Harmonic mode locking of the Nd:YAG laser

Abstract

We present experimental and theoretical results for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> th harmonic mode locking of a Nd:YAG laser with an intracavity phase modulator operating at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 2, 3, 4,</tex> and 5 times the fundamental <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c/2L</tex> frequency. The bandwidths of the resulting mode-locked spectra depend upon modulation frequency, modulation depth, and laser cavity losses in good agreement with the Gaussian-pulse analysis of Kuizenga and Siegman [5]. For modulation at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N(c/2L)</tex> the resulting pulse-repetition frequency is also <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N(c/2L)</tex> in all cases. However, in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 2</tex> case, for example, the mode-locked optical spectrum includes every adjacent axial mode component if the laser rod is located near the center of the laser cavity, but only every other axial mode when the rod is located at the end of the laser cavity. This behavior is explained by a Lamb-type theoretical analysis taking into account the competition between the two "hypermodes," or sets of interleaved next-adjacent axial modes, that can oscillate separately or simultaneously in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 2</tex> case.