Walk-off Length Research Articles

Designing an OAM fiber with a two-layer seven-core structure to support 322 OAM-mode transmissions

In this paper, a two-layer seven-core structural fiber (TLSCSF) is proposed to support and improve the propagation of more orbital angular momentum (OAM) mode beams, thus increasing the transmission capacity and spectrum efficiency (SE) of an optical communication system. The TLSCSF is composed of seven sub-cores, each containing two inner and outer layers of core rings and a central air hole. The two core rings are prepared using two materials with different doping concentrations. The supported OAM modes can be propagated in the fiber core ring. A finite element method (FEM) is used to analyze the designed fiber, and the calculated results show that the TLSCSF can stably transmit 322 OAM modes without higher order radial modes in the wavelength range of 1.5∼1.6 um. The corresponding effective refractive index difference between two adjacent vector modes (HE/EH) is more than 10−4. The measured effective mode areas (Aeff) and the confinement losses (CL) of HE or EH modes are larger than 54 um2 and smaller than 10−10 dB m−1, respectively. Moreover, the calculated dispersion variations and the mode qualities are lower than 230 ps nm−1 km−1 and more than 90%, respectively. Finally, the 10ps walk-off lengths of all vector modes supported by TLSCSF at a wavelength of 1.55 um are also evaluated, where the measured results show that except for HE2,1 and EH1,1, all other modes achieve a 10ps walk-off length of the order of 103 to 105. Consequently, the TLSCSF can contributes to improving the channel capacity and SE by supporting 322 fundamental radial OAM modes with robust performances in an optical communication system.

Improving orbital angular momentum mode transmission with imperfect ring–core fiber

Orbital angular momentum (OAM), inherent to light beams characterized by helical phase fronts, represents an alternative spatial degree of freedom for photons. In recent years, OAM-based communication has gained significant attention as a potential solution to increase the capacity and spectral efficiency of optical fiber communication systems. In optical fibers, OAM modes can be generated and manipulated by utilizing specialized optical components and techniques. One approach involves using specially designed optical fibers, such as ring–core fibers, which have the capability to support multiple OAM modes. In the manufacturing process, the ring fiber is hardly made perfectly, especially the doped-cores. The introduced defect breaks the symmetry of the ring–core, which has a serious impact on OAM mode transmission. Using a material with a slightly higher refractive index than the cladding to wrap the ring–core is effective in reducing impairment of defects. After numerical simulation, the proposed method improves the walk-off length by a factor of 2–40.

Intermodal effective phase matching for second harmonic generation of ultrashort pulses in high index contrast optical fibers

Second harmonic generation (SHG) in glass optical fibers calls for creating a second order susceptibility in the fiber glass and for achieving phase matching between the pump and the second harmonic signal. The latter is very challenging when using ultrashort pulses, given that the group velocities of the pump and the second harmonic should also be matched. We have shown in previous work that it is possible to achieve simultaneous modal phase matching (MPM) and group velocity matching (GVM) when the pump and the second harmonic are propagating in the LP01 and LP02 modes, respectively, in high GeO2-content double-clad optical fibers. However, simultaneous MPM and GVM can only be obtained in optical fibers with dedicated designs and within very tight geometrical tolerances. In this paper, we show that instead of considering the matching of phase and group velocities separately, we can consider a more general or “effective” phase matching approach, in which we consider all the dispersion terms up to the second order in the expressions of the propagation constants of the pump and second harmonic signals. This allows introducing the pulse duration as a controllable parameter that helps to enforce the said effective phase matching in fibers with designs that deviate by as much as 10% from the target, while providing for temporal walk-off lengths in excess of several centimeters. The impact of this finding goes beyond SHG only and can be applied to other ultrashort laser pulse-based nonlinear optical processes in fibers and waveguides.

Analytical solution to incident angle quasi-phase-matching engineering for second harmonic generation in a periodic-poled lithium niobate crystal

Phase matching or quasi-phase matching (QPM) is of significant importance to the conversion efficiency of second harmonic generation (SHG) in artificial nonlinear crystals like lithium niobate (LN) crystal or microstructured nonlinear crystals like periodic-poled lithium niobate (PPLN) crystals. In this paper, we propose and show that the incident angle of pump laser light can be harnessed as an alternative versatile tool to engineer QPM for high-efficiency SHG in a PPLN crystal, in addition to conventional means of period adjusting or temperature tuning. A rigorous model is established and analytical solution of the nonlinear conversion efficiency under the small and large signal approximation theory is obtained at different incident angles. The variation of phase mismatching and walk-off length with incident angle or incident wavelength are also explored. Numerical simulations for a PPLN crystal with first order QPM structure are used to confirm our theoretical predictions based on the exact analytical solution of the general large-signal theory. The results show that the narrow-band tunable SHG output covers a range of 532 nm–552.8 nm at the ideal incident angle from 0° to 90°. This theoretical scheme, fully considering the reflection and transmission at the air-crystal interface, would offer an efficient theoretical system to evaluate the nonlinear frequency conversion and help to obtain the maximum SHG conversion efficiency by selecting an optimum incident wavelength and incident angle in a specially designed PPLN crystal, which would be very helpful for the design of tunable narrow-band pulse nanosecond, picosecond, and femtosecond laser devices via PPLN and other microstructured LN crystals.

Polymer negative curvature ring-core fiber for OAM modes guidance.

In this paper, a novel, to the best of our knowledge, polymer-based negative curvature ring-core fiber (NC-RCF) is proposed and investigated. The hollow-core NC-RCF is composed of TOPAS as background material. The inner and outer negative curvature structure layers are connected to the annular area, and the orbital angular momentum (OAM) modes can propagate in the annular core. In the frequency region of 1.0-1.5THz, the designed NC-RCF can stably transmit 82 OAM modes. Investigation results indicate that the effective refractive index differences between the corresponding HE and EH modes are above 10-4. The confinement losses of EH or HE modes are smaller than 10-8 d B/m, and the dispersion variations are lower than 0.31ps/THz/cm. Effective mode areas are larger than 5.14m m 2. Additionally, the highest mode purity of all vector modes is 99.78%. In addition, modal birefringence, also known as the walk-off length, has also been discussed. All these operation performances indicate that the designed NC-RCF make contributions to the optical communication systems.

Air-Core Ring Fiber Guiding >400 Radially Fundamental OAM Modes Across S + C + L Bands

In this paper, we propose and design a Ge-doped air-core ring fiber, which can support a large amount of OAM modes for mode-division multiplexing (MDM) in optical fiber communications. By varying the mole fraction of GeO2 and adjusting the structure parameter, including the air-core radius and the GeO2-doped ring width, we investigate the influence of different fiber parameters on the total supported OAM mode number. The hollow silica fiber with a 50- $\mu \text{m}$ air core and a 1.5- $\mu \text{m}$ thickness of Ge-doped ring is designed in simulation to support fiber eigenmodes up to HE112,1 and EH107,1. This provides 436 OAM modes at 1550 nm while maintaining radially single mode condition. Moreover, it can support more than 400 radially fundamental OAM modes for the wavelength from 1460 nm to 1625 nm, covering entire S, C and L bands. The optical parameters of the guided OAM modes in the fiber are also numerically analyzed, including effect of material loss, optical field distribution, effective refractive index profile and chromatic dispersion, etc. The simulation results show that the higher-order OAM modes have longer $2\pi $ and 10-ps walk-off length in the air-core ring fiber with ellipticity or bending compared with low-order modes.

Analytic Expressions for Orbital Angular Momentum Modal Crosstalk in a Slightly Elliptical Fiber

Assuming weakly guiding approximation, we examine orbital angular momentum (OAM) mode mixing on account of ellipticity in a fiber and derive a complete set of analytic expressions for spatial crosstalk, using scalar perturbation theory that incorporates fully the existing degeneracy between a spatial OAM mode and its degenerate partner characterized by a topological charge of opposite sign. These expressions, consequently, include an explicit formula for calculating the 2 pi walk-off length over which an input OAM mode converts into its degenerate partner, and back into itself. We further explore the applicability of the derived expressions in the presence of spin-orbit interaction. The expressions constitute a useful mathematical tool in the analysis and design of fibers for spatially-multiplexed mode transmissions. Their utility is demonstrated with application to a few mode and a multimode step-index fiber.

Orbital Angular Momentum (OAM) Mode Mixing in a Bent Step Index Fiber in Perturbation Theory

Within the framework of perturbation theory, we explore in detail the mixing of orbital angular momentum(OAM) modes due to a fiber bend in a step-index multimode fiber. Using scalar wave equation, we develop a complete set of analytic expressions for mode-mixing, including those for the $2\pi$ walk-off length, which is the distance traveled within the bent fiber before an OAM mode transforms into its negative topological charge counterpart, and back into itself. The derived results provide insight into the nature of the bend effects, clearly revealing the mathematical dependence on the bend radius and the topological charge. We numerically simulate the theoretical results with applications to a few-mode fiber and a multimode fiber, and calculate bend-induced modal crosstalk with implications for mode-multiplexed systems. The presented perturbation technique is general enough to be applicable to other perturbations like ellipticity and easily extendable to other fibers with step-index-like profile as in the ring fiber.

Efficient middle-infrared generation in LiGaS2 by simultaneous spectral broadening and difference-frequency generation.

We report a surprisingly broadband and efficient midinfrared pulse generation in LiGaS2 (Langasite, LGS) by invoking a simultaneous interplay of intrapulse difference-frequency generation, self-phase modulation, and dispersion. This cascaded mechanism expands the output bandwidth and output power at the same time. With 30-fs driving pulses centered at 1030-nm wavelength we obtain a broadband middle-infrared spectrum of 8-11μm with an LGS crystal as thick as 4mm, which is eight times longer than the walk-off length.

Characterization of Red/Green/Blue Orbital Angular Momentum Modes in Conventional G.652 Fiber

The space domain of lightwaves has attracted increasing interest in optical communications. Lightwaves having helical phase front and carrying orbital angular momentum (OAM) have seen potential applications both in free-space and fiber-based optical communications. The widely deployed conventional ITU-T G.652 fiber is single mode fiber at 1550 nm, which, however, might support high-order modes as well as OAM modes at short wavelength. In this paper, we present detailed theoretical analyses on the mode properties of circularly polarized OAM modes in conventional G.652 fiber at three RGB wavelengths (red at 632.8 nm, green at 532 nm, and blue at 476.5 nm). The G.652 fiber has a 4.6-μm core radius, a 62.5-μm cladding radius, and 0.277% refractive index difference between the core and the cladding. We first study all the cylindrical vector modes (fiber eigenmodes) and synthesize the circular OAM modes by proper linear combination of degenerate fiber eigenmodes supported in the G.652 fiber at three RGB wavelengths. We then calculate the effective mode area and nonlinearity and discuss the tolerance to fiber ellipticity and bending (n eff differences, 2π walk-off length, 10-ps walk-off length, loss, and OAM crosstalks) for red, green, and blue OAM modes. Additionally, we investigate the OAM modes properties at another three wavelengths of conventional semiconductor lasers, i.e., 780, 650, and 405 nm. Moreover, we also estimate the fiber attenuation, propagation loss, and communication bandwidth/capacity. The obtained results may stimulate wide interesting OAM related applications using conventional G.652 fiber, especially for hundreds of meters or km-scale short reach/distance applications.

Group velocity matching in high-order harmonic generation driven by mid-infrared lasers

We analyze the role of group-velocity matching (GVM) in the macroscopic build up of the high-harmonic signal generated in gas targets at high pressures. A definition of the walk-off length, associated with GVM, in the non-perturbative intensity regime of high-harmonic generation is given. Semiclassical predictions based on this definition are in excellent agreement with full quantum simulations. We demonstrate that group velocity matching is a relevant factor in high harmonic generation and the isolation of attosecond pulses driven by long wavelength lasers and preferentially selects contributions from the short quantum trajectories.

Stimulated Raman scattering in AsSe2-As2S5 chalcogenide microstructured optical fiber with all-solid core.

The effects of stimulated Raman scattering (SRS) is demonstrated in chalcogenide microstructured optical fiber (MOF) with all-solid AsSe2 core and As2S5 cladding. The first-order Raman Stokes wave is investigated in the MOFs with different core diameters pumped by the picosecond pulses at 1958 nm. The maximum conversion efficiency of -15.0 dB from the pump to first-order Raman Stokes wave is obtained in the MOF with the core diameter of 2.6 μm. The conversion efficiency decreases when the core diameter deviates from 2.6 μm. When the fiber core is larger, the effective nonlinearity is decreased. When the fiber core is smaller, the mode field is difficult to be confined in the core. The walk-off length between the pump and Stokes wave is crucial to the process of SRS according to the analysis of the experimental data. The Raman effects are simulated numerically. The simulated results can agree well with the experiments. It is the first time to demonstrate the Raman effect in AsSe2-As2S5 MOF, to the best of our knowledge.

Mode Properties and Propagation Effects of Optical Orbital Angular Momentum (OAM) Modes in a Ring Fiber

We simulate and analyze the mode properties and propagation effects of orbital angular momentum (OAM) modes in a ring fiber. A ring fiber with 0.05 up-doping is designed in simulation to support up to 10 OAM modes while maintaining single-mode condition radially. With a multiple-ring fiber, tens of OAM modes can be potentially multiplexed to greatly enhance the system capacity and spectral efficiency. The mode index difference can be maintained above 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> over hundreds of nanometers optical bandwidth. Higher order OAM modes' azimuthal intensity and odd-order OAM modes' azimuthal phase show better tolerance to the fiber ellipticity. Moreover, higher order OAM modes also have longer 2π and 10-ps walk-off length. After 600-km propagation, OAM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,4</sub> mode shows <; 10-ps mode walk- off, even in a ring fiber with 1% ellipticity. Also, in such an elliptical fiber, the well-aligned OAM modes with different charges have <;-20 dB intermode crosstalk. The improvement of the circularity for the ring fiber is expected to reduce the crosstalk and increase the demultiplexing efficiency.

Terahertz generation with tilted-front laser pulses: dynamic theory for low-absorbing crystals

A theory of terahertz emission from a femtosecond laser pulse with a tilted intensity front propagating through a prism-shaped electro-optic crystal is developed. The theory accounts for transient effects at the entrance boundary of the crystal and allows us to explore the dynamics of terahertz generation in the crystal. In particular, transverse walkoff length is introduced as an important parameter of the terahertz field formation process. Two typical experimental situations—LiNbO3 excited with a Ti:sapphire laser (0.8 μm wavelength) at room and cryogenic temperatures—are considered, and new schemes, in which GaAs at room temperature is excited at 1.8 and 3.5 μm, are proposed and analyzed. The parameters of the laser pulse (transverse size, tilt angle, and pulse duration) and crystal size maximizing the terahertz yield are calculated.

Influence of self- and cross-phase modulation on 40 Gbaud dual polarization DQPSK/D8PSK signals in 10 Gbit/s OOK WDM systems

This paper, for the first time, investigates the nonlinear degradation of 40 Gbaud single- and dual polarization RZ-DQPSK/D8PSK signals caused by SPM and XPM-induced crosstalk from neighboring 10 Gbit/s NRZ-OOK channels in an WDM upgrade scenario. The investigations were numerically and experimentally conducted over a 320 km transmission link with three different wavelength configurations to address the impact of the walk-off length. The paper also presents the first numerical analysis of the XPM dependence on the relative state of polarization of the D8PSK with respect to the neighbors.

Delivery of picosecond lasers in multimode fibers for coherent anti-Stokes Raman scattering imaging

We investigated the possibility of using standard commercial multimode fibers (MMF), Corning SMF28 fibers, to deliver picosecond excitation lasers for coherent anti-Stokes Raman scattering (CARS) imaging. We theoretically and/or experimentally analyzed issues associated with the fiber delivery, such as dispersion length, walk-off length, nonlinear length, average threshold power for self-phase modulations, and four-wave mixing (FWM). These analyses can also be applied to other types of fibers. We found that FWM signals are generated in MMF, but they can be filtered out using a long-pass filter for CARS imaging. Finally, we demonstrated that MMF can be used for delivery of picosecond excitation lasers in the CARS imaging system without any degradation of image quality.

The study of narrow-band terahertz-wave generation by difference frequency mixing in periodical-inverted GaAs crystal with ps pump pulses

In this paper, the tuning of walk-off length and the optimal period of periodical-inverted GaAs crystal in narrow-band terahertz-wave generation by difference frequency mixing was numerical simulated and analyzed in the condition of different wavelengths and durations of pump pulse.The influence of the number of domains of periodically-inverted GaAs crystal on the THz-wave spectrum was also studied.The temperature tuning properties in periodical-inverted GaAs crystal were calculated and analyzed with the temperature dependent Sellmeier function of GaAs crystal; the influence of temperature tuning on the THz-wave spectrum was also studied.The simulation showed a new way to generate the wide-tunable narrow-band THz wave with temperature tuning.These theoretical calculations served for the subsequent experiment as theoretical basis and reference.

Self calibration in a fiber optic sensing system using the entangled photon states walk-off compensation

We present a concept of a self calibration of the classical and quantum parameters measurement using a fiber optic system. The measurement of the change in phase of the optimum entangled states visibility, which is performed in term of a walk-off length, i.e. birefringence. The applied two physical parameters (i.e. force/stress and temperature) on the sensing fiber can be simultaneously measured, whereas the self calibration respecting to the entangled photon walk-off length can be performed. The scheme of the entangled photons generation in fiber optic is reviewed and the walk-off on the polarization entangled states presented. The potential of self calibration and simultaneous measurement using an interferometric sensing technique and fiber grating sensor are proposed and discussed. The entangled photon walk-off compensation when the sensing fiber was in the thermal controlled environment presented and discussed.

Self-calibration in a fiber optic sensing system using the walk-off compensation

We firstly present a concept of a self-calibration of the classical and quantum parameters’ measurement using a fiber optic system. The measurement of the change in phase of the optimum entangled states’ visibility is performed in terms of a walk-off length, i.e. birefringence. The applied physical parameters on the sensing fiber can be simultaneously measured and the self-calibration respecting the birefringence performed. The scheme of the entangled photons generation in fiber optic is reviewed and the walk-off on the polarization entangled states presented. The potential of self-calibration and simultaneous measurement using an interferometric sensing technique and fiber grating sensor are proposed and discussed. The walk-off on the entangled states in the thermal-controlled environment is presented and discussed.

Fiber optic sensing applications using the entangled states walk-off compensations

This paper presents a new concept of the measurement of the entangled photon states timing walk-off in fiber optic systems. The relationship between the applied physical parameter on fiber optic and timing walk-off compensation can be performed. When polarized light pulse propagates into a fiber optic length, a pair of the entangled photons introduces the change in phase difference, i.e. birefringence, which can be recovered and detected. The potential of use in applications such as quantum interferometer and fiber optic remote sensing is proposed and described. The increase in measurement resolution in terms of the entangled photon walk-off length is analyzed and discussed.