Second-harmonic Distortion Research Articles

Modeling of generating ultra-high frequency oscillations in VCSEL integrated with cascaded transverse coupled cavities

We report on the design and modeling of vertical-cavity surface-emitting laser (VCSEL) integrated in the lateral direction with a cascade of multiple passive cavities. The scheme is proposed to increase the bandwidth of the VCSEL in the mm-waveband to generate ultra-high-frequency oscillations with low-frequency chirp. The model treats the transverse feedback induced by the cascaded transverse coupled cavities (TTCs) as time delay of the transverse slow light due to round trips in these cavities. The simulation is based on numerical integration of the modified time-delay rate equations of the intensity and phase of the electric field. The simulation results are used to optimize the TCCs parameters, including the coupling ratio and TCC length, for generating ultra-high-frequency signals with high intensity, low chirping and low distortion. The obtained results show that the proposed structure could achieve 300% enhancement of the modulation bandwidth of the C-VCSEL due to either extended carrier-photon resonance (CPR) frequencies of photon–photon resonance (PPR). Signals with frequencies as high as (40–49 GHz) with second-harmonic distortion lower than − 30 dB are presented.

Nonlinearity in a Medical Ultrasound Probe Under High Excitation Voltage

Tissue harmonic imaging is often the preferred ultrasound imaging modality due to its ability to suppress reverberations. The method requires good control of the transmit stage of the ultrasound scanner, as harmonics in the transmitted ultrasound pulses will interfere with the harmonics generated in the tissue during nonlinear propagation, degrading image quality. In this study, a medical ultrasound probe used in tissue harmonic imaging was experimentally characterized for transmitted second-harmonic distortion to identify and compare the sources of nonlinear distortion in the probe and transmit electronics. The system was tested up to amplitudes above what is found during conventional operation, pushing the system to the limits in order to investigate the phenomenon. Under these conditions, second-harmonic levels up to -20 dB relative to the fundamental frequency were found in the ultrasound pulses transmitted from the probe. The transmit stage consists of high-voltage transmit electronics, cable, tuning inductors, and the acoustic stack. The contribution from the different stages in the ultrasound transmit chain was quantified by separating and measuring at different positions. Nonlinearities in the acoustic transducer stack were identified as the dominating source for second harmonics in the transmitted ultrasound pulses. Contribution from other components, e.g., transmit electronics and cable and tuning circuitry, were found to be negligible compared with that from the acoustic stack. Investigation of the stack's electrical impedance at different driving voltages revealed that the impedance changes significantly as a function of excitation voltage. The second-harmonic peak in the transmitted pulses can be explained by this nonlinear electrical impedance distorting the driving voltage and current.

A Column-Row-Parallel Ultrasound Imaging Architecture for 3D Plane-wave Imaging and Tx 2nd-Order Harmonic Distortion (HD2) Reduction.

We propose a Column-Row-Parallel imaging frontend architecture for integrated and low-power 3D medical ultrasound imaging. The Column-Row-Parallel architecture offers linear-scaling interconnection, acquisition and programming time with row-by-row or column-by-column operations, while supporting volumetric imaging functionality and fault-tolerance against possible transducer element defects with per-element controls. The combination of column-parallel selection logic, row-parallel selection logic, and per-element selection logic reaches a balance between flexible imaging aperture definition and manageable imaging data / control interface to a 2D array. A 16×16 CMUT-ASIC Column-Row-Parallel prototype is fabricated and assembled with a flip-chip bonding process. It facilitates the 3D plane-wave coherent compounding algorithm for volumetric imaging with a fast frame rate of 62.5 Hz and 46% improved lateral resolution with 10-angle compounding and a field of view volume of 2.3mm in both azimuth and elevation, 8.5mm in depth. At a hypothetically scaled up 64x64 array size, the frame rate can still be kept at 31.2 Hz for a volume of 40mm in both azimuth and elevation, 150mm in depth. An interleaved checker board pattern with in-phase (I) and quadrature (Q) excitations is also demonstrated for reducing CMUT second harmonic distortion (HD2) emission by up to 25 dB at the loss of 3 dB fundamental energy reduction. The method reduces nonlinear effects from both transducers and circuits and is a wide band technique that is applicable to arbitrary pulse shapes.

Broad tunable photonic microwave generation based on period-one dynamics of optical injection vertical-cavity surface-emitting lasers.

Photonic microwave generation based on period-one dynamics of an optically injected VCSEL has been study experimentally. The results have shown that the frequency of the generated microwave signal can be broadly tunable through the adjustment of the injection power and the frequency detuning. Strong optical injection power and higher frequency detuning are favorable for obtaining a high frequency microwave signal. These results are similar to those found in systems based on distributed feedback lasers and quantum dot lasers. The variation of the microwave power at the fundamental frequency and the second-harmonic distortion have also been characterized.

Method to improve the linearity of the silicon Mach-Zehnder optical modulator by doping control.

We optimize the linearity performance of silicon carrier-depletion Mach-Zehnder optical modulator through controlling the doping concentration. The optical field distribution in the waveguide is a Gaussian-like distribution. As the doping concentration increases, the dynamic depletion width of the PN junction under the same modulation signal will decrease, and the integration width of the overlap between the Gaussian-like optical field distribution and the depletion region will become smaller. Therefore the modulated signal has less nonlinear components. Our simulation results proved this analysis. We also fabricated different devices with different doping concentrations. By adopting a ten times doping concentration, the spurious free dynamic range (SFDR) for third-order intermodulation distortion (TID) increases from 109.2 dB.Hz2/3 to 113.7 dB.Hz2/3 and the SFDR for second harmonic distortion (SHD) increases from 87.6 dB.Hz1/2 to 97.5 dB.Hz1/2 at a driving frequency of 2 GHz. When the driving frequency is 20 GHz, the SFDRs for TID and SHD distortions are 110.3 dB.Hz2/3 and 96 dB.Hz1/2, respectively.

Optically injected InAs/GaAs quantum dot laser for tunable photonic microwave generation.

We present an experimental investigation on the period-one dynamics of an optically injected InAs/GaAs quantum dot laser as a photonic microwave source. It is shown that the microwave frequency of the quantum dot laser's period-one oscillation is continuously tunable through the adjustment of the frequency detuning. The microwave power is enhanced by increasing the injection strength providing that the operation is away from the Hopf bifurcation, whereas the second-harmonic distortion of the electrical signal is well reduced by increasing the detuning frequency. Both strong optical injection and high detuning frequency are favorable for obtaining a single sideband optical signal. In addition, particular period-one oscillation points of low sensitivity to the frequency detuning are found close to the Hopf bifurcation line.

Output-Impedance Shaping of Bidirectional DAB DC–DC Converter Using Double-Proportional-Integral Feedback for Near-Ripple-Free DC Bus Voltage Regulation in Renewable Energy Systems

This paper investigates the design and implementation of virtual-output-impedance shaping on an inverter-loaded, fuel-cell-battery-powered dc–dc converter system for achieving near-ripple-free dc bus voltage regulation. The method is based on the insertion of a second output-voltage feedback loop as can be inferred from the Mason's gain formula. Three basic modes of virtual-output-impedance shaping (proportional, derivative, integral) are discussed and the closed-loop output-impedance characteristics due to each of them are analyzed in detail and with their Thevenin equivalent circuits derived. Despite the suitability of integral feedback for minimizing converter's output impedance, it can give rise to an unwanted resonance peak near the converter's crossover frequency, thus potentially destabilizing the system. The solution to the problem using combination of basic virtual-output-impedance shaping modes and its practical implementation are discussed. When implemented on a fuel-cell-battery-powered dual-active-bridge dc–dc converter, the second-harmonic distortion of dc bus voltage is shown to have been reduced by 85.5% compared to a conventionally PI-compensated system.

Neighborhood induced reader bias shift in perpendicular recording

A spin-stand technique to determine the influence of the neighborhood on readback in perpendicular recording is presented. A square wave was recorded on an ac erased medium. Stray fields from neighboring tracks resulted in reader bias shift and thereby second-harmonic distortion in the spectrum of the square wave. An external perpendicular field applied to compensate the distortion provided a measure of the neighborhood effect on readback. A dc magnetized track written approximately a track width away was found to change the required compensating field by 5 Oe. Additional dc tracks further enhanced or diminished the compensating field depending on their relative magnetization direction. The immediate neighborhood was proven to have a dominating influence on the reader bias.

Digital synthetic-heterodyne interferometric demodulation

Synthetic-heterodyne demodulation is a very useful technique for signal detection in interferometric sensors. The demodulation process is usually accomplished using analogue circuits. Improved functionality can be obtained by using a digital signal processor. In this paper, an expression is derived for the sensor sensitivity where both laser phase noise and signal acquisition quantization noise are considered. The demodulation technique requires modulation of the laser frequency, usually accomplished by modulation of the laser current. An expression is derived for the second-harmonic distortion caused by the laser power modulation. The detection scheme was implemented on a digital signal processor and used to detect dynamic pressure signals with a bandwidth of 550 Hz.

A simplified surface photoreflectance measurement system

We present a simple and economical photoreflectance measurementmethodology that can easily be adapted to conventional scanning opticalmicroscopes. In this design, the laser source is sine-wave modulated so thatthe second-harmonic modulation distortion within the optical probe beam beforeand after reflection off the sample surface can be monitored. The desiredphotoreflectance measurement, which is taken as the change of reflectance as aresult of varying the incident optical power, is then obtained from the changein the ratio of the fundamental and second-harmonic signals. We demonstrateour set-up and technique by measuring the implantation damage innitrogen-implanted silicon samples.

Analog ALC crystal oscillators for high-temperature applications

Fundamental mode and third-harmonic mode integrated high-performance automatic level controlled (ALC) crystal oscillators for high-temperature applications (up to 250/spl deg/C), are described in this paper. These oscillators were designed for a pressure measurement system in high-temperature environments, where the output signal is the difference between both generated frequencies. Frequency variations smaller than 0.0001 ppm/s for each oscillator and a frequency drift of about 2.5 ppm/year of the frequency difference are the measured performance concerning, respectively, the short-term (1 s) and long-term frequency stability of these integrated high performance crystal oscillators over the 30/spl deg/C-225/spl deg/C temperature range. Other important characteristics are the very stable and constant oscillation levels (/spl sim/1.1 Vpp), the small second-harmonic distortion (/spl sim/60 dR), and the phase noise (/spl sim/95 dB at 50 kHz shift). The characteristics of these oscillators make them also suitable for many other measurement systems (time, temperature, and other physical and chemical quantities), especially if they are constrained to operate under severe temperature conditions.

Robust, accurate seven-sample phase-shifting algorithm insensitive to nonlinear phase-shift error and second-harmonic distortion: a comparative study

A new seven-sample algorithm is derived, based on the Sur- rel six-sample algorithm, by using the averaging technique. The sensitivities of phase-shifting algorithms to phase-shift error and harmonics of nonsinusoidal waveforms are analyzed by the Fourier description method. Plots of the root-mean-square phase error, produced by computer simulation, are presented in order to compare the new algorithm with the other four well-known phase-shifting algorithms. It is shown that the new algorithm is the least sensitive to linear phase-shift error and to quadratic nonlinear phase-shift error with linear compensation, when the fringe signal contains the second-harmonic distortion. A 3-D fringe projection phase-shifting profilometer was constructed using a white light source and projecting a quasisinusoidal grating with some second- harmonic distortion. Experiments were carried out to compare the five phase-shifting algorithms when different phase-shift errors exist, and the shape of a 3-D object was measured using the new seven-sample algorithm.

Improved intrinsic dynamic distortions in directly modulated semiconductor lasers by optical injection locking

The effects of optical injection locking on the nonlinear distortions of directly modulated semiconductor distributed feedback (DFB) lasers are investigated experimentally. The second harmonic distortion (SHD) and third harmonic distortion (THD), as well as the third-order intermodulation distortion (IMD3), are measured as functions of modulation frequency for both the free-running and injection-locked lasers. Under strong injection locking with -8-dB injection ratio, the SHD and THD of the DFB laser have been suppressed by 15 dB from 2 to 4 GHz. Moreover, nearly 15-dB reduction in IMD3 has been observed from 1.4 to 3.0 GHz with the same injection conditions. We also found that the injection locking is not effective in reducing the low-frequency distortions.

Second-harmonic distortion in vertical-cavity surface-emitting lasers with lateral loss effects

The influence of lateral loss effects on the second-harmonic distortion (SHD) of vertical-cavity surface-emitting lasers is investigated theoretically. Two parameters, differential confinement factor and differential cavity loss, are defined for the consideration of self-focusing and diffraction loss. It is found that SHD increases at low modulation frequencies due to the presence of differential cavity loss, especially for lasers with small core radius.

Improved Analysis for Distortion in Emitter-Driven Variable Gain Pairs

This article presents an improved analysis for the distortion in emitter-driven variable-gain pairs owing to the Early-voltage effect. The analysis shows that, by careful design, it is possible to reduce the second-order distortion components resulting from the Early-voltage effect. The analysis shows also that, under large signal conditions, the value of the normalized input amplitude at which the second-harmonic distortion is minimum is different from the value of the normalized input amplitude at which the second-order intermodulation distortion is minimum.

Experimental validation of Volterra series nonlinear modelling for microwave subcarrier optical systems

A detailed comparative experimental and theoretical study of nonlinear distortion in laser diodes is undertaken to provide practical proving of the effectiveness and utility of the Volterra series method. The observed harmonic and intermodulation distortion levels are compared with the results given by the Volterra series nonlinear laser model using intrinsic parameters extracted from reflection and small-signal frequency response measurements. Second-harmonic, two-tone and three-tone intermodulation distortion data are all found to be in good agreement with the theoretical results, providing endorsement of the Volterra series approach for the study of distortion in microwave subcarrier optical systems.

The Effect of Non-Linear MR Read-back Distortion on a PRML Channel

The effect of the nonlinear readback process of an MR head on a PRML digital magnetic recording channel was studied. Although the combination of a highly sensitive MR read head and a PRML channel is promising for high areal-density recording, nonlinearity in the MR readback process is a critical issue in the case of a channel in which linearity is assumed. We theoretically analyzed the characteristics of SHD (second harmonic distortion) as an index of the nonlinearity. Then, the effect of nonlinearity on the error rate was studied by computer simulation and in experiments. The results show that an SHD of less than -25 dB is required in order for the channel to be free of nonlinear distortion.

Volterra functional series expansions for semiconductor lasers under modulation

An analytical model based on Volterra nonlinear functionals applied to semiconductor lasers has been developed. Analytical expressions are obtained for different laser diode responses, giving powerful tools for analysis. For harmonic input, the response is given including the gain compression factor /spl epsiv/. Second-harmonic distortion (2HD) shows two maxima at half relaxation oscillation frequency /spl Omega//sub R//2 and at /spl Omega//sub R/, in agreement with experiments; the residual dc component due to nonlinearities is estimated and experimentally verified. Dynamic frequency deviation as function of bias current shows resonant characteristics. Relaxation frequency and damping rate /spl Gamma//sub R/ reveal their precise dependence on /spl epsiv/ and differential gain A. For step input, the turn-on delay t/sub on/ and the overshoot P/sub P//P/sub on/ expressions of our model are only functions of /spl Gamma//sub R/ and /spl Omega//sub R/. P/sub P//P/sub on/, and the ringing phenomena decrease with increasing bias current level. >

ＭＲヘッド非線形歪みがＰＲＭＬチャンネルに及ぼす影響

Although the combination of a highly sensitive MR read head and a PRML channel is promising for high areal density recrding, non-linear distortion in the MR read-back process is a critical issue for the channel in which linearity is known to be essential. First, we theoretically analyzed the characteristics of SHD (Second Harmonic Distortion) as a gauge of non-linearity. Next, the effect of non-linearity on error rates was studied by computer simulation and examined by experiments. Results show that SHD of less than -25 dB is required for the channel to be free from non-linear distoriton.

Performance characteristics of a 4-terminal vertical magnetoresistive/inductive head

A 4-terminal vertical magnetoresistive (MR)/inductive head using the current bias technique has been developed. In the new head, a bias current conductor is connected to the rear lead of the MR element in series. With this design, this type of MR/inductive head can have a second harmonic distortion (SHD) of less than -25 dB with a 6 to 16 mA sense current. The linear recording density at D/sub 50/ is about 3.15 kfr/mm. The effective track width of the MR sensor is almost the same as its optical track width (2.5 /spl mu/m), so high track density (TPI) is possible. The stability of an MR element with a 2 /spl mu/m track width was also investigated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>