Regular Article

Physics of the sapphire whispering-gallery-mode solid-state MASER oscillator

¹ Department of Physics, Faculty of Sciences I & V, Lebanese University, Hadat and Nabatieh, Lebanon
² Laboratoire FEMTO-ST, 26 Chemin de l’Epitaphe, 25000 Besançon, France

^* e-mail: mohamadmrad84@gmail.com

Received: 17 April 2020
Received in final form: 14 June 2020
Accepted: 10 August 2020
Published online: 22 September 2020

Abstract

The Cryogenic Sapphire Oscillator (CSO) is currently the best available technology that can provide a relative frequency stability better than 10⁻¹⁵ with integration times between 1 s and 10,000 s. But, the CSO remains a complex instrument that requires multiple loop controls to achieve the best frequency stability. The possibility to use the sapphire resonator in a self-sustained MASER oscillator presents an elegant alternative to the CSO. Here, sustaining the amplification is achieved through the interaction between a high-Q factor whispering gallery mode and the paramagnetic Fe³⁺ ions, which are present in small concentration in the sapphire crystal. The Fe³⁺ ion exhibits three energy states enabling to realize a self-sustaining solid-state maser. Although, this principle has been already experimentally demonstrated few years ago, its development as a truly usable ultra-stable source has not yet been completed, mainly due to the lack of control of the complex physical phenomena involved. This paper complements the previous theoretical work based on the rate equations model. Here we derive the full quantum equations describing the evolution of the Fe³⁺ ions inside the sapphire lattice and submitted to a pump and a maser signal. The influence of the ions concentration and spin-spin relaxation time will be pointed out.