Glossary entry

Evanescent wave

An optical field that decays exponentially away from a boundary instead of propagating, found beyond a totally reflecting interface and outside the core of every guided mode. Typical 1/e depths are 100–300 nm for glass–air TIR and about 125 nm for a silicon wire waveguide at 1550 nm.

Optics fundamentals Integrated photonicsUpdated October 2026

An evanescent wave is an electromagnetic field that sits next to an interface or guiding structure, oscillates at the optical frequency and travels along the surface, but decays exponentially in the direction away from it. It carries no net power across the boundary. The decay length is set by the index contrast and the angle, and is usually a fraction of a wavelength: for BK7 glass against air at 633 nm and 60° incidence the field falls to 1/e in 119 nm, and around a silicon-on-insulator strip waveguide at 1550 nm it falls to 1/e in about 125 nm.

Evanescent fields appear in two closely related situations:

In the lower-index medium during total internal reflection, when the incidence angle exceeds the critical angle.
Outside the core of any dielectric waveguide, as the tail of the bound mode. The fraction of mode power in this tail is the complement of the confinement factor.

Mathematical form

For light incident at $θ_{1} > θ_{c}$ on a boundary between $n_{1}$ and $n_{2} < n_{1}$ , with the surface at $z = 0$ , the field in medium 2 is

E_{2} = E_{0} e^{- κ z} e^{i (k_{x} x - ω t)},

with $k_{x} = n_{1} k_{0} \sin θ_{1}$ and $k_{0} = ω / c$ . Conservation of $k_{x}$ across the boundary, the same condition that gives Snell's law, forces the normal component of the wavevector in medium 2 to be imaginary:

κ = k_{0} \sqrt{n_{1}^{2} \sin^{2} θ_{1} - n_{2}^{2}} .

The 1/e field penetration depth is $d = 1 / κ$ . Intensity falls as $e^{- 2 κ z}$ , so the intensity depth is $d / 2$ ; papers differ on which they quote, which is a common source of factor-of-two disagreements.

For a guided mode of effective index $n_{eff}$ the same expression applies with $n_{1} \sin θ_{1}$ replaced by $n_{eff}$ .

Typical penetration depths

Case	$λ_{0}$	Field depth $d$
BK7 (1.5151) to air, 45°	633 nm	262 nm
BK7 (1.5151) to air, 50°	633 nm	171 nm
BK7 (1.5151) to air, 60°	633 nm	119 nm
Fused silica (1.45) to air, 60°	633 nm	133 nm
SOI strip, $n_{eff}$ 2.44, in SiO₂	1550 nm	125 nm
Single-mode fiber LP01 in cladding	1550 nm	≈ 2.5 μm

The fiber value uses core radius 4.1 μm and NA 0.14, which give $V = 2.33$ ; the normalized propagation constant from the standard approximation $b \approx (1.1428 - 0.996 / V)^{2}$ is 0.51, the cladding decay parameter is $W = V \sqrt{b} = 1.66$ , and the asymptotic decay length is $a / W$ . Close to the critical angle the depth grows without limit: at 42° in BK7, just above $θ_{c} = 41.3 °$ , it is 604 nm.

Energy flow

The time-averaged Poynting vector of the evanescent wave has a component along the surface, carrying energy forward with the reflected beam, and zero component normal to the surface. Energy enters medium 2 during part of each optical cycle and returns during the rest.

Frustrated total internal reflection

If a second high-index medium is brought within a few penetration depths of the reflecting surface, the evanescent field couples into a propagating wave on the far side, and power tunnels across the gap. For gaps much larger than $d$ , the transmitted power falls roughly as $e^{- 2 κ g}$ with gap $g$ . Variable-ratio prism beamsplitters, prism couplers for slab waveguides and the Otto and Kretschmann configurations for surface plasmon resonance all use this effect. It is the optical analog of quantum-mechanical barrier tunneling.

Coupling on photonic chips

Most power transfer between neighboring waveguides on a photonic chip is evanescent.

Directional couplers: two parallel waveguides exchange power at a rate set by the overlap of their evanescent tails.
Ring resonators: the bus-to-ring gap sets the coupling coefficient and therefore whether the ring is under-, over- or critically coupled.
Adiabatic couplers: slowly tapered widths transfer a mode between guides through a gradually changing evanescent overlap.
Multimode interference couplers work differently, by self-imaging in a wide section, and are therefore less sensitive to gap variation.

The coupling coefficient between two guides scales approximately as $e^{- κ g}$ . For the silicon strip in the table, $κ = 7.97 μ m^{- 1}$ , so each extra 100 nm of gap multiplies the coupling by 0.45, and at a 1 μm gap the field overlap is reduced by a factor of about $3 \times 10^{- 4}$ relative to touching guides. This is why a typical strip waveguide layout keeps unrelated guides about 1 μm or more apart, and why coupler performance is sensitive to lithographic gap errors of a few nanometers.

Sensing and microscopy

TIRF microscopy: with a coverslip of $n = 1.518$ and cells at $n \approx 1.38$ , the critical angle is 65.4°. At 488 nm and 70° incidence the field depth is 215 nm and the intensity depth 108 nm, so only fluorophores near the membrane are excited.
Near-field scanning optical microscopy (NSOM): a sub-wavelength aperture or tip couples to evanescent components of the sample field, reaching resolution below 100 nm.
Evanescent fiber and waveguide sensors: removing or thinning cladding exposes the tail to the surroundings, so changes in the surrounding refractive index shift the mode's effective index or absorption.
Whispering-gallery and photonic crystal resonators: light is confined by TIR or band gaps, and evanescent fields couple it in and out.

Common questions

Does an evanescent wave carry energy?

It stores energy near the surface and carries it along the surface, but it transports no time-averaged power away from the boundary unless a second medium frustrates the reflection.

How is it observed?

By placing something within its reach: a fluorophore (TIRF), a second prism (frustrated TIR), a scanning tip (NSOM), or an absorbing film whose loss can be read from the reflected beam in attenuated total reflection spectroscopy.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), chapters on polarization optics and guided-wave optics; Born & Wolf, Principles of Optics (7th ed., 1999); Novotny & Hecht, Principles of Nano-Optics (2nd ed., 2012), for the near-field treatment.