Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform.

This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression.

Parametric Signal Estimation Using the Cumulative Distribution Transform.

We present a new method for estimating signal model parameters using the Cumulative Distribution Transform (CDT). Our approach minimizes the Wasserstein distance between measured and model signals. We derive some useful properties of the CDT and show that the resulting estimation problem, while nonlinear in the original signal domain, becomes a linear least squares problem in the transform domain.

Calculation of the impulse response and phase noise of a high-current photodetector using the drift-diffusion equations.

We describe a procedure to calculate the impulse response and phase noise of high-current photodetectors using the drift-diffusion equations while avoiding computationally expensive Monte Carlo simulations. We apply this procedure to a modified uni-traveling-carrier (MUTC) photodetector. In our approach, we first use the full drift-diffusion equations to calculate the steady-state photodetector parameters.

Frequency dependent harmonic powers in a modified uni-traveling carrier photodetector.

We use a drift-diffusion model to study frequency dependent harmonic powers in a modified uni-traveling carrier (MUTC) phododetector. The model includes external loading, incomplete ionization, the Franz-Keldysh effect, and history-dependent impact ionization. In three-tone measurements, the bias voltage at which a null occurs (bias null) in the second-order intermodulation distortion (IMD2) is different for the sum frequency and difference frequency.

Impact of the Coulomb interaction on the Franz-Keldysh effect in high-current photodetectors.

The Franz-Keldysh effect has been recognized as the largest contributor to oscillations in the responsivity of high-current photodetectors as a function of the applied bias or the incident light wavelength and to device nonlinearity. Prior work only considered the effect of the electric field without considering the Coulomb interaction. We show that it is not possible to obtain agreement with experiments at all optical wavelengths without including this effect in the effective mass equation.

Power photodiodes for high dynamic range photonic links.

High-power photodiode applications for multioctave high dynamic range links are presented. A review of modulator and photodiode distortion analysis is given as well as an introduction to polarization-dependent loss distortion as it pertains to such systems. A new analysis of the photodiode distortion contributed degradation of spurious free dynamic range (SFDR) is developed.

Simulation of a partially depleted absorber (PDA) photodetector.

We use a 2D drift-diffusion model to study the nonlinear response of a partially depleted absorber (PDA) phododetector. The model includes external loading, incomplete ionization, the Franz-Keldysh effect, and history-dependent impact ionization. It also takes into account heat flow in the device.

Procedure for aligning polarization modulator link for amplitude modulation applications.

A procedure is detailed for aligning the transmitted output states of a polarization modulated signal to the analyzer states of a polarizing discriminator in an analog photonic link. The steps in the procedure insure optimal amplitude modulation in the link. Experimental results are presented for biasing in two ways: either the DC bias on the modulator or a rotatable half-wave plate can be used.

Analysis of magnitude and relative phase of photodiode IMD2 using amplitude matched MZM-distortion cancellation technique.

We present a detailed look at using Mach-Zehnder modulator generated distortion for identifying the magnitude and relative sign of photodiode generated second order intermodulation distortion (IMD2). Previous discussions introduced the concept for characterizing a test device. Analysis is expanded to IMD2 as a function of voltage, photocurrent and frequency.

Suppression of even-order photodiode distortions via predistortion linearization with a bias-shifted Mach-Zehnder modulator.

A new technique to cancel photodiode-induced even-order distortion in microwave photonic links is demonstrated. A single Mach-Zehnder modulator, biased slightly away from the quadrature point, is shown to suppress photodiode second-order intermodulation distortion in excess of 40 dB without affecting the fundamental power. The technique is theoretically described with supporting experimental results.