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December 3, 2019 September 9, 2026

Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances - Notes

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Published abstract

Planck’s law constitutes one of the cornerstones in physics. It explains the well-known spectrum of an ideal blackbody consisting of a smooth curve, whose peak wavelength and intensity depend on the temperature of the body. This scenario changes drastically, however, when the size of the emitting object is comparable to the wavelength of the emitted radiation. Here we show that a silicon microsphere (2-3 μm in diameter) heated to around 800 °C yields a thermal emission spectrum consisting of pronounced peaks that are associated with Mie resonances. We experimentally demonstrate in the near-infrared the existence of modes with an ultrahigh quality factor, Q, of 400, which is substantially higher than values reported so far, and set a new benchmark in the field of thermal emission. Simulations predict that the thermal response of the microspheres is very fast, about 15 μs. Additionally, the possibility of achieving light emission above the Planck limit at some frequency ranges is envisaged.

Figures

Panel a shows the arrangement used to heat an individual silicon microsphere on a silica substrate with a 405 nm laser and collect its near-infrared thermal emission parallel to the surface. The finite-element results in panel b predict heating to 750 °C in about 10 µs and cooling in about 15 µs for a 3.5 µm sphere. Panel c resolves the steady-state temperature distribution and the small vertical gradient produced mainly by heat conduction into the substrate, linking the measurement geometry to the thermal response of the emitter.
Figure 1. Summary. Panel a shows the arrangement used to heat an individual silicon microsphere on a silica substrate with a 405 nm laser and collect its near-infrared thermal emission parallel to the surface. The finite-element results in panel b predict heating to 750 °C in about 10 µs and cooling in about 15 µs for a 3.5 µm sphere. Panel c resolves the steady-state temperature distribution and the small vertical gradient produced mainly by heat conduction into the substrate, linking the measurement geometry to the thermal response of the emitter.

© 2019 American Chemical Society. Source: R. Fenollosa et al., ACS Photonics 6(12), 3174-3179 (2019), DOI 10.1021/acsphotonics.9b01513. Reused by the authors on a personal website under the ACS author reuse policy.

Figure 2 from Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances
Figure 2. Summary. Thermal emission spectra of silicon microspheres. (a) Measured spectrum in the NIR for a 3595 nm diameter (Φ) silicon microsphere (black curve in right panel).

© 2019 American Chemical Society. Source: R. Fenollosa et al., ACS Photonics 6(12), 3174-3179 (2019), DOI 10.1021/acsphotonics.9b01513. Reused by the authors on a personal website under the ACS author reuse policy.

Figure 3 from Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances
Figure 3. Summary. Optical absorption parameters for silicon at high temperature. The green curve corresponds to the imaginary part of the refractive index at 756 °C, the temperature of the measurement of Figure 2a.

© 2019 American Chemical Society. Source: R. Fenollosa et al., ACS Photonics 6(12), 3174-3179 (2019), DOI 10.1021/acsphotonics.9b01513. Reused by the authors on a personal website under the ACS author reuse policy.

Figure 4 from Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances
Figure 4. Summary. Demonstration of a resonance tuning by temperature and its high Q. (a) Measured resonance TE10,5 of the microsphere of Figure 2a at 756 °C (red dots) and at 792 °C (black dots).

© 2019 American Chemical Society. Source: R. Fenollosa et al., ACS Photonics 6(12), 3174-3179 (2019), DOI 10.1021/acsphotonics.9b01513. Reused by the authors on a personal website under the ACS author reuse policy.

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Article access and reuse

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Related publications

Connections within F. Ramiro-Manzano's publication record, selected from shared research topics and evidence reviewed in the source papers.

Original embedded field-emission scanning electron micrograph of a typical hydrogenated amorphous silicon microsphere with a one micrometre scale bar
Journal article
Int. J. Therm. Sci. 213, 109829 (2025)
Thermal emission of hydrogenated amorphous silicon microspheres in the mid-infrared
R. Fenollosa and F. Ramiro-Manzano

What the related paper adds

This later paper extends the research direction developed in Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances. This paper distinguishes a new mid-infrared emission mechanism in hydrogenated amorphous silicon spheres. Vibrations of silicon-hydrogen bonds create a pronounced phononic band that can couple to the sphere resonances, while controlled laser heating reveals bond reconfiguration and the onset of transformation towards polycrystalline silicon.

What this paper adds to the related work

This paper provides an earlier basis for the later development reported in Thermal emission of hydrogenated amorphous silicon microspheres in the mid-infrared. This study turns a single silicon microsphere into a resonant thermal emitter in the near infrared. Heating produces discrete Mie peaks instead of a smooth black-body spectrum, with quality factors around 400 and a predicted microsecond response, and points towards emission above the Planck limit in selected spectral intervals.

SEM image showing a side view of as-synthesized polycrystalline silicon microspheres.
Journal article
Adv. Opt. Mater. 11(15), 2300135 (2023)
Silicon Microspheres for Super-Planckian Light Sources in the Mid Infrared
R. Fenollosa, F. Ramiro-Manzano, M. Garín and F. Meseguer

What the related paper adds

This later paper extends the research direction developed in Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances. This work carries resonant thermal emission into the mid infrared, where the lowest-order modes of two-to-three-micrometre silicon spheres are widely separated and approach the absorption-emission matching condition. Several peaks exceed the calculated black-body limit, establishing the spheres as compact, spectrally selective mid-infrared sources.

What this paper adds to the related work

This paper provides an earlier basis for the later development reported in Silicon Microspheres for Super-Planckian Light Sources in the Mid Infrared. This study turns a single silicon microsphere into a resonant thermal emitter in the near infrared. Heating produces discrete Mie peaks instead of a smooth black-body spectrum, with quality factors around 400 and a predicted microsecond response, and points towards emission above the Planck limit in selected spectral intervals.

Protocol Exchange
Protocol
Protocol Exchange (2013)
Processing and Characterization of Monodisperse Silicon Colloids
L. Shi, X. Lu, R. Fenollosa, I. Rodriguez, J. T. Harris, F. Ramiro-Manzano, B. A. Korgel and F. Meseguer

What the related paper adds

This earlier paper establishes a scientific basis for Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances. This protocol makes the silicon-colloid platform reproducible at smaller and more uniform sizes. It describes how to fabricate monodisperse spheres in the 300 to 500 nanometre range and how to characterize individual particles with a purpose-built confocal microscope, linking controlled processing to well-resolved electric and magnetic Mie modes.

What this paper adds to the related work

Building on the earlier contribution Processing and Characterization of Monodisperse Silicon Colloids, this paper advances the research line. This study turns a single silicon microsphere into a resonant thermal emitter in the near infrared. Heating produces discrete Mie peaks instead of a smooth black-body spectrum, with quality factors around 400 and a predicted microsecond response, and points towards emission above the Planck limit in selected spectral intervals.

Two silicon nanocavities illustrating mirror-image-induced magnetic modes
Article
ACS Nano 7(1), 664-668 (2013)
Mirror-Image-Induced Magnetic Modes
E. Xifré-Pérez, L. Shi, U. Tuzer, R. Fenollosa, F. Ramiro-Manzano, R. Quidant and F. Meseguer

What the related paper adds

This earlier paper establishes a scientific basis for Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances. This paper shows that a silicon nanocavity can acquire a strongly enhanced magnetic-like optical response through interaction with its own image in a metallic mirror. The real particle and its virtual counterpart form an effective magnetic dipole, providing a route to amplify scattering without assembling two perfectly matched physical particles.

What this paper adds to the related work

Building on the earlier contribution Mirror-Image-Induced Magnetic Modes, this paper advances the research line. This study turns a single silicon microsphere into a resonant thermal emitter in the near infrared. Heating produces discrete Mie peaks instead of a smooth black-body spectrum, with quality factors around 400 and a predicted microsecond response, and points towards emission above the Planck limit in selected spectral intervals.

Complete original Figure 2 composition extracted directly from the article PDF
Journal article
J. Appl. Phys. 109, 102424 (2011)
Silicon colloids: A new enabling nanomaterial
F. Meseguer, R. Fenollosa, I. Rodriguez, E. Xifre-Perez, F. Ramiro-Manzano, M. Garin and M. Tymczenko

What the related paper adds

This earlier paper establishes a scientific basis for Thermal Emission of Silicon at Near-Infrared Frequencies Mediated by Mie Resonances. This paper defines silicon colloids as a material platform rather than a single device. It surveys polycrystalline, amorphous and porous spherical particles, explains their strong low-order Mie resonances and infrared light confinement, and opens applications ranging from optical filtering to light-controlled forces between particles.

What this paper adds to the related work

Building on the earlier contribution Silicon colloids: A new enabling nanomaterial, this paper advances the research line. This study turns a single silicon microsphere into a resonant thermal emitter in the near infrared. Heating produces discrete Mie peaks instead of a smooth black-body spectrum, with quality factors around 400 and a predicted microsecond response, and points towards emission above the Planck limit in selected spectral intervals.

Research fields

Bottom-up

Polycrystalline silicon microspheres supply wavelength-scale resonators with smooth curved boundaries. Their particle-based formation avoids defining the cavity by planar lithography while retaining a high refractive-index optical volume.

Simulations & fits

Mie-theory fits assign the measured near-infrared emission peaks and determine the sphere temperature. Finite-element heat-transfer calculations map the steady temperature distribution and predict microsecond heating and cooling, linking optical resonances with the thermal dynamics of one particle.

Characterization

A focused blue laser heats an individual sphere while its near-infrared spectrum is collected parallel to the substrate. The experiment resolves modes with quality factors around 400 and compares their intensity with the blackbody emission expected from the sphere's projected area.

RESEARCH TOPICS

EmissionThe peaks coincide with calculated Mie modes, demonstrating that thermal radiation is filtered by the particle's own electromagnetic resonances. The work also identifies spectral intervals where the absorption cross-section could support super-Planckian emission.MaterialsTheir high refractive-index contrast provides confinement, while the temperature-dependent carrier population supplies loss and emission. The experiment therefore relies on a controlled balance: enough absorption to radiate, but not so much that the resonances are washed out.ResonatorsBecause the sphere is comparable to the emitted wavelength in all three dimensions, it behaves as a compact photonic cavity rather than an extended patterned surface. The same particle can therefore combine micrometre dimensions, high-Q emission and rapid heating-cooling dynamics.SetupsA 405 nm laser is focused onto one sphere supported on silica, and the emitted light is collected in a plane parallel to the substrate to reduce contamination from reflected pump light. That thermal modelling is essential because the laser power is controlled directly, whereas the resonant emission must be interpreted at the sphere's actual temperature.
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