High-coherence hybrid Si/III-V semiconductor lasers

The relentlessly increasing demand for network bandwidth, driven primarily by Internet-based services such as mobile computing, cloud storage and video-on-demand, calls for more efficient utilization of the available communication spectrum, as that afforded by the resurging DSP-powered coherent optical communications. Encoding information in the phase of the optical carrier, using multilevel phase modulationformats, and employing coherent detection at the receiver allows for enhanced spectral efficiency and thus enables increased network capacity. The distributed feedback semiconductor laser (DFB) has served as the near exclusive light source powering the fiber optic, long-haul network for over 30 years. The transition to coherent communication systems is pushing the DFB laser to the limits of its abilities. This is due to its limited temporal coherence that directly translates into the number of different phases that can be imparted to a single optical pulse and thus to the data capacity. Temporal coherence, most commonly quantified in the spectral linewidth Δν, is limited by phase noise, result of quantum-mandated spontaneous emission of photons due to random recombination of carriers in the active region of the laser.

In this work we develop a generically new type of semiconductor laser with the requisite coherence properties. We demonstrate electrically driven lasers characterized by a quantum noise-limited spectral linewidth as low as 18 kHz. This narrow linewidth is result of a fundamentally new laser design philosophy that separates the functions of photon generation and storage and is enabled by a hybrid Si/III-V integration platform. Photons generated in the active region of the III-V material are readily stored away in the low loss Si that hosts the bulk of the laser field, thereby enabling high-Q photon storage. The storage of a large number of coherent quanta acts as an optical flywheel, which by its inertia reduces the effect of the spontaneous emission-mandated phase perturbations on the laser field, while the enhanced photon lifetime effectively reduces the emission rate of incoherent quanta into the lasing mode. Narrow linewidths are obtained over a wavelength bandwidth spanning the entire optical communication C-band (1530-1575nm) at only a fraction of the input power required by conventional DFB lasers. The results presented in this thesis hold great promise for the large scale integration of lithographically tuned, high-coherence laser arrays for use in coherent communications, that will enable Tb/s-scale data capacities.

Random response of nonlinear continuous systems

This thesis presents a technique for obtaining the stochastic response of a nonlinear continuous system. First, the general method of nonstationary continuous equivalent linearization is developed. This technique allows replacement of the original nonlinear system with a time-varying linear continuous system. Next, a numerical implementation is described which allows solution of complex problems on a digital computer. In this procedure, the linear replacement system is discretized by the finite element method. Application of this method to systems satisfying the one-dimensional wave equation with two different types of constitutive nonlinearities is described. Results are discussed for nonlinear stress-strain laws of both hardening and softening types.

Part 1: Longitudinal static and dynamic effects in semiconductor lasers. Part II: Spectral characteristics of passively mode-locked quantum well lasers

In the first part of this thesis a study of the effect of the longitudinal distribution of optical intensity and electron density on the static and dynamic behavior of semiconductor lasers is performed. A static model for above threshold operation of a single mode laser, consisting of multiple active and passive sections, is developed by calculating the longitudinal optical intensity distribution and electron density distribution in a self-consistent manner. Feedback from an index and gain Bragg grating is included, as well as feedback from discrete reflections at interfaces and facets. Longitudinal spatial holeburning is analyzed by including the dependence of the gain and the refractive index on the electron density. The mechanisms of spatial holeburning in quarter wave shifted DFB lasers are analyzed. A new laser structure with a uniform optical intensity distribution is introduced and an implementation is simulated, resulting in a large reduction of the longitudinal spatial holeburning effect.

A dynamic small-signal model is then developed by including the optical intensity and electron density distribution, as well as the dependence of the grating coupling coefficients on the electron density. Expressions are derived for the intensity and frequency noise spectrum, the spontaneous emission rate into the lasing mode, the linewidth enhancement factor, and the AM and FM modulation response. Different chirp components are identified in the FM response, and a new adiabatic chirp component is discovered. This new adiabatic chirp component is caused by the nonuniform longitudinal distributions, and is found to dominate at low frequencies. Distributed feedback lasers with partial gain coupling are analyzed, and it is shown how the dependence of the grating coupling coefficients on the electron density can result in an enhancement of the differential gain with an associated enhancement in modulation bandwidth and a reduction in chirp.

In the second part, spectral characteristics of passively mode-locked two-section multiple quantum well laser coupled to an external cavity are studied. Broad-band wavelength tuning using an external grating is demonstrated for the first time in passively mode-locked semiconductor lasers. A record tuning range of 26 nm is measured, with pulse widths of typically a few picosecond and time-bandwidth products of more than 10 times the transform limit. It is then demonstrated that these large time-bandwidth products are due to a strong linear upchirp, by performing pulse compression by a factor of 15 to a record pulse widths as low 320 fs.

A model for pulse propagation through a saturable medium with self-phase-modulation, due to the a-parameter, is developed for quantum well material, including the frequency dependence of the gain medium. This model is used to simulate two-section devices coupled to an external cavity. When no self-phase-modulation is present, it is found that the pulses are asymmetric with a sharper rising edge, that the pulse tails have an exponential behavior, and that the transform limit is 0.3. Inclusion of self-phase-modulation results in a linear upchirp imprinted on the pulse after each round-trip. This linear upchirp is due to a combination of self-phase-modulation in a gain section and absorption of the leading edge of the pulse in the saturable absorber.

Application of microwave diagnostics to copper chloride and carbon dioxide lasers

Part A

A problem restricting the development of the CuCl laser has been the decrease in output power with increases of tube temperature above 400°C. At that temperature the CuCl vapor pressure is about .1 torr. This is a small fraction of the buffer gas pressure (He at 10 torr).

The aim of the project was to measure the peak radiation temperature (assumed related to the mean energy of electrons) in the laser discharge as a function of the tube temperature. A 24 gHz gated microwave radiometer was used.

It was found that at the tube temperatures at which the output power began to deteriorate, the electron radiation temperature showed a sharp increase (compared with radiation temperature in pure buffer).

Using the above result, we have postulated that this sudden increase is a result of Penning ionization of the Cu atoms. As a consequence of this process the number of Cu atoms available for lasing decrease.

PART B

The aim of the project was to study the dissociation of CO₂ in the glow discharge of flowing CO₂ lasers.

A TM₀₁₁ microwave (3 gHz) cavity was used to measure the radially averaged electron density n_e and the electron-neutral collision frequency in the laser discharge. An estimate of the electric field is made from these two measurements. A gas chromatograph was used to measure the chemical composition of the gases after going through the discharge. This instrument was checked against a mass spectrometer for accuracy and sensitivity.

Several typical laser mixtures were .used: CO₂-N₂-He (1,3,16), (1,3,0), (1,0,16), (1,2,10), (1,2,0), (1,0,10), (2,3,15), (2,3,0), (2,0,15), (1,3,16)+ H₂O and pure CO₂. Results show that for the conditions studied the dissociation as a function of the electron density is uniquely determined by the STP partial flow rate of CO₂, regardless of the amount of N₂ and/or He present. The presence of water vapor in the discharge decreased the degree of dissociation.

A simple theoretical model was developed using thermodynamic equilibrium. The electrons were replaced in the calculations by a distributed heat source.

The results are analyzed with a simple kinetic model.

A fundamental approach to phase noise reduction in hybrid Si/III-V lasers

Spontaneous emission into the lasing mode fundamentally limits laser linewidths. Reducing cavity losses provides two benefits to linewidth: (1) fewer excited carriers are needed to reach threshold, resulting in less phase-corrupting spontaneous emission into the laser mode, and (2) more photons are stored in the laser cavity, such that each individual spontaneous emission event disturbs the phase of the field less. Strong optical absorption in III-V materials causes high losses, preventing currently-available semiconductor lasers from achieving ultra-narrow linewidths. This absorption is a natural consequence of the compromise between efficient electrical and efficient optical performance in a semiconductor laser. Some of the III-V layers must be heavily doped in order to funnel excited carriers into the active region, which has the side effect of making the material strongly absorbing.

This thesis presents a new technique, called modal engineering, to remove modal energy from the lossy region and store it in an adjacent low-loss material, thereby reducing overall optical absorption. A quantum mechanical analysis of modal engineering shows that modal gain and spontaneous emission rate into the laser mode are both proportional to the normalized intensity of that mode at the active region. If optical absorption near the active region dominates the total losses of the laser cavity, shifting modal energy from the lossy region to the low-loss region will reduce modal gain, total loss, and the spontaneous emission rate into the mode by the same factor, so that linewidth decreases while the threshold inversion remains constant. The total spontaneous emission rate into all other modes is unchanged.

Modal engineering is demonstrated using the Si/III-V platform, in which light is generated in the III-V material and stored in the low-loss silicon material. The silicon is patterned as a high-Q resonator to minimize all sources of loss. Fabricated lasers employing modal engineering to concentrate light in silicon demonstrate linewidths at least 5 times smaller than lasers without modal engineering at the same pump level above threshold, while maintaining the same thresholds.

Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

The search for gravitational waves from the coalescence of black hole binary systems in data from the LIGO and Virgo detectors. Or: A dark walk through a random forest

The LIGO and Virgo gravitational-wave observatories are complex and extremely sensitive strain detectors that can be used to search for a wide variety of gravitational waves from astrophysical and cosmological sources. In this thesis, I motivate the search for the gravitational wave signals from coalescing black hole binary systems with total mass between 25 and 100 solar masses. The mechanisms for formation of such systems are not well-understood, and we do not have many observational constraints on the parameters that guide the formation scenarios. Detection of gravitational waves from such systems — or, in the absence of detection, the tightening of upper limits on the rate of such coalescences — will provide valuable information that can inform the astrophysics of the formation of these systems. I review the search for these systems and place upper limits on the rate of black hole binary coalescences with total mass between 25 and 100 solar masses. I then show how the sensitivity of this search can be improved by up to 40% by the the application of the multivariate statistical classifier known as a random forest of bagged decision trees to more effectively discriminate between signal and non-Gaussian instrumental noise. I also discuss the use of this classifier in the search for the ringdown signal from the merger of two black holes with total mass between 50 and 450 solar masses and present upper limits. I also apply multivariate statistical classifiers to the problem of quantifying the non-Gaussianity of LIGO data. Despite these improvements, no gravitational-wave signals have been detected in LIGO data so far. However, the use of multivariate statistical classification can significantly improve the sensitivity of the Advanced LIGO detectors to such signals.

Aperiodic structures in optics and integrated optics and the transverse Bragg reflector laser

The first part of this work describes the uses of aperiodic structures in optics and integrated optics. In particular, devices are designed, fabricated, tested and analyzed which make use of a chirped grating corrugation on the surface of a dielectric waveguide. These structures can be used as input-output couplers, multiplexers and demultiplexers, and broad band filters.

Next, a theoretical analysis is made of the effects of a random statistical variation in the thicknesses of layers in a dielectric mirror on its reflectivity properties. Unlike the intentional aperiodicity introduced in the chirped gratings, the aperiodicity in the Bragg reflector mirrors is unintentional and is present to some extent in all devices made. The analysis involved in studying these problems relies heavily on the coupled mode formalism. The results are compared with computer experiments, as well as tests of actual mirrors.

The second part of this work describes a novel method for confining light in the transverse direction in an injection laser. These so-called transverse Bragg reflector lasers confine light normal to the junction plane in the active region, through reflection from an adjacent layered medium. Thus, in principle, it is possible to guide light in a dielectric layer whose index is lower than that of the surrounding material. The design, theory and testing of these diode lasers are discussed.

Stationary random response of multidegree-of-freedom systems

An approximate approach is presented for determining the stationary random response of a general multidegree-of-freedom nonlinear system under stationary Gaussian excitation. This approach relies on defining an equivalent linear system for the nonlinear system. Two particular systems which possess exact solutions have been solved by this approach, and it is concluded that this approach can generate reasonable solutions even for systems with fairly large nonlinearities. The approximate approach has also been applied to two examples for which no exact or approximate solutions were previously available.

Also presented is a matrix algebra approach for determining the stationary random response of a general multidegree-of-freedom linear system. Its derivation involves only matrix algebra and some properties of the instantaneous correlation matricies of a stationary process. It is therefore very direct and straightforward. The application of this matrix algebra approach is in general simpler than that of commonly used approaches.