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.

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{dI}{dz} \;=\; -\alpha_1 I - \beta_\text{TPA} I^2,

where $\alpha_1$ is the linear absorption coefficient and $\beta_\text{TPA}$ is the TPA coefficient (cm/W). The TPA contribution is intensity-squared and so dominates linear absorption only at high intensities — typically megawatts per cm² or higher.

TPA coefficients at relevant wavelengths.

Material	Wavelength	$\beta_\text{TPA}$ (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	0.05 – 0.1	Approaching $E_g/2$ cutoff; TPA dropping rapidly
Silicon	2200 nm	~0	Below $E_g/2$ ; no TPA
Germanium	1550 nm	$\sim 0$	Below $E_g/2 = 0.33$ eV
InGaAs (telecom)	1550 nm	1 – 5	Significant TPA
GaAs	1064 nm	25	Very strong (near $E_g$ )
AlGaAs	1550 nm	< 0.01	Far below $E_g/2$ ; negligible
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 $\sim 10$ mW of input power:

I \;=\; \frac{P}{A_\text{eff}} \;\approx\; \frac{10 \text{ mW}}{0.1 \, \mu\text{m}^2} \;=\; 10 \text{ GW/cm}^2.

With $\beta_\text{TPA} = 0.6$ cm/GW: $\alpha_\text{TPA} \approx 6$ cm $^{-1}$ — adding 2.6 dB/mm of effective loss. For 1-mm-long silicon devices, this represents a substantial power-handling limit.

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 ( $\geq 2200$ nm) where silicon has no TPA — used in some Si photonic 2 μm-band 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 Ge or III-V at high-power locations — Ge has no TPA at 1550 nm, III-V has TPA but designed for different power regimes
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).
Mid-IR detection: TPA-based silicon photodetectors detect mid-IR wavelengths where single-photon absorption is forbidden.

References: Bristow, Rotenberg, van Driel, Two-photon absorption and Kerr coefficients of silicon for 850 – 2200 nm, Appl. Phys. Lett. 2007 (the canonical Si TPA characterization); Reed & Knights, Silicon Photonics, Ch. 5 for the silicon-specific treatment.