Origin of terminal voltage variations due to self-mixing in terahertz frequency quantum cascade lasers

Andrew Grier,Lianhe H Li,Iman Kundu,Gary Agnew,Yah Leng Lim,James Keeley,Dragan Indjin,Thomas Taimre,Karl Bertling,Aleksandar D Rakić,A Giles Davies,Alexander Valavanis,Edmund H Linfield,Zoran Ikonić,Paul Harrison,Jonathan D Cooper,Paul Dean

doi:10.1364/oe.24.021948

Abstract

We explain the origin of voltage variations due to self-mixing in a terahertz (THz) frequency quantum cascade laser (QCL) using an extended density matrix (DM) approach. Our DM model allows calculation of both the current-voltage (I-V) and optical power characteristics of the QCL under optical feedback by changing the cavity loss, to which the gain of the active region is clamped. The variation of intra-cavity field strength necessary to achieve gain clamping, and the corresponding change in bias required to maintain a constant current density through the heterostructure is then calculated. Strong enhancement of the self-mixing voltage signal due to non-linearity of the (I-V) characteristics is predicted and confirmed experimentally in an exemplar 2.6 THz bound-to-continuum QCL.

Highlights

Quantum cascade lasers (QCLs) are compact semiconductor sources of terahertz (THz) frequency radiation that are capable of emission powers of up to 1 W [1] and maximum operating temperatures of 200 K [2]
The SM effect is described using the excess phase equation, obtained from the steady-state solution to the Lang–Kobayashi model [8,9,10]. This approach has been a mainstay of laser feedback interferometry (LFI) for more than three decades, and even though the model was developed for a generic diode laser, the resulting variation of the self-mixing signal, with respect to external cavity length agrees remarkably well with experimental observations for all semiconductor lasers including QCLs and interband cascade lasers (ICLs) [11]
We note that ∆L = −0.3 cm−1 corresponds to a power modulation of approximately 5 %, which is consistent with that observed experimentally [13]. In both the simulated and experimental data, a strong enhancement of the SM signal occurs near where the QCL turns off due to the onset of the negative differential resistance (NDR) region at I ≈ 257 A/cm2

Summary

Introduction

Quantum cascade lasers (QCLs) are compact semiconductor sources of terahertz (THz) frequency radiation that are capable of emission powers of up to 1 W [1] and maximum operating temperatures of 200 K [2]. The SM effect is described using the excess phase equation, obtained from the steady-state solution to the Lang–Kobayashi model [8,9,10] This approach has been a mainstay of LFI for more than three decades, and even though the model was developed for a generic diode laser, the resulting variation of the self-mixing signal, with respect to external cavity length (or small frequency shifts) agrees remarkably well with experimental observations for all semiconductor lasers including QCLs and interband cascade lasers (ICLs) [11]. The full details of the DM model are described in Ref. [16] here we reiterate some relevant details for clarity of the present work

Density matrix model

Free-running QCL characteristics

Self-mixing interferometry

Results

Conclusion