Modulation instability in lossy silicon optical waveguide

Taking into account the small linear loss of silicon-on-insulator(SOI) waveguide, conditions and gain spectra of modulation instability(MI) induced by combined effects of self-phase modulation and waveguide dispersions are investigated. The impacts of various parameters to gain spectra of MI are analyzed theoretically. Results show that strong MI takes place even in the existence of low light power. The MI peak gain is 2 to 3 orders of magnitude larger than that achieved in optical fibers with the same light power. The linear loss of waveguide impacts gain spectra of MI, even within ultra-short propagation distance. The peak gain, peak gain frequency and bandwidth of gain spectra decrease to 66.828%, 41.683% and 41.6879% of their maxima at propagation distance z = 5mm, respectively.     

Thermally tunable EDFA gain equalizer using point symmetric cascaded Mach-Zehnder coupler

In this paper, a thermally tunable EDFA gain equalizer filter based on point symmetric cascaded Mach-Zehnder (CMZ) filter based two mode interference (TMI) coupler is presented with its mathematical model. Transmission characteristics of these CMZ couplers are analyzed and compared with Y symmetric CMZ couplers by using this model. For EDFA gain equalizer, point symmetric CMZ circuit is chosen due to its higher wavelength flattening width than Y symmetric CMZ circuit. The ripples of equalized EDFA gain spectrum are formulated and estimated from the equalized gain spectrum of point symmetric CMZ filters. It is found that 2 stage point symmetric CMZ coupler with binomial coupler distribution (2PB CMZ) using Δn = 5% provides gain equalized width of 35 nm with ripple of 0.4-0.6 dB and bending loss of 0.24 dB and device length is ∼15 times lower than that of the existing EDFA gain equalizer based CMZ filter. It is also seen that if during the fabrication process, waveguide core width w is increased or decreased by 0.1 μm (in percentage ∼±6.6%), the power imbalance of TMI based 2PB CMZ filter is slightly increased by ∼8% in comparison to that based on directional coupler (DC) by 40%. Low power thermooptic structure of varying gap between two waveguide cores with silicon trench just below the heater is used and it requires ∼1.5 times less heating power than the conventional structure for thermal tuning of EDFA gain equalization.     

Semi-elliptical dielectric-loaded surface plasmon-polariton waveguides

Semi-elliptical dielectric-loaded surface plasmon-polariton waveguide (DLSPPW) is proposed. The mode effective index, field confinement, and propagation length of the fundamental mode supported by it are calculated at the telecom wavelength λ = 1.55 μm for different dimensions of a polymer ridge (with the refractive index of 1.535) placed on a gold film surface. The waveguide structure is found to exhibit 23% increase of the propagation length while showing similar confinement as compared to conventional rectangular DLSPPW when ridge thickness t < 450 nm (ridge width w = 600 nm) and ridge width w < 320 nm (ridge thickness t = 600 nm).     

Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides

The propagation of electromagnetic energy via coupled surface plasmon polariton modes in a metal-insulator-metal heterostructure is analyzed analytically for a core material exhibiting optical gain. It is shown that a sufficiently large gain can completely compensate for the absorption losses due to energy dissipation in the metallic boundaries, enabling long-range transport with a confinement below the diffraction limit for on-chip switching and sensing applications. For a free-space wavelength of 1500 nm, lossless propagation in a gold-semiconductor-gold waveguide with a core size of 50 nm is predicted for a gain coefficient γ = 4830 cm⁻¹, comparable to that of semiconductor gain media. The gain requirements decrease with the use of low-index nanocrystal-doped glasses or polymers as core materials.     

Transmission performance of 20 × 10 Gb/s WDM signals using cascaded optimized SOAs with OOK and DPSK modulation formats

We investigated 20 channels at 10 Gb/s wavelength division multiplexing (WDM) transmission over 1190 km single mode fiber and dispersion compensating fiber using cascaded inline semiconductor optical amplifier at a span of 70 km for RZ-DPSK (return zero differential phase-shift keying) modulation format by using same channel spacing, i.e. 100 GHz. We show for RZ-OOK (return zero on-off keying) format a transmission distance of up to 1050 km with Q factor more than 15 dB, without any power drops. We developed the SOA model for inline amplifier having minimum cross-talks and ASE (amplified spontaneous emission) noise power with sufficient gain. At optimal bias current of 400 mA, a high constant gain of 36.5 dB is obtained up to a saturation power of 21.36 mW. So reduction of cross-talk and distortion is possible by decreasing the bias current at appropriate amplification factor.The DPSK modulation format has less cross-talk as compared to OOK format for nonlinearities and saturation case. The impact of optical power received and Q factor at different distance for both RZ-OOK and RZ-DPSK modulation format has been illustrated. We have shown the optical spectrum and clear Eye diagram at the transmission distance of 1190 km in RZ-DPSK system and 1050 km in RZ-OOK systems.The bit error rate (BER) for all channels observed is less than 10⁻¹⁰ up to gain saturation for both DPSK and OOK systems. Finally, we investigated that the transmission distance decreases with a decrease in channel spacing of up to 20 GHz.     

32-channel arrayed waveguide grating multiplexer using low loss fluorinated polymer operating around 1550 nm

A 32 × 32 arrayed waveguide grating (AWG) multiplexer operating around the 1550 nm wavelength has been designed and fabricated using highly fluorinated polyethers. The propagation loss of the slab waveguide is about 0.3 dB/cm at 1550 nm wavelength. The channel spacing of the AWG multiplexer is 0.8 nm (100 GHz). The insertion loss of the multiplexer is 10.3-15.3 dB and the crosstalk is less than −20 dB.     

Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement

Single mode silicon photonic wire waveguides allow low-loss sharp micro-bends, which enables compact photonic devices and circuits. The circuit compactness is achieved at the cost of loss induced by micro-bends, which can seriously affect the device performance. The bend loss strongly depends on the bend radius, polarization, waveguide dimension and profile. In this paper, we present the effect of waveguide profile on the bend loss. We present waveguide profile improvement with optimized etch chemistry and the role of etch chemistry in adapting the etch profile of silicon is investigated. We experimentally demonstrate that by making the waveguide sidewalls vertical, the bend loss can be reduced up to 25% without affecting the propagation loss of the photonic wires. The bend loss of a 2 μm bend has been reduced from 0.039dB/90° bend to 0.028dB/90° bend by changing the sidewall angle from 81° to 90°, respectively. The propagation loss of 2.7 ± 0.1dB/cm and 3 ± 0.09dB/cm was observed for sloped and vertical photonic wires respectively was obtained.     

A polymeric optical switch array based on arrayed waveguide grating structure

A novel 1 × N optical switch array based on arrayed waveguide grating (AWG) structure is presented in this paper. The device is designed for polymeric materials with a large negative thermooptic (TO) coefficient, which is employed to change the imaging effect and to realize optical switching. When input wavelength is located in a special waveband, the optical signal will image at different output channel as temperature changes. The two-dimensional finite difference beam propagation method (FD-BPM) has been used to simulate a 1 × 9 optical switch array. The insertion loss of this switch array is below 1.37 dB and the extinction ratio is better than 31 dB at 1550 nm, when the coupling and propagation loss is neglected. The optimum design and the simulation results show that this structure could be a multiple wavelengths switching at the same time.     

Extrinsic surface scattering and intrinsic absorption loss of vinyl based hybrid organic–inorganic materials for optical waveguides applications

Hybrid photosensitive materials were prepared by using vinyltriethoxysilane (VTES), tetraethoxysilane (TEOS) and tetrabutoxytitanate (TTBu) precursors through sol–gel technique. The materials are intended for optical telecommunication applications. Thus, high optical transmissions at the second and third optical telecommunication windows are essential. Extrinsic surface scattering due to surface roughness and intrinsic absorption due to aliphatic CH and OH groups are always ascribable to the optical power attenuations at aforementioned optical telecommunication windows. Optical waveguide based on hybrid sol–gel materials were fabricated, characterized and analyzed in order to investigate the extrinsic and intrinsic sources of attenuation and their contributions. The fabricated samples were characterized for propagation loss, surface condition, and Fourier transform IR (FTIR) absorption spectra. Propagation loss were measured by means of cut-back method as 1.6 and 6.9 dB/cm at 1310 and 1550 nm wavelengths, respectively. Surface scattering loss was modeled based on measured rms roughness of 0.724 nm and turned out to contribute less than 0.01% of the total propagation loss. FTIR absorption spectra show the persistent existence of aliphatic CH and OH groups within the final hybrid sol–gel materials.     

Wave propagation in a waveguide with continuous right-angled corners: Numerical simulations and experiment measurements

This paper studied the acoustic wave propagation in a waveguide with continuous right-angled corners, with emphasis on the effect brought by the distance between the corners. The numerical analyses showed that at middle to high frequencies, the transmission loss (TL) of a multi-cornered waveguide was 2–5 dB higher than that of single-cornered and varied with frequency. To explain the performance at peaks and dips in the TL curve, analyses on eigenmodes and sound intensity distribution were conducted. The performance of multi-cornered waveguides was experimentally investigated, which fit well with the numerical results. The present study indicates that, for a waveguide with continuous corners, its acoustic performance is not simply a “summation” of two individual single-cornered ones. Both the standing wave modes and the evanescent modes between the corners lead to its complicated frequency performance.     

Modulation instability in metamaterials with fourth-order linear dispersion,second-order nonlinear dispersion,and three kinds of saturable nonlinearites

The linearized nonlinear propagation equation and its coefficients, gain spectrum of modulation instability (MI) in metamaterials (MMs) with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites, are analytically deduced by utilizing the linear stability analysis and Drude electromagnetic model. Then variations of gain spectra of MI with the normalized angular frequencies and the optical power densities are calculated in real units. In the negative refractive region, two kinds of gain spectra are discovered. The first (second) one is close to (far from) the zero perturbation frequencies and it corresponds to the lower (higher) normalized angular frequencies. Moreover, the second one has higher cutoff frequency, which is obviously beneficial to generation of high-repetition-rate pulse trains. While in the positive refractive region, only the first kind of gain spectra is found. With increase of the optical power densities, the peak gains and the spectral widths of MI increase before decrease, but they vary the most rapidly (slowly) for the exponential (conventional) saturable nonlinearities. The MI characteristics and their corresponding applications can be adjusted by several methods.     

Optimized design of a new three branch optical waveguide

A new type of 1 × 3 Y-branch optical waveguide structure with a cone transitional section is introduced in this paper. The symmetrical branch ratio of the 1 × 3 Y branch optical waveguide is obtained by changing the width of this waveguide. The loss and the uniformity are obtained by using the finite difference beam propagation methods, and their values are 0.2 dB and 0.05 dB, respectively. Therefore, it provides some experimental basis for production of three branch optical waveguide.     

The fabrication of polymer-based evanescent optical waveguide for biosensing

A polymer waveguide was fabricated to amplify the evanescent optical field for biosensing. The structure of waveguide was designed to propagate a normal single mode at the input and output regions for low loss beam coupling and propagation. A sensing region was formed in the middle of the waveguide to activate the evanescent mode and to induce high birefringence by depositing a thin dielectric film with a high refractive index on a single mode waveguide. A polymer waveguide with the dimensions of 7 μm-width and 2.5 μm-thickness was fabricated by photolithography and dry-etching. The active region of the TiO₂ thin film was fabricated with the dimensions of 20 mm-length, 20 nm-thickness and 2 mm-tapered tail. A polarimetric interference technique was used to evaluate the evanescent waveguide biosensor, and biomaterial such as glycerol was tested. The sensitivity of the sensor increased with increasing TiO₂ film thickness. For the fabricated waveguide with a 20 nm-thick TiO₂ film, the measured index change to the lead phase variation of 2π was 1.8 × 10⁻⁴.     

Application of obliquely interfering TE10 modes for electron energy gain

Two fundamental TE₁₀ modes are considered to interfere at a small angle θ and then propagate along the z-axis in an evacuated rectangular waveguide. The electron trajectory in the resultant field and the expressions for energy gain and the acceleration gradient are obtained, when the electron is injected along the z-axis. A 50 keV electron gains 718 keV energy in a 4.0 cm × 2.5 cm waveguide, when the microwave with intensity of 1 × 10¹⁰ W/cm² and frequency 5.577 GHz is used and the modes superpose at an angle of 10°; here the maximum acceleration gradient is obtained as 251 MeV/m. The energy gain and acceleration gradient are decreased with increasing width of the waveguide and microwave frequency. Higher gradient and larger energy gain are obtained for the higher microwave intensity, smaller angle of superposition and also when the electron is injected with larger initial energy.     

Low-loss, compact waveguiding with TE mode in metal/dielectric waveguides for planar lightwave circuit

We propose a low-loss metal/dielectric waveguide for compact planar lightwave circuit. The basic waveguide structure is a metal-defined high-index-contrast strip waveguide based on silicon/silica. As the guide is designed for TE single mode waveguiding, extremely low propagation loss (e.g. <0.04 dB/cm), very low bend loss (e.g. 0.0043 dB/90°-turn) and small waveguide pitch of zero-crosstalk are theoretically achievable, and can be further improved by compromising with component size and density. Examples of multi-bends and device integration are demonstrated with numerical simulations. The proposal is compatible with silicon technology and appealing for development of silicon-based planar lightwave circuit.     

Experimental and theoretical studies on ytterbium sensitized erbium-doped fiber amplifier

The performance of a high power erbium-ytterbium doped fiber amplifier (EYDFA) is investigated experimentally and theoretically. The EYDFA provides a flat gain with an output power higher than 23 dBm in the wavelength region from 1541 to 1565 nm using a multimode pumping at 927 nm. In the theoretical analysis, the rate and power propagation equations are solved to examine the effect of fiber length on the bandwidth of the gain spectra. In the C-band region, the small signal gain of the EYDFA varies from 30 to 34 dB with 10 m long erbium-ytterbium doped fiber (EYDF) while the 927 nm pump power is fixed at 3.5 W. It is shown that the calculated output power is in good agreement with the experimental results, verifying the feasibility of our theoretical model. However, the experimental result shows a relatively lower gain compared to the theoretical result due to the spurious reflection in the cavity and the insertion loss of the EYDF which were neglected in our theoretical model.     

Er-Yb co-doped glass waveguide amplifiers using ion exchange and field-assisted annealing

Er³⁺-Yb³⁺ co-doped waveguide amplifiers fabricated using thermal two-step ion-exchange are demonstrated. K⁺-Na⁺ ion-exchange process was first carried out in pure KNO₃ molten bath, and then field-assisted annealing (FAA) was used to make the buried waveguides. The effective buried depth is estimated to be ∼3.4 μm for the buried FAA waveguides. With the use of cut-back method, the fiber-to-guide coupling loss of ∼4.38 dB, the waveguide loss of ∼2.27 dB/cm, and Er³⁺ absorption loss ∼5.7 dB were measured for a ∼1.24-cm-long waveguide. Peak relative gain of ∼7.0 dB is obtained for a ∼1.24-cm-long waveguide. The potential for the fabrication of compact optical amplifiers operating in the range of 1520-1580 nm is also demonstrated.     

Optimal design of multimode interference couplers using an improved self-imaging theory

Self-imaging theory is widely accepted as a good method in designing 1 × N multimode interference (MMI) couplers, but it is also true that self-imaging theory is not suitable for low-contrast structures. An improved self-imaging theory is proposed in this paper for the optimal design of low-contrast 1 × N MMI couplers. The average effective width of MMI waveguide and the average effective propagation constant of MMI waveguide are used as the basis to modify the conventional self-imaging theory. A direct calculation of the average effective width of low-contrast MMIs is presented. We use this approach in the optimal design of a 1 × 4 silica MMI coupler, and the results show that the improved self-imaging theory is more accurate than conventional self-imaging theory for low-contrast structures, the results also show that if the material parameters and the width of an MMI waveguide are fixed, the average effective width of the MMI waveguide will increase with the decrease of the height of the core layer.     

Numerical analysis of amplification characteristics of ErxY2 − xSiO5

The gain characteristics of Er_xY_2 − xSiO₅ waveguide amplifiers have been investigated by solving rate equations and propagation equations. The gain at 1.53 μm as a function of waveguide length, Er³⁺ concentration and pump power is studied pumping at three different wavelengths of 654 nm, 980 nm and 1480 nm, respectively. The optimum Er³⁺ concentrations of 1 × 10²¹ cm^− 3-2 × 10²¹ cm^− 3 with the high gain are obtained for all three pump wavelengths. Pumping at 654 nm wavelength is shown to be the most efficient one due to weak cooperative upconversion. A maximum 16 dB gain at 1 mm waveguide length under a 30 mW pump with Er³⁺ concentration of 1 × 10²¹ cm^− 3 is demonstrated pumping at 654 nm wavelength.     

饱和非线性正折射异向介质中的调制不稳定性

直接从异向介质中包含饱和非线性、自陡峭和二阶非线性色散效应的非线性扩展传输方程出发,采用线性稳定性分析法,导出了调制不稳定性的色散关系、不稳定条件、无量纲的临界扰动频率和增益谱。计算和讨论了异向介质正折射区无量纲的增益谱随归一化角频率和入射功率密度的变化关系。结果表明,在异向介质正折射区,随归一化角频率和入射功率密度的不同,增益谱将会出现扰动频率大于零、扰动频率大于某个非零临界值、扰动频率大于零而小于某个非零临界值3种形式。在归一化角频率较小时,调制不稳定性可能出现阈值入射功率密度;且在较小的入射功率密度时,调制不稳定性只能出现在大于某个临界频率时。