Stimulated Raman scattering and molecular modulation processes are enhanced by higher Raman gain in the ultraviolet. Owing to the pressure-tunable normal dispersion landscape of the fiber-gas system in the ultraviolet, higher-order anti-Stokes bands are generated preferentially in higher-order fiber modes. The results pave the way towards tunable fiber-based sources of deep- and vacuum ultra…
We show how to apply tiling and pattern theory in the design of hollow-core photonic crystal fibers and guide light in multiple bandgaps. By combining two different glass apexes in a single [$3^6$;$3^2$.$4.3.4$] 2-uniform tiling, transmission regions with fundamental, second and third harmonic wavelengths are supported. This cladding design may also be an excellent candidate for high power beam delivery of Er/Yb, Nd:YAG and Ti:Sapphire laser sources.
We report on an easy-to-evaluate expression for the prediction of the bend-loss for a large mode area photonic crystal fiber (PCF) with a triangular air-hole lattice. The expression is based on a recently proposed formulation of the V-parameter for a PCF and contains no free parameters. The validity of the expression is verified experimentally for varying fiber parameters as well as bend radius. The typical deviation between the position of the measured and the predicted bend loss edge is within measurement uncertainty.
A polymer/liquid crystal-based fiber Bragg grating (PLC-FBG) is fabricated with visible two-beam holography by photo-induced modulation of a pre-polymer/LC solution infiltrated into the hollow channels of a solid core photonic crystal fiber (PCF). The fabrication process and effects related to the photonic bandgap guidance into the infiltrated PCF, and characterization of the PLC-FBG are discussed. Experimental data here presented, demonstrate that the liquid crystal inclusions of the PLC-FBG lead to high thermal and bending sensitivities. The microscopic behavior of the polymer/liquid crystal…
We study the sensitivity of fiber grating sensors in the applications of strain, temperature, internal label-free biosensing, and internal refractive index sensing. It is shown that optical dispersion plays a central role in determining the sensitivity, and the dispersion may enhance or suppress sensitivity as well as change the sign of the resonant wavelength shifts. We propose a quality factor, $Q$, for characterizing LPGs.
Based on the interplay between photoionization and Raman effect in gas-filled photonic crystal fibers, we propose a new optical device to control frequency-conversion of ultrashort pulses. By tuning the input-pulse energy, the output spectrum can be either down-converted, up-converted, or even frequency-shift compensated. For low input energies, Raman effect is dominant and leads to a redshift that increases linearly during propagation. For larger pulse energies, photoionization starts to take over the frequency conversion process, and induces a strong blueshift. We have found also that the fi…
We numerically study the possibilities for improved large-mode area endlessly single mode photonic crystal fibers for use in high-power delivery applications. By carefully choosing the optimal hole diameter we find that a triangular core formed by three missing neighboring air holes considerably improves the mode area and loss properties compared to the case with a core formed by one missing air hole. In a realized fiber we demonstrate an enhancement of the mode area by ~30 % without a corresponding increase in the attenuation.
Tunable photonic elements at the surface of an optical fiber with piezoelectric core are proposed and analyzed theoretically. These elements are based on whispering gallery modes whose propagation along the fiber is fully controlled by nanoscale variation of the effective fiber radius, which can be tuned by means of a piezoelectric actuator embedded into the core. The developed theory allows one to express the introduced effective radius variation through the shape of the actuator and the voltage applied to it. In particular, the design of a miniature tunable optical delay line and a miniature…
We consider photonic crystal fibers made from arbitrary base materials and derive a unified semi-analytical approach for the dispersion and modal properties which applies to the short-wavelength regime. In particular we calculate the dispersion and the effective index and comparing to fully-vectorial plane wave simulations we find excellent agreement. We also calculate asymptotic results for the mode-field diameter and the V-parameter and from the latter we predict that the fibers are endlessly single mode for a normalized air-hole diameter smaller than 0.42, independently of the base material…
We present two novel hybrid photonic structures made of silica that possess two well-separated frequency bandgaps. The addition of interstitial air holes in a precise location and size allows these bandgaps to open up with a ratio of ${\sim3}$ between their central frequencies at the air line ${ck_z/w=1}$, thus fulfilling the basic guidance condition for third harmonic generation in hollow-core fibers. In addition, these designs may serve as high-power laser delivery of two well-separated wavelengths, such as visible and near infrared.
Higher-order modes up to LP$_{33}$ are controllably excited in water-filled kagomé- and bandgap-style hollow-core photonic crystal fibers (HC-PCF). A spatial light modulator is used to create amplitude and phase distributions that closely match those of the fiber modes, resulting in typical launch efficiencies of 10-20% into the liquid-filled core. Modes, excited across the visible wavelength range, closely resemble those observed in air-filled kagomé HC-PCF and match numerical simulations. Mode indices are obtained by launching plane-waves at specific angles onto the fiber input-face and comp…
