total internal reflection

History

The phenomenon has been noticed since antiquity: when looking from underwater, the surface can appear mirror-like. In 1611, Kepler first described it mathematically, and later Snellius discovered the law of refraction, allowing the calculation of the critical angle.

How it works

Light travels at different speeds in different media - this is described by the refractive index. At the boundary between a 'slow' and a 'fast' medium, the beam bends. If the angle of incidence is too large, the bending becomes so strong that the light does not exit but returns. This happens only when transitioning from an optically denser medium to a less dense one.

History

The phenomenon has been noticed since antiquity: when looking from underwater, the surface can appear mirror-like. In 1611, Kepler first described it mathematically, and later Snellius discovered the law of refraction, allowing the calculation of the critical angle.

How it works

Light travels at different speeds in different media - this is described by the refractive index. At the boundary between a 'slow' and a 'fast' medium, the beam bends. If the angle of incidence is too large, the bending becomes so strong that the light does not exit but returns. This happens only when transitioning from an optically denser medium to a less dense one.

History

The first description of total internal reflection was given by Kepler in 'Dioptrice' (1611). In 1621, Snellius discovered the law of refraction, from which the critical angle is directly derived. In the 1820s, Fresnel developed the theory, including evanescent waves. In 1854, Tyndall demonstrated a light guide using a water jet - a prototype of optical fiber. In the 1960s, practical application of fiber optics began.

How it works

Condition for TIR: n₁ > n₂ and angle of incidence θ₁ > θ_c. Conservation of the tangential component of the wave vector gives k_x = (n₁ ω/c) sin θ₁. When θ₁ > θ_c, k_x exceeds n₂ ω/c, so the normal component k_z₂ becomes imaginary: k_z₂ = iκ. The field decays exponentially: exp(−κ z), penetration depth δ = 1/κ = λ₀/(2π n₁ √(sin²θ₁ − (n₂/n₁)²)). The evanescent wave carries energy along the boundary but not into the volume. The phase shift upon reflection differs for s- and p-polarizations. Frustrated TIR is analogous to quantum tunneling: when two prisms are brought within a distance of about δ, light partially penetrates into the second.

Open problems & fun facts

Reducing losses in optical fiber for ultra-long-distance communication; Development of waveguides for integrated photonics; Increasing the efficiency of sensors based on FTIR; Quantum effects in evanescent coupling with single emitters; Materials with record-low absorption for the mid-IR range

💡 In frustrated total internal reflection, photons tunnel through a narrow gap, which is a direct optical analog of the quantum mechanical tunnel effect. This experiment can be performed with two prisms and a laser pointer.