Showing papers on "Radiation mode published in 2016"

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

Abstract: 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.

Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides.

Abstract: Fiber-chip edge couplers are extensively used in integrated optics for coupling of light between planar waveguide circuits and optical fibers. In this work, we report on a new fiber-chip edge coupler concept with large mode size for silicon photonic wire waveguides. The coupler allows direct coupling with conventional cleaved optical fibers with large mode size while circumventing the need for lensed fibers. The coupler is designed for 220 nm silicon-on-insulator (SOI) platform. It exhibits an overall coupling efficiency exceeding 90%, as independently confirmed by 3D Finite-Difference Time-Domain (FDTD) and fully vectorial 3D Eigenmode Expansion (EME) calculations. We present two specific coupler designs, namely for a high numerical aperture single mode optical fiber with 6 µm mode field diameter (MFD) and a standard SMF-28 fiber with 10.4 µm MFD. An important advantage of our coupler concept is the ability to expand the mode at the chip edge without leading to high substrate leakage losses through buried oxide (BOX), which in our design is set to 3 µm. This remarkable feature is achieved by implementing in the SiO2 upper cladding thin high-index Si3N4 layers. The Si3N4 layers increase the effective refractive index of the upper cladding near the facet. The index is controlled along the taper by subwavelength refractive index engineering to facilitate adiabatic mode transformation to the silicon wire waveguide while the Si-wire waveguide is inversely tapered along the coupler. The mode overlap optimization at the chip facet is carried out with a full vectorial mode solver. The mode transformation along the coupler is studied using 3D-FDTD simulations and with fully-vectorial 3D-EME calculations. The couplers are optimized for operating with transverse electric (TE) polarization and the operating wavelength is centered at 1.55 µm.

A New Type Circular Photonic Crystal Fiber for Orbital Angular Momentum Mode Transmission

Abstract: We proposed a new circular photonic crystal fiber (C-PCF), which can support 14 orbital angular momentum (OAM) modes transmission, with the good features of wide bandwidth, low confinement loss, and all OAM modes at the same size. At 1.55 μm, the designed C-PCF has a very low confinement loss of 3.434 × 10 -9 dB/m for HE41 mode and a relatively low nonlinear coefficient of 3.979 W -1 km -1 for EH 31 mode. The common bandwidth for the four orders of OAM modes is as large as 560 nm (about 1.25 μm-1.81 μm), which does cover all bands of optical fiber communication. Flat dispersion (a total dispersion variation of <;46.38 ps nm -1 km -1 over a 750-nm bandwidth from 1.25 μm to 2 μm for TE 01 mode) is another feature. With all these good features, the proposed C-PCF could be a well-promising OAM fiber for mode division multiplexing in high capacity fiber communication systems.

Exceptional points and asymmetric mode conversion in quasi-guided dual-mode optical waveguides.

Abstract: Non-Hermitian systems host unconventional physical effects that be used to design new optical devices. We study a non-Hermitian system consisting of 1D planar optical waveguides with suitable amount of simultaneous gain and loss. The parameter space contains an exceptional point, which can be accessed by varying the transverse gain and loss profile. When light propagates through the waveguide structure, the output mode is independent of the choice of input mode. This “asymmetric mode conversion” phenomenon can be explained by the swapping of mode identities in the vicinity of the exceptional point, together with the failure of adiabatic evolution in non-Hermitian systems.

Realization of a compact polarization splitter-rotator on silicon

Abstract: A novel compact polarization splitter-rotator (PSR) is proposed and realized with silicon-on-insulator nanowires. The present PSR consists of an adiabatic taper, an asymmetric directional coupler (ADC), and a multimode interference (MMI) mode filter. The adiabatic taper enables an efficient mode conversion from the launched TM0 mode to the TE1 mode in a wide waveguide, which is then coupled to the TE0 mode of a narrow waveguide through the ADC. Meanwhile, the launched TE0 mode does not have mode conversion and outputs from the through port directly. The MMI mode filter is cascaded at the through port to filter out the residual power of the TE1 mode so that the extinction ratio of the PSR is improved greatly. The total length of the PSR is ∼70 μm and the fabricated PSR has an extinction ratio of ∼20 dB over a broadband ranging from 1547 to 1597 nm.

Broadband mode division multiplexer using all-fiber mode selective couplers.

Abstract: We report an all-fiber mode division multiplexer formed with cascaded mode selective couplers with significantly broadened bandwidth potentially spanning S, C and L band. This was achieved by matching the effective refractive indices over a wide wavelength range for the few mode fiber and the single mode fiber used in the coupler. The multiplexer provides high coupling efficiency (>55% for the worst case) for the 4 spatial modes over the entire wavelength range of 1515-1590 nm. The all-fiber construction provides mechanical stability. Experimental results for the coupling efficiency and the mode extinction ratio for each spatial mode are presented along with the far field radiation patterns.

Mode Coupling Effects in Ring-Core Fibers for Space-Division Multiplexing Systems

Abstract: An optical fiber with weak mode coupling is desirable for future ultrahigh capacity space-division multiplexing (SDM) systems because mode coupling in an optical fiber results in extrinsic loss of the fiber and crosstalk between guided optical modes. To study the feasibility of a ring-core fiber (RCF) for SDM systems, in this paper, we investigate the mode coupling in the RCF supporting five or seven guided mode groups (MGs) at a wavelength of 1550 nm. For this purpose, the coupled mode/power theory with identified spatial power spectrum of random perturbations of fiber axis is used to estimate the bend loss/crosstalk of the RCF due to microbending. It is shown that based on the identified parameters for the spatial power spectrum in the 5/7-MG RCF, the estimated bend loss/crosstalk of the RCF agrees well with experimental results. In addition, the impact of the gradient parameter α and refractive index contrast Δ of the fiber refractive index profile on bend loss and crosstalk of the RCF is explored. Simulation results indicate that the Δ instead of the α significantly affects bend loss and crosstalk of the RCF. The magnitude improvement in bend loss by increasing the Δ is dependent on the spatial power spectrum.

Optical vortex generation with wavelength tunability based on an acoustically-induced fiber grating.

Abstract: We presented a method to actualize the optical vortex generation with wavelength tunability via an acoustically-induced fiber grating (AIFG) driven by a radio frequency source. The circular polarization fundamental mode could be converted to the first-order optical vortex through the AIFG, and its topological charges were verified by the spiral pattern of coaxial interference between the first-order optical vortex and a Gaussian-reference beam. A spectral tuning range from 1540 nm to 1560 nm was demonstrated with a wavelength tunability slope of 4.65 nm/kHz. The mode conversion efficiency was 95% within the whole tuning spectral range.

Design and fabrication of elliptical-core few-mode fiber for MIMO-less data transmission

Abstract: We propose a design strategy of elliptical core few-mode fiber (e-FMF) that supports three spatial modes with enhanced mode spacing between LP11a and LP11b, to suppress intra-mode coupling during mode-division multiplexing (MDM) transmission. Our theoretical investigations show that there exist two optimization regimes for the e-FMF, as a comparison with traditional circular core FMF(c-FMF). At the regime of three-mode operation, there occurs a trade-off between mode spacing and bending-induced loss. Meanwhile, in terms of five-mode regime, a trade-off between mode spacing and high-order mode crosstalk happens. Finally, we fabricate 7.94 km e-FMF with the optimal parameters, based on the commercial fiber manufacture facility. The primary characterizations at 1550 nm show that three spatial modes of e-FMF can be transmitted with a loss less than 0.3 dB/km. Meanwhile, −22.44 dB crosstalk between LP11a and LP11b is observed, even when the 2 km e-FMF is under stress-induced strong perturbation.

Environmentally isolated waveguide display

Abstract: A waveguide display is provided comprising: an input image generator providing image light projected over a field of view; a waveguide having first and second external surfaces; and at least one grating optically coupled to the waveguide for extracting light towards a viewer. The waveguide has a lateral refractive index variation between said external surfaces that prevents any ray propagated within the waveguide from optically interacting with at least one of the external surfaces.

Supermodes in Coupled Multi-Core Waveguide Structures

Abstract: Optical supermode dynamics are nowadays receiving an ever increasing attention in mode-division multiplexing applications. In this paper, we systematically analyze and characterize these modes in various structures based on coupled-mode theory. In particular, we investigate the structure of supermodes in honeycomb multi-ring arrangements of any size. In addition, we show that higher order supermodes in coupled few-mode multi-core waveguide arrays can be strongly affected by angle-dependent couplings, leading to different modal field profiles. Analytical solutions are provided for linear, rectangular, and ring arrays. Higher order supermodes are observed for the first time in a coupled few-mode three-core fiber system using the S2 imaging method.

Optimizing high-power Yb-doped fiber amplifier systems in the presence of transverse mode instabilities.

Abstract: The average output power of Yb-doped fiber amplifier systems is currently limited by the onset of transverse mode instabilities. Besides, it has been recently shown that the transverse mode instability threshold can be significantly reduced by the presence of photodarkening in the fiber. Therefore, reducing the photodarkening level of the core material composition is the most straightforward way to increase the output average power of fiber amplifier systems but, unfortunately, this is not always easy or possible. In this paper we present guidelines to optimize the output average power of fiber amplifiers affected by transverse mode instabilities and photodarkening. The guidelines derived from the simulations do not involve changes in the composition of the active material (except for its doping concentration), but can still lead to a significant increase of the transverse mode instability threshold. The dependence of this parameter on the active ion concentration and the core conformation, among others, will be studied and discussed.

Tunable Fiber Polarization Filter by Filling Different Index Liquids and Gold Wire Into Photonic Crystal Fiber

Abstract: A tunable fiber polarization filter by filling different index liquids into the central hole of photonic crystal fiber (PCF) is proposed and demonstrated. The dispersion characteristics and loss spectra of the polarization filter are evaluated by finite element method (FEM). The gold wires are selectively filled into the cladding air holes of the PCF. When the phase matching condition is satisfied, the liquid-core mode couples to surface plasmon polaritons (SPP) mode intensely. The resonance wavelength varies with the change of the structural parameters and liquids. By adjusting the refractive index of the liquid, we realize the polarization filter at the wavelength of 1.31, 1.49, and 1.55 $\mu$ m, respectively, under the optimized structural parameters. This is the first time to propose the narrowband polarization filter at the communication wavelength of 1.31 $\mu$ m to our best knowledge based on the coupling between liquid-core mode and SPP mode, and the full width half maximum (FWHM) is only 16 nm. The loss of X-polarized mode is 44336 dB/m at $\lambda$ = 1.31 $\mu$ m, and the corresponding loss of Y-polarization mode is 224 dB/m. By comparison, we find the birefringence in our structure is further better than that in conventional structure. High birefringence is helpful to separate the resonance wavelength positions of the two orthogonal polarized modes. The result also reveals that resonance loss becomes small with increasing the distance between liquid core and gold wire.

Fiber Twisting- and Bending-Induced Adiabatic/Nonadiabatic Super-Mode Transition in Coupled Multicore Fiber

Abstract: The characteristics of power transfer between super-modes in coupled multicore fiber are investigated numerically and experimentally. We reveal that fiber twisting and macrobending cause mode coupling through an adiabatic/nonadiabatic process, which is different from the mode coupling caused by structural perturbation, namely microbending. We also investigate the impulse response characteristics of coupled two-core fibers, and find that there is an optimum core pitch for minimizing the complexity of the MIMO processing. Finally, we conduct a 4 × 4 MIMO transmission experiment using two-core fibers to evaluate their transmission characteristics. We show that strongly coupled multicore fiber can reduce the quality difference between the received signals even when the transmission line has large core-dependent gain/loss values.

High-birefringence photonic crystal fiber polarization filter based on surface plasmon resonance

Abstract: In this paper, we designed a C2v-symmetry-structured photonic crystal fiber with triangular lattice and Au-filled air holes. The finite element method is used to analyze the dispersion and confinement loss characteristics of the core mode and the surface plasmon mode of the metal wire. In this work, we found that the positions of resonance peaks and the resonance strength of core mode and surface plasmon mode can be well adjusted by changing the pitch between the cladding air holes and the diameters of the air holes or metal wires around the core. By optimizing the parameters of the fiber structure, a polarization filter at the communication band is designed. At the wavelength of 1.31 μm, which is located in the communication band, the fundamental mode in X pol can be filtered with the diameter of the metal wire d(m)=1.2 μm. When d(m)=1.4 μm, the fundamental mode in Y pol can be filtered at the wavelength of 1.55 μm, which is also located in the communication band. Compared with the ordinary single-polarization and single-mode photonic crystal fiber, the fiber we proposed in this paper can selectively filter out the polarized light in one direction by adjusting the wire diameter. It is meaningful for the development of the polarization filter in the communication band.

Deep-subwavelength plasmonic mode converter with large size reduction for Si-wire waveguide

Abstract: If we are to utilize deep-subwavelength plasmonic waveguides in photonic integrated circuit applications, highly efficient three-dimensional (3D) mode conversion must be achieved between deep-subwavelength plasmonic waveguides and conventional dielectric waveguides such as Si-wire waveguides. Here, we describe 3D mode conversion from a Si-wire waveguide (the core size is 400 nm×200 nm) to a plasmonic slot waveguide (the air core size is 50 nm×20 nm) with a coupling loss of 1.7 dB. Our mode converter has only a two-dimensional laterally tapered structure even with the presence of a large discontinuity in the thickness, and can still produce efficient full 3D mode conversion with a very short taper length (600 nm). Calculation results obtained with the finite element method agreed well with the experimental results. We believe our mode converter will provide a new deep-subwavelength photonic platform.

Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide

Abstract: A graphene-based cylindrical hybrid surface plasmon polariton waveguide, composed of a silicon nanowire core surrounded by a silica layer and then a graphene layer, is investigated using the finite-difference time-domain method. The analytical solutions and the numerical simulation show that an ultra-small mode area and a large propagation length can be achieved with this waveguide. Utilizing the perturbation theory of coupled mode, we demonstrate that the six lowest-order coupling modes originate from the coupling of the three lowest-order single-waveguide modes, and the m = 1 order yy-coupling mode possesses the maximum coupling length and the minimum crosstalk. This waveguide can be used for photonic integrated circuits in the mid-infrared range.

Mode crosstalk matrix measurement of a 1 km elliptical core few-mode optical fiber

Abstract: The spatial modes of a 1 km elliptical core few-mode optical fiber (6 spatial modes) are analyzed by using liquid crystal on silicon spatial light modulators to measure the fiber's mode crosstalk matrix in Hermite-Gaussian, Laguerre-Gaussian, and linearly polarized spatial mode bases. It is shown that the fiber's spatial modes can be described by Hermite-Gaussian modes, which can propagate 1 km over the optical fiber with <-20 dB (1%) average mode crosstalk even when the fiber has multiple 1 cm diameter bends. The use of elliptical core few-mode optical fibers for space division multiplexing in data centers is discussed.

Bend Resistant Large Mode Area Fiber With Multi-Trench in the Core

Abstract: A bend resistant large mode area fiber with multitrench in the core is proposed. Four layers of trenches with high refractive index are introduced to modulate the mode field distribution. Low refractive index trenches in traditional designs are replaced with pure silica trenches to reduce the difficulty of manufacture. Meanwhile, the core region with a refractive index higher than pure silica cladding conforms to the practical requirement for active fibers. Numerical investigations show that single mode operation with a mode field area of 1100 μm2 is achieved at a bend radius of 15 cm. This design shows the potential of mode field scaling for multitrench fibers and makes a contribution to compact high power fiber lasers.

Highly efficient silicon optical polarization rotators based on mode order conversions.

Abstract: We design and demonstrate the novel silicon optical polarization rotators (PRs) based on the TM(0)-TE(n)-TE(0) mode conversions inside the waveguide. The TM(0)-TE(n) mode converters are realized by the mode hybridization of the tapered rib waveguides. The TE(n)-TE(0) mode converters based on the beam shaping method are followed to complete the PRs function. By using the TE(1), TE(2), and TE(3) mode as the transitional mode, the fabricated PRs show the insert losses of less than 0.4, 0.5, and 1 dB, respectively. The corresponding polarization extinction ratios of larger than 21, 18, and 23 dB, over a wavelength range of 100 nm.

Theory and modeling of photodarkening-induced quasi static degradation in fiber amplifiers

Abstract: A theory of photodarkening-induced quasi-static degradation in fiber amplifiers is presented. As the doped core of a fiber photodarkens and continues to absorb more power converting it to heat, the intensity grating created by higher order mode interference with the fundamental mode moves toward the input end. This creates a persistent absorption grating that remains phase-shifted from the modal interference pattern. This leads to power transfer from the fundamental mode to a higher order mode with a very small frequency offset that occurs on a time scale of minutes to hours. This process is modeled in large mode area step index and photonic crystal fibers and is found to produce reasonable threshold values.

Low Loss Fiber-to-Waveguide Converter With a 3-D Functional Taper for Silicon Photonics

Abstract: We demonstrate a low-loss and broad-bandwidth fiber-to-waveguide converter with a 3-D functional SiO2 taper for silicon photonics. The converter is composed of a cantilevered SiO2 waveguide and Si nano-tapers. In order to reduce the loss from the cleaved fiber, a 3-D functional SiO2 taper is designed to compress the size of optical mode field. Using cleaved optical fibers with a mode field diameter of 10.5 $\mu \text{m}$ at 1550 nm, we characterized the optical performances of the converter. With an index-matching liquid, the lowest coupling loss of TE mode is 1.5 dB/facet and the lowest coupling loss of TM mode is 2.1 dB/facet. For both TE and TM modes, the 1-dB bandwidth is more than 100 nm, and the alignment tolerances for 1-dB excess loss are, respectively, ±2.5 and $\pm 2~\mu \text{m}$ in horizontal and vertical directions.

Theoretical study of mode evolution in active long tapered multimode fiber.

Abstract: A concise and effective model based on coupled mode theory to describe mode evolution in long tapered active fiber is presented in this manuscript. The mode coupling due to variation of core radius and slight perturbation have been analyzed and local gain with transverse spatial hole burning (TSHB) effect, loss and curvature have been taken into consideration in our model. On the base of this model, the mode evolution behaviors under different factors have been numerically investigated. Our model and results can provide instructive suggestions when designing long tapered fiber based laser and amplifiers.

Robust polarization-insensitive strip-slot waveguide mode converter based on symmetric multimode interference

Abstract: Strip-slot waveguide mode converters for TE0 have been widely investigated. Here we demonstrate a polarization-insensitive converter numerically and experimentally. The polarization-insensitive performance is achieved by matching the optical field distribution of the 2-fold image of the Multimode Interference (MMI) and the TE0 (TM0) mode of a slot waveguide. The working principle for this MMI-based mode converter is thoroughly analyzed with the quantitatively evaluated optical field overlap ratio that is theoretically derived from the orthonormal relation of eigenmodes. Based on the analysis, the MMI-based polarization-insensitive converters are then simulated and fabricated. The simulation and measurement results indicate that the proposed scheme is a robust design since it is not only polarization-insensitive but also wavelength-insensitive and fabrication-tolerant. Moreover, the mode converter is as small as 1.22 μm × 4 μm while the measured conversion efficiencies are 95.9% for TE0 and 96.6% for TM0. All these excellent properties make the proposed mode converter an ideal solution for coupling light between strip and slot waveguides when both TE and TM polarizations are considered.

Mode coupling in hybrid square-rectangular lasers for single mode operation

Abstract: Mode coupling between a square microcavity and a Fabry-Perot (FP) cavity is proposed and demonstrated for realizing single mode lasers. The modulations of the mode Q factor as simulation results are observed and single mode operation is obtained with a side mode suppression ratio of 46 dB and a single mode fiber coupling loss of 3.2 dB for an AlGaInAs/InP hybrid laser as a 300-μm-length and 1.5-μm-wide FP cavity connected to a vertex of a 10-μm-side square microcavity. Furthermore, tunable single mode operation is demonstrated with a continuous wavelength tuning range over 10 nm. The simple hybrid structure may shed light on practical applications of whispering-gallery mode microcavities in large-scale photonic integrated circuits and optical communication and interconnection.

Graphene-induced unique polarization tuning properties of excessively tilted fiber grating

Abstract: By exploiting the polarization-sensitive coupling effect of graphene with the optical mode, we investigate the polarization modulation properties of a hybrid waveguide of graphene-integrated excessively tilted fiber grating (Ex-TFG). The theoretical analysis and experimental results demonstrate that the real and imaginary parts of complex refractive index of fewlayer graphene exhibit different effects on transverse electric (TE) and transverse magnetic (TM) cladding modes of the Ex-TFG, enabling stronger absorption in the TE mode and more wavelength shift in the TM mode. Furthermore, the surrounding refractive index can modulate the complex optical constant of graphene and then the polarization properties of the hybrid waveguide, such as resonant wavelength and peak intensity. Therefore, the unique polarization tuning property induced by the integration of the graphene layer with Ex-TFG may endow potential applications in all-in-one fiber modulators, fiber lasers, and biochemical sensors.

Large-mode-area single-polarization single-mode photonic crystal fiber: design and analysis.

Abstract: A rectangular core photonic crystal fiber structure has been presented and analyzed for single-polarization single-mode operation. Single-polarization is obtained with asymmetric design and by introducing different loss for x-polarization and y-polarization of fundamental modes. Single-polarization single-mode operation of the proposed photonic crystal fiber is investigated in detail by using a full vector finite element method with an anisotropic perfectly matched layer. The variations of the confinement loss and effective mode area of x-polarization and y-polarization of fundamental modes have been simulated by varying the structural parameters of the proposed photonic crystal fiber. At the optimized parameters, confinement loss and effective mode area is obtained as 0.94 dB/m and 60.67 μm2 for y-polarization as well as 26.67 dB/m and 67.23 μm2 for x-polarization of fundamental modes, respectively, at 1.55 μm. Therefore simulation results confirmed that, 0.75 m length of fiber will be sufficient to get a y-polarized fundamental mode with an effective mode area as large as 60.67 μm2.

Optical coupling scheme

Abstract: The present invention provides a waveguide structure 100 for optical coupling. The waveguide structure 100 includes a first waveguide 101 embedded in a cladding 102 of a lower refractive index than the first waveguide 101, a second waveguide 103 of a higher refractive index than the cladding 102, and an intermediate waveguide 104. The first 5 waveguide 101 and the second waveguide 103 are physically arranged at the same side 104u of the intermediate waveguide 104 to establish an optical coupling between the first waveguide 101 and the second waveguide 103 through the intermediate waveguide 104. The first waveguide material has a refractive index value smaller than or equal to 3.

Dynamic Fano Resonance in Thin Fiber Taper Coupled Cylindrical Microcavity

Abstract: Fano resonance results from interference between a background and a resonant scattering, which produces the asymmetrical lineshape. A cylindrical microcavity naturally possesses localized whispering gallery mode (WGM) and delocalized radiation mode, and a thin fiber taper can excite these two modes simultaneously. The localized WGM can interfere with the weak delocalized background to generate Fano resonance in the thin fiber taper coupled cylindrical microcavity. In addition, the Fano parameter can be adjusted by changing the gap between fiber taper and microcylinder cavity or the coupling diameter of fiber taper. The experimental results agree well with the quantum scattering theory.

Influence of a backward reflection on low-threshold mode instability in Yb 3+ -doped few-mode fiber amplifiers

Abstract: An influence of backward reflection on spatio-temporal instability of the fundamental mode in Yb3+-doped few-mode polarization maintaining fiber amplifiers with a core diameter of 10 μm was studied experimentally and theoretically. The mode instability threshold was registered to decrease dramatically in the presence of a backward reflection of the signal from the output fiber end; an increase of the signal bandwidth or input power resulted in the increase of the threshold. Numerical simulation revealed a self-consistent growth of the higher-order mode LP11 and a traveling index grating accompanying the population grating induced by the mode interference field (due to different polarizability of the excited and unexcited Yb3+ ions). The presence of the backward-propagating wave resulted in four-wave mixing on the common index grating induced by the interference field of pairs of the fundamental LP01 and LP11 modes.