Steffen Wittek

Enhanced sensitivity at higher-order exceptional points

Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce. In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency, unidirectional invisibility, band merging, topological chirality and laser mode selectivity. Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations. Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies, their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement—specifically, a ternary, parity–time-symmetric photonic laser molecule—with a carefully tailored gain–loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics, microwaves and atomic physics.

Topological insulator laser: Experiments

Topological protection for lasers Ideas based on topology, initially developed in mathematics to describe the properties of geometric space under deformations, are now finding application in materials, electronics, and optics. The main driver is topological protection, a property that provides stability to a system even in the presence of defects. Harari et al. outline a theoretical proposal that carries such ideas over to geometrically designed laser cavities. The lasing mode is confined to the topological edge state of the cavity structure. Bandres et al. implemented those ideas to fabricate a topological insulator laser with an array of ring resonators. The results demonstrate a powerful platform for developing new laser systems. Science, this issue p. eaar4003, p. eaar4005 Lasing is observed in an edge mode of a designed optical topological insulator. INTRODUCTION Physical systems that exhibit topological invariants are naturally endowed with robustness against perturbations, as was recently demonstrated in many settings in condensed matter, photonics, cold atoms, acoustics, and more. The most prominent manifestations of topological systems are topological insulators, which exhibit scatter-free edge-state transport, immune to perturbations and disorder. Recent years have witnessed intense efforts toward exploiting these physical phenomena in the optical domain, with new ideas ranging from topology-driven unidirectional devices to topological protection of path entanglement. But perhaps more technologically relevant than all topological photonic settings studied thus far is, as proposed by the accompanying theoretical paper by Harari et al., an all-dielectric magnet-free topological insulator laser, with desirable properties stemming from the topological transport of light in the laser cavity. RATIONALE We demonstrate nonmagnetic topological insulator lasers. The topological properties of the laser system give rise to single-mode lasing, robustness against fabrication defects, and notably higher slope efficiencies compared to those of the topologically trivial counterparts. We further exploit the properties of the active topological platform by assembling topological insulator lasers from S-chiral microresonators that enforce predetermined unidirectional lasing even in the absence of magnetic fields. RESULTS Our topological insulator laser system is an aperiodic array of 10 unit cell–by–10 unit cell coupled ring resonators on an InGaAsP quantum wells platform. The active lattice uses the topological architecture suggested in the accompanying theoretical paper. This two-dimensional setting is composed of a square lattice of ring resonators coupled to each other by means of link rings. The intermediary links are judiciously spatially shifted to introduce a set of hopping phases, establishing a synthetic magnetic field and two topological band gaps. The gain in this laser system is provided by optical pumping. To promote lasing of the topologically protected edge modes, we pump the outer perimeter of the array while leaving the interior lossy. We find that this topological insulator laser operates in single mode even considerably above threshold, whereas the corresponding topologically trivial realizations lase in multiple modes. Moreover, the topological laser displays a slope efficiency that is considerably higher than that in the corresponding trivial realizations. We further demonstrate the topological features of this laser by observing that in the topological array, all sites emit coherently at the same wavelength, whereas in the trivial array, lasing occurs in localized regions, each at a different frequency. Also, by pumping only part of the topological array, we demonstrate that the topological edge mode always travels along the perimeter and emits light through the output coupler. By contrast, when we pump the trivial array far from the output coupler, no light is extracted from the coupler because the lasing occurs at stationary modes. We also observe that, even in the presence of defects, the topological protection always leads to more efficient lasing compared to that of the trivial counterpart. Finally, to show the potential of this active system, we assemble a topological system based on S-chiral resonators, which can provide new avenues to control the topological features. CONCLUSION We have experimentally demonstrated an all-dielectric topological insulator laser and found that the topological features enhance the lasing performance of a two-dimensional array of microresonators, making them lase in unison in an extended topologically protected scatter-free edge mode. The observed single longitudinal-mode operation leads to a considerably higher slope efficiency as compared to that of a corresponding topologically trivial system. Our results pave the way toward a new class of active topological photonic devices, such as laser arrays, that can operate in a coherent fashion with high efficiencies. Topological insulator laser. (A) Top-view image of the lasing pattern (topological edge mode) in a 10 unit cell–by–10 unit cell array of topologically coupled resonators and the output ports. (B) Output intensity versus pump intensity for a topological insulator laser and its trivial counterpart. The enhancement of the slope efficiency is about threefold. Comparing the power emitted in the single mode of the topological array to that of the highest power mode in the trivial array, the topological outperforms the trivial by more than a factor of 10

Fiber chirped pulse amplifier at 2.08 μm emitting 383-fs pulses at 10 nJ and 7 MHz.

An all-polarization maintaining (PM) fiber chirped pulse amplifier system at 2.08 μm based on thulium:holmium codoped gain fibers is reported. An inhouse built oscillator emits pulses at a repetition rate of 7 MHz with a spectral full width at half-maximum (FWHM) bandwidth of 23.5 nm at 2.8 mW average output power. The pulses are temporally stretched and subsequently amplified in a double-stage amplifier setup. The stretched pulses are compressed to 383 fs by use of a Martinez-style setup at an output pulse energy of 10.2 nJ. By neglecting temporal stretching, high peak powers in a single amplifier stage led to Raman soliton formation at 2.3 μm.

Mode-selective amplification in a large mode area Yb-doped fiber using a photonic lantern

We demonstrate selective spatial mode amplification in a few mode, double-clad Yb-doped large mode area (LMA) fiber, utilizing an all-fiber photonic lantern. Amplification to multi-watt output power is achieved while preserving high spatial mode selectivity. We observe gain values of over 12 dB for all modes: LP01, LP11a, and LP11b, when amplified individually. Additionally, we investigate the simultaneous amplification of LP01+LP11a and LP11a+LP11b, and the resultant mode competition. The proposed architecture allows for the reconfigurable excitation of spatial modes in the LMA fiber amplifiers, and represents a promising method that could enable dynamic spatial mode control in high power fiber lasers.

Topological Photonics and Topological Insulator Lasers

We present, in theory and experiments, the first Topological Insulator Lasers: lasers where the cavity acts as a “superconductor for light”, maintaining slope high efficiency even in the presence of defects and disorder.

Erratum: Enhanced sensitivity at higher-order exceptional points

This corrects the article DOI: 10.1038/nature23280

Higher-order exceptional points in photonic systems (Conference Presentation)

Student contribution: In recent years, non-Hermitian degeneracies, also known as exceptional points (EPs), have emerged as a new paradigm for engineering the response of optical systems. This class of degeneracies represents points in parameter space where the eigenvalues and their corresponding eigenvectors simultaneously coalesce [1,2]. Among the large set of non-conservative photonic systems, parity-time (PT) symmetric arrangements are of particular interest since they provide an excellent platform to study the physics and properties of non-Hermitian degeneracies [3,4]. So far, the abrupt nature of the phase transitions at EPs has led to a number of new functionalities such as loss-induced transparency [5], unidirectional invisibility [6,7], and single mode lasing [8-11]. In addition, it has been suggested that the bifurcation properties associated with second-order exceptional points can be utilized to achieve enhanced sensitivity in micro-resonator arrangements [11]. Of interest is to use even higher-order exceptional points that in principle could further amplify the effect of perturbations. While such higher-order singularities have been theoretically studied in a number of recent works [13,14], their experimental realization in the optical domain has so far remained out of reach. In this paper, for the first time, we show the emergence of third order exceptional points in ternary parity-time-symmetric coupled resonator lasers by judiciously designing the gain/loss distribution and coupling strengths following a recursive bosonic quantization procedure. Subsequently, the nature of the third order exceptional point is confirmed through the cubic root response of this ternary system to external perturbations. Our work may pave the way towards the utilization of higher order exceptional points in designing ultrasensitive photonic arrangements. References [1] W. D. Heiss, J. of Phys. A: Mathematical and Theoretical 45, 444016 (2012). [2] N. Moiseyev, Non-Hermitian Quantum Mechanics. (Cambridge University Press, 2011). [3] K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 103904 (2008). [4] C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010). [5] A. Guo et al., Phys. Rev. Lett. 103, 093902 (2009). [6] B. Peng et al., Nat. Phys. 10, 394 (2015). [7] A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012). [7] M. Miri, P. Likamwa, D. N. Christodoulides, Opt. Lett. 37, 764 (2012) [8] H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Science 346, 975 (2014). [9] L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, X. Zhang, Science 346, 972 (2014). [11] H. Hodaei et al., Laser & Photon. Rev. 10, 494 (2016). [12] J. Wiersig, Phys. Rev. Lett. 112, 203901 (2014). [13] G. Demange, and E.-M. Graefe, J. Phys. Math. Theor. 45, 25303 (2012). [14] M.H. Teimourpour, R. El-Ganainy, A. Eisfeld, A .Szameit, D.N. Christodoulides, Phys. Rev. A 90, 053817 (2014).

FCPA System at 2.08 µm and 7 MHz in All-PM Design Delivering Pulses at 10 nJ and 390 fs Pulse Duration

We report on an all-PM fiber oscillator-CPA system at 2.08 μm running at 7 MHz pulse repetition rate with 10 nJ pulse energy and 390 fs pulse duration behind external compression.