Two-mode Fiber Research Articles

An Injection-Locked Single-Longitudinal-Mode Fiber Ring Laser With Cylindrical Vector Beam Emission

We demonstrate a fiber ring laser with narrow bandwidth single-longitudinal-mode cylindrical vector beam (CVB) output at C-band wavelength range for the first time to the best of our knowledge. A step index two-mode fiber Bragg grating is used as a transverse mode selector for CVB generation, while both the injection-locking technique and narrow bandwidth of the fiber Bragg grating lead to single-longitudinal-mode operation. The 3-dB bandwidth of the laser output is measured to be 60 dB. Mode distribution and optical spectra of few-mode fibers with periodic modulated refractive index profile, namely the few-mode fiber Bragg gratings with bent radius, are investigated theoretically and experimentally, which provide a comprehensive exploration of CVB's generation.

Generation of femtosecond optical vortex pulse in fiber based on an acoustically induced fiber grating.

We proposed a method for generation of a femtosecond optical vortex pulse in a two-mode fiber based on an acoustically induced fiber grating (AIFG) driven by a radio frequency source. Theoretical analysis and experimental results demonstrated that the left- and right-handed circular polarization fundamental modes of the femtosecond optical pulse could be converted to the linearly polarized ±1-order optical vortex modes through the AIFG with the mode conversion efficiency of ∼95%. The off-axial interference experiment and the polarization angle-dependent intensity examination were performed to verify the topological charge and the polarization state of the femtosecond optical vortex, respectively.

Vector bright soliton behaviors of the coupled higher-order nonlinear Schrödinger system in the birefringent or two-mode fiber.

Studied in this paper are the vector bright solitons of the coupled higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber. With the help of auxiliary functions, we obtain the bilinear forms and construct the vector bright one- and two-soliton solutions via the Hirota method and symbolic computation. Two types of vector solitons are derived. Single-hump, double-hump, and flat-top solitons are displayed. Elastic and inelastic interactions between the Type-I solitons, between the Type-II solitons, and between the two combined types of the solitons are revealed, respectively. Especially, from the interaction between a Type-I soliton and a Type-II soliton, we see that the Type-II soliton exhibits the oscillation periodically before such an interaction and becomes the double-hump soliton after the interaction, which is different from the previously reported.

Simulation of a long-haul fiber optic link with a two-mode optical fiber

Modern telecommunication networks approach the capacity crunch, which is associated with the so-called nonlinear Shannon limit. So, the passage to fiber optic links with few-mode optical fibers is considered as an alternative solution of the described problem concerned with high nonlinearity of conventional commercial single-mode optical fibers. Presently, various designs of few-mode optical fibers have been known, with the recently published works presenting experimental results demonstrating their potentialities for long-haul fiber optic links. A lot of models of long-haul fiber optic links with few-mode optical fibers have been developed based on which features of a few-mode optical fiber transport network were numerically simulated. This work presents the results of simulation of a 6000-km long-haul fiber optic link with a two-mode optical fiber and 100-km-per-span Erbium doped fiber optic amplifiers system under 100 Gbps DP-DQPSK data transmission. We studied the use of particular linearly polarized modes and optical vortices for signal transmission. The computation results were compared with the simulation of the same fiber optic link with a single-mode optical fiber under the identical conditions.

Inter-modal four-wave mixing study in a two-mode fiber.

We demonstrate efficient four-wave mixing among different spatial modes in a 1-km long two-mode fiber at telecommunication wavelengths. Two pumps excite the LP01 and LP11 modes, respectively, while the probe signal excites the LP01 mode, and the phase conjugation (PC) and Bragg scattering (BS) idlers are generated in the LP11 mode. For these processes we experimentally characterize their phase matching efficiency and bandwidth and find that they depend critically on the wavelength separation of the two pumps, in good agreement with the numerical study we carried out. We also confirm experimentally that BS has a larger bandwidth than PC for the optimum choice of the pump wavelength separation.

Simultaneous control of orbital angular momentum and beam profile in two-mode polarization-maintaining fiber.

We report simultaneous control of the orbital angular momentum (OAM) and beam profile of vortex beams generated in two-mode polarization-maintaining optical fiber. Two higher-order eigenmodes of the fiber are combined to form optical vortices. Reduced coherence between the fiber modes decreases the mode purity. Varying the coherence of the fiber modes changes the average OAM while maintaining a constant annular intensity profile. Additionally, a donut mode has been shown to be insensitive to bends and twists in the fiber.

Ultrafast, all-optical control of modal phases in a few-mode fiber for all-optical switching.

The phase differences between the transverse modes of an optical fiber can be altered all-optically by intermodal cross-phase modulation. In this Letter, we experimentally demonstrate this effect with ultrashort laser pulses. An ultrashort probe pulse, guided in both modes of a two-mode fiber, is co-propagating and temporally overlapping with an ultrashort control pulse, guided in the fundamental mode only and centered at a separate wavelength. The use of ultrashort pulses allows for a notable phase shift at a 33-fold reduced control pulse energy and a 173-fold reduced fiber length, compared to previous experiments. A total phase shift of 0.285π between the two probe modes was achieved at a 9 nJ control pulse energy in a 19 cm long two-mode graded-index fiber. Additionally, the capability of this scheme to switch ultrashort pulses in an all-optical manner was investigated. A modulation depth of 50% was achieved, limited by temporal nonlinear effects.

Effective Mode Field Diameter for LP11Mode and Its Measurement Technique

The effective mode field diameter (MFD) for the second-order (LP11) mode in two-mode fibers is determined to allow estimation of the coupling efficiencies at a splice with axial misalignment. Simulations are performed to verify its validity. In addition, we propose a novel technique for measuring the effective MFD distribution for the LP11 mode along two-mode fibers. The technique is based on optical time-domain reflectometry; it conducts measurements in the two-mode region of test fibers and individually observes the LP01 and LP11 modes of the backscattered light. Its feasibility is demonstrated experimentally.

Modulation instabilities in randomly birefringent two-mode optical fibers**Project supported by the Natural Science Foundation of Jiangsu Provincial Universities (Grant No. 14KJB140009), the National Natural Science Foundation of China (Grant No. 11447113), and the Startup Foundation for Introducing Talent of NUIST (Grant No. 2241131301064).

Modulation instabilities in the randomly birefringent two-mode optical fibers (RB-TMFs) are analyzed in detail by accounting the effects of the differential mode group delay (DMGD) and group velocity dispersion (GVD) ratio between the two modes, both of which are absent in the randomly birefringent single-mode optical fibers (RB-SMFs). New MI characteristics are found in both normal and anomalous dispersion regimes. For the normal dispersion, without DMGD, no MI exists. With DMGD, a completely new MI band is generated as long as the total power is smaller than a critical total power value, named by Pcr, which increases significantly with the increment of DMGD, and reduces dramatically as GVD ratio and power ratio between the two modes increases. For the anomalous dispersion, there is one MI band without DMGD. In the presence of DMGD, the MI gain is reduced generally. On the other hand, there also exists a critical total power (Pcr), which increases (decreases) distinctly with the increment of DMGD (GVD ratio of the two modes) but varies complicatedly with the power ratio between the two modes. Two MI bands are present for total power smaller than Pcr, and the dominant band can be switched between the low and high frequency bands by adjusting the power ratio between the two modes. The MI analysis in this paper is verified by numerical simulation.

Design and Fabrication of Low Loss Hole-Assisted Few-Mode Fibers With Consideration of Surface Imperfection of Air Holes

We designed and fabricated a low loss hole-assisted few-mode fiber (HA-FMF) taking the surface imperfections of air holes into consideration. We employed a simulation model with a “defective layer” to estimate the modal loss dependence on the surface imperfections of air holes. We confirmed that the experimental result agrees well with the theoretical calculation. The theoretical studies suggest that the radius of an inscribed circle linking the air holes C has the greatest influence on the additional loss due to the surface imperfections of the air holes in the HA-FMF. We designed and fabricated the hole-assisted two-mode fibers (HA-TMF) according to our theoretical study. We obtained an HA-TMF with losses of 0.20 dB/km in the $\rm{LP}_{\rm{01}}$ mode and 0.26 dB/km in the $\rm{LP}_{\rm{11}}$ mode in the 1550 nm band. The additional loss induced by surface imperfections can be reduced by controlling the parameter C and this improves the bending properties of the $\rm{LP}_{\rm{11}}$ mode even without employing a polishing process for the air holes. Our results show the great potential of the HA-FMF for space-division multiplexing applications.

Experimental characterization of Raman overlaps between mode-groups.

Mode-division multiplexing has the potential to further increase data transmission capacity through optical fibers. In addition, distributed Raman amplification is a promising candidate for multi-mode signal amplification due to its desirable noise properties and the possibility of mode-equalized gain. In this paper, we present an experimental characterization of the intermodal Raman intensity overlaps of a few-mode fiber using backward-pumped Raman amplification. By varying the input pump power and the degree of higher order mode-excitation for the pump and the signal in a 10 km long two-mode fiber, we are able to characterize all intermodal Raman intensity overlaps. Using these results, we perform a Raman amplification measurement and demonstrate a mode-differential gain of only 0.25 dB per 10 dB overall gain. This is, to the best of our knowledge, the lowest mode differential gain achieved for amplification of mode division multiplexed signals in a single fiber.

All-Fiber Tunable LP11Mode Rotator With 360° Range

We propose and experimentally demonstrate an all-fiber tunable ${\rm{LP}}_{11}$ mode rotator with 360° range, based on the bending and twisting of the two-mode fiber (TMF). A theoretical model of TMF perturbation and its effect on the spatial pattern of ${\rm{LP}}_{11}$ mode is put forward. We experimentally characterize the implementation of the ${\rm{LP}}_{11}$ mode rotator by an all-fiber polarization controller configuration. The results agree well with the theoretical investigations. We are able to demonstrate arbitrary ${\rm{LP}}_{11}$ mode rotation with 360° range. The insertion loss is less than 0.4 dB when the operation wavelength is varied from 1540 to 1560 nm.

Relationship Between Mode Coupling and Fiber Characteristics in Few-Mode Fibers Analyzed Using Impulse Response Measurements Technique

When few-mode fibers are employed in mode-division multiplexing (MDM), mode coupling between the propagation modes must be suppressed. In this study, the impulse response for a two-mode fiber (TMF) is theoretically described to estimate the mode coupling in the fiber and at a splice point. We then propose a technique for measuring the mode-coupling coefficient in a TMF based on the impulse response technique. The mode-coupling behavior in a fiber and at splice points is measured experimentally using the proposed technique for several fabricated TMFs. We clarify the relationship between the effective-index difference $\Delta n_{{\rm{eff}}}$ between ${\text{LP}}_{{01}}$ and ${\text{LP}}_{{11}}$ modes and the mode-coupling coefficient h for our fabricated TMFs.

Coupling analysis of non-circular-symmetric modes and design of orientation-insensitive few-mode fiber couplers

We study the coupling between two identical weakly-coupled few-mode fibers based on coupled-mode theory. The coupling behavior of non-circular-symmetric modes, such as LP11 and LP21, is investigated analytically and numerically. By carefully choosing the fiber core separation and coupler length, we can design orientation-insensitive fiber couplers for non-circular-symmetric modes at arbitrary coupling ratios. Based on the design method, we propose an orientation-insensitive two-mode fiber coupler at 850nm working as a mode multiplexer/demultiplexer for two-mode transmission using standard single-mode fiber. Within the band from 845 to 855nm, the insertion losses of LP01 and LP11 modes are less than 0.03dB and 0.24dB, respectively. When the two-mode fiber coupler is used as mode demultiplexer, the LP01/LP11 and LP11/LP01 extinction ratios in the separated branches are respectively above 12.6dB and 21.2dB. Our design method can be extended to two-mode communication or sensing systems at other wavelengths.

High Sensitivity Twist Sensor Based on Helical Long-Period Grating Written in Two-Mode Fiber

We demonstrate the fabrication of the helical long-period grating (HLPG) in a two-mode fiber (TMF) with CO2 laser. The torsion characteristics of the helical gratings are experimentally investigated. It was found that the resonance wavelength of the TMF-HLPG linearly shifts with a twist sensitivity of 0.47 nm/(rad/m), which is an order magnitude higher than that of the conventional long-period fiber gratings (LPFGs). The temperature sensitivity of the TMF-HPFG was measured to be 23.9 pm/°C, which is one third of that of the conventional LPFGs. The proposed TMF-HLPG-based twist sensor would have a promising application for the twist monitor.

LP01–LP11Cross-Mode Interference in a Chirped Grating Inscribed in Two-Mode Fiber

We have demonstrated LP01-LP11 cross-mode interference in a single chirped grating (CG) inscribed in a two-mode fiber (TMF). With the aid of a binary phase plate, LP01 mode and LP11 mode can be selectively excited in the CG. By offsetting the position of the phase plate from the center of the input beam, we can simultaneously excite both the spatial modes at different LP01:LP11 intensity ratios in the TMF. The excited modes lead to the formation of different interference patterns in the output spectra. The measured output spectra are found to be in good agreement with the simulation based on a coupled mode theory.

Demonstration of Bidirectional PON Based on Mode Division Multiplexing

Recently, mode division multiplexing (MDM) has been introduced into optical transmission systems and networks for capacity enhancement. In this letter, we propose a bidirectional passive optical network (PON) architecture based on MDM. The bidirectional optical distribution network of the MDM-PON consists of few-mode fiber, passive mode multiplexer/demultiplexer, and few-mode circulators, all of which are characterized by low modal-crosstalk. Signals in different modes are able to be transmitted and received independently for both downstream and upstream transmission. We experimentally demonstrate the bidirectional MDM-PON transmission over 10-km two-mode optical fiber. The 10-Gb/s ON–OFF-keying signals can be independently transmitted and directly detected without coherent receiver and multiple-input multiple-output processing. Moreover, nonlinear transmission impairments are experimentally investigated.

Characterization of Rayleigh backscattering arising in various two-mode fibers.

We experimentally characterize the mode dependent characteristics of Rayleigh backscattering (RB) arising in various two-mode fibers (TMFs). With the help of an all-fiber photonic lantern, we are able to measure the RB power at individual modes. Consequently, mode dependent power distribution of RB light caused by arbitrary forward propagation mode superposition can be obtained. The total RB power of the TMFs under test is higher than that of single mode fiber by at least 2 dB over the C band. Meanwhile, the RB light occurs among all guided modes in the TMFs with specific power ratios. The experimental characterization agrees well with the theoretical calculations.

Rational solitary wave and rogue wave solutions in coupled defocusing Hirota equation

We derive and study a general rational solution of a coupled defocusing Hirota equation which can be used to describe evolution of light in a two-mode fiber with defocusing Kerr effect and some certain high-order effects. We find some new excitation patterns in the model, such as M-shaped soliton, W-shaped soliton, anti-eye-shaped rogue wave and four-petaled flower rogue wave. The results are compared with the solutions obtained in other coupled systems like vector nonlinear Schrödinger equation, coupled focusing Hirota and Sasa–Satsuma equations. We explain the new characters by modulational instability properties. This further indicates that rational solution does not necessarily correspond to rogue wave excitation dynamics and the quantitative relation between nonlinear excitations and modulational instability should exist.

Mode converter based on the long-period fiber gratings written in the two-mode fiber.

We demonstrate the fabrication of long-period fiber gratings (LPFGs) written in the two-mode fiber (TMF) by CO2 laser. Both uniform and tilted LPFGs were fabricated to provide the light coupling between LP01 mode and LP11 mode with a coupling efficiency of more than 99%. The writing efficiency and the bandwidth of the LPFG mode converter can be adjusted by changing the tilt angle of the tilted TMF-LPFGs. The torsion sensitivity of conventional and tilted LPFG mode converters were measured to be 0.37 nm/(rad/m) and 0.50 nm/(rad/m), respectively. Two orthogonal vector modes (the HEeven 21and HEodd 21 modes) and corresponding orbital angular momentum state were successfully obtained at the resonance wavelength. The proposed LPFG mode converter could be used as not only a high efficiency wavelength tunable mode converter in the mode division multiplexing system but also a high sensitive torsion sensor in the field of optical sensing.