Control Systems and Laser Frequency Stabilization (2/2)
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Video Lecture 44 of 69
Copyright Information: This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen. The full course, including this and many other lecture videos, exercises, solutions to exercises, and lists of relevant reading, are available on the web at http://elmer.caltech.edu/ph237/
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### Lecture Description

Control Systems and Laser Frequency Stabilization - Week 13, Lecture 23  [by Erik Black]

1. Introduction
1. What a control system is
2. Uses of control systems
3. Simple control system (input, amplifier K, feedback, and output); its oscillatory instability due to time delay

General, linear control theory

1. Laplace transforms
2. Transfer function (Kernel) for a linear system, in time domain and in (Laplace-transform) s-space
3. Poles of the transfer function in s-space; their relationship to system's stability
4. Transfer function for simple control system with s-dependent amplifier, K(s)
1. Open-loop transfer function K(s); closed-loop transfer function K/(1+K)
2. Nyquist diagram for analyzing stability
3. Gain margin, phase margin
4. Bode plot for analyzing stability; stability diagnosed via phase at unity gain point (phase margin)
5. Bode's gain-phase relations

Laser frequency stabilization via locking to eigenmode of an optical cavity (Pound-Drever-Hall [PDH] locking): an example of linear control theory

1. Laser frequency adjusted via PZT attached to mirror of laser cavity
2. Stable Fabry Perot cavity to which laser frequency is locked
3. Frequency-modulated laser light reflected off locking cavity, demodulated and fed back to laser
4. Analysis of stability of this PDH  feedback system
1. Influence of locking cavity's storage time (time delay)

Spectral density of frequency fluctuations for PDH-stabilized laser; magnitude of stabilization

### Course Description

Caltech's Physics 237-2002: Gravitational Waves
A Web-Based Course organized and Designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen.

This course contains all the materials from a graduate-student-level course on Gravitational Waves taught at the California Institute of Technology, January through May of 2002. The materials include Quicktime videos of the lectures, lists of suggested and supplementary reading, copies of some of the readings, many exercises, and solutions to all exercises. The video files are so large that it may not be possible to stream them from most sites, but they can be downloaded. Alternatively, the course materials on DVD's can be borrowed via Interlibrary Loan from the Caltech Library (click on CLAS, then on Call Number, then enter QC179.T56 2002 ).

Questions and issues about this course and website can be directed to Mihai Bondarescu or Yanbei Chen.