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Non-Stationary Photodetection Shot Noise in Frequency Combs: a Signal Processing Perspective

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Non-Stationary Photodetection Shot Noise in Frequency Combs: a Signal Processing Perspective Non-stationary photodetection shot noise in frequency combs: a signal processing perspective Thèse Jean-Daniel Deschênes Doctorat en génie électrique Philosophiae Doctor (Ph.D.) Québec, Canada © Jean-Daniel Deschênes, 2014 Résumé Cette thèse examine le bruit de photon lors de la détection d’impulsions provenant d’un peigne de fréquences. En premier lieu, nous faisons abstraction du mécanisme physique produisant le bruit de photon, réduisant son effet à celui d’une source de bruit additif non-stationnaire (avec des statistiques variables dans le temps). Ce modèle de traitement de signal est ensuite utilisé dans l’analyse de deux expériences importantes pour l’utilisation d’un peigne de fréquence comme mécanisme de compteur de fréquence dans une horloge optique : la conversion du train d’impulsions optiques en un train d’impulsions électriques, et le battement hétérodyne entre un peigne de fréquences et un laser à onde continue. Nous démontrons en premier lieu que le bruit de photon lié à la photodétection produit principalement du bruit d’amplitude, et une quantité presque négligeable de jigue aléatoire de temps sur le signal électrique détecté. Des résultats expérimentaux viennent confirmer nos prédictions théoriques. Nous explorons ensuite les limites de ce mécanisme en considérant la physique de la photodétection, ce qui révèle un étalement du temps de transit qui peut affecter la jigue aléatoire produite par cette conversion. Dans un deuxième temps, nous démontrons que la nature pulsée du peigne de fréquences peut être utilisée pour donner un rapport signal-sur-bruit plus élevé que celui qui est prédit en considérant seulement le battement d’un seul mode du peigne avec le laser à onde continue. La première technique développée, le GATOR, rejette une grande partie du bruit de photon produit par le laser à onde continue afin d’améliorer le rapport signal-sur-bruit lorsque la puissance du peigne est faible. Avec cette technique, nous démontrons un rapport signal-sur- bruit 100 fois plus élevé que la limite en admettant l’utilisation d’un seul mode. Nous démontrons ensuite un raffinement de cette technique qui utilise le glissement de fréquence de l’impulsion optique afin d’utiliser efficacement tous les photons du peigne dans une bande passante déterminée. Cette technique nous a permis de produire un battement avec le plus grand rapport signal-sur- bruit parmi les résultats dans la littérature, 68.3 dB, obtenu en normalisant dans une bande passante commune de 100 kHz. iii Abstract This thesis is a study of shot noise in the photodetection of pulses from a frequency comb. We first make abstraction of the physical mechanism of shot noise to reduce its effects to that of an additive, non-stationary (meaning with time-varying statistics) noise source. This signal processing model is then used to analyze two experiments of importance for the operation of optical clockwork based on frequency combs: the conversion of the optical pulse train into an electrical pulse train by a photodetector, and the heterodyne (or beating) experiment between a frequency comb and a continuous wave laser. For the detection of the optical pulse train, we show that photodetection shot noise yields mostly amplitude noise and vanishingly low timing jitter on the electrical signal. Experimental results confirm our theoretical predictions. We then explore the limits of this jitter when considering practical photodetection physics. This reveals a transit time spread parameter that can affect the jitter produced by this conversion. Next, we turn our attention to the heterodyne experiment. We show that the pulsed nature of the frequency comb can be exploited in different schemes to yield higher signal-to-noise ratio (SNR) that is predicted by the use of the beating of a single comb mode with the continuous wave laser. The first technique that we develop, the GATOR, gates out shot noise from the continuous wave, and improves the SNR in the case of low comb power. Using this technique, we have demonstrated a factor of 100 higher SNR than the single-mode limit. We then show a further refinement of the technique which uses chirping of the optical pulse to effectively use all the available photons from the comb in a given bandwidth. This technique enabled us to produce the beating with the highest SNR reported in the literature of 68.3 dB, when normalizing to the common detection bandwidth of 100 kHz. v Table of Contents Résumé ....................................................................................................... iii Abstract ....................................................................................................... v Table of Contents ....................................................................................... vii List of Tables .............................................................................................. ix List of Figures ............................................................................................. xi Abbreviations and acronyms .................................................................... xvii Remerciements ......................................................................................... xix 1 Introduction .......................................................................................... 1 1.1 Motivation ............................................................................................... 1 1.2 Methodology and scope of this thesis ...................................................... 3 1.2.1 We deal with photodetection shot noise ............................................. 3 1.2.2 Distinction from noise from the laser and photodetection shot noise . 4 1.2.3 Semi-classical model ......................................................................... 4 1.2.4 Two main thrusts: Shot noise in electrical clock output, shot noise in comb-CW beat ............................................................................................... 6 1.3 What is shot noise, what is noise stationarity and why should we care? .. 7 1.3.1 Shot noise definition ......................................................................... 7 1.3.2 Noise stationarity ............................................................................ 12 2 Shot noise in the detection of the repetition rate: operation as output of an optical clock ......................................................................................... 15 2.1.1 Timing jitter on a single pulse due to photodetection shot noise ...... 15 2.1.2 Phase noise and timing jitter on a sine wave ................................... 17 2.1.3 Quadrature splitting ratios in the literature .................................... 26 2.1.4 Experimental results ....................................................................... 29 2.1.5 Additional factors influencing the I-Q noise split ............................. 35 2.1.6 Conclusion and outlook .................................................................. 48 3 The effect of shot noise in a comb-CW heterodyne experiment: gated optical noise reduction and chirped pulse heterodyne ............................... 49 3.1 SNR limit for a single comb mode beating with a CW laser .................... 50 3.2 Gated optical noise reduction (GATOR) .................................................. 53 3.2.1 The gated optical noise reduction concept in the time domain ........ 53 3.2.2 The GATOR concept in the frequency domain ................................. 57 3.2.3 Experimental results ....................................................................... 59 3.3 Optimal detection bandwidth for GATOR ............................................... 69 3.3.1 Interpretation of the theoretical result ............................................. 78 3.4 Chirped pulse heterodyne...................................................................... 79 3.4.1 Case of a single chirped pulse beating with a CW laser ................... 81 3.4.2 Case of a chirped pulse train beating with a CW laser ..................... 86 3.4.3 Interpretation of the results and observations ................................. 87 3.4.4 Signal detection strategies .............................................................. 89 3.4.5 Experimental results ....................................................................... 98 3.5 Comparison of beat SNRs in the literature .......................................... 107 3.6 Alternative filter topology for pulse stretching ...................................... 110 vii Conclusion .............................................................................................. 115 Bibliography ............................................................................................ 117 Annex A - Deriving the SNR given in [REI99] ........................................... 125 Annex B - Using an adjustable beam splitter at the optimum point yields the same SNR as using a 50-50 beam splitter with a balanced photodetector. 127 viii List of Tables Table 3-1 Definition of parameters for the derivation of the snr.......................... 70 Table 3-2 definition of Parameters for the derivation of the snr in the chirped pulse case .................................................................................................. 82 Table 3-3 Comparison of the comb-CW beat SNRs reported in the literature. ... 108 ix List of Figures Figure 1-1 - High-level block diagram of one type of optical clock. The output of this particular clock is the electrical pulse train
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