Band-pass filter with flat time delay response based on fiber grating Sagnac loop

We have developed the analytic expressions for the phase response and time delay of FBGSL of arbitrary grating structure and found that the results from the modelling are in excellent agreement with that of the experimentally measured real devices. The theoretical and experimental investigation clearly reveals that FBGSLs utilizing uniform and linearly chirped gratings exhibit a near-constant time delay in the passbands. Such multi-channel bandpass filters should be highly attractive to WDM applications as they are operating in transmission regime and offering near-zero dispersion.

Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

Design of few-mode fibers with up to 12 modes and low differential mode delay

In this paper, we investigate the design of few-mode fibers (FMFs) guiding 4 to 12 non-degenerate linearly polarized (LP) modes with low differential mode delay (DMD) over the C-band, suitable for long-haul transmission. The refractive index profile considered is composed by a graded-core with a cladding trench (GCCT). The optimization of the profile parameters aims the lowest possible DMD and macro-bend losses (MBL) lower than the ITU-T standard recommendation. The optimization results show that the optimum DMD and the MBL scale with the number of modes. Additionally, it is shown that the refractive-index relative difference at the core center is one of the most preponderant parameters, allowing to reduce the DMD at the expense of increasing MBL. Finally, the optimum DMD obtained for 12 LP modes is lower than 3 ps/km. © 2014 IEEE.

Design of few-mode fibers with M-modes and low differential mode delay

In this paper, we investigate the design of few-mode fibers (FMFs) guiding 2 to 12 linearly polarized (LP) modes with low differential mode delay (DMD) over the C-band, suitable for long-haul transmission. Two different types of refractive index profile have been considered: a graded-core with a cladding trench (GCCT) profile and a multi-step-index (MSI) profile. The profiles parameters are optimized in order to achieve: the lowest possible DMD and macro-bend losses (MBL) lower than the ITU-T standard recommendation. The optimization results show that the MSI profiles present lower DMD than the minimum achieved with a GCCT profile. Moreover, it is shown that the optimum DMD and the MBL scale with the number of modes for both profiles. The optimum DMD obtained for 12 LP modes is lower than 3 ps/km using a GCCT profile and lower than 2.5 ps/km using a MSI profile. The optimization results reveal that the most preponderant parameter of the GCCT profile is the refractive index relative difference at the core center, Δnco. Reducing Δn co, the DMD is reduced at the expense of increasing the MBL. Regarding the MSI profiles, it is shown that 64 steps are required to obtain a DMD improvement considering 12 LP modes. Finally, the impact of the fabrication margins on the optimum DMD is analyzed. The probability of having a manufactured FMF with 12 LP modes and DMD lower than 12 ps/km is approximately 68% using a GCCT profile and 16% using a MSI profile. © 2013 IEEE.

Design of few-mode fibers with arbitrary and flattened differential mode delay

This letter proposes the use of a refractive index profile with a graded core and a cladding trench for the design of few-mode fibers, aiming an arbitrary differential mode delay (DMD) flattened over the C+ L band. By optimizing the core grading exponent and the dimensioning of the trench, a deviation lower than 0.01 ps/km from a target DMD is observed over the investigated wavelength range. Additionally, it is found that the dimensioning of the trench is almost independent of the target DMD, thereby enabling the use of a simple design rule that guarantees a maximum DMD deviation of 1.8 ps/km for a DMD target between-200 and 200 ps/km. © 2012 IEEE.

Phase noise influence in long-range coherent optical OFDM systems with delay detection, IFFT multiplexing and FFT demodulation

We present a study of the influence of dispersion induced phase noise for CO-OFDM systems using FFT multiplexing/IFFT demultiplexing techniques (software based). The software based system provides a method for a rigorous evaluation of the phase noise variance caused by Common Phase Error (CPE) and Inter-Carrier Interference (ICI) including - for the first time to our knowledge - in explicit form the effect of equalization enhanced phase noise (EEPN). This, in turns, leads to an analytic BER specification. Numerical results focus on a CO-OFDM system with 10-25 GS/s QPSK channel modulation. A worst case constellation configuration is identified for the phase noise influence and the resulting BER is compared to the BER of a conventional single channel QPSK system with the same capacity as the CO-OFDM implementation. Results are evaluated as a function of transmission distance. For both types of systems, the phase noise variance increases significantly with increasing transmission distance. For a total capacity of 400 (1000) Gbit/s, the transmission distance to have the BER < 10-2 for the worst case CO-OFDM design is less than 800 and 460 km, respectively, whereas for a single channel QPSK system it is less than 1400 and 560 km.

Existence Results for Fractional Functional Differential Inclusions with Infinite Delay and Applications to Control Theory

Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05

Stabilization of standing waves through time-delay feedback

Standing waves are studied as solutions of a complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms. The onset is described as an instability of the uniform oscillations with respect to spatially periodic perturbations. The solution of the standing wave pattern is given analytically and studied through simulations. © 2013 American Physical Society.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Oscillation Criteria for First Order Delay Differential Equations

2000 Mathematics Subject Classification: 34K15.

Management of slow light dispersion and delay time characteristics with SNAP bottle resonators

The nanoscale radius variation of a bottle microresonator with the required dispersion characteristics is determined theoretically. Experimentally, a microresonator with the footprint 0.08 mm2 exhibiting 20 ns/nm dispersion compensation of 100 ps pulses is demonstrated. © 2014 OSA.

Record small and low loss slow light delay lines and dispersion compensators

Record small and low loss slow light optical signal processing devices are proposed and demonstrated using the recently invented Surface Nanoscale Axial Photonics (SNAP) technology.

Comments on multiple oscillatory solutions in systems with time-delay feedback

A complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms is considered. In particular, multiple oscillatory solutions and their properties are studied. We present novel results regarding the disappearance of limit cycle solutions, derive analytical criteria for frequency degeneration, amplitude degeneration, frequency extrema. Furthermore, we discuss the influence of the phase shift parameter and show analytically that the stabilization of the steady state and the decay of all oscillations (amplitude death) cannot happen for global feedback only. Finally, we explain the onset of traveling wave patterns close to the regime of amplitude death.

Oscillation of Nonlinear Neutral Delay Differential Equations

2000 Mathematics Subject Classification: 34K15, 34C10.

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.