Photonic Crystals: Building a Bandgap for Light

A periodic potential for light, not electrons

A photonic crystal is a periodic dielectric structure with a period comparable to the wavelength of light — the optical analogue of a semiconductor crystal lattice for electrons. Just as a periodic atomic potential opens an electronic bandgap that forbids certain electron energies, a periodic refractive-index modulation opens a photonic bandgap that forbids certain frequencies of light from propagating. First proposed independently by Eli Yablonovitch and Sajeev John in 1987, photonic crystals now underpin distributed-feedback lasers, photonic-crystal fibres, and on-chip waveguides that route light around corners with almost no loss. Maxwell's equations in such a periodic medium reduce to a Bloch-wave eigenvalue problem — mathematically identical to electrons in a crystal — producing a discrete, ordered band structure ω_n(k).

The 1D case: a quarter-wave Bragg mirror

This simulation models the simplest photonic crystal: alternating layers of high index n₁ and low index n₂, each sized to a quarter-wavelength at the design wavelength λ_center so their reflections add constructively.

Quarter-wave condition:   n1·d1 = n2·d2 = λ0 / 4
Centre wavelength:        λ0 = 2·Λ·n_avg      (Λ = d1 + d2, normal incidence)
Fractional bandwidth:     Δω/ω0 ≈ (4/π)·arcsin[(n2−n1)/(n2+n1)]

Example: SiO2/Ta2O5 stack, λ0 = 1550 nm
  d1 ≈ 267 nm, d2 ≈ 185 nm — 20-30 layer pairs give >99.9% reflectance

The Transfer Matrix Method gets the transmission spectrum exactly, with no approximation: each layer becomes a 2×2 characteristic matrix built from its index, thickness and wavelength, all the matrices in the stack are multiplied in order, and the result combines with the optical admittances of the incident medium and substrate to give the exact reflection and transmission for every wavelength.

Beyond 1D: waveguides, cavities and fibres

2D photonic crystals use a periodic array of holes or rods in a slab, where TE and TM polarisations can have different gaps; a "complete" gap needs both to overlap. A point or line defect — a missing hole, an extra rod — locally breaks the periodicity and can pull a discrete mode into the bandgap: a point defect traps light as a microcavity with quality factors above 10⁶, while a line defect guides light along a channel and routes it through 90° bends with near-zero radiative loss, something total-internal-reflection waveguides cannot do at sharp corners. The same physics enables hollow-core photonic bandgap fibre, where light is confined in a low-index air core purely by the surrounding bandgap, with no total internal reflection involved at all.

Scale invariance

Maxwell's equations in a lossless dielectric have no fundamental length scale: rescale every length by a factor s and the band structure simply scales as ω_new(k) = ω_old(k)/s. A photonic crystal designed and tested at microwave frequencies (centimetre-scale, easy to fabricate) can be shrunk by a factor of 10⁴-10⁵ to work at optical frequencies with an identical relative band structure — which is why microwave prototyping remains standard practice before optical fabrication.

Frequently asked questions

Try it live

Everything above runs in your browser — open Photonic Crystal, load a preset material pair, and watch the wave decay evanescently inside the bandgap or sail straight through outside it. Nothing is installed, nothing is uploaded.