Optical parametric amplifier (OPA)

An optical parametric amplifier passes an intense pump beam and a weak signal beam together through a crystal with a second-order nonlinearity. Each pump photon that splits produces one signal photon and one idler photon, so the signal grows and a new beam, the idler, appears at the frequency difference between pump and signal. With an 800 nm pump from a Ti:sapphire laser and a 1300 nm signal, the idler is at 2080 nm. Single-pass gains of 10³ to 10⁶ are reached in 1–5 mm of crystal at pump intensities of tens of GW/cm², which is why OPAs are almost always pumped by femtosecond or picosecond pulses. No energy is stored in the medium: the gain exists only while the pump pulse is present.

Energy and momentum conservation

Photon energy is conserved in each splitting event:

$$\frac{1}{\lambda_p} = \frac{1}{\lambda_s} + \frac{1}{\lambda_i}.$$

For $\lambda_p$ = 800 nm and $\lambda_s$ = 1300 nm this gives $\lambda_i$ = 2080 nm; the photon energies are 1.550 eV, 0.954 eV and 0.596 eV, which sum correctly. The fraction of each converted pump photon's energy that goes to the signal is $\lambda_p/\lambda_s$ = 61.5%, with 38.5% going to the idler. Which pair of wavelengths actually grows is decided by phase matching, $\mathbf{k}_p = \mathbf{k}_s + \mathbf{k}_i$, set by crystal angle, temperature or poling period. The process is the amplifying form of difference-frequency generation: with a weak signal and strong pump, the idler generated by DFG beats with the pump to create more signal, and the two waves grow together.

Gain formula and a worked number

With no pump depletion and perfect phase matching, a seeded signal grows as $G = \cosh^2(\Gamma L)$, approaching $\tfrac14 e^{2\Gamma L}$ for large $\Gamma L$. The gain coefficient is

$$\Gamma^2 = \frac{8\pi^2 d_\text{eff}^2\, I_p} {n_p n_s n_i\, \varepsilon_0 c\, \lambda_s \lambda_i},$$

where $d_\text{eff}$ is the effective nonlinear coefficient and $I_p$ the pump intensity. For β-barium borate (BBO) with $d_\text{eff}$ ≈ 2 pm/V, refractive indices near 1.66, and a pump intensity of 50 GW/cm², the 800 → 1300 + 2080 nm case gives $\Gamma$ ≈ 2.2 mm⁻¹. A 2.3 mm crystal then reaches $\Gamma L$ = 5 and $G = \cosh^2 5$ ≈ 5500, about 37 dB. Because the gain is exponential in $\sqrt{I_p}$, pump fluctuations are magnified; operating in saturation, with the pump depleted, stabilizes the output.

Gain bandwidth and pulse effects

The gain bandwidth is set by how fast the phase mismatch grows as the signal is detuned, which is governed by the difference between the signal and idler group velocities. Near degeneracy, or in a noncollinear geometry where a small angle between pump and signal makes the signal and idler group velocities match along the signal direction, the bandwidth becomes very large. Noncollinear OPAs (NOPAs) in BBO pumped at 400 nm amplify bandwidths that support sub-10 fs pulses in the visible. Group-velocity mismatch between pump and signal limits the useful crystal length for femtosecond pulses, and spatial walk-off limits it further for small beams.

OPCPA

In optical parametric chirped-pulse amplification (OPCPA), a stretched seed pulse is amplified in an OPA by a synchronized pump pulse of similar duration and then recompressed, the parametric analogue of chirped-pulse amplification. Because the crystal stores no energy, the energy difference between pump and signal photons leaves as the idler instead of heating the crystal, the gain bandwidth is set by phase matching instead of an atomic transition and can be far broader than in laser amplifiers, and no amplified spontaneous emission after the pump has passed; the only background is parametric superfluorescence during the pump pulse, which degrades temporal contrast only inside that window. OPCPA is used for few-cycle, high-peak-power systems and for pulses at wavelengths where no broadband laser medium exists, and the idler from an OPCPA is passively stable in carrier-envelope phase when pump and signal are derived from the same laser.

Relation to the OPO

An optical parametric oscillator is the same gain process inside a resonant cavity: the signal or idler recirculates and builds up from noise once round-trip gain exceeds loss. An OPA has no cavity and needs either a seed or a very high single-pass gain. Without a seed, an OPA amplifies vacuum fluctuations, a process called optical parametric generation, whose low-gain limit is spontaneous parametric down-conversion. Femtosecond OPAs usually seed from a white-light continuum generated in sapphire or YAG by part of the driving laser.

Common questions

What is the difference between an OPA and an OPO?

Both use the same second-order parametric gain. An OPA is single-pass or multipass with no resonator and is driven by amplified ultrafast lasers at kHz to hundreds of kHz rates with µJ–mJ pulse energies. An OPO uses a cavity to reach threshold at much lower pump intensity, which suits continuous-wave pumps and MHz-rate mode-locked oscillators.

Why is an idler produced even when only the signal is seeded?

Every amplified signal photon comes from a pump photon splitting, and the other half of that split is an idler photon. Signal and idler photon numbers therefore grow by the same amount, and the idler phase is fixed by the pump and signal phases, $\phi_i = \phi_p - \phi_s - \pi/2$.

References: R. W. Boyd, Nonlinear Optics, 4th ed. (Academic Press, 2020); G. Cerullo and S. De Silvestri, Rev. Sci. Instrum. 74, 1 (2003); A. Dubietis, G. Jonušauskas, A. Piskarskas, Opt. Commun. 88, 437 (1992); Saleh & Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).