Field-resolved high-order sub-cycle nonlinearities in a terahertz semiconductor laser

Abstract

The exploitation of ultrafast electron dynamics in quantum cascade lasers (QCLs) holds enormous potential for intense, compact mode-locked terahertz (THz) sources, squeezed THz light, frequency mixers, and comb-based metrology systems. Yet the important sub-cycle dynamics have been notoriously difficult to access in operational THz QCLs. Here, we employ high-field THz pulses to perform the first ultrafast two-dimensional spectroscopy of a free-running THz QCL. Strong incoherent and coherent nonlinearities up to eight-wave mixing are detected below and above the laser threshold. These data not only reveal extremely short gain recovery times of 2 ps at the laser threshold, they also reflect the nonlinear polarization dynamics of the QCL laser transition for the first time, where we quantify the corresponding dephasing times between 0.9 and 1.5 ps with increasing bias currents. A density-matrix approach reproducing the emergence of all nonlinearities and their ultrafast evolution, simultaneously, allows us to map the coherently induced trajectory of the Bloch vector. The observed high-order multi-wave mixing nonlinearities benefit from resonant enhancement in the absence of absorption losses and bear potential for a number of future applications, ranging from efficient intracavity frequency conversion, mode proliferation to passive mode locking.

The 2023 terahertz science and technology roadmap

“…ISBs also display atomic-like absorption from the subbands possessing the same parobolicity, which results in giant optical nonlinearities. This has led to room-temperature THz operation using intra-cavity difference-frequency mixing in MIR QCLs [132], FCs through four-wave mixing [126], nonlinear detectors [133], as well as recent demonstrations of high-order wave mixing in QCLs [134] and intersubband polaritons [135] (coupling between a ISB and a cavity mode). Further, ISB transitions have extremely short lifetimes, owing to interactions of electrons with scattering mechanisms of the materials, resulting in ultrafast dynamics that is of importance for active modelocking for THz pulse generation [127] and ultrafast detection using the QCL itself as a detector [136].…”

Modeling of short pulse generation in THz quantum cascade lasers with embedded graphene saturable absorber

“…Ensemble Monte-Carlo simulations carried out in a previous work resulted in τ g = 2.6 ps, 13 in agreement with recent measurements. 20 However, previous works of bound-to-continuum and heterogenous QCL designs measured significantly longer recovery times, ranging up to several tens of picoseconds. [21][22][23] The gain saturation intensity is directly influenced by the recovery time…”

“…[14][15][16][17] Employing several layers of the two-dimensional carbon material is especially suitable due to an enhanced saturation effect and increased adhesion to the surface of the waveguide. 14,18 THz QCLs exhibit intersubband gain dynamics on a picosecond timescale, [19][20][21][22][23] thus shorter than the cavity round trip time t rt (typically several ten picoseconds), such that established models of mode-locking with a slow absorber only allow for stable pulses in a very restricted parameter range. 24 Our Maxwell-Bloch-type simulation approach extends the classical mode-locking equations to include optical interference effects, such as spatial hole burning (SHB), 3,25 broadening the parameter range where pulse formation is possible.…”

Theory of Hybrid Microwave–Photonic Quantum Devices

“…The latter applies, for example, to QCLs where the gain recovery time is typically much shorter than the roundtrip time. [ 21,80 ] The modulated part of the gain coefficient can then approximately be written as $$g_{\Delta }(x,t) =g_{u}u_{\Delta }(x,t)$$, with some proportionality factor $$g_{u}$$. To evaluate the modulation in the vicinity of the optical pulse, a co‐moving reference frame is introduced via the retarded time coordinate $$t^{\prime }=t-xn_{\omega }/c$$.…”