Photonic Crystal Band Structure Simulator

simulator intermediate ~10 min
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Band gap centered at 980 nm — Gap-midgap ratio: 18.7%. 400 nm period Si/SiO2 stack.

A 1D photonic crystal with 400 nm period, alternating silicon (n=3.4) and silica (n=1.5) layers at 50% fill fraction, produces a band gap centered near 980 nm wavelength.

Formula

λ_mid = 2a(n₁f + n₂(1−f))
Δω/ω_mid = (4/π) arcsin((n₁−n₂)/(n₁+n₂))
R = tanh²(N · ln(n₁/n₂)) for N bilayers

Photonic Band Gaps

Photonic crystals are periodic arrangements of dielectric materials that create band gaps — frequency ranges where electromagnetic wave propagation is forbidden. First proposed by Yablonovitch and John in 1987, these structures provide unprecedented control over light, enabling waveguides, filters, and cavities at the wavelength scale.

1D Bragg Stacks

The simplest photonic crystal is a one-dimensional stack of alternating high- and low-index layers, known as a distributed Bragg reflector. Constructive interference of reflections from each interface produces a stop band whose width depends on the index contrast and whose center wavelength scales with the optical path length per unit cell.

Gap Engineering

The band gap can be tuned by adjusting the lattice period (shifting center wavelength), index contrast (widening or narrowing the gap), and fill fraction (optimizing gap width). For a 1D crystal, maximum gap-midgap ratio occurs near 50% fill. Two-dimensional and three-dimensional photonic crystals offer omnidirectional gaps but require higher index contrasts.

Applications in Photonics

Photonic crystals enable vertical-cavity surface-emitting lasers (VCSELs), wavelength-division multiplexing filters, photonic crystal fibers with engineered dispersion, and slow-light devices for optical buffering. Their ability to confine light to volumes smaller than a cubic wavelength makes them essential for integrated photonic circuits and quantum optical devices.

FAQ

What is a photonic band gap?

A photonic band gap is a range of frequencies where light cannot propagate through a periodic dielectric structure, analogous to electronic band gaps in semiconductors. Light at these frequencies is perfectly reflected regardless of incident angle.

How does refractive index contrast affect the band gap?

Higher index contrast between the two materials produces wider band gaps. A minimum contrast of about 2:1 is needed for useful 2D band gaps, while 1D structures can have gaps at any contrast. Silicon-air (3.4:1) provides some of the widest achievable gaps.

What are photonic crystals used for?

Photonic crystals are used in high-reflectivity mirrors (distributed Bragg reflectors), waveguides that bend light around sharp corners, optical filters, low-threshold lasers, and sensors. They also appear naturally in opals and butterfly wings.

What is the relationship between lattice period and band gap wavelength?

The band gap center wavelength scales linearly with lattice period. The midgap wavelength approximately equals twice the optical path length per unit cell: lambda = 2a(n1*f + n2*(1-f)), where a is the period and f is the fill fraction.

Sources

Embed

<iframe src="https://homo-deus.com/lab/photonics/photonic-crystal/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub