Optical Kerr effect field measurements and ad hoc engineering model comparisons.

Optical Kerr effects induced by the propagation of high peak-power laser beams through real atmospheres have been a topic of interest to the nonlinear optics community for several decades. This paper proposes a new analytical model for predicting the filamentation/light channel onset distance in real atmospheres based on modulation instability model considerations. The normalized intensity increases exponentially as the beam propagates through the medium. It is hypothesized that this growth can be modeled as a weighted ratio of the Gaussian beam diameter at range to the lateral coherence radius and can be used to set the power ratio for an absorbing, turbulent, nonlinear media to estimate the beam collapse distance. Comparison of onset distance predictions with those found from computer simulation and deduced from field experiments will be presented. In addition, this model will be used with an analytical approach to quantify the expected radius of light channels resulting from self-focusing both with and without the production of a plasma filament. Finally, this paper will describe a set of 1.5-micron, variable focal length USPL field experiments. Comparisons of theoretical radius calculations to measurements from field experiments will be presented.

Engineering equations for the filamentation collapse distance in lossy, turbulent, nonlinear media.

The propagation of high peak-power laser beams in real atmospheres has been an active research area for a couple of decades. Atmospheric turbulence and loss will induce decreases in the filamentation self-focusing collapse distance as the refractive index structure parameter and volume extinction coefficient, respectively, increase. This paper provides a validated analytical method for predicting the filamentation onset distance in lossy, turbulent, nonlinear media. It is based on a modification of Petrishchev's and Marburger theories. It postulates that the ratio of the peak power to critical power at range in turbulence is modified by a multiplicative, rather than additive, gain factor. Specifically, this new approach modifies the Petrishchev's turbulence equation to create the required multiplicative factor. This is necessary to create the shortened filamentation onset distance that occurs when a laser beam propagates through the cited nonlinear medium. This equation then is used with the Marburger distance and the Karr et al loss equations to yield the filamentation onset distance estimate in lossy, turbulent, nonlinear environment. Theory validation is done against two independent sets of computer simulation results. One comes from the NRL's HELCAP software and the other from MZA's Wave Train modeling software package. This paper also shows that once the zero-turbulence onset distance is set based on link loss, the addition of turbulence creates essentially the same PDFs at similar median distances for each loss case. This result had not been previously reported. This is the first quantitative comparison between closed form equations and computer simulation results characterizing filament generation in a lossy, turbulent, nonlinear medium.

Engineering equation for filamentation self-focusing collapse distance in atmospheric turbulence.

The propagation of high peak-power laser beams in real atmospheres will be affected by both linear and nonlinear effects contained therein. Atmospheric turbulence usually will induce decreases in the filamentation self-focusing collapse distance for refractive index structure parameter increases. This paper provided the first validated analytical equation for predicting the nonlinear self-focusing collapse distance based on a modification of Petrishchev's and Marburger's theories. It shows that the estimate of the peak power to critical power at range in turbulence is modified to be the product of the transmitted peak power to critical power ratio times a multiplicative factor derived from Petrishchev's turbulence equations. This estimate is used in the Marburger distance equation to yield a predicted self-focusing collapse distance. This approach was compared to previous NRL's HELCAP computer simulation results and showed good agreement. The HELCAP simulations capability has shown good agreement between its results and a previously published laboratory-scale experiment. The analytical approach in this paper may provide a guide for further numerical simulations, more formal theoretical developments and field experiments.

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. We obtained agreement with the experimental results. The bias null that appears in the IMD2 is due to the Franz-Keldysh effect. The bias voltage at which the bias null is located depends on the electric field in the intrinsic region, and the difference in the location of the bias null for the sum frequency and difference frequency is due to the displacement current in the intrinsic region. When the frequency is large, the displacement current is large and has a large effect on the harmonic powers. We also found that the bias null depends on the recombination rate in the p-absorption region because the electric field decreases in the intrinsic region when the recombination rate in the p-region decreases.

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. We find the maxima and minima in the absorption of the applied electric field shift when the Coulomb interaction is included. We then use the calculated absorption with the drift-diffusion equations to calculate the responsivity in a partially depleted absorber (PDA) photodetector, and we obtain excellent agreement with experiments at all biases and optical wavelengths.

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. Experimental data covers high-power photodiodes for zero-bias high dynamic range links, showing significant improvement in SFDR. A link is presented showing the degradation of link performance when polarization-dependent loss is added into the system. A summary of state-of-the-art device performance is covered as well as the outlook on future applications for power photodiodes in analog photonic links requiring high SFDR.

Microwave photonic delay line signal processing.

This paper provides a path for the design of state-of-the-art fiber-optic delay lines for signal processing. The theoretical forms for various radio-frequency system performance metrics are derived for four modulation types: X- and Z-cut Mach-Zehnder modulators, a phase modulator with asymmetric Mach-Zehnder interferometer, and a polarization modulator with control waveplate and polarizing beam splitter. Each modulation type is considered to cover the current and future needs for ideal system designs. System gain, compression point, and third-order output intercept point are derived from the transfer matrices for each modulation type. A discussion of optical amplifier placement and fiber-effect mitigation is offered. The paper concludes by detailing two high-performance delay lines, built for unique applications, that exhibit performance levels an order of magnitude better than commercial delay lines. This paper should serve as a guide to maximizing the performance of future systems and offer a look into current and future research being done to further improve photonics technologies.

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. With all these effects included, we obtain excellent agreement with experiments for the responsivity and for the harmonic power at different modulation frequencies. The role of these different physical effects is elucidated, and we find that both the Franz-Keldysh effect and the load resistance play a key role in generating higher harmonic power at larger reverse biases. Increasing the size of the p-region absorption layers reduces the impact of the Franz-Keldysh effect. Decreasing the effective load resistance also decreases the higher harmonic powers. We also show that the model can suggest design changes that will improve device performance.

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. The corresponding theory is included.

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.

Bias-dependent distortion in optical comb-based analog optical links.

We provide the first experimental demonstration of the impact of bias-frequency on second-order distortion in sampled analog optical links. We show proper selection of bias frequency yields >48 dB improvement in second-order distortion performance. In addition, we demonstrate that measurement of the average frequency of the optical comb may be used to determine the optimum bias frequency - without the need for involved radio-frequency distortion measurements.

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.

Cancellation of photodiode-induced second harmonic distortion using single side band modulation from a dual parallel Mach-Zehnder.

We have theoretically and experimentally investigated using a dual parallel Mach-Zehnder modulator (DP-MZM) in an RF photonic link to cancel the second harmonic distortion due to the photodiode. Biasing the DP-MZM for single sideband modulation, the second harmonic generated by the DP-MZM can be set out of phase with the second harmonic generated at the photodiode. We measure the output intercept point of the second harmonic distortion of the link to be 55.3 dBm, which is an improvement of over 32 dB as compared to only the photodiode.

Demonstration of a mode-conversion cavity add-drop filter.

We experimentally demonstrate a new type of add-drop filter incorporating an asymmetric Y-branch waveguide coupler and a shifted-grating mode-conversion cavity. The device relies on mode separation in the asymmetric Y-branch and wavelength-selective mode conversion upon reflection from the shifted-grating cavity. Add-drop functionality is demonstrated in a three-port integrated silicon-on-insulator device.

Even-order harmonic cancellation for off-quadrature biased Mach-Zehnder modulator with improved RF metrics using dual wavelength inputs and dual outputs.

We present a technique using a dual-output Mach-Zehnder modulator (MZM) with two wavelength inputs, one operating at low-bias and the other operating at high-bias, in order to cancel unwanted even-order harmonics in analog optical links. By using a dual-output MZM, this technique allows for two suppressed optical carriers to be transmitted to the receiver. Combined with optical amplification and balanced differential detection, the RF power of the fundamental is increased by 2 dB while the even-order harmonic is reduced by 47 dB, simultaneously. The RF noise figure and third-order spurious-free dynamic range (SFDR(3)) are improved by 5.4 dB and 3.6 dB, respectively. Using a wavelength sensitive, low V(pi) MZM allows the two wavelengths to be within 5.5 nm of each other for a frequency band from 10 MHz to 100 MHz and 10 nm for 1 GHz.