Scalable numerical approach for the steady-state<i>ab initio</i>laser theory

Esterhazy, S.; Liu, Dazhi; Liertzer, Matthias; Cerjan, Alexander; Li, Ge; Makris, Konstantinos G.; Stone, A. Douglas; Melenk, Jens Markus; Johnson, Steven G.; Rotter, Stefan

doi:10.1103/physreva.90.023816

Cited by 54 publications

(103 citation statements)

References 66 publications

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“…Due to their time-dependent nature these equations are, however, usually difficult to solve for all but the most simple cases. In recent years, a much more efficient approach named steady state ab initio lasing theory (SALT) has emerged, which can be used to describe the steady-state lasing of lasers [17][18][19][20][21][22][23]. Among other advances, this new framework has shed light on weakly-scattering random lasers [24], on pump-induced exceptional points [11,12,25,26] and on coherent perfect absorption [27,28] and has opened up new ways of controlling the emission patterns of random as well as of microcavity lasers [29,30].…”

Section: Introductionmentioning

confidence: 99%

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

et al. 2015

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We investigate the range of validity of the recently developed steady-state ab-initio laser theory (SALT). While very efficient in describing various microlasers, SALT is conventionally believed not to be applicable to lasers featuring fully or nearly degenerate pairs of resonator modes above the lasing threshold. Here we demonstrate how SALT can indeed be extended to describe such cases as well, with the effect that we significantly broaden the theory's scope. In particular, we show how to use SALT in conjunction with a linear stability analysis to obtain stable single-mode lasing solutions that involve a degenerate mode pair. Our flexible and efficient approach is tested on one-dimensional ring lasers as well as on two-dimensional microdisk lasers with broken symmetry.

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Section: Introductionmentioning

confidence: 99%

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

et al. 2015

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“…4(c). To determine the net-polarization of modes from the 3D simulations on a quantitative level, we expect that taking into account non-linear interactions between the laser modes [26] as well as effects, which are specific to the employed quantum cascade structures [27] will be necessary. An incoherent far-field superposition of 20 modes with the highest PNet is depicted in Fig.…”

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confidence: 99%

Random lasers for broadband directional emission

Schönhuber

Brandstetter

Hisch

et al. 2016

Optica

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Broadband coherent light sources are becoming increasingly important for sensing and spectroscopic applications, especially in the mid-infrared and terahertz (THz) spectral regions, where the unique absorption characteristics of a whole host of molecules are located. The desire to miniaturize such light emitters has recently lead to spectacular advances with compact on-chip lasers that cover both of these spectral regions. The long wavelength and the small size of the sources result in a strongly diverging laser beam that is difficult to focus on the target that one aims to perform spectroscopy with. Here, we introduce an unconventional solution to this vexing problem relying on a random laser to produce coherent broadband THz radiation as well as an almost diffraction limited far-field emission profile. Our random lasers do not require any fine-tuning and thus constitute a promising example of practical device applications for random lasing.Various spectroscopic techniques rely on the specific absorption features of numerous molecules within the midinfrared and terahertz (THz) spectral regions, which allow their unambiguous identification. Although broadband coherent sources of radiation are already available within these frequency regions [1][2][3][4][5], a compact size and electrically pumped operation are additionally desired for actual applications. These criteria are fulfilled by quantum cascade lasers (QCLs), semiconductor sources which are able to provide broadband emission at mid-infrared [6,7] and THz [8,9] frequencies. However, for typically used THz QCL waveguides the output aperture is on the order of 10 µm, while the emission wavelength is about 100 µm. This, in fact, leads to a very divergent output beam, which is additionally distorted by interference effects [10,11]. Since external optical elements such as lenses or antennas are difficult to handle on a large scale [12,13], several monolithic concepts have been pursued to address this issue. To improve the far-field for facet emission, e.g., a 3rd order distributed feedback (DFB) grating can be used [14]. Another approach is to coherently emit from a large area on the laser surface. In contrast to interband semiconductor lasers, QCLs can only generate in-plane radiation due to intersubband selection rules, preventing the realization of VCSELtype resonators. Thus several concepts have been developed to couple out the in-plane cavity mode in vertical direction, including 2nd order DFB gratings [15,16] , and photonic crystal (PhC) cavities [17]. Recently, also non-periodic resonator structures such as graded photonic heterostructures [18], or quasicrystal cavities [19,20] have been developed. However, all on-chip techniques providing surface emission demonstrated so far are designed to support a single laser mode only, while for many spectroscopic applications a broadband coherent light source is necessary. To achieve the objective of a broadband and at the same time very collimated laser light emission in the THz regime, we propose here a radical ...

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“…Our perturbative solution near threshold confirms an ansatz in the earlier degenerate SALT work [7], in which the circulating and standing-wave solutions were guessed as starting points for a SALT solver and it was conjectured that the resulting four solutions were the only possibilities. Furthermore, we have presented an efficient numerical scheme to track these solutions far above threshold via numerical SALT solvers [14] combined with a simple technique to correct for numerical symmetry breaking. And finally, we have shown that the degeneracy of the C n group Sec.…”

Section: Discussionmentioning

confidence: 99%

“…As explained in Ref. [14], the process for solving for lasing modes begins with the linear problem for the passive poles. Because both the real and imaginary parts of the passive poles are split by the discretization error, the modes will lase at different pump strengths, and even after both modes lase we cannot construct a linear combination of them because the two modes satisfy equations with different real eigenfrequencies.…”

Section: C Nv Symmetry Broken By Discretizationmentioning

confidence: 99%

“…This equation can be efficiently solved numerically by adapting standard techniques from computational electromagnetism [14]. As described below and also in previous work [2,7], the SALT framework applies very naturally to lasing of degenerate microcavities, assuming a stable degenerate steady state exists, but it turns out that there are two complications.…”

Section: Introductionmentioning

confidence: 99%

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Symmetry, stability, and computation of degenerate lasing modes

Liu

Zhen

et al. 2017

Phys. Rev. A

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We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its "chiral" intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.

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Scalable numerical approach for the steady-stateab initiolaser theory

Cited by 54 publications

References 66 publications

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

Random lasers for broadband directional emission

Symmetry, stability, and computation of degenerate lasing modes

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