Measurement of phase and amplitude error distributionsin InP-based arrayed-waveguidegrating multi/demultiplexers

The crosstalk performance of an arrayed-waveguide grating (AWG) multiplexer or demultiplexer is primarily caused by random optical phase errors introduced in the arrayed waveguides. Because the layout of waveguides on a wafer is patterned via photomask through the photolithography process, the resolution of a photomask has a direct influence on the phase errors of an AWG. The paper presents a theoretical analysis on the phase error caused by photomask resolution and other basic design parameters. Both calculation and measurement results show that a high-resolution photomask (better than 25 nm) is a critical requirement to produce low-crosstalk (less than -30 dB) AWG demultiplexers. We also investigate the effect of nonideal power distribution in the arrayed waveguides because it contributes considerable phase errors when material impurity is not well controlled during wafer fabrication. Basic criteria of power profile truncation, number of grating waveguides, and material index variation are also summarized.

A statistical model is proposed for estimating the chromatic dispersion in the passband of a filter using an arrayed waveguide grating (AWG) with random phase errors. The model is derived without assuming the independence of random errors and can be applied to AWGs with frequency-dependent array amplitude coefficients as well as conventional AWGs. The average and variance of the chromatic dispersion in the passband can be calculated by using simple expressions without random computation once the standard deviation and correlation of random phase errors are given. The behavior of the chromatic dispersion in a synchronized-router-based flat-passband filter consisting of a multiple-input AWG and cascaded Mach-Zehnder interferometers (MZIs) was investigated. The standard deviation of the chromatic dispersion monotonically increases with the standard deviation of random phase errors, and has a distinctive dependence on frequency. The average and standard deviation of the chromatic dispersion in the passband obtained by the model are in good agreement with those obtained by random simulation for both a synchronized-router-based flat-passband filter and conventional AWGs.

Low sidelobe levels may be a crucial factor in the success of achieving high gain using linear receiving arrays, since the level of the sidelobes determines the degree to which noisy nearby sources can be prohibited from interfering with the detection of a weak source on a different azimuth. In real world experiments at sea, one frequently operates with an array which has not only errors in amplitude and phase between channels but also dead elements. The effect of random errors in both amplitude and phase is to yield a sidelobe level of the average beam pattern which is the sum of the error-free pattern and an additional level due to the random errors. The sidelobe level due to the random errors depends upon the details of the amplitude shading function, the distribution function from which the random errors are drawn, and increases with the mean square value of the errors. Thus, given rms values of amplitude and phase errors, there is a practical limit to which the sidelobes can be reduced by amplitude shading the array. The effect of element failure on the sidelobe level can be drastic and depends on the sum of the amplitude weights of the dead elements. Thus, a failure of a highly-weighted element will have a greater effect on the sidelobe level than the failure of two or three whose combined weights are less. [Work supported by NAVMAT.]

This paper studies the influence of random phase and amplitude fabrication errors on the performance of optical filters based on fiber Bragg gratings (FBG's). In particular, we analyze two effects of particular importance for optical communications: the excess crosstalk induced in apodized gratings commonly used in wavelength-division-multiplexing (WDM) systems, and the time-delay fluctuations that appear in chirped gratings employed to compensate the fiber dispersion. A statistical model is presented to explain these effects in terms of the coherence length of the grating fabrication procedure.

A silicon arrayed‐waveguide grating (AWG) with 1.6‐nm channel spacing is proposed and realized with high performances for dense wavelength‐division (de)multiplexing systems. For the present AWG, the arrayed waveguides are broadened uniformly to be far beyond the singlemode regime, so that random phase errors and propagation loss are minimized even without any additional requirement for the fabrication process. Particularly, Euler‐bends are introduced for the arrayed waveguides to shrink the device footprint and suppress any excitation of higher‐order modes. As an example, a 16 × 16 AWG (de)multiplexer is realized with a compact footprint of 600 × 800 µm2 by using single‐etched 220‐nm‐thick silicon photonic waveguides. When using the fabricated AWG to demultiplex the channels launched from the central input port, the excess loss and the adjacent‐channel crosstalk of the central output port are ≈2.2 and ≈−31.7 dB, respectively. Such an AWG is one of the best among silicon implementations.

A mathematical analysis is made of two synchronizing systems which might be used in "dot" color television to synchronize the dotting or sampling frequency in the receiver. Synchronizing information is transmitted in bursts of carrier cohered in phase of approximately 3 Mc during line fly-back time. The two systems analyzed are (1) a simple high-Q resonant filter and (2) an oscillator with automatic frequency control (afc). In order to maintain sufficient phase accuracy in the sampling frequency, crystal control at the transmitter is necessary. Since the variations of the frequency response of a particular crystal filter with time may be made essentially negligible, the problem resolves itself into calculating the parameters of the synchronizing system to keep below an acceptable value the random phase error due to noise together with the phase error caused by variations in frequency (static phase error) from crystal to crystal. Rather than attempt to minimize the sum of the random and static phase errors, the two have been dealt with separately because of their different character. A fundamental parameter in the calculations is the power carrier-to-noise ratio in the intermediate frequency, the carrier being measured at the sync tips. Calculations are made for values of this ratio of 1, 3, 5, this being considered the critical range. Results of the calculation show that when the phase error due to noise alone is fixed, the simple resonant filter and the afc with single time constant suffer the same static phase error.

Statistical properties of phase-shift algorithms are investigated for the case of additive Gaussian intensity noise. Based on a bivariate normal distribution, a generally valid probability-density function for the random phase error is derived. This new description of the random phase error shows properties that cannot be obtained through Gaussian error propagation. The assumption of a normally distributed phase error is compared with the derived probability-density function. For small signal-to-noise ratios the assumption of a normally distributed phase error is not valid. Additionally, it is shown that some advanced systematic-error-compensating algorithms have a disadvantageous effect on the random phase error.

PHASARs or Arrayed Waveguide Grating (AWG) multiplexers for application in Dense Wavelength Division Multiplexing optical networks have been realized using silica-waveguide technology. Using waveguide tapers, a flat-top passband characteristic is obtained. Using Fourier transform spectroscopy employing a low coherence interferometer, the power-distribution coefficients and the phase error distribution in such components is evaluated. Because of the coherence length of the used light source being smaller than the optical path length difference in the PHASAR, it is possible to resolve individual waveguides of the array. Thus, the transfer functions of the individual optical paths are accessible to the measurement, enabling the full simulation of the PHASAR transmission spectrum. It is demonstrated that the measured phase error distribution in tapered PHASAR devices consists of contributions from both tapered waveguides and arrayed waveguide grating regions. An evaluation method suitable for investigating both contributions separately is developed. Phase shift introduced by the waveguide tapers is in good agreement with simulation calculations based on the Beam Propagation Method. An analytic transmission calculation based on measured phase and power-distribution coefficients enables a full simulation of PHASARs including insertion loss, bandwidth and crosstalk performance. Excellent agreement with transmission measurements is performed.

The amplitude and phase errors deteriorate the low-sidelobe level characteristic of phased array antenna, which degrades radar performance seriously. Therefore an improved calibration method of amplitude and phase errors based on diagonal loading is proposed to address the problem of amplitude and phase errors in this paper. Initially, the mathematical models of amplitude and phase errors are developed and the impact of amplitude and phase errors is analyzed. It is found that although the interference can be suppressed when there is amplitude and phase errors in the array, the low-sidelobe level characteristic of adaptive antenna is badly deteriorated. An improved calibration method of amplitude and phase errors based on diagonal loading is proposed. Compared with traditional calibration method, proposed method can reduce the sidelobe level efficiently. At last simulations were carried out to verify the effectiveness of proposed method.

Joint sonar-communication (SonarCom) systems offer interesting and promising perspectives for target detection in military or civilian applications. Compared to the traditional sonar systems, orthogonal frequency division multiplexing (OFDM) SonarCom system suffers from frequency offset. The fluctuation due to array uncertainty and acoustic propagation characteristics lead to random phase errors, which heavily impair the estimation accuracy. To deal with this drawback, we present a compressed sensing-based range-angle estimation algorithm when phase errors are present for OFDM SonarCom systems. In order to overcome multitarget interference, cyclic prefix (CP)-based OFDM technique is applied. Exploiting the structure of the CP-OFDM signal model, the redundant dictionary and minimization problem are defined. The coupling information of sparse data are considered as a global metric to minimize the effect of phase errors and recover super-resolution range-angle estimation. Regardless the presence of random phase errors and strong noise, the approach returns high-quality estimates of range and angle. Moreover, a low complexity solution algorithm is developed to improve the computational complexity and memory requirements. The performance assessment underlines that the proposed approach can be a viable means to solve the joint range and angle estimation problem.

On the quadrature accuracy of in-phase coupled quadrature LC oscillator

Optically pumped magnetometer (OPM) has gained popularity as a viable alternative to the superconducting quantum interference device (SQUID) for biomagnetic measurements. However, the presence of amplitude and phase errors in the OPM can degrade the signal quality of, e.g., magnetoencephalography (MEG) signals. This study presents a dual-PI closed-loop control (DPCC) method aimed at suppressing amplitude and phase errors of the OPM when operated in the spin-exchange relaxation-free (SERF) regime, thereby enhancing MEG localization accuracy. The main sources of the amplitude and phase errors in the OPM are identified through a theoretical analysis of the inertial element characteristics and static residual magnetic fields. The experimental results demonstrate that the utilization of DPCC for the OPM reduces the amplitude and phase errors in static MEG measurements by 94.2% and 95.6%, respectively. At a residual magnetic field of 6.5 nT, the amplitude and phase errors are further suppressed by 97.8% and 87.2%, respectively. Furthermore, the fluctuation of the residual magnetic field is reduced by a factor of 25, significantly enhancing the robustness of the OPM. This straightforward and effective arrangement of the OPM holds promise in the field of biomagnetism and is expected to enhance the localization and calibration accuracy of OPM-based MEG (OPM-MEG) systems.

We describe a method for measuring the phase error distribution of an arrayed waveguide grating (AWG) in the frequency domain when the free spectral range (FSR) of the AWG is so wide that it cannot be covered by one tunable laser source. Our method is to sweep the light frequency in the neighborhoods of two successive peaks in the AWG transmission spectrum by using two laser sources with different tuning ranges. The method was confirmed experimentally by applying it to a 160 GHz spaced AWG with a FSR of 11 THz. The variations in the derived phase error data were very small at +/-0.02 rad around the central arrayed waveguides.

We present a numerical and experimental study of the impact of phase errors on the performance of large, high-resolution arrayed waveguide gratings (AWG) for applications in astronomy. We use a scalar diffraction model to study the transmission spectrum of an AWG under random variations of the optical waveguide lengths. We simulate phase error correction by numerically trimming the lengths of the optical waveguides to the nearest integer multiple of the central wavelength. The optical length error distribution of a custom-fabricated silica AWG is measured using frequency-domain interferometry and Monte-Carlo fitting of interferogram intensities. In the end, we give an estimate for the phase-error limited size of a waveguide array manufactured using state-of-the-art technology. We show that post-processing eliminates phase errors as a performance limiting factor for astronomical spectroscopy in the H-band.

This paper deals with considerations in the design of an electronically steered IFF antenna which is to provide sidelobe suppression through the use of a difference beam with gain higher than that of the sum beam everywhere outside of the mainlobe region. The influence of the suppression requirement upon illumination design tradeoffs in beamwidth, sidelobe levels, and taper efficiency is demonstrated theoretically for an array restricted to 16 elements. The sidelobe suppression performance for this array, with appropriate choices for amplitude taper, number of phase shifter bits and randomizing phase function, is examined in detail for susceptibility to failures in elements, failures in individual phase shifter bits, and random phase and amplitude illumination errors. In the case of random errors, performance variability with steering direction is examined and a criterion involving the radiation patterns at both the transmit and receive RF frequencies is defined as a measure of performance. It is seen that the design analyzed is successful in reducing the corresponding performance degradation to very low levels in even the worst cases. Expressions are presented for estimating the effects of increasing the number of elements upon improvements in performance in the presence of component failures or random errors.