Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend: comment.

To estimate the intercore crosstalk in uncoupled multicore fibers with cores' propagation constants perturbed by bending, twist, and structure fluctuations, in the paper [Opt. Express21, 5401 (2013)10.1364/OE.21.005401] entitled "Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend," Hayashi et al. derived an intuitively interpretable expression of the average power-coupling coefficient as the convolution of the arcsine and Lorentzian distributions, and calculated the derived expression numerically by performing the fast Fourier transform. In the present paper, we derive a closed-form solution of the convolution of the arcsine and Lorentzian distributions, and point out that the closed-form analytical expression derived here is exactly equivalent to the previously reported closed-form expression.

Mode multi/demultiplexing with parallel waveguide for mode division multiplexed transmission.

We propose a planar lightwave circuit (PLC)-based mode multi/demultiplexer (MUX/DEMUX) with an asymmetric parallel waveguide for mode division multiplexed (MDM) transmission. The PLCb-ased mode MUX/DEMUX has advantage of selectively exciting higher-order mode. We realize three-mode (LP(01), LP(11)a, and LP(21)a) multiplexing by using an asymmetric parallel waveguide. We then design and fabricate a PLC-based mode MUX/DEMUX on one chip by using our proposed LP(11) mode rotator to allow us to utilize the LP(11)b mode. We successfully multiplex the LP(01), LP(11)a, and LP(11)b modes and achieve a relatively low insertion loss over the C-band using our fabricated mode MUX/DEMUX. Our results indicate that the PLC-based mode MUX/DEMUX with a uniform height has the potential to increase the mode number by using an LP(11)b mode.

Two-mode PLC-based mode multi/demultiplexer for mode and wavelength division multiplexed transmission.

We proposed a PLC-based mode multi/demultiplexer (MUX/DEMUX) with an asymmetric parallel waveguide for mode division multiplexed (MDM) transmission. The mode MUX/DEMUX including a mode conversion function with an asymmetric parallel waveguide can be realized by matching the effective indices of the LP(01) and LP(11) modes of two waveguides. We report the design of a mode MUX/DEMUX that can support C-band WDM-MDM transmission. The fabricated mode MUX/DEMUX realized a low insertion loss of less than 1.3 dB and high a mode extinction ratio that exceeded 15 dB. We used the fabricated mode MUX/DEMUX to achieve a successful 2 mode x 4 wavelength x 10 Gbps transmission over a 9 km two-mode fiber with a penalty of less than 1 dB.

409-Tb/s + 409-Tb/s crosstalk suppressed bidirectional MCF transmission over 450 km using propagation-direction interleaving.

We demonstrate bidirectional transmission over 450 km of newly-developed dual-ring structured 12-core fiber with large effective area and low crosstalk. Inter-core crosstalk is suppressed by employing propagation-direction interleaving, and 409-Tb/s capacities are achieved for both directions.

Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend.

We have derived an intuitively interpretable expression of the average power-coupling coefficient for estimating the inter-core crosstalk of the multicore fiber. Based on the derived expression, we discuss how the structure fluctuation and macrobend can affect the crosstalk, and organize previously reported methods for crosstalk suppression. We also discuss how the microbending can affect the crosstalk in homogeneous and heterogeneous MCFs, based on the derived expression and previously reported measurement results.

Large-effective-area uncoupled few-mode multi-core fiber.

Characteristics of few-mode multi-core fiber (FM-MCF) were numerically analyzed and experimentally confirmed. The cores of FM-MCF were designed to support transmission of LP(01) and LP(11) modes from the point of bending loss of LP(11) and LP(21) modes. Inter-core crosstalk between LP(11) mode was calculated to determine core pitch of fibers. It was confirmed that the fabricated fibers was two-mode transmission over C-band and L-band with the effective area of LP(01) mode of about 110 µm(2) at 1550 nm. The crosstalk of the fibers was estimated to be smaller than -30 dB at 1550 nm after 100-km propagation. The crosstalk dependence on wavelength was also measured and matched well with the simulated results.

Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber.

Based on the overlap integral of electromagnetic fields in neighboring cores, a calculating method is proposed for obtaining the coupling coefficient between two adjacent trench-assisted non-identical cores. And a kind of heterogeneous trench-assisted multi-core fiber (Hetero-TA-MCF) with 12 cores is proposed to achieve large effective area (A(eff)) and high density of cores. As bending radius becomes larger than 50 mm, the crosstalk value at 1550-nm wavelength of the Hetero-TA-MCF is about -42 dB after 100-km propagation and the A(eff) of this Hetero-TA-MCF can reach 100 µm(2).

Large-effective-area ten-core fiber with cladding diameter of about 200 µm.

A multicore fiber with two-pitch layout is proposed to overcome the trade-off between core number and a cladding diameter of a standard hexagonal layout with a single-core pitch. A fabricated ten-core fiber simultaneously realizes effective area of about 120 µm(2) at 1550 nm, small crosstalk, and cladding diameter of 204 µm. The crosstalk between the center core and outer cores is about 30 dB smaller than that between outer cores. The small crosstalk of the center core would help to keep the transmission quality of the center core at the same level as that of the outer cores.

A design method of lithium niobate on insulator ridge waveguides without leakage loss.

We evaluate structural dependency of leakage losses in lithium niobate on insulator ridge waveguides. Generally, shallow ridge waveguides based on isotropic materials have inherent leakage loss for TM-like mode. On the other hand, lithium niobate is anisotropic material, thus the optical properties of lithium niobate based ridge waveguides are different from those of isotopic material based ridge waveguides. In this paper, we investigate leakage losses of lithium niobate on insulator ridge waveguides. We show that the shallow ridge waveguide structure without leakage loss can be realized by choosing the waveguide parameters adequately.

Strong infrared radiation through passive dispersive wave generation and its control.

We observe strong infrared (IR) radiation as a result of passive dispersive wave generation for a realistic microstructured fiber having two zero-dispersion wavelengths. The IR radiation frequency can be suitably controlled by varying the operational wavelength, which falls in the first normal dispersion regime. The amplitude of the radiation can be significantly increased by introducing a suitable amount of chirp in the input pulse. This strong phase-matching radiation can be considered as an alternative solution for the IR laser for different applications.

Dynamics of Raman soliton during supercontinuum generation near the zero-dispersion wavelength of optical fibers.

We observe unique dynamics of Raman soliton during supercontinuum process when an input pulse experiences initially normal group-velocity dispersion with a negative dispersion slope. In this situation, the blue components of the spectrum form a Raman soliton that moves faster than the input pulse and eventually decelerates because of Raman-induced frequency downshifting. In the time domain, the soliton trajectory bends and becomes vertical when the Raman shift ceases to occur as the spectrum of Raman soliton approaches the zero dispersion point. Parts of the red components of the pulse spectrum are captured by the Raman soliton through cross-phase modulation and they travel with it. The influence of soliton order, input chirp and dispersion slope on the dynamics of Raman soliton is discussed thoroughly.

Investigation on multi-core fibers with large Aeff and low micro bending loss.

To realize large effective area (Aeff) multi-core fibers (MCFs), the design to suppress the cross-talk and the influence of the cladding diameter on the micro bending loss were investigated. As a result, the MCFs with large Aeff over 100 µm(2) and low micro bending loss were successfully fabricated. The results indicate the importance of fiber design to realize large Aeff MCFs including fiber diameters, which largely affect the micro bending loss property. Additionally, MCF with large Aeff, low attenuation loss and suppressed cross-talk was successfully realized by optimizing the fiber design. The cross-talk properties could be estimated by the simulation based on the coupling power theory taking the influences of the longitudinal fluctuation of core diameter into account.

Multiple resonant coupling mechanism for suppression of higher-order modes in all-solid photonic bandgap fibers with heterostructured cladding.

In this paper, we propose a novel mechanism for suppression of higher-order modes (HOMs), namely multiple resonant coupling, in all-solid photonic bandgap fibers (PBGFs) with effectively large core diameters. In an analogy to the well-known tight-binding theory in solid-state physics, multiple anti-resonant reflecting optical waveguide (ARROW) modes bound in designedly arranged defects in the cladding make up Bloch states and resultant photonic bands with a finite effective-index width, which contribute to the suppression of HOMs. In particular, contrary to the conventional method for the HOM suppression using the index-matching of the HOMs in the core of the PBGF and the defect mode arranged in the cladding, the proposed mechanism guarantees a broadband HOM suppression without a precise structural design. This effect is explained by the multiple resonant coupling, as well as an enhanced confinement loss mechanism which occurs near the condition satisfying the multiple resonant coupling. Moreover, we show that the proposed structure exhibits a lower bending loss characteristic when compared to the conventional all-solid PBGFs. The simultaneous realization of the single-mode operation and the low bending loss property is due to the novel cladding concept named as heterostructured cladding. The proposed structure also resolves the issue for the increased confinement loss property in the first-order photonic bandgap (PBG) at the same time.

Polarization characteristics of photonic crystal fibers selectively filled with metal wires into cladding air holes.

We numerically investigate the polarization characteristics of photonic crystal fibers selectively filled with metal wires into cladding air holes, through a full-vector modal solver based on the finite-element method (FEM). Firstly, we investigate the fundamental coupling properties between the core guided light and surface plasmon polaritons (SPPs) excited on the surface of metal wire. Secondly, we show that we can obtain highly polarization-dependent transmission characteristics in PCFs by introducing several metal wires closely aligned into the cladding, and reveal the strongly polarization-dependent coupling properties between the core guided modes and the SPP supermodes, which consist of discrete SPP modes. Finally, we show the importance of arranging the metal wires close to each other for high polarization-dependence.

Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory.

Coupled-mode and coupled-power theories are described for multi-core fiber design and analysis. First, in order to satisfy the law of power conservation, mode-coupling coefficients are redefined and then, closed-form power-coupling coefficients are derived based on exponential, Gaussian, and triangular autocorrelation functions. Using the coupled-mode and coupled-power theories, impacts of random phase-offsets and correlation lengths on crosstalk in multi-core fibers are investigated for the first time. The simulation results are in good agreement with the measurement results. Furthermore, from the simulation results obtained by both theories, it is confirmed that the reciprocity is satisfied in multi-core fibers.

A large effective area multi-core fiber with an optimized cladding thickness.

The cladding thickness of trench-assisted multi-core fibers was theoretically and experimentally investigated in terms of excess losses of outer cores. No significant micro-bending loss increase was observed on multi-core fibers with the cladding thickness of about 30 µm. The tolerance for the micro-bending loss of a multi-core fiber is larger than that of the single core fiber. However, the cladding thickness will be limited by the occurrence of the excess loss on outer cores. The reduction of cladding thickness is probably limited around 40 µm in terms of the excess loss. The multi-core fiber with an effective area of 110 µm(2) at 1.55 µm and 181-µm cladding diameter was realized without any excess loss.

A design method of a fiber-based mode multi/demultiplexer for mode-division multiplexing.

In the mode-division multiplexing (MDM) optical transmission system, a mode multi/demultiplexer is an important key device for excitation, multiplication, and separation of light signals which have distinct modes. In this report, we propose a fiber-type mode multi/demultiplexer based on selective phase matching between different cores/modes. Design method and device characteristics of 1x4 mode multi/demultiplexer are investigated through finite element analysis. In order to expand operating wavelength range, we reveal the structural parameters that satisfy phase matching conditions over wide wavelength range. Our numerical results demonstrate that the mode multi/demultiplexer with broadband, polarization-insensitive operation can be realized by applying the proposed fiber structure.

Detailed theoretical investigation of bending properties in solid-core photonic bandgap fibers.

In this paper, detailed properties of bent solid-core photonic bandgap fibers (SC-PBGFs) are investigated. We propose an approximate equivalent straight waveguide (ESW) formulation for photonic bandgap (PBG) edges, which is convenient to see qualitatively which radiation (centripetal or centrifugal radiation) mainly occurs and the impact of bend losses for an operating wavelength. In particular, we show that cladding modes induced by bending cause several complete or incomplete leaky mode couplings with the core mode and the resultant loss peaks. Moreover, we show that the field distributions of the cladding modes are characterized by three distinct types for blue-edge, mid-gap, and red-edge wavelengths in the PBG, which is explained by considering the cladding Bloch states or resonant conditions without bending. Next, we investigate the structural dependence of the bend losses. In particular, we demonstrate the bend-loss dependence on the number of the cladding rings. Finally, by investigating the impacts of the order of PBG and the core structure on the bend losses, we discuss a tight-bending structure.

Design of all-solid leakage channel fibers with large mode area and low bending loss.

We investigate a novel design for all-solid large mode area (LMA) leakage channel fibers (LCFs) for high-power Yb-doped fiber lasers and amplifiers, based on a single down-doped-silica rod ring surrounding a seven-cell pure-silica core, aiming for effectively single-mode behavior and low bending loss characteristics. Through detailed numerical simulations based on the finite element method (FEM), we find that the proposed all-solid LMA-LCFs, having a seven-cell core and two different sizes of down-doped rods, can achieve sufficient differential mode loss and much lower bending loss, as compared with a previously-reported LCF with a one-cell core and six large down-doped-silica rods.

Design of miniaturized silicon wire and slot waveguide polarization splitterbased on a resonant tunneling.

We propose an ultra-small polarization splitter based on a resonant tunneling phenomenon. This polarization splitter consists of two identical horizontally oblong silicon wire waveguides separated by a vertical slot waveguide. The structural parameters of the central resonant slot waveguide are designed to couple only the TM-like mode between the left and right side silicon wire waveguides. Results from numerical simulation with the full-vectorial beam propagation method show that a 16-mum-long polarization splitter with extinction ratio better than -20 dB on the entire C-band is achieved.