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			<titleStmt><title level='a'>Dynamical Methods for Studying Noise in Frequency Comb Sources</title></titleStmt>
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				<date>03/01/2022</date>
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				<bibl> 
					<idno type="par_id">10326041</idno>
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					<title level='j'>Twelfth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory,</title>
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					<author>Curtis R. Menyuk</author><author>Shaokang Wang</author>
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			<abstract><ab><![CDATA[Frequency combs have revolutionized the measurement of time and frequency since theirinvention in 2000, and have a wide array of applications to applications that range from basicscience applications, to a wide array of sensing applications, to commercial applications, tomilitary applications, and the list goes on. Noise poses a fundamental limit to these systems,and calculating its impact play a critical role in system design. Frequency combs are createdby modelocked laser systems that emit a periodic train of short pulses. Laser systems arecomplex nonlinear systems and the usual method for determining the impact of noise is tocarry out computationally-expensive Monte Carlo methods. That limits the parameter rangeover which it is possible to study the noise impact. We have developed a new approachbased on dynamical systems methods. In our approach, we determine a stationary stateof the laser system as parameters vary solving a root-finding problem [Wang1]. Startingfrom a stationary state, we determine all the eigenvalues and eigenvalues of the linearizedsystem. The variance of the amplitudes of the eigenvalues obey either random walk ofLangevin equations [Menyuk]. Starting from that point, we can determine the power spectraldensity of the key laser parameters (amplitude jitter, timing jitter, frequency jitter, phasejitter) [Wang2]. We applied this approach to SESAM lasers and found that we were able toreproduce a computation that took 20 minutes on a cluster with 256 cores with a computationthat took less than 4 minutes on a desktop computer.]]></ab></abstract>
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