Farid Kalhor, Thomas Thundat, and Zubin Jacob. 2/8/2016.

Universal spin-momentum locked optical forces

. Applied Physics Letters, 108.

Evanescent electromagnetic waves possess spin-momentum locking, where the direction of propagation (momentum) is locked to the inherent polarization of the wave (transverse spin). We study the optical forces arising from this universal phenomenon and show that the fundamental origin of recently reported non-trivial optical chiral forces is spin-momentum locking. For evanescent waves, we show that the direction of energy flow, the direction of decay, and the direction of spin follow a right hand rule for three different cases of total internal reflection, surface plasmon polaritons, and HE11 mode of an optical fiber. Furthermore, we explain how the recently reported phenomena of lateral optical force on chiral and achiral particles are caused by the transverse spin of the evanescent field and the spin-momentum locking phenomenon. Finally, we propose an experiment to identify the unique lateral forces arising from the transverse spin in the optical fiber and point to fundamental differences of the spin density from the well-known orbital angular momentum of light. Our work presents a unified view on spin-momentum locking and how it affects optical forces on chiral and achiral particles.

See also: Spin, Photonics
Sarang Pendharker, Yu Guo, Farhad Khosravi, and Zubin Jacob. 3/17/2017.

PT-symmetric spectral singularity and negative-frequency resonance

. PHYSICAL REVIEW A, 95, 3.

Vacuum consists of a bath of balanced and symmetric positive- and negative-frequency fluctuations. Media in relative motion or accelerated observers can break this symmetry and preferentially amplify negative-frequency modes as in quantum Cherenkov radiation and Unruh radiation. Here, we show the existence of a universal negative-frequency-momentum mirror symmetry in the relativistic Lorentzian transformation for electromagnetic waves. We show the connection of our discovered symmetry to parity-time (PT) symmetry in moving media and the resulting spectral singularity in vacuum fluctuation-related effects. We prove that this spectral singularity can occur in the case of two metallic plates in relative motion interacting through positive- and negative-frequency plasmonic fluctuations (negative-frequency resonance). Our work paves the way for understanding the role of PT-symmetric spectral singularities in amplifying fluctuations and motivates the search for PT symmetry in novel photonic systems.

See also: Photonics, Quantum
Prashant Shekhar, Marek Malac, Vaibhav Gaind, Neda Dalili, Al Meldrum, and Zubin Jacob. 3/31/2017.

Momentum-Resolved Electron Energy Loss Spectroscopy for Mapping the Photonic Density of States

. ACS Photonics, 4, 4, Pp. 1009-1014.

Strong nanoscale light–matter interaction is often accompanied by ultraconfined photonic modes and large momentum polaritons existing far beyond the light cone. A direct probe of such phenomena is difficult due to the momentum mismatch of these modes with free space light, however, fast electron probes can reveal the fundamental quantum and spatially dispersive behavior of these excitations. Here, we use momentum-resolved electron energy loss spectroscopy (q-EELS) in a transmission electron microscope to explore the optical response of plasmonic thin films including momentum transfer up to wavevectors (q) significantly exceeding the light line wave vector. We show close agreement between experimental q-EELS maps, theoretical simulations of fast electrons passing through thin films and the momentum-resolved photonic density of states (q-PDOS) dispersion. Although a direct link between q-EELS and the q-PDOS exists for an infinite medium, here we show fundamental differences between q-EELS measurements and the q-PDOS that must be taken into consideration for realistic finite structures with no translational invariance along the direction of electron motion. Our work paves the way for using q-EELS as the preeminent tool for mapping the q-PDOS of exotic phenomena with large momenta (high-q) such as hyperbolic polaritons and spatially dispersive plasmons.

See also: Photonics
Li-Ping Yang, Hong X. Tang, and Zubin Jacob. 1/22/2018.

Concept of quantum timing jitter and non-Markovian limits in single-photon detection

. Physical Review A, 97.

Single atoms form a model system for understanding the limits of single-photon detection. Here, we develop a non-Markovian theory of single-photon absorption by a two-level atom to place limits on the absorption (transduction) time. We show the existence of a finite rise time in the probability of excitation of the atom during the absorption event which is infinitely fast in previous Markov theories. This rise time is governed by the bandwidth of the atom-field interaction spectrum and leads to a fundamental jitter in time stamping the absorption event. Our theoretical framework captures both the weak and strong atom-field coupling regimes and sheds light on the spectral matching between the interaction bandwidth and single-photon Fock state pulse spectrum. Our work opens questions whether such jitter in the absorption event can be observed in a multimode realistic single-photon detector. Finally, we also shed light on the fundamental differences between linear and nonlinear detector outputs for single-photon Fock-state vs coherent-state pulses.

See also: Photonics, Quantum
Saman Jahani, Sangsik Kim, Jonathan Atkinson, Justin C. Wirth, Farid Kalhor, Abdullah Al Noman, Ward D. Newman, Prashant Shekhar, Kyunghun Han, Vien Van, Raymond G. DeCorby, Lukas Chrostowski, Minghao Qi, and Zubin Jacob. 5/14/2018.

Controlling evanescent waves using silicon photonic all-dielectric metamaterials for dense integration

. Nature Communications, 9.

Ultra-compact, densely integrated optical components manufactured on a CMOS-foundry platform are highly desirable for optical information processing and electronic-photonic co-integration. However, the large spatial extent of evanescent waves arising from nanoscale confinement, ubiquitous in silicon photonic devices, causes significant cross-talk and scattering loss. Here, we demonstrate that anisotropic all-dielectric metamaterials open a new degree of freedom in total internal reflection to shorten the decay length of evanescent waves. We experimentally show the reduction of cross-talk by greater than 30 times and the bending loss by greater than 3 times in densely integrated, ultra-compact photonic circuit blocks. Our prototype all-dielectric metamaterial-waveguide achieves a low propagation loss of approximately 3.7±1.0 dB/cm, comparable to those of silicon strip waveguides. Our approach marks a departure from interference-based confinement as in photonic crystals or slot waveguides, which utilize nanoscale field enhancement. Its ability to suppress evanescent waves without substantially increasing the propagation loss shall pave the way for all-dielectric metamaterial-based dense integration.

Saman Jahani, Hangqi Zhao, and Zubin Jacob. 7/12/2018.

Switching Purcell effect with nonlinear epsilon-near-zero media

. Applied Physics Letters, 113.

An optical topological transition is defined as the change in the photonic iso-frequency surface around epsilon-near-zero (ENZ) frequencies which can considerably change the spontaneous emission of a quantum emitter placed near a metamaterial slab. Here, we show that due to the strong Kerr nonlinearity at ENZ frequencies, a high-power pulse can induce a sudden transition in the topology of the iso-frequency dispersion curve, leading to a significant change in the transmission of propagating as well as evanescent waves through the metamaterial slab. This evanescent wave switch effect allows for the control of spontaneous emission through modulation of the Purcell effect. We develop a theory of the enhanced nonlinear response of ENZ media to s and p polarized inputs and show that this nonlinear effect is stronger for p polarization and is almost independent of the incident angle. We perform finite-difference time-domain simulations to demonstrate the transient response of the metamaterial slab to an ultrafast pulse and fast switching of the Purcell effect at the sub-picosecond scale. The Purcell factor changes at ENZ by almost a factor of three which is an order of magnitude stronger than that away from ENZ. We also show that due to the inhomogeneous spatial field distribution inside the multilayer metal-dielectric super-lattice, a unique spatial topological transition metamaterial can be achieved by the control pulse induced nonlinearity. Our work can lead to ultra-fast control of quantum phenomena in ENZ metamaterials.

TODD VAN MECHELEN and Zubin Jacob. 8/21/2018.

Quantum gyroelectric effect: Photon spin-1 quantization in continuum topological bosonic phases

. Physical Review A, 98.

Topological phases of matter arise in distinct fermionic and bosonic flavors. The fundamental differences between them are encapsulated in their rotational symmetries—the spin. Although spin quantization is routinely encountered in fermionic topological edge states, analogous quantization for bosons has proven elusive. To this end, we develop the complete electromagnetic continuum theory characterizing 2+1D topological bosons, taking into account their intrinsic spin and orbital angular momentum degrees of freedom. We demonstrate that spatiotemporal dispersion (momentum and frequency dependence of linear response) captures the matter-mediated interactions between bosons and is a necessary ingredient for topological phases. We prove that the bulk topology of these 2+1D phases is manifested in transverse spin-1 quantization of the photon. From this insight, we predict two unique bosonic phases—one with even parity C = ±2 and one with odd C = ±1. To understand the even parity phase C = ±2, we introduce an exactly solvable model utilizing nonlocal optical Hall conductivity and reveal a single gapless photon at the edge. This unidirectional photon is spin-1 helically quantized, immune to backscattering, defects, and exists at the boundary of the C = ±2 bosonic phase and any interface-even vacuum. The contrasting phenomena of transverse quantization in the bulk, but longitudinal (helical) quantization on the edge is addressed as the quantum gyroelectric effect. We also validate our bosonic Maxwell theory by direct comparison with the supersymmetric Dirac theory of fermions. To accelerate the discovery of such bosonic phases, we suggest two probes of topological matter with broken time-reversal symmetry: momentum-resolved electron energy-loss spectroscopy and cold atom near-field measurement of nonlocal optical Hall conductivity.

Sarang Pendharker, Farid Kalhor, TODD VAN MECHELEN, Saman Jahani, Neda Nazemifard, Thomas Thundat, and Zubin Jacob. 8/30/2018.

Spin photonic forces in non-reciprocal waveguides

. Optics Express, 26, 18, Pp. 23898-23910.

Optical forces acting on particles - controlled by the intensity, polarization and direction of optical beams - have become an important tool in manipulation, sorting and analysis of nano/micro-particles. The nature of these forces has been well understood in reciprocal structures exhibiting time-reversal symmetries. Here, we investigate the nature of optical forces in non-reciprocal structures with non-degenerate counter-propagating modes. We consider the specific case of non-reciprocity induced via translational motion and show that the two counter-propagating modes in a moving slab-waveguide are not degenerate which results in a non-zero lateral and longitudinal force on a nanoparticle. We prove that these anomalous forces are fundamentally connected to near-field photonic spin in optical waveguides and explain their directionality using universal spin-momentum locking of evanescent waves. The presented results show that the interplay of photon spin and non-reciprocity can lead to unique avenues of controlling nanoscale optical forces on-chip.

See also: Spin, Photonics
Cristian L. Cortes and Zubin Jacob. 7/23/2018.

Fundamental figures of merit for engineering Förster resonance energy transfer

. Optics Express, 26, 15, Pp. 19371-19387.

Over the past 15 years there has been an ongoing debate regarding the influence of the photonic environment on Förster resonance energy transfer (FRET). Disparate results corresponding to enhancement, suppression and null effect of the photonic environment have led to a lack of consensus between the traditional theory of FRET and experiments. Here we show that the quantum electrodynamic theory (QED) of FRET near an engineered nanophotonic environment is exactly equivalent to an effective near-field model describing electrostatic dipole-dipole interactions. This leads to an intuitive and rigorously exact description of FRET, previously unavailable, bridging the gap between experimental observations and theoretical interpretations. Furthermore, we show that the widely used concept of Purcell factor variation is only important for understanding spontaneous emission and is an incorrect figure of merit (FOM) for analyzing FRET. To this end, we analyze the figures of merit which characterize FRET in a photonic environment 1) the FRET rate enhancement factor (FET), 2) FRET efficiency enhancement factor (Feff) and 3) Two-point spectral density (SEE) which is the photonic property of the environment governing FRET analogous to the local density of states that controls spontaneous emission. Counterintuitive to existing knowledge, we show that suppression of the Purcell factor is in fact necessary for enhancing the efficiency of the FRET process. We place fundamental bounds on the FRET figures of merit arising from material absorption in the photonic environment as well as key properties of emitters including intrinsic quantum efficiencies and orientational dependence. Finally, we use our approach to conclusively explain multiple recent experiments and predict regimes where the FRET rate is expected to be enhanced, suppressed or remain the same. Our work paves for a complete theory of FRET with predictive power for designing the ideal photonic environment to control FRET.

See also: Quantum, Photonics
TODD VAN MECHELEN and Zubin Jacob. 1/1/2019.

Photonic Dirac monopoles and skyrmions: spin-1 quantization

. Optical Materials Express, 9, 1, Pp. 95-111.

We introduce the concept of a photonic Dirac monopole, appropriate for photonic crystals, metamaterials and 2D materials, by utilizing the Dirac-Maxwell correspondence. We start by exploring the vacuum where the reciprocal momentum space of both Maxwell’s equations and the massless Dirac equation (Weyl equation) possess a magnetic monopole. The critical distinction is the nature of magnetic monopole charges, which are integer valued for photons but half-integer for electrons. This inherent difference is directly tied to the spin and ultimately connects to the bosonic or fermionic behavior. We also show the presence of photonic Dirac strings, which are line singularities in the underlying Berry gauge potential. While the results in vacuum are intuitively expected, our central result is the application of this topological Dirac-Maxwell correspondence to 2D photonic (bosonic) materials, as opposed to conventional electronic (fermionic) materials. Intriguingly, within dispersive matter, the presence of photonic Dirac monopoles is captured by nonlocal quantum Hall conductivity–i.e., a spatiotemporally dispersive gyroelectric constant. For both 2D photonic and electronic media, the nontrivial topological phases emerge in the context of massive particles with broken time-reversal symmetry. However, the bulk dynamics of these bosonic and fermionic Chern insulators are characterized by spin-1 and spin-½ skyrmions in momentum space, which have fundamentally different interpretations. This is exemplified by their contrasting spin-1 and spin-½ helically quantized edge states. Our work sheds light on the recently proposed quantum gyroelectric phase of matter and the essential role of photon spin quantization in topological bosonic phases.

See also: Photonics, Topological, Spin
Sean Molesky and Zubin Jacob. 3/18/2019.

Definition of polaritonic fluctuations in natural hyperbolic media

. Physical Review A, 99, 3.

The discovery of photonic hyperbolic dispersion surfaces in certain van der Waals bonded solids, such as hexagonal boron nitride and bismuth selenide (a topological insulator), offers intriguing possibilities for creating strongly modified light-matter interactions. However, open problems exist in quantifying electromagnetic field fluctuations in these media, complicating typical approaches for modeling photonic characteristics. Here, we address this issue by linking the identifying traits of hyperbolic response to a coupling between longitudinal and transverse fields that cannot occur in isotropic media. This description allows us to formulate a gauge theoretic description of the influence of hyperbolic response on electromagnetic fluctuations without explicitly imposing a characteristic size (model of nonlocality)—leading to formally bounded expressions so long as material absorption is included. We then apply this framework to two exemplary areas: the optical sum rule for modified spontaneous emission enhancement in a general uniaxial medium and thermal electromagnetic field fluctuations in hexagonal boron nitride and bismuth selenide. We find that while the sum rule is satisfied, it does not constrain the enhancement of light-matter interactions in either case. We also show that both hexagonal boron nitride and bismuth selenide possess broad spectral regions where the magnitude of electromagnetic field fluctuations are over 120 times larger, and over 800 times larger along specific angular directions, than they are in vacuum.

Prashant Shekhar, Sarang Pendharker, Douglas Vick, Marek Malac, and Zubin Jacob. 3/4/2019.

Fast electrons interacting with a natural hyperbolic medium: bismuth telluride

. Optics Express, 27, 5, Pp. 6970-6975.

Fast electrons interacting with matter have been instrumental for probing bulk and surface photonic excitations including Cherenkov radiation and plasmons. Additionally, fast electrons are ideal to investigate unique bulk and longitudinal photonic modes in hyperbolic materials at large wavevectors difficult to probe optically. Here, we use momentum-resolved electron energy loss spectroscopy (k-EELS) to perform the first experimental demonstration of high-k modes and hyperbolic Cherenkov radiation in the natural hyperbolic material Bi2Te3. This work establishes Bi2Te3 as one of the few viable natural hyperbolic materials in the visible and paves the way for k-EELS as a fundamental tool to probe hyperbolic media.

Farhad Khosravi, Cristian L. Cortes, and Zubin Jacob. 5/20/2019.

Spin photonics in 3D whispering gallery mode resonators

. Optics Express, 27, 11, Pp. 15846-15855.

Whispering gallery modes are known for possessing orbital angular momentum, however the interplay of local spin density, orbital angular momentum, and the near-field interaction with quantum emitters is far less explored. Here, we study the spin-orbit interaction of a circularly polarized dipole with the whispering gallery modes (WGMs) of a spherical resonator. Using an exact dyadic Green’s function approach, we show that the near-field interaction between the photonic spin of a circularly polarized dipole and the local electromagnetic spin density of whispering gallery modes gives rise to unidirectional behaviour where modes with either positive or negative orbital angular momentum are excited. We show that this is a manifestation of spin-momentum locking with the whispering gallery modes of the spherical resonator. We also discuss requirements for possible experimental demonstrations using Zeeman transitions in cold atoms or quantum dots, and outline potential applications of these previously overlooked properties. Our work firmly establishes local spin density, momentum and decay as a universal right-handed electromagnetic triplet for near-field light-matter interaction.

See also: Spin, Photonics
TODD VAN MECHELEN and Zubin Jacob. 6/19/2019.

Unidirectional Maxwellian spin waves

. Nanophotonics, 8, 8.

In this article, we develop a unified perspective of unidirectional topological edge waves in nonreciprocal media. We focus on the inherent role of photonic spin in nonreciprocal gyroelectric media, i.e. magnetized metals or magnetized insulators. Due to the large body of contradicting literature, we point out at the outset that these Maxwellian spin waves are fundamentally different from well-known topologically trivial surface plasmon polaritons. We first review the concept of a Maxwell Hamiltonian in nonreciprocal media, which immediately reveals that the gyrotropic coefficient behaves as a photon mass in two dimensions. Similar to the Dirac mass, this photonic mass opens bandgaps in the energy dispersion of bulk propagating waves. Within these bulk photonic bandgaps, three distinct classes of Maxwellian edge waves exist – each arising from subtle differences in boundary conditions. On one hand, the edge wave solutions are rigorous photonic analogs of Jackiw-Rebbi electronic edge states. On the other hand, for the exact same system, they can be high frequency photonic counterparts of the integer quantum Hall effect, familiar at zero frequency. Our Hamiltonian approach also predicts the existence of a third distinct class of Maxwellian edge wave exhibiting topological protection. This occurs in an intriguing topological bosonic phase of matter, fundamentally different from any known electronic or photonic medium. The Maxwellian edge state in this unique quantum gyroelectric phase of matter necessarily requires a sign change in gyrotropy arising from nonlocality (spatial dispersion). In a Drude system, this behavior emerges from a spatially dispersive cyclotron frequency that switches sign with momentum. A signature property of these topological electromagnetic edge states is that they are oblivious to the contacting medium, i.e. they occur at the interface of the quantum gyroelectric phase and any medium (even vacuum). This is because the edge state satisfies open boundary conditions – all components of the electromagnetic field vanish at the interface. Furthermore, the Maxwellian spin waves exhibit photonic spin-1 quantization in exact analogy with their supersymmetric spin-1/2 counterparts. The goal of this paper is to discuss these three foundational classes of edge waves in a unified perspective while providing in-depth derivations, taking into account nonlocality and various boundary conditions. Our work sheds light on the important role of photonic spin in condensed matter systems, where this definition of spin is also translatable to topological photonic crystals and metamaterials.

See also: Topological, Spin, Photonics
Ryan Starko-Bowes, Xueji Wang, Zhujing Xu, Sandipan Pramanik, Na Lu, Tongcang Li, and Zubin Jacob. 10/3/2019.

High-Temperature Polaritons in Ceramic Nanotube Antennas

. Nano letters, 19, 12, Pp. 8565-8571.

High-temperature thermal photonics presents unique challenges for engineers as the database of materials that can withstand extreme environments are limited. In particular, ceramics with high temperature stability that can support coupled light-matter excitations, that is, polaritons, open new avenues for engineering radiative heat transfer. Hexagonal boron nitride (hBN) is an emerging ceramic 2D material that possesses low-loss polaritons in two spectrally distinct mid-infrared frequency bands. The hyperbolic nature of these frequency bands leads to a large local density of states (LDOS). In 2D form, these polaritonic states are dark modes, bound to the material. In cylindrical form, boron nitride nanotubes (BNNTs) create subwavelength particles capable of coupling these dark modes to radiative ones. In this study, we leverage the high-frequency optical phonons present in BNNTs to create strong mid-IR thermal antenna emitters at high temperatures (938 K). Through direct measurement of thermal emission of a disordered system of BNNTs, we confirm their radiative polaritonic modes and show that the antenna behavior can be observed even in a disordered system. These are among the highest-frequency optical phonon polaritons that exist and could be used as high-temperature mid-IR thermal nanoantenna sources.

Chinmay Khandekar and Zubin Jacob. 10/15/2019.

Thermal spin photonics in the near-field of nonreciprocal media

. New Journal of Physics, 21.

The interplay of spin angular momentum and thermal radiation is a frontier area of interest to nanophotonics as well as topological physics. Here, we show that a thick planar slab of a nonreciprocal material, despite being at thermal equilibrium with its environment, can exhibit nonzero photon spin angular momentum and nonzero radiative heat flux in its vicinity. We identify them as the persistent thermal photon spin and the persistent planar heat current respectively. With a practical example system, we reveal that the fundamental origin of these phenomena is connected to the spin-momentum locking of thermally excited evanescent waves. We also discover spin magnetic moment of surface polaritons that further clarifies these features. We then propose an imaging experiment based on Brownian motion that allows one to witness these surprising features by directly looking at them using a lab microscope. We further demonstrate the universal behavior of these near-field thermal radiation phenomena through a comprehensive analysis of gyroelectric, gyromagnetic and magneto-electric nonreciprocal materials. Together, these results expose a surprisingly little explored research area of thermal spin photonics with prospects for new avenues related to non-Hermitian topological photonics and radiative heat transport.

Farhad Khosravi, TODD VAN MECHELEN, and Zubin Jacob. 10/3/2019.

Dirac wire: Fermionic waveguides with longitudinal spin

. Physical Review B, 100, 15.

The interplay of photon spin and orbital angular momentum (OAM) in the optical fiber (one-dimensional waveguide) has recently risen to the forefront of quantum nanophotonics. Here, we introduce the fermionic dual of the optical fiber, the Dirac wire, which exhibits unique electronic spin and OAM properties arising from confined solutions of the Dirac equation. The Dirac wires analyzed here represent cylindrical generalizations of the Jackiw-Rebbi domain wall and the minimal topological insulator, which are of significant interest in spintronics. We show the unique longitudinal spin arising from electrons confined to propagation in a wire, an effect which is fundamentally prohibited in planar geometries. Our work sheds light on the universal spatial dynamics of electron spin in confined geometries and the duality between electronic and photonic spin.

See also: Photonics, Spin
Zubin Jacob. 8/15/2012.

Quantum Plasmonics

. MRS Bulletin, 37, 8, Pp. 761-767.

Surface plasmon polaritons, combined excitations of light and free electrons of a metal, have emerged as an alternative information carrier for nanoscale circuitry due to their ability to confine light far below the size of the wavelength. They hold the potential to act as a revolutionary bridge between current diffraction-limited microphotonics and bandwidth-limited nanoelectronics. Interestingly, the nanoscale confinement achievable by plasmons also increases the interaction with quantum emitters, paving the way for quantum applications. Exotic non-classical properties of light such as entanglement and squeezing can be embedded into plasmons and faithfully transmitted and received. Recently, it was also shown that unique coupled plasmonic excitations can be engineered on the nanoscale with artificial media (metamaterials) to enhance and control light-matter interaction. A major departure from the conventional classical description of the plasmon is under development. The aim is to incorporate the “wave” nature of matter manifested in ultra-small metallic nanoparticles and the “particle” nature of light, which can play a role in future integrated circuits with capabilities of quantum information processing. This article reviews developments in the field of quantum nanophotonics, an exciting frontier of plasmonic applications ranging from single photon sources and quantum information transfer to single molecule sensing.

T. Galfsky, H. N. S. Krishnamoorthy, W. Newman, E. E. Narimanov, Z. Jacob, and V. M. Menon. 2015.

Active hyperbolic metamaterials: enhanced spontaneous emission and light extraction

. Optica, 2, 1, Pp. 62-65.

Hyperbolic metamaterials (HMMs) have recently garnered much attention because they possess the potential for broadband manipulation of the photonic density of states and subwavelength light confinement. These exceptional properties arise due to the excitation of electromagnetic states with high momentum (high-𝑘k modes). However, a major hindrance to practical applications of HMMs is the difficulty in coupling light out of these modes because they become evanescent at the surface of the metamaterial. Here we report the first demonstration, to our knowledge, of simultaneous spontaneous emission enhancement and outcoupling of high-𝑘k modes in an active HMM using a high-index-contrast bullseye grating. Quantum dots embedded inside the metamaterial are used for local excitation of high-𝑘k modes. This demonstration could pave the way for the development of photonic devices such as single-photon sources, ultrafast LEDs, and true nanoscale lasers.