skip to main content

Explore Research Products in the NSF-PAR

Title: Dynamical Methods for Studying Stability and Noise in Frequency Comb Sources
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
Award ID(s):
1807272
NSF-PAR ID:
10247905
Author(s) / Creator(s):
Date Published:
Journal Name:
SIAM Conference on Applied Dynamical Systems
Page Range / eLocation ID:
MS-15
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ( , AMS Fall Western Virtual Sectional Meeting 2021)
    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
  2. ( , Progress in Electromagnetics Research Symposium 2021)
    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
  3. ( , Colloquium talk: Boston University, Columbia University, Cornell University, University of West Virginia)
    Frequency combs have revolutionized the measurement of time and frequency and impacted a wide range of applications spanning basic physics, astrophysics, medicine, and defense. The key theoretical issues in understanding and designing frequency combs are finding regions in the adjustable parameter space where combs operate stably, determining their noise performance, and optimizing them for high power, low noise, and/or large bandwidth. Here, we present a unique set of computational tools that we have developed that allow us to efficiently address these issues. These tools combine 400-year-old dynamical systems theory with modern computational methods, and they are 3–5 orders of magnitude faster than standard evolutionary methods and provide important physical insight. We have applied these tools to frequency combs from passively modelocked lasers with fast and with slow saturable absorbers and to frequency combs from microresonators. Our methods predict improved operating regimes for combs that are produced from both the passively modelocked lasers and the microresonators. 
    more » « less
  4. ; ; ; ; ( , Optics Express)

    Modulation-based control and locking of lasers, filters and other photonic components is a ubiquitous function across many applications that span the visible to infrared (IR), including atomic, molecular and optical (AMO), quantum sciences, fiber communications, metrology, and microwave photonics. Today, modulators used to realize these control functions consist of high-power bulk-optic components for tuning, sideband modulation, and phase and frequency shifting, while providing low optical insertion loss and operation from DC to 10s of MHz. In order to reduce the size, weight and cost of these applications and improve their scalability and reliability, modulation control functions need to be implemented in a low loss, wafer-scale CMOS-compatible photonic integration platform. The silicon nitride integration platform has been successful at realizing extremely low waveguide losses across the visible to infrared and components including high performance lasers, filters, resonators, stabilization cavities, and optical frequency combs. Yet, progress towards implementing low loss, low power modulators in the silicon nitride platform, while maintaining wafer-scale process compatibility has been limited. Here we report a significant advance in integration of a piezo-electric (PZT, lead zirconate titanate) actuated micro-ring modulation in a fully-planar, wafer-scale silicon nitride platform, that maintains low optical loss (0.03 dB/cm in a 625 µm resonator) at 1550 nm, with an order of magnitude increase in bandwidth (DC - 15 MHz 3-dB and DC - 25 MHz 6-dB) and order of magnitude lower power consumption of 20 nW improvement over prior PZT modulators. The modulator provides a >14 dB extinction ratio (ER) and 7.1 million quality-factor (Q) over the entire 4 GHz tuning range, a tuning efficiency of 162 MHz/V, and delivers the linearity required for control applications with 65.1 dB·Hz2/3and 73.8 dB·Hz2/3third-order intermodulation distortion (IMD3) spurious free dynamic range (SFDR) at 1 MHz and 10 MHz respectively. We demonstrate two control applications, laser stabilization in a Pound-Drever Hall (PDH) lock loop, reducing laser frequency noise by 40 dB, and as a laser carrier tracking filter. This PZT modulator design can be extended to the visible in the ultra-low loss silicon nitride platform with minor waveguide design changes. This integration of PZT modulation in the ultra-low loss silicon nitride waveguide platform enables modulator control functions in a wide range of visible to IR applications such as atomic and molecular transition locking for cooling, trapping and probing, controllable optical frequency combs, low-power external cavity tunable lasers, quantum computers, sensors and communications, atomic clocks, and tunable ultra-low linewidth lasers and ultra-low phase noise microwave synthesizers.

     
    more » « less
  5. ; ( , Twelfth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory,)
    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
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email