Beat Length Research Articles

Polarization-dependent gain and gain fluctuations in a fiber Raman amplifier

We report a new vector model of a fiber Raman amplifier with a randomly varying birefringence. We find that the analysis of gain fluctuations and polarization-dependent gain can be used for measurements of beat and birefringence correlation lengths and the polarization mode dispersion value on a long single-mode fiber. Results are consistent with a standard technique based on differential group delay measurements.

Ultrahigh birefringence of elliptic core fibers with irregular air holes

We have investigated experimentally and theoretically the birefringence of the elliptic core fiber with irregular air holes. The wavelength dependence of the beat length and the birefringence was measured by the wavelength scanning method. The fiber exhibits ultrahigh birefringence of 1.12×10−2 at 1550 nm. We also calculated the modal birefringence of the fundamental modes in the fiber by using the plane wave expansion method. The calculated birefringence is in excellent agreement with the measured one.

Determination of the wavelength dependence of the coupling effect in twin-core microstructured polymer optical fibers

A simple and straightforward method is applied to experimentally obtain the wavelength dependence of the intercore beat length for two different types of twin-core microstructured polymer optical fiber. The results are compared with numerical calculations using a full-vectorial plane-wave expansion method, which shows good agreement.

Compact multimode interference coupler with tapered waveguide geometry

In this paper, a novel MMI coupler, based on general interference, with tapered waveguide geometry has been proposed for reduction of coupling length. The coupling characteristics and power imbalance of the proposed structure are compared with conventional MMI structures by using a mathematical model based on sinusoidal modes. It is seen that the beat length for tapered MMI coupler with angle of taper ∼1.05° is reduced by ∼24% of that of conventional MMI coupler and the coupling characteristics obtained with the mathematical model, match well with those obtained by more sophisticated BPM computer aided design software. The power imbalance for tapered 3 dB MMI coupler is more sensitive to the wavelength than that for conventional 3 dB MMI coupler and variation of power imbalance with fabrication tolerance for both the MMI coupler is almost same.

Reducing polarization mode dispersion with controlled polarization rotations

One of the fundamental limitations to high bit rate, long distance telecommunication in optical fibres is polarization mode dispersion (PMD). Here we introduce a conceptually new method to reduce PMD in optical fibres by carrying out controlled rotations of polarization at predetermined locations along the fibre. The distance between these controlled polarization rotations must be less than both the beat length and the correlation length of the birefringence of the fibre. This method can also be combined with the method in which the fibre is spun while it is drawn.

A novel 1 × 2 multimode interference optical wavelength filter based on photodefinable benzocyclobutene (BCB 4024–40) polymer

AbstractA novel 1 × 2 multimode interference (MMI) optical wavelength filter for 1310 and 1550 nm operation based on photodefinable BenzoCyclobutene (BCB 4024–40) polymer is demonstrated. The device is fabricated on BK7 glass substrate with thin layer of SiO2 as cover. A cost effective chemical etching technique is used in the fabrication process to take advantage of the photosensitive nature of the polymer. The filter length is significantly reduced by adopting the restricted MMI scheme, lower beat length ratio, and cascaded MMI couplers. At 1550 nm filtering operation, the measured crosstalk is −20.6 dB and at 1310 nm filtering is −14.4 dB. The measured insertion loss is around 3.2–3.5 dB for both ports. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1024–1028, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22327

2 Assessing ventricular function in patients with atrial fibrillation

The Frank-Starling law states that the stroke volume of a regular cardiac beat increases in response to an increase in the volume of blood filling the heart. If this law applies in atrial fibrillation (AF) as well as in sinus rhythm (SR) then cardiac function will depend on the duration of diastole in the preceding beat as well as the duration of the indexed beat. Aim: The aim of this thesis was to develop a series of tools which would allow an assessment of the changes in cardiac function from one beat to the next in AF and SR. A secondary aim was to find a means of describing rhythm in a way that reflected possible functional change. Methods: List-mode radionuclide ventriculography, RNVG, acquisitions of 373 patients in AF and a comparative group of 385 patients in SR were made. Software was written which allowed tightly defined preceding and indexed beat selection criteria to be established. Left ventricular ejection fraction (LVEF) and other functional parameters (pre-systolic volume, systolic time, the ratio of pre-systolic to end-diastolic volume, peak filling rate and first third filling fraction) were calculated for images created using different beat selection criteria based on the quartiles of beat length. Assessment used both variable and fixed time formatting and included a comparison of results achieved in the first and second half of the scan. Traditional linear measures of heart rate variability together with descriptors of the Poincar´e plot and cycle length entropy were used to describe rhythm in both AF and SR patients. Results: Substantial variation with indexed and preceding beat length was seen in both SR and AF in all the systolic parameters measured and in particular in LVEF where the standard deviation of LVEF for any one patient was found to be 8.2% in SR and 14.1% in AF. A combination of descriptors of rhythm was found to have good correlation with the range of LVEF measured. Examination of the results for LVEF in several clinical sub-groups suggests that the range of LVEF may have clinical interest. The techniques were applied in a small clinical study which considered the value of radio-frequency ablation in patients with AF and heart failure. In this study, measures of Sample entropy and the range of LVEF appeared to have prognostic value. Conclusion: A tool which allows the investigation of beat-to-beat functional variation in RNVG has been produced. It has been shown that the functional variation depending on beat selection criteria is substantial and may have clinical significance both in patients with underlying pathology and prognostically in patients undergoing radiofrequency ablation (RFA).

Analysis of a gained nonlinear directional coupler pulse switch

We have investigated the switching performance of a gained (nonlinear directional coupler) NLDC switch in the presence of both 2nd and 4th order gain nonlinearities. In this system, we have achieved a nearly complete pulse switching at half beat length of the coupler which implies about 40% reduction in the switching length as compared to the switching length reported in Trillo et al. (1988). We have shown that at the half beat length the output energy of each branch is equal to that of the input energy and hence the gained NLDC switches have ability to be cascaded. Our initial investigations reveal that this gained NLDC switch has remarkable performance and potential to be used in ultra-fast optical communication systems.

Multimode interference wavelength multi/demultiplexer for 1310 and 1550 nm operation based on BCB 4024-40 photodefinable polymer

A 1310 and 1550 nm coarse wavelength multi/demultiplexer based on benzocyclobutene (BCB 4024-40) polymer is demonstrated for the first time. The device is designed based on a combination of general interference and paired interference mechanisms of multimode interference (MMI). It is fabricated on BK7 glass substrate with a thin layer of SiO 2 as cover. A cost effective chemical etching technique is used in the fabrication process to take advantage of the photosensitive nature of the polymer. The device length was significantly reduced by adopting the restricted multimode interference scheme, lower beat length ratio and cascaded MMI couplers. The measured crosstalk at 1310 nm was 14.4 dB and at 1550 nm was 20.6 dB. The measured insertion loss is around 3.2–3.5 dB for both ports.

Tunable acoustic gratings in solid-core photonic bandgap fiber

We investigate acousto-optic long period grating resonances in a fluid-filled solid-core photonic bandgap fiber (PBGF). The acoustic grating design enables electrically tunable notches in each of the PBGF transmission bands, where both the center frequency and depth of the resonances can be varied. The measured intermodal beat length and resonance bandwidth are in good agreement with numerical simulations based on multipole method. We show that the highly dispersive nature of PBGF modes results in very narrow-band rejection for a given grating pitch.

Characterization of Polarization-Maintaining Fiber Using High-Sensitivity Optical-Frequency-Domain Reflectometry

Optical-frequency-domain reflectometry is used to measure the group-index difference and the refractive-index difference (i.e., beat length) between the fast and slow modes in polarization-maintaining optical fiber. The Rayleigh scatter normally present in the fiber is measured in reflection. This measurement, in turn, enables a distributed measurement of the fiber's birefringence that is rapid and completely nondestructive

High dynamic polarization-OTDR for the PMD mapping in optical fiber links

We describe a new algorithm based on the level-crossing rate analysis of the POTDR trace which enables the distributed measurement of the beat length, the coupling length and the PMD in long optical fiber links. This analysis allows using 500ns pulses which significantly improves the measurement dynamic compared to classical POTDR.

Leakage loss and phase variation of a buried directional coupler on a silicon substrate

Effects of the presence of a silicon substrate on the leakage loss and phase variation of silica-based parallel waveguides are investigated using the imaginary-distance beam-propagation method. The leakage loss is evaluated as a function of the distance between the core and the substrate. Calculation shows that the loss of the directional coupler can be estimated using the single waveguide with the same cross section. It is also found that the beat length becomes longer than that without the substrate except the case where the core is extremely close to the substrate. In terms of the loss reduction, the insertion of a SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> film with a 1-μm thickness corresponds to an increase in the distance between the core and the substrate without the SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> film by about 2 μm.

Design and Fabrication of Multi-Mode Interference Hollow Waveguide Optical Switch with Variable Air Core

We present the design and fabrication of a novel hollow waveguide optical switch composed of a multi-mode interference (MMI) coupler with a variable air core. The numerical simulation and measurement of the proposed optical switch is carried out for investigating switch performances. Switching operation can be obtained by mechanical displacement of the air core of an MMI hollow waveguide. The switching operation is based on the variation of the mode-field associated with the mechanical displacement. Our modeling shows a possibility of a compact optical switch with a sub-mm switching length. We fabricated an MMI hollow waveguide optical switch consisting of Au mirrors deposited on two GaAs substrates. One of the substrates is mechanically moved, resulting in the change of the beat length of the MMI waveguide. We observed optical switching of about 85% optical power fraction with a switch length of 1.1 mm and small displacement of an air core thickness.

Short-crested waves in deep water: a numerical investigation of recent laboratory experiments

A numerical study of quasi-steady doubly periodic monochromatic short-crested wave patterns in deep water is conducted using a high-order Boussinesq-type model. Simulations using linear wavemaker conditions in the nonlinear model are initially used to approximate conditions from recent laboratory experiments. The computed patterns share many features with those observed in wavetanks, including bending (both frontwards and backwards) of the wave crests, dipping at the crest centrelines, and a pronounced long modulation in the direction of propagation. A new and simple explanation for these features is provided, involving the release of spurious free first harmonics, due to the neglect of steady third-order components in the three-dimensional wave generation. A comparison with the experimentally observed beat length and amplitude matches the theoretical/numerical predictions well. Additionally, direct inclusion of steady third-order components in the wave generation is shown to reduce significantly the modulations (and other unsteady features), further confirming the explanation. This numerical work makes apparent some previously unknown difficulties associated with the physical generation of even the simplest three-dimensional waves, adding significant insight into the interpretation of recent experimental observations.

Numerical and experimental analysis of the birefringence of large air fraction slightly unsymmetrical holey fibres

Careful numerical computations show that very slight geometrical imperfections of the cross-section of actual large air-fraction holey fibres (d/Λ>0.6) may induce surprisingly high birefringence, corresponding to beat lengths as short as few millimeters. The spectral variations of this birefringence obeys laws similar to those of elliptical core Hi-Bi holey fibres with low air-fraction. For all the tested fibres, the group birefringence numerically deduced from the only shape birefringence is in good agreement with the measured one that does not varies when strongly heating the fibres. These computations and measurements show that the contribution of possible inner stress to the birefringence is negligible.

Distributed measurements of fiber birefringence and diametric load using optical low-coherence reflectometry and fiber gratings

Polarization sensitive optical low-coherence reflectometry (OLCR) is used for measuring the complex fiber Bragg gratings (FBG) reflection coefficient. We determine the beat length directly from oscillations in the OLCR amplitude with a resolution of 10(-6) and a spatial resolution only limited by the minimum beat length or the coherence length of the light source. Using the OLCR amplitude and phase in combination with an inverse scattering algorithm the birefringence is retrieved with a resolution of 2x10(-5) while the spatial resolution is 25 mum. The two developed techniques are applied for measuring position, magnitude and footprint of induced birefringence of an FBG under uniform and non-uniform diametric loading.

Principles and application of reduced beat length in MMI couplers

A unified method was proposed to reduce the beat length of a multimode interference (MMI) coupler. By properly adjusting the phase difference of the N-fold images, the mode evolution is changed to generate self-images at a much shorter distance. The effect of adjusting the phase difference can be regarded as dividing the original MMI coupler into multiple sub-MMI couplers. Such an effect can be applied for both symmetric- and paired-interference cases. We applied the principle to design compact optical splitters operating at dual wavelength bands. The simulation shows that excellent performance with reduced coupler length can be obtained for splitters operating at both 1.3 and 1.55 mum bands.

Design of a compact photonic-crystal-based polarizing beam splitter

A compact polarizing beam splitter based on a photonic crystal (PC) directional coupler with a triangular lattice of air holes is designed and simulated. In the employed PC structure, transverse-electric (TE) light is confined with the photonic bandgap effect, while transverse-magnetic (TM) light is guided through an index-like effect. Due to the different guiding mechanisms, TM and TE light have strikingly different beat lengths, which is utilized to separate the two polarizations in a directional coupler no longer than 24.2 μm. The two-dimensional finite-difference time-domain method of computation is used to evaluate the device performance. The extinction ratios are found to be around 20 dB for both TE and TM polarized light.

Two-wave mixing of orthogonally polarized waves via anisotropic dynamic gratings in erbium-doped optical fiber

We report on observations of transient two-wave mixing (TWM) of orthogonally polarized waves counterpropagating through an Er-doped single-mode optical fiber. Experiments were performed in a 2-m-long moderately birefringent (with beat length approximately 2 cm) Er-doped fiber without optical pumping at the laser wavelength 1549 nm. The transient TWM signal observed for crossed linear polarizations of the recording waves oriented along two orthogonal birefringence axes of the fiber (i.e., for the interference pattern with spatially modulated state of light polarization only) proved to be approximately half of that observed for parallel polarizations. Direct measurements of the transient polarization hole-burning effect (i.e., that observed for fast switching of the input light linear polarization between two orthogonal orientations of the doped fiber birefringence axes) allow us to attribute formation of the corresponding anisotropic dynamic grating to this effect.