Title: Semi-classical derivation of the laser linewidth
Abstract:
Based on the assumption that stimulated emission occurs in phase with the incident field, whereas spontaneous emission occurs under an arbitrary phase difference with respect to an incident field, Lax and Haken derived quantum-mechanically the Schawlow-Townes laser linewidth and predicted its narrowing by a factor of two around the laser threshold, and Henry predicted its re-broadening due to amplitude-phase coupling, resulting in the a-factor. However, Maxwell’s equations suggest that both stimulated and spontaneous emission would violate the law of energy conservation. I will show semi-classically that the phase of the emitted field is 90° in lead of the incident field.
When combining Weisskopf’s idea that vacuum fluctuations trigger spontaneous emission with Einstein’s semi-classical rate-equation approach to Planck’s law of blackbody radiation, a direct consequence is that an optical mode contains a vacuum energy of hn. This result contradicts with Heisenberg’s proof that a quantum-harmonic oscillator contains a zero-point energy of ½ hn. I will show that this factor-of-two difference and the factor-of-two narrowing of the laser linewidth have the same origin.
Both findings question the quantum-mechanical derivation of the laser linewidth. I will present a simple semi-classical explanation.
Biography:
Markus Pollnau is a Professor in Photonics at the Advanced Technology Institute (ATI), at the University of Surrey. He received an MSc from the University of Hamburg, Germany, in 1992, and a PhD from the University of Bern, Switzerland, in 1996, both in physics. After postdoctoral positions with the University of Southampton, UK, until 1998 and the University of Bern, Switzerland, until 1999, he worked as a Project and Research Group Leader with the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland. In 2004, he became a Full Professor and Chair of the Integrated Optical MicroSystems Group, MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands. After a short stay at KTH - Royal Institute of Technology, Stockholm, Sweden, he joined the University of Surrey and the ATI in 2017. He was a visiting researcher at the University of Manchester, UK, in 1998-2000, on sabbatical leave to Harvard University, Cambridge, MA, in 2009, and a visiting Professor at the University of Jena, Germany, in 2013.
Prof Pollnau has contributed to more than 140 reviewed journal articles, more than 400 international conference and proceedings papers, among them 14 plenary/tutorial/keynote lectures and more than 70 invited papers, more than 10 book chapters, and more than 50 summer school lectures in the fields of thin-film growth, rare-earth-ion spectroscopy in dielectric solids, bulk, fiber, and waveguide lasers, integrated optics, and bio-medical applications. He held a “Human Capital and Mobility” Research Fellowship of the European Union (1996-1998), a “Profil” Research Fellowship of the Swiss National Science Foundation (1999-2004), and a “Vici” Research Fellowship of the Netherlands Organisation for Scientific Research (2006-2011), obtained numerous National and European Research Grants, and coordinated the EU STREP project “PI-Oxide” (2005-2008). In 2014, he started the ERC Advanced Grant “Optical Ultra-Sensor” of the European Research Council.
Prof Pollnau has been involved in the organization of major international conferences, e.g., as a Program and General Co-chair of the Conference on Lasers and Electro- Optics (2006/2008) and the Conference on Lasers and Electro-Optics Europe (2009/2011), inaugurated and steered the Europhoton Conference (2004-2008). He served as Topical Editor for the Journal of the Optical Society of America B and on the editorial board of the journal Laser Physics Letters, and was the chair and member of several prize committees. In 1995, he was awarded the Annual Physics Prize of the Faculty of Natural Sciences of the University of Bern, Switzerland, for research results obtained during his Ph.D. thesis. He was elected a Fellow of the Optical Society of America in 2013 and a Fellow of the European Physical Society in 2014.