Glossary entry

Two-photon absorption (TPA)

A nonlinear absorption process in which two photons are simultaneously absorbed to excite an electron across a bandgap larger than either photon's individual energy. Limits high-power operation of silicon photonic devices at telecom wavelengths.

Integrated photonics Optics fundamentalsUpdated September 2026

Two-photon absorption is a third-order nonlinear optical process in which a material absorbs two photons simultaneously, exciting an electron from the valence band to the conduction band. Unlike single-photon absorption (which requires photon energy $\geq E_{g}$ ), TPA occurs at photon energies above $E_{g} / 2$ but below $E_{g}$ , where single-photon absorption is forbidden.

Mathematical form. The change in transmitted intensity per unit propagation length due to TPA:

\frac{d I}{d z} = - α_{1} I - β_{TPA} I^{2},

where $α_{1}$ is the linear absorption coefficient and $β_{TPA}$ is the TPA coefficient (cm/W). The TPA contribution is intensity-squared and so dominates linear absorption only at high intensities, in a silicon waveguide with a few dB/cm of linear loss, several hundred MW/cm² or more.

TPA coefficients at relevant wavelengths.

Material	Wavelength	$β_{TPA}$ (cm/GW)	Notes
Silicon	1550 nm	0.45 – 0.9	$E_{g} / 2 = 0.56$ eV; 1550 nm is 0.80 eV; strong TPA
Silicon	2000 nm	–	Below the 1550 nm value; approaching the $E_{g} / 2$ edge, TPA falling toward zero
Silicon	2200 nm	~0	At the $E_{g} / 2$ edge (2.21 μm); TPA vanishes
Germanium	1550 nm	n/a	0.80 eV exceeds $E_{g} = 0.66$ eV; linear absorption dominates
In $_{0.53}$ Ga $_{0.47}$ As	1550 nm	n/a	0.80 eV exceeds $E_{g} \approx 0.75$ eV; linear absorption dominates
GaAs	1064 nm	25	Very strong (near $E_{g}$ )
AlGaAs, Al fraction above 0.15	1550 nm	–	$E_{g} / 2$ above 0.80 eV; TPA weak, three-photon absorption remains
Fused silica	1550 nm	< $10^{- 3}$	Negligible

Why TPA matters for silicon photonics. Silicon photonic waveguides at 1550 nm have very small effective area (typically $\sim 0.1$ μm²), concentrating optical intensity to very high levels even at modest input powers. At 100 mW of input power:

I = \frac{P}{A_{eff}} \approx \frac{100 mW}{0.1 μ m^{2}} = 0.1 {GW/cm}^{2} .

With $β_{TPA} = 0.6$ cm/GW: $α_{TPA} = β_{TPA} I \approx 0.06$ cm $^{- 1}$ , adding 0.26 dB/cm of effective loss. At 1 W this rises to 2.6 dB/cm, comparable to or larger than the linear propagation loss, and the free carriers TPA generates add more (below).

TPA-induced free-carrier absorption (TPA + FCA). TPA generates free carriers, which then cause free-carrier absorption. The combined effect produces a power-dependent loss that scales as $I^{2}$ (TPA itself) plus a long-lived $I^{3}$ contribution (TPA-generated carriers absorbing the light over their lifetime). For silicon photonic devices, this is the dominant power-handling limit.

Mitigation strategies:

Operate at longer wavelengths (beyond about 2.2 μm) where silicon has no TPA, used in mid-infrared silicon photonics research
Use lateral p-i-n junctions with reverse bias to sweep TPA-generated carriers out of the waveguide rapidly, reducing carrier lifetime and FCA contribution
Switch to silicon nitride for high-power passive sections: SiN has bandgap of $\sim 5$ eV, so 1550 nm photons cannot do TPA

Applications of TPA (not just a nuisance):

Two-photon microscopy: deep-tissue fluorescence imaging using TPA-excited fluorescent probes. Avoids out-of-focus excitation because TPA requires high local intensity, providing intrinsic optical sectioning.
Two-photon polymerization (TPP) / 3D direct-laser-writing: photoresist hardening at the focal spot of a tightly-focused femtosecond laser, achieving sub-100 nm 3D feature size.
Optical limiting: protective optical elements that pass low-power light but absorb high-power destructive pulses via TPA.
All-optical switching: TPA-induced absorption modulation in silicon for ultrafast all-optical processing (research; not deployed).
Sub-bandgap detection: silicon photodiodes respond to 1.1–2.2 μm light through TPA, where single-photon absorption is forbidden; this is the basis of simple pulse autocorrelators.

References: A. D. Bristow, N. Rotenberg and H. M. van Driel, "Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm," Appl. Phys. Lett. 90, 191104 (2007); Q. Lin, O. J. Painter and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: modeling and applications," Opt. Express 15, 16604 (2007).