Non-Lorentzian Local Density of States in Coupled Photonic Crystal Cavities Probed by Near- and Far-Field Emission

Pellegrino, Daniele; Balestri, Dario; Granchi, Nicoletta; Ciardi, Matteo; Intonti, Francesca; Pagliano, Francesco; Silov, A. Yu.; Otten, F. W. M. van; Wu, Tong; Vynck, Kevin; Lalanne, Philippe; Fiore, Andrea; Gurioli, Massimo

doi:10.1103/physrevlett.124.123902

Cited by 20 publications

(22 citation statements)

References 28 publications

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“…In addition to generating subradiance or superradiance, the CDOS contribution in the interferometric emission process may also influence the spectral lineshape. An interesting situation is that of two coupled photonic cavities generating a LDOS with a non-Lorentzian spectrum, which can be achieved by selecting two L3 cavities with unbalanced losses [28]. This situation goes beyond the high-Q model used above, and the expansion (18) for the LDOS and CDOS has to be replaced by a more general expansion in QNMs (for an introduction to QNMs in photonics, see for example [27]).…”

Section: B Coupled Cavities With Non-lorentzian Spectrummentioning

confidence: 99%

Purcell effect with extended sources: The role of the cross density of states

Carminati,

Gurioli

2021

Preprint

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We analyze the change in the spontaneous decay rate, or Purcell effect, of an extended quantum emitter in a structured photonic environment. Based on a simple theory, we show that the crossdensity of states is the central quantity driving interferences in the emission process. Using numerical simulations in realistic photonic cavity geometries, we demonstrate that a structured cross-density of states can induce subradiance or superradiance, and change subtantially the emission spectrum. Interestingly, the spectral lineshape of the Purcell effect of an extended source cannot be predicted from the sole knowledge of the spectral dependence of the local density of states.

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Section: B Coupled Cavities With Non-lorentzian Spectrummentioning

confidence: 99%

Purcell effect with extended sources: The role of the cross density of states

Carminati,

Gurioli

2021

Preprint

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“…This result can be easily understood by formulating Equations (1) and (2) in terms of Fano asymmetry parameters, following the approach of ref. [31]. It is lengthy but straightforward (see Supporting Information) to show (here:

ε = false(ω_{X} - ω_{n} false) / {normalΓ}_{n}

)

\begin{matrix} true \\ right γ^{*} ((), ω_{X}, boldr) & = & left \sum_{n} γ_{n}^{*} ((), ω_{X}, boldr) \\ = & left \sum_{n} \frac{6 π c^{3} ε_{o}}{{ω_{X}}^{2} ε {(boldr)}^{1 / 2}} γ_{X} \frac{{(||, ({\overset{E}{true}}_{n} (boldr) \cdot u))}^{2}}{{normalΓ}_{n}} F_{q_{n} ((), r)} ((), ε) \end{matrix}

\begin{matrix} true \\ right normalΔ ω ((), ω_{X}, boldr) & = & left \sum_{n} normalΔ ω_{n} ((), ω_{X}, boldr) \\ = & left - \sum_{n} \frac{3 π c^{3} ε_{o}}{{ω_{X}}^{2} ε {(boldr)}^{1 / 2}} γ_{X} \frac{{(||, ({\overset{E}{true}}_{n} (boldr) \cdot u))}^{2}}{{normalΓ}_{n}} F_{{q^{'}}_{n} ((), r)} ((), ε) \end{matrix}

...

…”

Section: Vacuum Optical Trapmentioning

confidence: 99%

“…The two Fano parameters

q_{n} false(boldr false)

and

q_{n}^{'} false(boldr false)

for Purcell effect and resonant Lamb shift are interconnected, both associated to the spatial phase of the n ‐th QNM, which is fully defined by the normalization and it is a physical observable. [ 25,31 ]

q_{n} (boldr) = - \frac{Re [((), {\tilde{boldE}}_{n} ((), r) \cdot boldu)]}{Im [((), {\tilde{boldE}}_{n} ((), r) \cdot boldu)]}; q_{n}^{'} (boldr) = - \frac{1 - q_{n} (boldr)}{1 + q_{n} (boldr)}

…”

Section: Vacuum Optical Trapmentioning

confidence: 99%

“…It has been shown that for two coupled QNMs of unbalanced losses, the imaginary part of the modal volumes can be large even for very high Q. [ 31 ] In addition this relevant non‐Hermitian effect can be quantitatively predicted with an analytic coupled mode theory. [ 31 ] Starting from these results, here we extend the coupled mode theory to the hybrid systems with quite large detuning by benchmarking it via FDTD simulations (see Supporting Information).…”

Section: Vacuum Optical Trapmentioning

confidence: 99%

“…It has been shown that, when only the cavity # j (being j = 1 or 2) is driven by

P_{j}

, the spectral dependence of

Im (c_{j} / P_{j})

(

c_{j}

represents the electric field amplitude inside the j ‐th cavity) is representative of the

γ^{*} false(ω_{X}, r_{j} false)

lineshapes at the at the antinodes

r_{j}

of cavity #j . [ 31 ] In addition, the coupled mode theory also gives the correct expression for the complex modal volumes of the QNM. Therefore (see the Supporting Information), we use the spectral dependence of

Re (c_{j} / P_{j})

to predict the resonant Lamb shift

Δ ω false(ω_{X}, r_{j} false)

lineshapes.…”

Section: Vacuum Optical Trapmentioning

confidence: 99%

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Vacuum Field Photonic Trap for Excitons

Gurioli

2021

Adv Quantum Tech

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The spectral and spatial dependence of the resonant Lamb shift of an exciton inside a photonic vacuum field landscape is considered to predict an optical dipole potential generated via virtual photons quantum fluctuations. This trapping potential can be exploited for exciton self-positioning in electric field hotspots at the nanoscale in view of quantum electrodynamics effects. By non Hermitian decomposition of the electromagnetic Green tensor in terms of quasi normal modes, the resonant part of the Lamb shift is expressed as Fano profile strictly interlinked to the Purcell enhancement of the exciton radiative lifetime. This approach explains how to tailor the depth of the vacuum photonic potential in several possible scenarios.

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Tailoring Fano Lineshape in Photonic Local Density of States by Losses Engineering

Granchi,

Gurioli

2023

Adv Quantum Tech

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Non‐Hermitian theory in photonics revolutionized the understanding of optical resonators, thanks to the concept of quasi‐normal modes (QNM) and to a deep revision of the Purcell factor expression. Counterintuitive effects followed, such as complex modal volumes and non‐Lorentzian local density of states (LDOS) of QNMs. One of the fascinating aspects of non‐Hermitian theory is the analogy with quantum mechanics for autoionizing electronic levels where the absorption cross'section is characterized by Fano lineshapes, caused by interference between the probability of absorption in the continuum and in the bound states. In photonics Fano lineshapes can arise from QNM normalization through the complex modal volume. The link between Fano lineshapes in photonic LDOS of QNMs and in the case of autoionizing states needs to be clarified. Here, by developing an analytical model based on the role of losses in the QNM normalization, they clarify the meaning of the phase of QNM normalized fields (qFano parameter),linking QNMs normalization to the concept of interference among the resonant and the leaky modes. This inspired the design of photonic crystal (PhC) cavity that exhibits LDOS with Fano character inside the itself, providing a proof of principle on how to mold the radiative lifetime by Purcell effect.

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Non-Lorentzian Local Density of States in Coupled Photonic Crystal Cavities Probed by Near- and Far-Field Emission

Cited by 20 publications

References 28 publications

Purcell effect with extended sources: The role of the cross density of states

Purcell effect with extended sources: The role of the cross density of states

Vacuum Field Photonic Trap for Excitons

Tailoring Fano Lineshape in Photonic Local Density of States by Losses Engineering

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