Steady-state<i>ab initio</i>laser theory for fully or nearly degenerate cavity modes

Burkhardt, Stephan; Liertzer, Matthias; Krimer, Dmitry O.; Rotter, Stefan

doi:10.1103/physreva.92.013847

Cited by 19 publications

(40 citation statements)

References 52 publications

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“…Thus, by transiting from one EP to another EP the direction of unidirectional emission is completely reversedan effect demonstrated to our knowledge for the first time here. The fact that the maximum possible chirality values for the lasing system are reached here very robustly can be attributed to the fact that the nonlinear interactions in a laser tend to reinforce a modal chirality already predetermined by the resonator geometry (34).…”

Section: Controlling Emission Direction Of a Wgm Microlaser At Epsmentioning

confidence: 95%

Chiral modes and directional lasing at exceptional points

Peng

Özdemir

Liertzer

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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534

395

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Controlling the emission and the flow of light in micro-and nanostructures is crucial for on-chip information processing. Here we show how to impose a strong chirality and a switchable direction of light propagation in an optical system by steering it to an exceptional point (EP)-a degeneracy universally occurring in all open physical systems when two eigenvalues and the corresponding eigenstates coalesce. In our experiments with a fiber-coupled whispering-gallery-mode (WGM) resonator, we dynamically control the chirality of resonator modes and the emission direction of a WGM microlaser in the vicinity of an EP: Away from the EPs, the resonator modes are nonchiral and laser emission is bidirectional. As the system approaches an EP, the modes become chiral and allow unidirectional emission such that by transiting from one EP to another one the direction of emission can be completely reversed. Our results exemplify a very counterintuitive feature of nonHermitian physics that paves the way to chiral photonics on a chip.exceptional points | asymmetric backscattering | chiral modes | directional lasing | whispering-gallery-mode resonator C hirality lies at the heart of the most fascinating and fundamental phenomena in modern physics like the quantum Hall effect (1), Majorana fermions (2), and the surface conductance in topological insulators (3) as well as in p-wave superconductors (4). In all of these cases chiral edge states exist, which propagate along the surface of a sample in a specific direction. The chirality (or handedness) is secured by specific mechanisms, which prevent the same edge state from propagating in the opposite direction. For example, in topological insulators the backscattering of edge states is prevented by the strong spin-orbit coupling of the underlying material.Transferring such concepts to the optical domain is a challenging endeavor that has recently attracted considerable attention. Quite similar to their electronic counterparts, the electromagnetic realizations of chiral states typically require either a mechanism that breaks time-reversal symmetry (5) or one that gives rise to a spinorbit coupling of light (6-8). Because such mechanisms are often not available or difficult to realize, alternative concepts have recently been proposed, which require, however, a careful arrangement of many optical resonators in structured arrays (9,10).Here, we demonstrate explicitly that the above demanding requirements on the realization of chiral optical states propagating along the surface of a system can all be bypassed by using a single resonator with non-Hermitian scattering. The key insight in this respect is that a judiciously chosen non-Hermitian outcoupling of two near-degenerate resonator modes to the environment leads to an asymmetric backscattering between them [an effect that has been ignored in previous models based on coupled mode theory (11)] and thus to an effective breaking of the time-reversal symmetry that supports chiral behavior (12). More specifically, we show that a strong spatia...

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Section: Controlling Emission Direction Of a Wgm Microlaser At Epsmentioning

confidence: 95%

Chiral modes and directional lasing at exceptional points

Peng

Özdemir

Liertzer

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

534

395

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“…In this work, we show rigorously using degenerate perturbation theory on the SALT equations that the circulating modes used in Ref. [7], along with standing-wave modes that are linear combinations of the clockwise and counterclockwise circulating modes, are the only solutions to * daveliu@mit.edu † stevenj@math.mit.edu SALT in the C nv degenerate case. We complement those results with semianalytical closed-form expressions for the stability eigenvalues of the Maxwell-Bloch equations linearized about these lasing solutions (Sec.…”

Section: Introductionmentioning

confidence: 99%

“…V A, generalizing earlier SALT methods, where a numerical nonlinear solver is the only option; in this regime, our focus is on finding a degenerate lasing mode in SALT (if one exists), and we defer to the results of Ref. [7] for checking its stability after a solution far above threshold is found.…”

Section: Introductionmentioning

confidence: 99%

“…Figure 1 gives examples of degenerate lasing modes in C nv geometries. Previous work [7] showed how the steady-state degenerate solutions of SALT (steady-state ab initio lasing theory [8][9][10][11][12]) could be found from an educated guess of a superposition of the threshold degenerate modes, and how their stability could be computed numerically. In this work, we show rigorously using degenerate perturbation theory on the SALT equations that the circulating modes used in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…[7], a full linear-stability analysis (Sec. III B) was applied numerically to the Maxwell-Bloch equations of lasing in order to check whether the steady state was stable, and stability of the solution was also analyzed when the degeneracy was broken by a perturbation.…”

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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Continuum-atomistic simulation of picosecond laser heating of copper with electron heat capacity from ab initio calculation

Zhang

2016

Chemical Physics Letters

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On the basis of ab initio quantum mechanics (QM) calculation, the obtained electron heat capacity is implemented into energy equation of electron subsystem in two temperature model (TTM). Upon laser irradiation on the copper film, energy transfer from the electron subsystem to the lattice subsystem is modeled by including the electron-phonon coupling factor in molecular dynamics (MD) and TTM coupled simulation. The results show temperature and thermal melting difference between the QM-MD-TTM integrated simulation and pure MD-TTM coupled simulation. The successful construction of the QM-MD-TTM integrated simulation provide a general way that is accessible to other metals in laser heating.

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

Cited by 19 publications

References 52 publications

Chiral modes and directional lasing at exceptional points

Chiral modes and directional lasing at exceptional points

Symmetry, stability, and computation of degenerate lasing modes

Continuum-atomistic simulation of picosecond laser heating of copper with electron heat capacity from ab initio calculation

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