Mode Coupling Coefficients Research Articles

5 kW single-mode oscillating-amplifying integrated fiber laser through tightly bent confined ytterbium-doped fiber

We demonstrated a 5 kW single-mode oscillating-amplifying integrated fiber laser by tightly bending a homemade 25/400 µm confined YDF. Simulation results showed that tightly bending the confined YDF could decrease the mode coupling coefficient and increase the TMI threshold. By optimizing the doping ratio and bending radius of the confined YDF, a TMI-free 5.1 kW laser output was achieved based on the confined YDF and non-wavelength stable 976 nm LD. The beam quality factor M2 was 1.2 and maintained in the 5.5 hours full power operation. In comparison, the 976 nm pumped oscillating-amplifying integrated fiber laser with the conventional 25/400 YDF was limited by the quantum defect induced TMI at 3.1 kW, while the 915 nm pumped oscillating-amplifying integrated fiber laser with the conventional 25/400 YDF experienced the photodarkening induced TMI at 3.8 kW. To our knowledge, this is the highest output power of the single-mode confined doped all-fiber laser. This work also proves that tightly bending the confined YDF is an effective method to suppress the TMI induced by the quantum defect and the photodarkening.

Inter-Mode Crosstalk Estimation between Cores for LPmn Modes in Weakly Coupled Few-Mode Multicore Fiber with Perturbations.

A novel inter-mode crosstalk (IMXT) model of LPmn mode for weakly coupled few-mode multicore fiber is proposed based on the coupled mode theory (CMT) with bending and twisting perturbations. A universal expression of the mode coupling coefficient (MCC) between LPmn modes is derived. By employing this MCC, the universal semi-analytical model (USAM) of inter-core crosstalk (ICXT) can be applied to calculate the IMXT. Simulation results show that our model is generally consistent with previous theories when stochastic perturbations are absent. Moreover, our model can work effectively when stochastic perturbations are present, where former theories are not able to work properly. It has been theoretically found that the MCC has an intimate relationship with core pitch. Our model, based on the CMT, can provide physical characteristics in detail, which has not been reported clearly by former theories. In addition, our model is applicable to phase-matching and non-phase-matching regions of both real homogeneous and heterogeneous few-mode multicore fibers (FM-MCFs) with a wider range of applications.

Simultaneous generation of first- to fourth-order OAM modes based on a cascaded preset-twist long-period fiber grating.

We propose and demonstrate the simulation and fabrication of an all-fiber orbital angular momentum (OAM) mode converter capable of generating first- to fourth-order modes simultaneously, which is realized by inscribing a cascaded preset-twist long-period fiber grating (CPT-LPFG) in a six-mode fiber utilizing a CO2 laser. A new segmented Runge-Kutta method is proposed to simulate the preset-twist long-period fiber gratings. By calculating the twist angle and relative coupling coefficient for each pitch and then solving the coupled mode equations utilizing the Runge-Kutta algorithm. The simulation illustrates that the preset-twist method significantly improves the coupling coefficient of higher-order modes, thereby reducing coupling difficulty. In the experiment, by twisting the fiber at an angle of 1080° and fabricating cascaded gratings with periods of 745 μm, 310 μm, 204 μm, and 146 μm, it is feasible to generate first- to fourth-order OAM modes simultaneously, at wavelengths of 1635 nm, 1548 nm, 1460 nm, and 1334 nm, respectively. The insertion loss is less than 1 dB, and the mode purity is over 90 %. To the best of our knowledge, this is the first time that first- to fourth-order OAM modes are simultaneously generated utilizing a single long-period fiber grating.

Design of low crosstalk homogeneous multicore few mode fiber for future high-capacity optical transmission

Many researches are diligently striving to develop a multi-core optical fiber with minimal signal distortion and reduced issues. The current study proposed few designs for homogeneous multicore few mode fiber which is characterized by the combination of high index ring and trench. This study also added four air holes surrounding each core. We considered pure silica for both the outer clad and the inner clad of the fiber. To calculate the crosstalk, a two-core model was used and the mode coupling coefficient was determined using coupled-mode and couple-power theory. For the current work we considered only the fundamental mode (LP01) to compute the crosstalk between neighboring cores. The proposed structure was simulated using the wave optics module of COMSOL Multiphysics (Version 6.1), a well-known commercial software tool based on finite element method (FEM). MATLAB (Version R2018a) was used to calculate the mode coupling coefficient and crosstalk after extracting the mode field data from COMSOL. Obtained results revealed that the proposed structure can offer lower crosstalk which was attractive for future high-capacity fiber optic communication using multicore fiber technology.

Transverse mode distribution in multimode diode-pumped Raman fiber laser

Raman lasers based on multimode graded-index fibers may generate high-quality (M2∼2) Stokes beams when pumped by highly multimode (M2>30) laser diodes. Here we, examine, both experimentally and theoretically, the energy distribution of the output Stokes beam across the principal quantum mode number n in a bent multimode fiber operating well above the Raman threshold. In contrast to Kerr spatial beam cleaning, leading to a Rayleigh–Jeans mode power distribution, in a multimode Raman fiber laser, we find that the output mode powers approach an exponential distribution. We introduce a coupled-mode equations model, including random linear coupling between neighboring mode groups, and obtain a good agreement between numerical simulations and experimental results. The model shows that, for typical mode coupling coefficients, the randomization of the mode power distribution is compensated by both nonlinear (Raman and Kerr) effects and linear filtering from the fs-inscribed fiber Bragg grating, both acting on the Stokes beam over successive round trips. When random coupling becomes the dominating factor, the mode power distribution of the Stokes beam tends to equipartition, similar to what is observed with large-size highly multimode beams of low intensity (and nonlinearity) in the absence of any filtering.

A direct method for measuring modal coupling and attenuation coefficients of few-mode fibers

A direct method for measuring modal coupling and attenuation coefficients of few-mode fibers

Simultaneous Efficient Excitation of Multiple Higher-Order OAM Modes Using a Single Long-Period Fiber Grating

In this paper, a method for the simultaneous generation of multiple higher-order orbital angular momentum (OAM) modes in a few-mode fiber (FMF) using a single long-period fiber grating (LPFG) is proposed and demonstrated. The high diffraction order of the grating is used to achieve the resonant coupling of multiple modes, and the coupling coefficients of different order modes are balanced by a preset-twist method. This solves the two coupling problems of over-coupling for lower-order modes and difficult excitation of higher-order modes faced by multi-order mode generation, and overcomes the challenge of balanced excitation of multiple modes with high coupling efficiency. In the experiment, the simultaneous generation and flexible combination of first-order, second-order and third-order OAM modes are successfully achieved in a six-mode fiber, in which the mode order, resonant wavelength and wavelength interval can be flexibly controlled. By fabricating with grating periods of 2300 μm, 782 μm and 990 μm, respectively, high conversion efficiency of first-order and second-order modes, first-order and third-order modes, second-order and third-order modes can be generated simultaneously. In addition, for the first time, the first-order, second-order and third-order modes are generated simultaneously at a grating period of 1630 μm with conversion efficiencies of 98.61%, 99.11% and 98.89%, respectively. The mode profiles and interference patterns of different order modes show that multiple higher-order OAM modes with insertion loss less than 1 dB and mode purity over 95% are successfully generated.

Mode coupling coefficients between the convective core and radiative envelope of γ Doradus and slowly pulsating B stars

Context. Signatures of coupling between an inertial mode in the convective core and a gravito-inertial mode in the envelope have been found in four-year Kepler light curves of 16 rapidly rotating γ Doradus (γ Dor) stars. This makes it possible to obtain a measurement of the rotation frequency in their convective core. Despite their similar internal structure and available data, inertial modes have not yet been reported for slowly pulsating B (SPB) stars. Aims. We aim to provide a numerical counterpart of the recently published theoretical expressions for the mode-coupling coefficients, ε and ε̃. These coefficients represent the two cases of a continuous and a discontinuous Brunt-Väisälä frequency profile at the core-envelope interface, respectively. We consider γ Dor and SPB stars to shed light on the difference between these two classes of intermediate-mass gravito-inertial mode pulsators in terms of core and envelope mode coupling. Methods. We used asteroseismic forward models of two samples consisting of 26 SPB stars and 37 γ Dor stars to infer their numerical values of ε and ε̃. For both samples, we also computed: the linear correlation coefficients between ε or ε̃ and the near-core rotation frequency, the chemical gradient, the evolutionary stage, the convective core masses and radii, and the Schönberg-Chandrasekhar limiting mass representing the maximum mass of an inert helium core at central hydrogen exhaustion that can still withstand the pressure of the overlaying envelope. Results. The asteroseismically inferred values of ε and ε̃ for the two samples are between 0.0 and 0.34. While ε is most strongly correlated with the near-core rotation frequency for γ Dor stars, the fractional radius of the convective core instead provides the tightest correlation for SPB stars. We find ε to decrease mildly as the stars evolve. For the SPB stars, ε and ε̃ have similar moderate correlations with respect to the core properties. For the γ Dor stars, ε̃ reveals systematically lower and often no correlation to the core properties; their ε is mainly determined by the near-core rotation frequency. The Schönberg-Chandrasekar limit is already surpassed by the more massive SPB stars, while none of the γ Dor stars have reached it yet. Conclusions. Our asteroseismic results for the mode coupling support the theoretical interpretation and reveal that young, fast-rotating γ Dor stars are most suitable for undergoing couplings between inertial modes in the rotating convective core and gravito-inertial modes in the radiative envelope. The phenomenon has been found in 2.4% of such pulsators with detected period spacing patterns, whereas it has not been seen in any of the SPB stars so far.

Design and Analysis of Lithium–Niobate-Based Laterally Excited Bulk Acoustic Wave Resonator with Pentagon Spiral Electrodes

In this paper, we present a comprehensive study on the propagation and dispersion characteristics of A1 mode propagating in Z-cut LiNbO3 membrane. The A1 mode resonators with pentagon spiral electrodes utilizing Z-cut lithium niobate (LiNbO3) thin film are designed and fabricated. The proposed structure excites the A1 mode waves in both x- and y-direction by utilizing both the piezoelectric constants e24 and e15 due to applying voltage along both the x- and y-direction by arranging pentagon spiral electrode. The fabricated resonator operates at 5.43 GHz with no spurious mode and effective electromechanical coupling coefficient (Keff2) of 21.3%, when the width of electrode is 1 µm and the pitch is 5 µm. Moreover, we present a comprehensive study of the effect of different structure parameters on resonance frequency and Keff2 of XBAR. The Keff2 keeps a constant with varied thickness of LiNbO3 thin film and different electrode rotation angles, while it declines with the increase of p from 5 to 20 µm. The proposed XBAR with pentagon spiral electrodes realize high frequency response with no spurious mode and tunable Keff2, which shows promising prospects to satisfy the needs of various 5 G high-band application.

Dual-Passband SAW Filter Based on a 32°YX-LN/SiO2/SiC Multilayered Substrate.

To meet the demands of highly integrated and miniaturized radio frequency front-end (RFFE) modules, multi-passband filters which support multi-channel compounding come to the foreground. In this work, we proposed a new design of a dual-passband surface acoustic wave (SAW) filter based on a 32°YX-LiNbO3 (LN)/SiO2/SiC multilayered structure. The filter is of a standalone ladder topology and comprises dual-mode resonators, in which the shear horizontal (SH) mode and high-order SH mode are simultaneously excited through electrode thickness modulation. The impact of electrode thickness on the performance of the dual-mode resonator was systematically investigated by the finite element method (FEM), and resonators were prepared and verified the simulation results. The electromechanical coupling coefficients (K2) of the SH modes are 15.1% and 17.0%, while the maximum Bode-Q (Qmax) values are 150 and 247, respectively, for the fabricated resonators with wavelengths of 1 μm and 1.1 μm. In terms of the high-order SH modes in these resonators, the K2 values are 9.8% and 8.4%, and Qmax values are 190 and 262, respectively. The fabricated dual-band filter shows the center frequencies (fc) of 3065 MHz and 4808 MHz as two bands, with 3-dB fractional bandwidths (FBW) of 5.1% and 5.9%, respectively. Such a dual-band SAW filter based on a conventional ladder topology is meaningful in terms of its compact layout and diminished area occupancy. This work provides a promising avenue to constitute a high-performance dual-passband SAW filter for sub-6 GHz RF application.

Theoretical analysis of mode evolution in a tapered double clad fiber based on the coupled local mode theory

Mode characteristics of a tapered double clad fiber should be analyzed based on three-layer waveguide model, so it is more complicated than that of a single clad fiber. In this paper, a method based on coupled local mode theory is introduced to calculate the mode evolution process in a tapered double clad fiber. Mode field characteristics of double clad fiber are calculated analytically with weak guidance approximation, and the expression of mode coupling coefficient is derived. Based on this, the local mode characteristics and mode coupling characteristics in a tapered double clad fiber are analyzed. The mode evolution characteristics of tapered double clad fibers with different parameters are simulated. As an example, the structure optimization process of a tapered double clad fiber is introduced. High efficiency coupling with a six-mode single clad fiber is realized, and the theoretical transmission loss is less than 0.3 dB.

Design of Low-SAR and High On-Body Efficiency Tri-Band Smartwatch Antenna Utilizing the Theory of Characteristic Modes of Composite PEC-Lossy Dielectric Structures

A low specific absorption rate (SAR) and high on-body efficiency tri-band smartwatch antenna is designed utilizing the theory of characteristic modes (TCM) of composite perfect electric conductors and lossy dielectric structures. The antenna works in the GPS frequency band, WLAN 2.4 GHz/Bluetooth frequency band, and 5G frequency band. After analyzing the characteristic modes of the antenna and human body in the above three frequency bands, the characteristic modes with small modal coupling coefficients (MCCs) are selected and excited. Due to the small mutual coupling between the antenna and the human body, the proposed antenna has good performance on both SAR and on-body efficiency. Its measured 10 g average body SAR is lower than 1.3 W/kg. When it is placed 0 mm above the body, its on-body efficiency is 9.3%–9.88% in the GPS frequency band, 12%–14.2% in the WLAN 2.4 GHz/Bluetooth frequency band, and 17.3%–20.1% in the 5G frequency band.

Improvement of piezoelectric properties of relaxor type 0.695Pb(Mg1/3Nb2/3)O3−0.305 PbTiO3 single crystal plate and silver vibrator by alternating current poling

Alternating current poling (ACP) and direct current poling (DCP) on [001]-oriented 0.695Pb(Mg1/3Nb2/3)O3−0.305PbTiO3 (PMN-0.305PT) single crystal (SC) plates with a dimension of 12 × 4 × 0.3 mm and silver vibrators of 12 × 0.15 × 0.3 mm were investigated. The highest dielectric constant of 14500 and piezoelectric constant of 4200 pCN−1 were confirmed with the ACP SC plate manufactured by the conventional one charge Bridgman process. After array dicing into silver, the silver mode coupling coefficient k’ 33 = 94.3% was obtained from ACP SC. However, many spurious mode vibrations (SMV) were seen in the impedance spectra of the DCP and ACP SC silver vibrators. We consider that this SMV may be caused by array dicing damage. The PMN-0.305PT SC plate near the morphotropic phase boundary shows excellent piezoelectric and dielectric properties, however, these silvers tend to show SMV after dicing. This information is useful to select the PMN-PT composition for medical probe application.

SAW Resonators and Filters Based on Sc0.43Al0.57N on Single Crystal and Polycrystalline Diamond.

The massive data transfer rates of nowadays mobile communication technologies demand devices not only with outstanding electric performances but with example stability in a wide range of conditions. Surface acoustic wave (SAW) devices provide a high Q-factor and properties inherent to the employed materials: thermal and chemical stability or low propagation losses. SAW resonators and filters based on synthetized by reactive magnetron sputtering on single crystal and polycrystalline diamond substrates were fabricated and evaluated. Our SAW resonators showed high electromechanical coupling coefficients for Rayleigh and Sezawa modes, propagating at 1.2 GHz and 2.3 GHz, respectively. Finally, SAW filters were fabricated on /diamond heterostructures, with working frequencies above 4.7 GHz and ~200 MHz bandwidths, confirming that these devices are promising candidates in developing 5G technology.

A Novel Grating Coupling Coefficient Extraction Method for DFB Laser Diodes Based on Side Mode Spacing

A novel method to extract the grating coupling coefficient of distributed feedback (DFB) lasers by comparing the theoretical and experimental values of the side mode spacing is demonstrated. Compared with the traditional method, the proposed method in this paper transforms the solution process of the lasing model with multiple unknown parameters into that with only the side mode spacing and coupling coefficient, which significantly reduces the computational workload. Furthermore, the bias current of the measured spectrum can be much higher than the threshold current, which makes the method less affected by noise. This paper theoretically analyzes the changing relationship between multiple parameters by calculating the lasing mode distribution, and the results show that the side mode spacing is only sensitive to the coupling coefficient. In addition, the grating coupling coefficients (57–61 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> ) of the fabricated DFB laser diodes are experimentally extracted at 40-80 mA currents. The variation of the coupling coefficient with current is less than 2‰/mA, and the method exhibits pretty good stability. Meanwhile, the grating coupling coefficient extraction method for the complex grating types is also considered in this paper.

Brillouin optical time domain reflectometry for estimating loss and crosstalk at the splice point in few-mode fibers

We propose a technique using Brillouin optical time domain reflectometry for estimating the loss and crosstalk at a splice point in few-mode fibers. The technique measures the splice loss of a fundamental mode using a feature where the Brillouin gain spectrum differs depending on the mode. Then, the splice loss of the higher-order mode and the modal crosstalk at the splice point are estimated from the measured loss of the fundamental mode. We reveal the feasibility of our technique in a comparison of the experimental results with the numerically calculated ones. The fiber under test we used was two mode fibers with a graded-index profile. We found that the splice loss of the LP01 mode can be yielded by measuring the splice loss under the condition that the scattered light of the LP01 mode becomes larger than that of other modes. Moreover, we determined that the loss and crosstalk of the LP11 mode could be yielded using the measured loss of the LP01 mode and the approximate expression of the mode coupling coefficient at the splice point.

Basis expansion model for tracking and equalizing rapidly varying multimode fiber channels

In multi-mode fibers, environmental perturbations induce changes in the channel transfer matrix at rates proportional to the total length of affected segments and the number of modes; potentially reaching levels where adaptive equalizers fail in tracking the channel state. We propose a technique that tracks the channel on a frame-by-frame basis by modeling variations in mode coupling coefficients over the period of a full frame of symbols as a linear combination of discrete prolate spheroidal sequences (DPSS). In simulations of rapidly varying channel scenarios where least-mean square (LMS) and recursive least squares (RLS) fail completely, our proposed approach consistently tracks and equalizes the channel variation; yielding a symbol error rate of 10-4 at 15-dB signal-to-noise ratio. DPSS, being matched to the dynamic channel behaviour, is a key factor in minimizing the pilot resources expended in channel estimation, with losses in spectral efficiency starting from 4% up to 20% in the worst case.

Analytical expression for mode-coupling coefficient between non-identical step-index cores and its application to multi-core fiber design within 125-[formula omitted]m cladding diameter

Analytical expression is derived for the mode-coupling coefficient between non-identical step-index (SI) cores, which enables a quick estimate of the crosstalk in the heterogeneous SI multi-core fibers (Hetero-SI-MCFs). The analytical results are in good agreement with the results obtained by numerical simulations by finite-element method (FEM). Using the derived analytical expression, the feasibility of Hetero-SI-MCF design within standard 125-μm cladding diameter is discussed. The designed MCFs have potential applications in space division multiplexing (SDM) systems.

Integrated acousto-optic interaction at ultrahigh frequencies

With the development of nanoscale transducers, surface acoustic wave (SAW) with frequencies above 10 GHz can now be excited on the optical waveguides. However, the fundamental mode is very difficult to be excited for SAW at ultrahigh frequencies. Moreover, as the wavelength of SAW is reduced to below the optical wavelength, the acoustic field across the optical waveguide can no longer be approximated as uniform but is spatially periodic. Here, we develop a discussion about integrated acousto-optic (AO) interaction at ultrahigh frequencies. The electromechanical coupling coefficients of different modes are evaluated for SAW at ultrahigh frequencies. The acousto-optic overlap is analyzed to evaluate integrated AO interaction for each given acoustic wavelength and optical waveguide size. An analytic model is presented for integrated AO interaction at ultrahigh frequencies. The research shows that it would be a trade-off for the design of an integrated AO device with ultrahigh frequencies.

Comparative analysis of void-containing and all-semiconductor 1.5 µm InP-based photonic crystal surface-emitting laser diodes

This paper analyzes 2D photonic crystal surface-emitting laser diodes with void-containing and all-semiconductor structures by comparing their simulated mode distribution, band structure, and coupling coefficients. A photonic crystal design with a square lattice and circle atoms is considered.