Mode Field Profiles Research Articles

Design of all-fiber 2D MMI based optical devices using 1D mode propagation method

We show that the mode propagation analysis in a 2D confined optical device can be bifurcated into two 1D problems. In our method, a given 2D launch field profile is divided into two 1D profiles and suitably aligned with the 1D waveguide, acting as independent launching conditions. This method shows that the complete propagation problem of a 2D waveguide, which involves the computation of 2D mode field profiles and their propagation constants, can indeed be solved as two 1D problems. Our method is verified with the beam propagation method through a commercial simulator. Based on our analysis, we design MMI-based optical devices using square core multimode optical fiber such as wideband power divider and combiner at 1550 nm. Furthermore, the practical considerations, such as fabrication tolerance and operation bandwidth for these devices, are investigated to ascertain operational advantages.

Temperature-Dependent Electromagnetic Surface Wave Supported by Graphene-Loaded Indium Antimonide Planar Structure

In this study, the propagation characteristics of EM surface waves supported by the graphene-coated indium antimonide (InSb) planar waveguide have been investigated theoretically and numerically. The modeling of graphene has been performed by use of Kubo formalism whereas the relative permittivity of indium antimonide has been calculated using Drude’s model. The results for transverse electric (TE) and transverse magnetic (TM) polarized surface waves have been computed analytically and numerically. The major challenge is to model the atomically thick graphene sheet over the InSb grounded slab. To get the temperature-dependent characteristic equation for the electromagnetic surface waves, the surface current boundary conditions’ approach has been employed. The numerical results have been computed for both the TE and TM polarization states and reported that the TE does not support the propagation of surface waves. The dispersion relation, effective mode index, phase speed, propagation length, and field profile have been computed in Mathematica under TM polarization. The graphene and indium antimonide have been found active for low and high Terahertz regions, respectively. As temperature increases, the plasma frequency of the InSb increases due to this reason with the increase of temperature and the resonance frequency, leading to a shift in the dispersion curve. Moreover, with the increase of temperature, the effective wave number of transverse magnetic polarized surface waves also increases. Resultantly, the confinement of such surface waves supported by graphene-loaded InSb increases. It is shown that with the variation of temperature of indium antimonide, the surface waves propagating across the interface can be tuned in the Terahertz region and can be exploited for thermo-optical sensing, near-field communications waveguides, and graphene-based temperature sensor designing.

Thermally tunable electromagnetic surface waves supported by graphene loaded indium antimonide (InSb) interface

The thermal agitation plays a vital role in tunability of optoelectronic, structural and chemical characteristics of the temperature sensitive materials. Graphene enables the THz optics, due to its unprecedent controlling characteristics over the traditional materials. The influence of temperature on the monolayer graphene is very negligible due to its low free charge carrier density, to enhance the thermal sensitivity of graphene, the graphene loaded temperature sensitive material interface has been proposed. A theoretical analysis has been carried out on temperature dependent propagation characteristics of electromagnetic surface waves supported by the graphene loaded semi-infinite indium antimonide (InSb). The InSb has been taken as temperature sensitive material. The Drude model has been used for the modeling of InSb in the THz region while the modeling of the graphene has been done by random phase approximation-based Kubo’s formulism. To realize the graphene loaded indium antimonide interface, the impedance boundary conditions (IBCs) have been employed. The numerical analysis has been conducted to analyze the influence of temperature on the characteristics of electromagnetic surface waves i.e., dispersion curve, effective mode index (Neff), penetration depth (δ), propagation length (Lp), phase speed (Vp) and field profile, propagating along the graphene loaded InSb. In all the numerical results, the temperature variation has been considered from 200 to 350 K. It has been concluded that the graphene–InSb interface provides more temperature assisted tunability to the interfacial surface modes, commonly known as surface waves, as compared to monolayer graphene. Further, the graphene parameters can play a vital role in the dynamical tuning of electromagnetic surface waves in THz to IR frequency range. The numerically computed results have potential applications in designing of thermo-optical waveguides, temperature assisted communication devices, thermo-optical sensors and near field thermal imaging platforms.

Design of photonic crystal fiber with large mode area for flat-top mode generation

We report a large mode area photonic crystal fiber with a flat-top mode field. The optical fiber has a multi-layer square structure with air holes and doped layer. A flat and top-hat-like mode intensity profile is provided through the reasonable design of the doped layer. The modal characteristics including effective mode area, dispersion, bending loss, confinement loss and field profile are investigated. The proposed fiber with a top-hat mode generation has potential applications in laser drilling, laser cleaning, imaging, spectroscopy, and so on.

Intermodal Four-Wave Mixing Process in Strain-Induced Birefringent Multimode Optical Fibers.

Our study investigated the partially degenerate intermodal four-wave mixing (IM-FWM) process in nonlinear multimode optical fibers with strain-induced birefringence. The difference in the refractive index along the two orthogonal directions was due to the photoelastic effect that occurred when the fiber under test (FUT) was subjected to uniformly applied diameter stress caused by winding on a cylinder of a given diameter. Our work analyzed how the nonlinear frequency conversion and the output modal field profiles depended on the degree of birefringence in FUT. The experimental results significantly affected the order of the excited moduli in fiber sections characterized by different amounts of birefringence. We also checked the efficiency of the FWM process for different polarizations of the pump beam to determine those for which the FWM process was most effective for the 532 nm sub-nanosecond pulses. More than 30% conversion efficiency was obtained for the FUTs with a length of tens of centimeters.

Ultra-Low Noise Figure in Optical Fiber Amplifier by Tailoring the Mode Field Profile of Erbium-Doped Fiber

We present a numerical analysis of noise performance improvement of the erbium-doped fiber amplifier by flatting the mode field intensity distribution within the interaction region of erbium ions. Three different refractive index types of erbium-doped fiber were used to study the effect of the pump mode intensity distribution on noise performance. The results show that taking advantage of the depressed refractive index erbium-doped fiber which has a flat mode distribution in the fiber core, the maximum reduction of nearly 0.53 dB for noise figure was achieved across the full C-band. Based on the center depressed refractive index profile, the noise figure was further decreased by about 0.1 dB by reducing the doping radius to 0.71 μm. Finally, maintaining the same gain level of ∼38.3 dB, a NF reduction of ∼0.63 dB was realized by introducing the center depressed refractive index profile and narrowing the erbium doping region. It is suggested that our investigation shows great potential for improving the noise performance of the erbium-doped fiber amplifier.

Ultralow-loss fusion splicing between negative curvature hollow-core fibers and conventional SMFs with a reverse-tapering method.

Negative curvature hollow-core fibers (NC-HCFs) can boost the excellent performance of HCFs in terms of propagation loss, nonlinearity, and latency, while retaining large core and delicate cladding structures, which makes them distinctly different from conventional fibers. Construction of low-loss all-fiber NC-HCF architecture with conventional single-mode fibers (SMFs) is important for various applications. Here we demonstrate an efficient and reliable fusion splicing method to achieve low-loss connection between a NC-HCF and a conventional SMF. By controlling the mode-field profile of the SMF with a two-step reverse-tapering method, we realize a record-low insertion loss of 0.88 dB for a SMF/NC-HCF/SMF chain at 1310 nm. Our method is simple, effective, and reliable, compared with those methods that rely on intermediate bridging elements, such as graded-index fibers, and can greatly facilitate the integration of NC-HCFs and promote more advanced applications with such fibers.

Wavelength Conversion Efficiency Enhancement in Modal Phase Matched $\chi^{\hbox{{(2)}}}$ Nonlinear Waveguides

Modal phase matching (MPM) is a widely used phase matching technique in Al$_x$Ga$_{1-x}$As and other $\chi^{(2)}$ nonlinear waveguides for efficient wavelength conversions. The use of a non-fundamental spatial mode compensates the material dispersion but also reduces the spatial overlap of the three interacting waves and therefore limits the conversion efficiency. In this work, we develop a technique to increase the nonlinear overlap by modifying the material nonlinearity, instead of the traditional method of optimizing the modal field profiles. This could eliminate the limiting factor of low spatial overlap inherent to MPM and significantly enhance the conversion efficiency. Among the design examples provided, this technique could increase the conversion efficiency by a factor of up to $\sim$290 in an Al$_x$Ga$_{1-x}$As waveguide. We further show that this technique is applicable to all $\chi^{(2)}$ material systems that utilize MPM for wavelength conversion.

Nanoscale Electrical Excitation of Distinct Modes in Plasmonic Waveguides.

The electrical excitation of guided plasmonic modes at the nanoscale enables integration of optical nanocircuitry into nanoelectronics. In this context, exciting plasmons with a distinct modal field profile constitutes a key advantage over conventional single-mode integrated photonics. Here, we demonstrate the selective electrical excitation of the lowest-order symmetric and antisymmetric plasmonic modes in a two-wire transmission line. We achieve mode selectivity by precisely positioning nanoscale excitation sources, i.e., junctions for inelastic electron tunneling, within the respective modal field distribution. By using advanced fabrication that combines focused He-ion beam milling and dielectrophoresis, we control the location of tunnel junctions with sub-10 nm accuracy. At the far end of the two-wire transmission line, the guided plasmonic modes are converted into far-field radiation at separate spatial positions showing two distinct orthogonal polarizations. Hence, the resulting device represents the smallest electrically driven light source with directly switchable polarization states with possible applications in display technology.

All‐Dielectric Toroidal Metasurfaces for Angular‐Dependent Resonant Polarization Beam Splitting

AbstractAn all‐dielectric metasurface exhibiting a strong toroidal resonance is theoretically designed and experimentally demonstrated as an angular‐dependent resonant polarization beam‐splitter in the microwave K‐band. The metasurface is fabricated by embedding a square periodic array of high‐permittivity ceramic cuboid resonators in a 3D‐printed substrate of polylactic acid. It is demonstrated that by properly selecting the resonator geometry and by tuning the angle of incidence through mechanical rotation, the metasurface can switch between a polarization beam splitting and bandpass or bandstop operation. Such performance is achieved by exploiting the highly asymmetric Fano spectral profile of the toroidal resonance and the very low (high) dispersion of the associated p‐(s‐) polarized mode resulting from the resonant toroidal dipole mode's field profile, as evidenced by both full‐wave and band structure simulations. Theoretically infinite extinction ratios are achievable for polarization beam splitting operation with very low insertion losses and adjustable bandwidth. The experimental demonstration of such a compact, all‐dielectric metasurface expands the research portfolio of resonant metasurfaces toward not only the investigation of the intriguing physics of toroidal modes but also to the engineering of functional millimeter‐wave components for polarization control, for instance, in the context of 5G wireless communication networks.

Mode analysis of in-line Mach-Zehnder interferometer with offset splicing

Mode excitation of in-line Mach-Zehnder interferometer (MZI) with offset splicing between standard single-mode fiber (SMF) and thin-core fiber (TCF) is investigated. Based on the mode field profiles of high order modes in TCF, dependence of mode excitation on core offset is researched firstly. It is revealed that which modes can be significantly excited is strongly dependent on the mode fields matching between LP01 mode in SMF and LP1n mode in TCF, by which the dominant excited modes can be predicted and this method can be expanded to any two fibers with offset splicing. Based on the energy distributions of excited modes with/without considering interference among cladding modes, transmission spectra can be calculated by interference equations theoretically. By comparing with experimental results, it can be concluded that for kind of MZIs based on offset splicing, it is difficult to make the calculated results to be identical with experimental results due to the large number of modes excited, so an equivalent mode approach is proposed to solve this problem and verified by the temperature sensing experiment. In addition, dependence of mode excitation on probing wavelength or refractive index (RI) of surroundings, and effect of fiber parameters on signal shape are also studied. The MZI proposed here shows advantages of low cost, easy fabrication, no special splicing equipment required, and relative high sensitivity. Results shown here will provide valuable information for kind of MZIs based on core-offset splicing between TCF and SMF, and afford useful references for other kinds of in-line MZIs based on the interference between core and cladding modes.

Spatiotemporal plane wave expansion method for arbitrary space-time periodic photonic media.

We have derived a systematic method to calculate the photonic band structures and mode field profiles of arbitrary space-time periodic media by adopting the plane wave expansion method and extending to the space-time domain. We have applied the proposed method to a photonic crystal with time periodic permittivity, i.e., the Floquet photonic crystal, and showed that the method efficiently predicts driving-induced opening of frequency and momentum gaps and breaking of mirror symmetry in the photonic band structures. This method enables systematic investigation of various optical phenomena in space-time periodic media, such as nonreciprocal propagation of light, parametric processes, and photonic Floquet topological phases.

Nanowire Oligomer Waveguide Modes towards Reduced Lasing Threshold.

Semiconductor nanowires offer a promising route of realizing nanolasers for the next generation of chip-scale optoelectronics and photonics applications. Established fabrication methods can produce vertical semiconductor nanowires which can themselves act both as a gain medium and as a Fabry–Pérot cavity for feedback. The lasing threshold in such nanowire lasers is affected by the modal confinement factor and end facet reflectivities, of which the substrate end reflectivity tends to be limited due to small refractive index contrast between the nanowire and substrate. These modal properties, however, also depend strongly on the modal field profiles. In this work, we use numerical simulations to investigate waveguide modes in vertical nanowire oligomers (that is, arrangements of few vertical nanowires close to each other) and their modal properties compared to single nanowire monomers. We solve for the oligomer waveguide eigenmodes which are understood as arising from interaction of monomer modes and further compute the reflectivity of these modes at the end facets of the nanowires. We consider either the nanowires or an additional coating layer as the gain medium. We show that both types of oligomers can exhibit modes with modal properties leading to reduced lasing threshold and also give directions for further research on the topic.

Perturbation theory for Kerr nonlinear leaky cavities.

In emerging open photonic resonators that support quasinormal eigenmodes, fundamental physical quantities and methods have to be carefully redefined. Here, we develop a perturbation theory framework for nonlinear material perturbations in leaky optical cavities. The ambiguity in specifying the stored energy due to the exponential growth of the quasinormal mode field profile is lifted by implicitly specifying it via the accompanying resistive loss. The capabilities of the framework are demonstrated by considering a third-order nonlinear ring resonator and verified by comparing against full-wave nonlinear finite element simulations. The developed theory allows for efficiently modeling nonlinear phenomena in contemporary photonic resonators with radiation and resistive loss.

Hybrid III-V Silicon Photonic Crystal Cavity Emitting at Telecom Wavelengths.

Photonic crystal (PhC) cavities are promising candidates for Si photonics integrated circuits due to their ultrahigh quality (Q)-factors and small mode volumes. Here, we demonstrate a novel concept of a one-dimensional hybrid III-V/Si PhC cavity which exploits a combination of standard silicon-on-insulator technology and active III-V materials. Using template-assisted selective epitaxy, the central part of a Si PhC lattice is locally replaced with III-V gain material. The III-V material is placed to overlap with the maximum of the cavity mode field profile, while keeping the major part of the PhC in Si. The selective epitaxy process enables growth parallel to the substrate, and hence in-plane integration with Si, and in-situ in-plane homo- and heterojunctions. The fabricated hybrid III-V/Si PhCs show emission over the entire telecommunication band from 1.2 to 1.6 μm at room temperature validating the device concept and its potential towards fully integrated light sources on silicon.

Semi-analytical approach for calculation of intercore crosstalk in multicore fibers

In this paper, a semi-analytical method to calculate intercore crosstalk (ICXT) in bent and twisted multicore fibers (MCFs) is proposed. The modified refractive index of bent MCF is first computed using geometrically exact beam theory (GEBT) and conformal mapping technique. The computed refractive index profile is used to obtain mode field profiles of bent MCF by solving the wave equation using vectorial finite element method in COMSOL. To take twisting of MCF into account, outer cores of the MCF are approximated to be helically bent around the central core. Using the mode field profiles, mode coupling coefficient between the MCF cores is calculated for different bend radii which is then used to calculate ICXT by using closed form analytical expressions reported in the literature. The ICXT values obtained using our proposed approach are in very good agreement with the experimental values reported in the literature. The effect of change in core pitch and change in relative refractive index contrast of MCF on the mode coupling coefficient between the MCF cores is analysed. The influence of twisting rate of MCF on the ICXT values for different bend radii is studied and it is shown that, ICXT is constant with respect to twisting rate of MCF for bending radii greater than the critical bending radius of the MCF. The proposed approach is also extended to calculate ICXT between different modes of trench assisted few-mode MCF (FM-MCF). The ICXT values obtained for the trench assisted FM-MCF follow the expected trend.

Multichannel mode-selective silicon photonic add/drop multiplexer with phase change material

A multichannel mode-selective silicon photonic add/drop multiplexer is proposed by introducing asymmetric directional couplers (ADCs) assisted with phase change material (PCM) strips. Each ADC consists of a multimode bus waveguide and a single-mode access waveguide with a thin PCM strip on the top. For the present mode-selective add/drop multiplexer, the PCM of G e 2 S b 2 S e 4 T e 1 (GSST) is used, and the PCM-loaded access waveguide is designed optimally by engineering the effective index and the modal field profile. When the switching state of the add/drop multiplexer is OFF with crystal GSST, all the mode channels go through with very low excess losses. Otherwise, when it is ON, by switching the GSST-PCM strip to be amorphous, the desired TE mode channel can be selectively added to or dropped from the multimode bus waveguide, while the other mode channels still stay and propagate in the multimode bus waveguide. The simulated results show that the designed mode-selective silicon photonic add/drop multiplexer utilizing a single ADC has low excess losses of < 0.5 d B and low intermodal crosstalk of < − 15 d B over the C-band for all the mode channels. Furthermore, using the design with cascaded ADCs for each mode-selective add/drop switch, the crosstalk can be suppressed to < − 20 d B , and the excess losses are less than 1 dB over an 80 nm broad wavelength band from 1505 to 1585 nm.

Hybrid multi-chip assembly of optical communication engines by in situ 3D nano-lithography

Three-dimensional (3D) nano-printing of freeform optical waveguides, also referred to as photonic wire bonding, allows for efficient coupling between photonic chips and can greatly simplify optical system assembly. As a key advantage, the shape and the trajectory of photonic wire bonds can be adapted to the mode-field profiles and the positions of the chips, thereby offering an attractive alternative to conventional optical assembly techniques that rely on technically complex and costly high-precision alignment. However, while the fundamental advantages of the photonic wire bonding concept have been shown in proof-of-concept experiments, it has so far been unclear whether the technique can also be leveraged for practically relevant use cases with stringent reproducibility and reliability requirements. In this paper, we demonstrate optical communication engines that rely on photonic wire bonding for connecting arrays of silicon photonic modulators to InP lasers and single-mode fibres. In a first experiment, we show an eight-channel transmitter offering an aggregate line rate of 448 Gbit/s by low-complexity intensity modulation. A second experiment is dedicated to a four-channel coherent transmitter, operating at a net data rate of 732.7 Gbit/s – a record for coherent silicon photonic transmitters with co-packaged lasers. Using dedicated test chips, we further demonstrate automated mass production of photonic wire bonds with insertion losses of (0.7 ± 0.15) dB, and we show their resilience in environmental-stability tests and at high optical power. These results might form the basis for simplified assembly of advanced photonic multi-chip systems that combine the distinct advantages of different integration platforms.

Efficient light coupling between an ultra-low loss lithium niobate waveguide and an adiabatically tapered single mode optical fiber

A lithium niobate on an insulator ridge waveguide allows constructing high-density photonic integrated circuits thanks to its small bending radius offered by the high index contrast. Meanwhile, the significant mode-field mismatch between an optical fiber and the single-mode lithium niobate waveguide leads to low coupling efficiencies. Here, we demonstrate, both numerically and experimentally, that the problem can be solved with a tapered single mode fiber of an optimized mode field profile. Numerical simulation shows that the minimum coupling losses for the TE and TM mode are 0.32 dB and 0.86 dB, respectively. Experimentally, though without anti-reflection coating, the measured coupling losses for TE and TM mode are 1.32 dB and 1.88 dB, respectively. Our technique paves a way for a broad range of on-chip lithium niobate applications.

Long period grating in a liquid crystal waveguide

This paper introduces, for the first time to the best of our knowledge we theoretically report the long period grating (LPG) in the liquid crystal (LC) layer of planar optical waveguide. LPG has the ability to couple the light between core and cladding modes of waveguide. LPG can be used for the development of band rejection filter, gain flattening in erbium-doped fiber amplifiers (EDFA) and for sensing applications. We have shown the realization of proposed LPG in temperature sensing. First, we theoretically analyzed the propagation of light through a 6-layer planar optical waveguide by analyzing its modal field profiles and effective index profile of fundamental mode TE0 and two higher order modes TE1 and TE2. Then we investigated in details the phase-matching curves of the long period grating, which supervise the association between the grating period and the resonance wavelength. Using phase matching curve to choose grating period, we have studied the transmission spectrum of the PLG which display evident elimination of bands at individual wavelengths, noted as the resonance wavelengths. High sensitivity of LC to the environmental temperature makes it a good choice for temperature sensing. The performance of LPG has been studied for the temperature ranging from 306 K to 329 K. The novelty of this structure is the realization of LPG in the LC, which is a key component of display devices. Hence, our structure can provide freedom to use this in variety of pragmatic applications.