Why a particle has two separate color-making resonances
A dielectric particle can hold light the way a bell holds sound. At certain wavelengths the light circulates inside and builds up instead of passing straight through, and the particle scatters that wavelength strongly. The lowest-order patterns of this buildup are the electric dipole resonance, where the internal field oscillates in step with the incoming light's electric field, and the magnetic dipole resonance, a second mode that appears at a different wavelength [5].
Because the two resonances peak at different wavelengths, a single particle can scatter strongly in two color bands at once. The overall color you see is the combined result, which is why controlling the two modes separately is a route to controlling the color rather than just the brightness. Silicon nanospheres show exactly this: spectrally narrow electric and magnetic dipole resonances in the visible range, producing vivid structural colors [1].
How size and dielectric constant move the resonances
The resonance wavelength scales with the particle's size and with how strongly the material concentrates light inside it, which is set by the dielectric constant. A larger particle, or one made of a higher-dielectric-constant material, pushes its resonances toward longer wavelengths. This is the practical tuning knob: the same geometry in a different material, or the same material at a different diameter, gives a different color. In silicon nanoparticles, the dielectric constant is what allows strong Mie resonances to appear at all [4].
The same size dependence shows up in other dielectric systems. In nanostructures built from transition metal dichalcogenides, the color spectra come from Mie resonances whose modes depend on the structure's size [5]. That makes size a design parameter for color across materials, not a silicon-specific quirk.
Choosing which resonance dominates the color
Knowing where the resonances sit is not the same as controlling which one you see. A platform using sparsely placed silicon nanospheres over a Fabry–Pérot-type spacer and mirror selectively excites the magnetic dipole and electric dipole resonances, and that selective excitation tunes the macroscopic color of the coating [2]. In other words, the substrate can decide which of the two modes speaks loudest, and therefore which color reaches the eye.
This matters because it separates two questions that are easy to confuse: what color a particle could produce, and what color a coating actually shows. The particle's size and dielectric constant set the available resonances; the surrounding structure determines how those resonances are excited and combined [2]. A coating can therefore be tuned without changing the particles themselves.
What this buys you in a real coating
The payoff is color that does not depend on pigments. Monolayers of dielectric nanoparticles can coat three-dimensional objects with a glossy finish while avoiding the rainbow shimmer, or iridescence, that usually comes with structural color, and the Mie resonances are what generate the color and help control the gloss [1]. Because the color comes from resonance rather than absorption, it is also a route to colors that resist fading.
The resonances can also be switched after the fact. Silicon nanoparticles manipulated optically scatter light whose color is modulated by Mie resonances, which allows color patterns to be created and changed dynamically [4]. That is a different capability from a fixed coating: the same particles can display different colors depending on how they are addressed.
One boundary is worth keeping in view. These studies establish that electric and magnetic dipole resonances generate and tune structural color, and that size-dependent Mie modes shape the color spectrum [1][2][5]. They do not, in the evidence available here, work out a quantitative rule linking a specific particle diameter and dielectric constant to a specific pair of resonance wavelengths. The direction of the dependence is clear; the exact mapping is still something a designer would have to measure or simulate.
Sources used in this answer
Glossy yet Noniridescent Conformal Structural Color Coating of Three‐Dimensional Objects With All‐Dielectric Nanoparticle Monolayers
Dielectric nanoparticle monolayers use spectrally narrow electric and magnetic dipole Mie resonances in the visible to produce glossy, noniridescent structural color coatings on three-dimensional objects.
Macroscopic Color Tuning by Selective Excitation of Electric and Magnetic Dipolar Mie‐Scattering of Silicon Nanospheres
A platform of sparsely placed silicon nanospheres over a Fabry–Pérot-type spacer and mirror tunes macroscopic structural color by selectively exciting the magnetic dipole and electric dipole Mie resonances.
Red and blue color production by flexible all-dielectric structure
Flexible all-dielectric metasurfaces can produce red and blue structural color, with the color described in terms of Mie resonances rather than metallic particle behavior.
Creating color patterns using optical manipulation and scattering of silicon nanoparticles
Optically manipulated silicon nanoparticles scatter light with strong Mie resonances, and their dielectric constant enables color patterns to be created and modulated.
Exploring Transition Metal Dichalcogenide Nanostructures for Electrically Tunable Structural Colors
In transition metal dichalcogenide nanostructures, size-dependent Mie modes, including electric and magnetic dipole contributions, generate the color spectra used for tunable structural colors.