skip to main content


Title: Dynamical Methods for Studying Noise in Frequency Comb Sources
Frequency combs have revolutionized the measurement of time and frequency since their invention in 2000, and have a wide array of applications to applications that range from basic science applications, to a wide array of sensing applications, to commercial applications, to military 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 created by modelocked laser systems that emit a periodic train of short pulses. Laser systems are complex nonlinear systems and the usual method for determining the impact of noise is to carry out computationally-expensive Monte Carlo methods. That limits the parameter range over which it is possible to study the noise impact. We have developed a new approach based on dynamical systems methods. In our approach, we determine a stationary state of the laser system as parameters vary solving a root-finding problem [Wang1]. Starting from a stationary state, we determine all the eigenvalues and eigenvalues of the linearized system. The variance of the amplitudes of the eigenvalues obey either random walk of Langevin equations [Menyuk]. Starting from that point, we can determine the power spectral density of the key laser parameters (amplitude jitter, timing jitter, frequency jitter, phase jitter) [Wang2]. We applied this approach to SESAM lasers and found that we were able to reproduce a computation that took 20 minutes on a cluster with 256 cores with a computation that took less than 4 minutes on a desktop computer.  more » « less
Award ID(s):
1807272
NSF-PAR ID:
10326041
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Twelfth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory,
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Coherent multimode instabilities are responsible for several phenomena of recent interest in semiconductor lasers, such as the generation of frequency combs and ultrashort pulses. These techonologies have proven disruptive in optical telecommunications and spectroscopy applications. While the standard Maxwell-Bloch equations (MBEs) encompass such complex lasing phenomena, their integration is computationally expensive and offers limited analytical insight. In this paper, we demonstrate an efficient spectral approach to the simulation of multimode instabilities via a quantitative analysis of the instability of single-frequency lasing in ring lasers, referred to as the Lorenz-Haken (LH) instability or the RNGH instability in distinct parameter regimes. Our approach, referred to as CFTD, uses generally non-Hermitian Constant Flux modes to obtain projected Time Domain equations. CFTD provides excellent agreement with finite-difference integration of the MBEs across a wide range of parameters in regimes of non-stationary inversion, including frequency comb formation and spatiotemporal chaos. We also develop a modal linear stability analysis using CFTD to efficiently predict multimode instabilities in lasers. The combination of numerical accuracy, speedup, and semi-analytic insight across a variety of dynamical regimes make the CFTD approach ideal to analyze multimode instabilities in lasers, especially in more complex geometries or coupled laser arrays.

     
    more » « less
  2. Frequency combs, invented in 2000, have revolutionized frequency measurement and thereby impacted a host of applications. These include applications to military systems, medicine, environmental sensing, astrophysics, and basic physics. The sources have improved dramatically in the past decade, evolving from laboratory-size lasers to fiber lasers to microresonators on a chip. However, the theoretical input to these developments has been surprisingly small. The key problem in designing frequency combs is to determine where in the experimentally-adjustable parameter space stable solutions exist, to determine how to access them, and to determine the impact that noise has on them. While analytical approaches to answer these questions exist, computational tools to implement these approaches in realistic settings have been lacking. Our research has developed computational tools to address these issues, focusing on fiber laser and microresonator combs. In this talk, we will review our progress to date and discuss open problems. 
    more » « less
  3. null (Ed.)
    Frequency combs, invented in 2000, have revolutionized frequency measurement and thereby impacted a host of applications. These include applications to military systems, medicine, environmental sensing, astrophysics, and basic physics. The sources have improved dramatically in the past decade, evolving from laboratory-size lasers to fiber lasers to microresonators on a chip. However, the theoretical input to these developments has been surprisingly small. The key problem in designing frequency combs is to determine where in the experimentally-adjustable parameter space stable solutions exist, to determine how to access them, and to determine the impact that noise has on them. While analytical approaches to answer these questions exist, computational tools to implement these approaches in realistic settings have been lacking. Our research has developed computational tools to address these issues, focusing on fiber laser and microresonator combs. In this talk, we will review our progress to date and discuss open problems. 
    more » « less
  4. Frequency combs, invented in 2000, have revolutionized frequency measurement and there- by impacted a host of applications. These include applications to military systems, medi- cine, environmental sensing, astrophysics, and basic physics. The sources have improved dramatically in the past decade, evolving from laboratory-size lasers to  ber lasers to mi- croresonators on a chip. However, the theoretical input to these developments has been surprisingly small. The key problem in designing frequency combs is to determine where in the experimentally-adjustable parameter space stable solutions exist, to determine how to access them, and to determine the impact that noise has on them. While analytical approaches to answer these questions exist, computational tools to implement these ap- proaches in realistic settings have been lacking. Our research has developed computational tools to address these issues, focusing on  ber laser and microresonator combs. In this talk, we will review our progress to date and discuss open problems. 
    more » « less
  5. Abstract

    Dissipative Kerr soliton (DKS) microcomb has emerged as an enabling technology that revolutionizes a wide range of applications in both basic science and technological innovation. Reliable turnkey operation with sub-optical-cycle and sub-femtosecond timing jitter is key to the success of many intriguing microcomb applications at the intersection of ultrafast optics and microwave electronics. Here we propose an approach and demonstrate the first turnkey Brillouin-DKS frequency comb to the best of our knowledge. Our microresonator-filtered laser design offers essential benefits, including phase insensitivity, self-healing capability, deterministic selection of the DKS state, and access to the ultralow noise comb state. The demonstrated turnkey Brillouin-DKS frequency comb achieves a fundamental comb linewidth of 100 mHz and DKS timing jitter of 1 femtosecond for averaging times up to 56 μs. The approach is universal and generalizable to various device platforms for user-friendly and field-deployable comb devices.

     
    more » « less