Abstract The aim of this thesis was to develop time-to-digital converters (TDC) for the integrated receiver of a pulsed time-of-flight (TOF) laser rangefinder aiming at cm-level accuracy over an input range of 10 m – 15 m. A simple structure, a high integration level and low power consumption are the desired features for such a TDC. From the pulsed TOF laser rangefinder point of view an integrated receiver consisting of both the TDC and the receiver channel on the same die offers the possibility of manufacturing these laser rangefinders with a high integration level and at a low price to fulfil the needs of mass industrial markets. The heart of the TDC is a CMOS ring oscillator, the clock frequency of which is used to calculate the full clock cycles between timing signals, the positions of the timing signals inside the clock period being determined by storing the state of the phase of the ring oscillator for each timing signal. This will improve the resolution of the TDC. Also, additional delay lines are used to generate multiple timing signals, each having a time difference of a fraction of that of the ring oscillator. This will further improve the resolution of the whole TDC. To achieve stable results regardless of temperature and supply voltage variations, the TDC is locked to an on-chip reference voltage, or the resolution of the TDC is calibrated before the actual time interval measurement. The systematic walk error in the receiver channel caused by amplitude variation in the received pulse is compensated for by the TDC measuring the slew rate of the received pulse. This time domain compensation method is not affected by the low supply voltage range of modern CMOS technologies. Three TDC prototypes were tested. A single-shot precision standard deviation of 16 ps (2.4 mm) and a power consumption of 5.3 mW/channel were achieved at best over an input range of 100 ns (15 m). The temperature drifts of an on-chip voltage reference-locked TDC and a TDC based on the calibration method were 90 ppm/°C and 0.27 ps/°C, respectively. The results also showed that a pulsed TOF laser rangefinder with cm-level accuracy over a 0 – 15 m input range can be realized using the integrated receiver with the time domain walk error compensation described here. / Tiivistelmä Väitöskirjatyön tavoitteena oli kehittää aika-digitaalimuunninrakenteita valopulssin kulkuajan mittaukseen perustuvan lasertutkan integroituun vastaanottimeen. Tavoitteena oli saavuttaa senttimetriluokan tarkkuus 10 m – 15 m mittausalueella koko lasertutkan osalta. Aika-digitaalimuuntimelta vaaditaan yksinkertaista rakennetta, korkeaa integroimisastetta ja matalaa tehonkulutusta. Integroitu vastaanotin sisältää sekä aika-digitaalimuuntimen että vastaanotinkanavan ja tarjoaa mahdollisuuden korkeasti integroidun lasertutkan valmistukseen halvalla teollisuuden massamarkkinoiden tarpeisiin. Aika-digitaalimuuntimen ytimenä toimii monivaiheinen CMOS-rengasoskillaattori. Aika-digitaalimuunnos perustuu rengasoskillaattorin täysien kellojaksojen laskentaan laskurilla ajoitussignaalien välillä. Lisäksi rengasoskillaatorin jokaisesta vaiheesta otetaan näyte ajoitussignaaleilla niiden paikkojen määrittämiseksi kellojakson sisällä, jolloin aika-digitaalimuuntimen erottelutarkkuutta saadaan parannettua. Erottelutarkkuutta parannetaan lisää viivästämällä ajoitussignaaleja viive-elementeillä ja muodostamalla näin useita erillisiä ajoitussignaaleja, joiden väliset viive-erot ovat murto-osa rengasoskillaattorin viive-elementin viiveestä. Aika-digitaalimuunnin stabiloidaan käyttöjännite- ja lämpötilavaihteluja vastaan lukitsemalla se integroidun piirin sisäiseen jännitereferenssiin, tai sen erottelutarkkuus määritetään ennen varsinaista aikavälinmittausta erillisellä kalibrointimittauksella. Vastaanotetun valopulssin amplitudivaihtelun aiheuttama systemaattinen ajoitusvirhe integroidussa vastaanotinkanavassa kompensoidaan mittaamalla vastaanotetun valopulssin nousunopeus aika-digitaalimuuntimella. Tällainen aikatasoon perustuva kompensointimetodi on myös suorituskykyinen nykyisissä matalakäyttöjännitteisissä CMOS-teknologioissa. Työssä valmistettiin ja testattiin kolme aika-digitaalimuunninprototyyppiä. Muuntimien kertamittaustarkkuuden keskihajonta oli parhaimmillaan 16 ps (2,4 mm) ja tehonkulutus alle 5,3 mW/kanava mittausetäisyyden olessa alle 100 ns (15 m). Sisäiseen jännitereferenssiin lukitun aika-digitaalimuuntimen lämpötilariippuvuudeksi mitattiin 90 ppm/°C ja kalibrointimenetelmällä saavutettiin 0,27 ps/°C lämpötilariipuvuus. Työssä saavutetut tulokset osoittavat lisäksi, että valopulssin kulkuajan mittaukseen perustuvalla lasertutkalla on saavutettavissa senttimetriluokan tarkkuus 0 – 15 m mittausalueella käyttämällä tässä työssä esitettyä integroitua vastaanotinta ja aikatason ajoitusvirhekompensointia.

Abstract This thesis describes the development of a high precision time-to-digital converter (TDC) in which the conversion is based on a counter and three-stage stabilised delay line interpolation developed in this work. The biggest design challenges in the design of a TDC are related to the fact that the arrival moment of the hit signals (start and stop) is unknown and asynchronous with respect to the reference clock edges. Yet, the time interval measurement system must provide an immediate and unambiguous measurement result over the full dynamic range. It must be made sure that the readings from the counter and the interpolators are always consistent with very high probability. Therefore, the operation of the counter is controlled with a synchronising logic that is in turn controlled with the interpolation result. Another synchronising logic makes it possible to synchronise the timing signals with multiphase time-interleaved clock signals as if the synchronising was done with a GHz-level clock, and enables multi-stage interpolation. Multi-stage interpolation reduces the number of delay cells and registers needed. The delay line interpolators are stabilised with nested delay-locked loops, which leads to good stability and makes it possible to improve single-shot precision with a single look-up table containing the integral nonlinearities of the interpolators measured at the room temperature. A multi-channel prototype TDC was fabricated in a 0.6 μm digital CMOS process. The prototype reaches state-of-the-art rms single-shot precision of better than 20 ps and low power consumption of 50 mW as an integrated TDC.

The mode-locked laser diode (MLLD) finds a lot of use in applications such as ultra high-speed data processing and sampling, large-capacity optical fiber communications based on optical time-division multiplexing (OTDM) systems. Integrating mode-locked lasers on silicon makes way for highly integrated silicon based photonic communication devices. The mode-locked laser being used in this thesis was built with Hybrid Silicon technology. This technology, developed by UC Santa Barbara in 2006, introduced the idea of wafer bonding a crystalline III- V layer to a Silicon-on-insulator (SOI) substrate, making integrated lasers in silicon chips possible. Furthermore, all mode-locked lasers produce phase noise, which can be a limiting factor in the performance of optical communication systems, specifically at higher bit rates. In this thesis, we design and discuss an impedance matching solution for a hybrid silicon mode-locked laser diode to lower phase noise and reduce the drive power requirements of the device. In order to develop an impedance matching solution, a thorough measurement and analysis of the impedance of the MLLD is necessary and was carried out. Then, a narrowband solution of two 0.1 pF chip capacitors in parallel is considered and examined as an impedance matching network for an operating frequency of 20 GHz. The hybrid silicon laser was packaged together in a module including the impedance- matching circuit for efficient RF injection. In conclusion, a 6 dB reduction of power required to drive the laser diode, as well as approximately a 10 dB phase noise improvement, was measured with the narrow-band solution. Also, looking ahead to possible future work, we discuss a step recovery diode (SRD) driven impulse generator, which wave-shapes the RF drive to achieve efficient injection. This novel technique takes into account the time varying impedance of the absorber as the optical pulse passes through it, to provide optimum pulse shaping.

Proprietary.

Diplomová práce přibližuje systémy LIDAR přímo měřící čas průletu a časově digitální převodníky určené k použití v těchto systémech. Představuje problematiku distribuce hodinových signálů napříč soubory časově digitálních převodníků v LIDAR systémech a věnuje se jednomu z nových řešení této problematiky, které je založené na injekcí zavěšených oscilátorech. Technika injekčního zavěšení oscilátorů je důkladně matematicky popsána. V programu Matlab byl vytvořen simulační model injekcí zavěšeného kruhového oscilátoru, který potvrzuje správnost uvedených analytických predikcí. Ve výrobní technologii ONK65 byl navržen injekcí zavěšený kruhový oscilátor stabilizovaný pomocí smyčky závěsu zpoždění, určený pro implementaci časově digitálního převodníku pro systém LIDAR. Navržený injekcí zavěšený kruhový oscilátor byl verifikován počítačovými simulacemi zohledňujícími vliv procesních, napěťových i teplotních variací. Oscilátor poskytuje specifikované časové rozlišení 50 pikosekund a dosahuje dvakrát nižší hodnoty fázového neklidu než ekvivalentní volnoběžný oscilátor v dané technologii.

Communication delays are common in many complex systems. It has been shown that these delays cannot be neglected when they are long enough compared to other timescales in the system. In systems of coupled phase oscillators discrete delays in the coupling give rise to effects such as multistability of steady states. However, variability in the communication times inherent to many processes suggests that the description with discrete delays maybe insufficient to capture all effects of delays. An interesting example of the effects of communication delays is found during embryonic development of vertebrates. A clock based on biochemical reactions inside cells provides the periodicity for the successive and robust formation of somites, the embryonic precursors of vertebrae, ribs and some skeletal muscle. Experiments show that these cellular clocks communicate in order to synchronize their behavior. However, in cellular systems, fluctuations and stochastic processes introduce a variability in the communication times. Here we account for such variability by considering the effects of distributed delays. Our approach takes into account entire intervals of past states, and weights them according to a delay distribution. We find that the stability of the fully synchronized steady state with zero phase lag does not depend on the shape of the delay distribution, but the dynamics when responding to small perturbations about this steady state do. Depending on the mean of the delay distribution, a change in its shape can enhance or reduce the ability of these systems to respond to small perturbations about the phase-locked steady state, as compared to a discrete delay with a value equal to this mean. For synchronized steady states with non-zero phase lag we find that the stability of the steady state can be altered by changing the shape of the delay distribution. We conclude that the response to a perturbation in systems of phase oscillators coupled with discrete delays has a sharper functional dependence on the mean delay than in systems with distributed delays in the coupling. The strong dependence of the coupling on the mean delay time is partially averaged out by distributed delays that take into account intervals of the past.:Abstract i Acknowledgement iii I. INTRODUCTION 1. Coupled Phase Oscillators Enter the Stage 5 1.1. Adjusting rhythms – synchronization . . . . . . . . . . . . . . . . . . 5 1.2. Historical remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3. Reducing variables – phase models . . . . . . . . . . . . . . . . . . . . 9 1.4. The Kuramoto order parameter . . . . . . . . . . . . . . . . . . . . . . 10 1.5. Who talks to whom – coupling topologies . . . . . . . . . . . . . . . . 12 2. Coupled Phase Oscillators with Delay in the Coupling 15 2.1. Communication needs time – coupling delays . . . . . . . . . . . . . . 15 2.1.1. Discrete delays consider one past time . . . . . . . . . . . . . . 16 2.1.2. Distributed delays consider multiple past times . . . . . . . . 17 2.2. Coupled phase oscillators with discrete delay . . . . . . . . . . . . . . 18 2.2.1. Phase locked steady states with no phase lags . . . . . . . . . 18 2.2.2. m-twist solutions: phase-locked steady states with phase lags 21 3. The Vertebrate Segmentation Clock – What Provides the Rhythm? 25 3.1. The clock and wavefront mechanism . . . . . . . . . . . . . . . . . . . 26 3.2. Cyclic gene expression on the cellular and the tissue level . . . . . . 27 3.3. Coupling by Delta-Notch signalling . . . . . . . . . . . . . . . . . . . . 29 3.4. The Delayed Coupling Theory . . . . . . . . . . . . . . . . . . . . . . . 30 3.5. Discrete delay is an approximation – is it sufficient? . . . . . . . . . 32 4. Outline of the Thesis 33 II. DISTRIBUTED DELAYS 5. Setting the Stage for Distributed Delays 37 5.1. Model equations with distributed delays . . . . . . . . . . . . . . . . . 37 5.2. How we include distributed delays . . . . . . . . . . . . . . . . . . . . 38 5.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6. The Phase-Locked Steady State Solution 41 6.1. Global frequency of phase-locked steady states . . . . . . . . . . . . . 41 6.2. Linear stability of the steady state . . . . . . . . . . . . . . . . . . . . 42 6.3. Linear dynamics of the perturbation – the characteristic equation . 43 6.4. Summary and application to the Delayed Coupling Theory . . . . . . 50 7. Dynamics Close to the Phase-Locked Steady State 53 7.1. The response to small perturbations . . . . . . . . . . . . . . . . . . . 53 7.2. Relation between order parameter and perturbation modes . . . . . 54 7.3. Perturbation dynamics in mean-field coupled systems . . . . . . . . 56 7.4. Nearest neighbour coupling with periodic boundary conditions . . . 62 7.4.1. How variance and skewness influence synchrony dynamics . 73 7.4.2. The dependence of synchrony dynamics on the number of oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7.5. Synchrony dynamics in systems with arbitrary coupling topologies . 88 7.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 8. The m-twist Steady State Solution on a Ring 95 8.1. Global frequency of m-twist steady states . . . . . . . . . . . . . . . . 95 8.2. Linear stability of m-twist steady states . . . . . . . . . . . . . . . . . 97 8.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 9. Dynamics Approaching the m-twist Steady States 105 9.1. Relation between order parameter and perturbation modes . . . . . 105 9.2. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 10.Conclusions and Outlook 111 vi III. APPENDICES A. 119 A.1. Distribution composed of two adjacent boxcar functions . . . . . . . 119 A.2. The gamma distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 124 A.3. Distribution composed of two Dirac delta peaks . . . . . . . . . . . . 125 A.4. Gerschgorin’s circle theorem . . . . . . . . . . . . . . . . . . . . . . . . 127 A.5. The Lambert W function . . . . . . . . . . . . . . . . . . . . . . . . . . 127 A.6. Roots of unity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 B. Simulation methods 129

This thesis presents methods for detecting consciousness in patients with complete locked-in syndrome (CLIS). CLIS patients are unable to speak and have lost all muscle movement. Externally, the internal brain activity of such patients cannot be easily perceived, but CLIS patients are considered to be still conscious and cognitively active. Detecting the current state of consciousness of CLIS patients is non-trivial, and it is difficult to ascertain whether CLIS patients are conscious or not. Thus, it is vital to develop alternative ways to re-establish communication with these patients during periods of awareness, and a possible platform is through brain–computer interface (BCI). Since consciousness is required to use BCI correctly, this study proposes a modus operandi to analyze not only in intracranial electrocorticography (ECoG) signals with greater signal-to-noise ratio (SNR) and higher signal amplitude, but also in non-invasive electroencephalography (EEG) signals. By applying three different time-domain analysis approaches sample entropy, permutation entropy, and Poincaré plot as feature extraction to prevent disease-related reductions of brainwave frequency bands in CLIS patients, and cross-validated to improve the probability of correctly detecting the conscious states of CLIS patients. Due to the lack a of 'ground truth' that could be used as teaching input to correct the outcomes, k-Means and DBSCAN these unsupervised learning methods were used to reveal the presence of different levels of consciousness for individual participation in the experiment first in locked-in state (LIS) patients with ALSFRS-R score of 0. The results of these different methods converge on the specific periods of consciousness of CLIS/LIS patients, coinciding with the period during which CLIS/LIS patients recorded communication with an experimenter. To determine methodological feasibility, the methods were also applied to patients with disorders of consciousness (DOC). The results indicate that the use of sample entropy might be helpful to detect awareness not only in CLIS/LIS patients but also in minimally conscious state (MCS)/unresponsive wakefulness syndrome (UWS) patients, and showed good resolution for both ECoG signals up to 24 hours a day and EEG signals focused on one or two hours at the time of the experiment. This thesis focus on consistent results across multiple channels to avoid compensatory effects of brain injury. Unlike most techniques designed to help clinicians diagnose and understand patients' long-term disease progression or distinguish between different disease types on the clinical scales of consciousness. The aim of this investigation is to develop a reliable brain-computer interface-based communication aid eventually to provide family members with a method for short-term communication with CLIS patients in daily life, and at the same time, this will keep patients' brains active to increase patients' willingness to live and improve their quality of life (QOL).

While the development of bright pulses produced in free space devices can be found in a large set of applications and research equipment all over the world. The production of dark pulses in a free-space device has not been shown prior to this work. In this work a method of producing free space mode-locked laser in a straight laser cavity using intra-cavity loss induced by periodic nonlinear interactions mediated by a mode-locked source. We are able to show the existence of a dark pulse propagating inside of the cavity. An extensive analysis of the generation of the dark pulse is made using a homemade cross correlator. A symmetric dark pulse with a 10 ps width is achieved with a 90% modulation depth. This work will be used in a continued project involving passive two-color pulse synchronization. / Framtagningen av ljusa pulser i kristall baserade lasrar finns i en stor utsträckning av tillämpningar inom forskning och industri. Utvecklandet av mörkpulskällor i kristall baserade kaviteter har till vår kunskap inte tagits fram. I detta arbete presenteras en metod att utveckla en modlåst mörkpuls laser i en rak kavitet som utnyttjar intrakavitär förlust som periodiskt induceras av en ickelinjär interaktion som styrs av en ljus modlåst källa. Vi kan visa att en mörk puls propagerar inuti kaviteten. En utförlig analys och experiment med hjälp av en hemagjord korskorrelator belyser hur den mörka pulsen kan formas. En symmetrisk mörk puls formas med en 10 ps bredd och över 90 % modulations djup. Detta arbete kommer användas i ett framtida projekt inom passiv tvåfärgs puls synkronisation.

A novel dispersion-managed breathing-mode semiconductor mode-locked ring laser is developed. The "breathing-mode" designation derives from the fact that intracavity pulses are alternately stretched and compressed as they circulate around the ring resonator. The pulses are stretched before entering the semiconductor gain medium to minimize the detrimental strong integrating self-phase modulation and to enable efficient pulse amplification. Subsequently compressed pulses facilitate bleaching the semiconductor saturable absorber. The intracavity pulse compression ratio is higher than 50. Down chirping when compared to up chirping allows broader mode-locked spectra and shorter pulse generation owing to temporal and spectral semiconductor gain dynamics. Pulses as short as 185 fs, with a peak power of ~230 w, and a focused intensity of ~4.6 gw/cm2 are generated by linear down chirp compensation and characterized by shg-frog method. To our knowledge, this is the highest peak power and the shortest pulse generation from an electrically pumped all-semiconductor system. The very good agreement between the simulated and the measured results verifies our understanding and ability to control the physical mechanisms involved in the pulse shaping within the ring cavity. Application trends such as continuum generation via a photonic crystal fiber, two-photon fluorescence imaging, and ultrafast pulse source for pump-probe experiments are demonstrated.

Harmonically mode-locked semiconductor lasers with external ring cavities offer high repetition rate pulse trains while maintaining low optical linewidth via long cavity storage times. Single frequency injection locking generates widely-spaced and tunable frequency combs from these harmonically mode-locked lasers, while stabilizing the optical frequencies. The output is stabilized long-term with the help of a feedback loop utilizing either a novel technique based on Pound-Drever-Hall stabilization or by polarization spectroscopy. Error signals of both techniques are simulated and compared to experimentally obtained signals. Frequency combs spaced by 2.5 GHz and ~10 GHz are generated, with demonstrated optical sidemode suppression of unwanted modes of 36 dB, as well as RF supermode noise suppression of 14 dB for longer than 1 hour. In addition to the injection locking of actively harmonically mode-locked lasers, the injection locking technique for regeneratively mode-locked lasers, or Coupled OptoElectronic Oscillators (COEOs), is also demonstrated and characterized extensively.