This project began with an experimental discovery of a new operation regime of quantum cascade lasers (QCLs)––the harmonic state––that is characterised by laser emission spectra featuring widely-spaced isolated modes, skipping multiples of the cavity free spectral range (FSR) [1]. Typical FSR for a QCL is about 10 GHz, while intermodal spacing in the harmonic state regime reaches hundreds of GHz corresponding to tens of cavity modes skipped by the laser. This ability of QCLs to skip modes is provided by their ultrafast gain recovery dynamics––a feature that distinguishes them from most of other lasers, optically or electrically pumped, semiconductor, gas or solid-state. Mode skipping at the onset of multimode operation is attributed to an inhomogeneous modification of the gain spectrum through an addition of a parametric gain contribution due to population pulsations in the QCL gain medium. Through theory and experiment we concluded that the harmonic state is inherent to all QCLs, regardless of the band structure design, however, cavity geometry was found out to play a role in the formation of the harmonic state. Next, we verified by a measurement of an extreme precision that the widely spaced modes of the harmonic state remain phase-coherent over laboratory timescales leading to formation of harmonic frequency combs in QCLs [2]. Finally, time-domain waveform profile of a QCLs in harmonic state was retrieved through a second-order nonlinear autocorrelation measurement combined with a phase-retrieval algorithm. It showed that QCL frequency combs obey variational principle that was postulated over 50 years before this research began [3]. We identified in experiment the conditions for the breakdown of this principle in QCLs with wider mode spacing. 

Our efforts in investigation of the harmonic state went hand in hand with research on fundamental QCL frequency combs with modes spaced by one FSR. There we have gained a great degree of understanding of the spatial properties of dynamic electronic transport in QCLs: we have shown that upper-state population of the laser responds dynamically to intensity modulation of the intracavity frequency comb field and that this response has a spatial dependence––phase and magnitude of population inversion oscillations are the function of position inside the cavity [4]. We have developed a simple experimental technique that allowed for detection of the spatial profiles of these dynamic oscillations, that we dub dynamic gratings, and that are confirmed by an analytical model that we derived to explain the occurrence of these oscillations. This model allows to predict dynamic grating profiles for a frequency comb field with an arbitrary spectrum and for an arbitrary cavity geometry [5]. The findings of dynamic gratings in QCL combs pave the way to complete understanding of fundamental and harmonic frequency comb formation in these lasers and allow to draw analogies with other laser systems, where mode-locking mechanisms are different from those present in QCLs, such as saturable absorption in quantum well or quantum dot lasers. Understanding of dynamic gratings will allow deterministic control of harmonic comb spacing in the future. This will in turn enable new applications for the lasers with fast gain medium, such as QCLs, whereby they are no longer used as a source of light, but as a source of high frequency radio waves, that can be sourced from the oscillations of population inversion ins response to modulation of the optical frequency comb field. Understanding internal structure of the dynamic gratings is quintessential to design and fabrication of efficient radiation outcouplers and might enable new, previously overseen use cases for laser frequency combs.  

[1] Mansuripur, Tobias S., et al. "Single-mode instability in standing-wave lasers:   The quantum cascade laser as a self-pumped parametric oscillator." Physical Review A 94.6 (2016): 063807.

[2] Kazakov, Dmitry, et al. "Self-starting harmonic frequency comb generation in a quantum cascade laser." Nature Photonics 11.12 (2017): 789-792.

[3] Piccardo, Marco, et al. "Frequency-Modulated Combs Obey a Variational Principle." Physical review letters 122.25 (2019): 253901.

[4] Piccardo, Marco, et al. "Time-dependent population inversion gratings in laser frequency combs." Optica 5.4 (2018): 475-478.

[5] Piccardo, Marco, et al. "Light and Microwaves in Laser Frequency Combs: An Interplay of Spatiotemporal Phenomena." IEEE Journal of Selected Topics in Quantum Electronics 25.6 (2019): 1-12.

Last Modified: 03/17/2020
Modified by: Federico Capasso