Terahertz generation

Terahertz generation covers the methods used to produce electromagnetic radiation between about 0.1 and 10 THz, the band between microwave electronics and infrared optics. Across that range the wavelength runs from 3 mm to 30 µm and the photon energy from 0.41 to 41 meV. One terahertz corresponds to a vacuum wavelength of 299.8 µm, a photon energy of 4.14 meV, a wavenumber of 33.36 cm⁻¹ and a temperature $h\nu/k_B$ of 48 K; the conversions follow from the relations in wavelength, frequency and wavenumber. Room-temperature thermal energy, 25.9 meV, corresponds to 6.25 THz, so terahertz photons are comparable to or smaller than $k_BT$. That is one reason neither transistor oscillators nor interband semiconductor lasers work well in this band, which has been called the terahertz gap. Most laboratory sources are optical: femtosecond pulses converted in a photoconductor or a nonlinear crystal, two lasers mixed together, or a quantum cascade laser.

Photoconductive antennas

A photoconductive antenna is a pair of biased metal electrodes on a semiconductor with a sub-picosecond carrier lifetime, typically low-temperature-grown GaAs. A femtosecond pulse from a Ti:sapphire laser or an erbium fiber laser creates carriers in the gap; the bias accelerates them, and the transient current, rising within the pulse and decaying within the carrier lifetime, radiates a single-cycle terahertz pulse through a silicon lens on the back of the chip. The spectrum usually peaks below 1 THz and extends to a few terahertz. Antennas are compact and efficient at low pump energies, and they are the most common emitter in terahertz time-domain spectroscopy (THz-TDS).

Optical rectification

In a crystal with a second-order nonlinearity, a femtosecond pulse produces a nonlinear polarization that follows its intensity envelope. This is difference-frequency generation among the frequency components within one pulse, and it radiates a broadband terahertz pulse. Efficient conversion requires the optical pulse envelope, moving at its group velocity, to keep pace with the terahertz phase velocity.

• ZnTe is nearly velocity-matched for 800 nm pulses, because its optical group index and terahertz refractive index are both close to 3.2. GaP plays the same role for drivers near 1 µm.
• Lithium niobate has a large nonlinear coefficient, but its terahertz index (about 5.0) is more than twice its optical group index (about 2.25). The tilted-pulse-front scheme of Hebling and coworkers tilts the intensity front of the pump with a grating so that only its component along the terahertz direction must match: $\cos\gamma = n_g/n_\text{THz}$, giving a tilt angle $\gamma \approx 63°$.

Tilted-pulse-front sources in LiNbO3 pumped by millijoule pulses provide single-cycle pulses with microjoule energies and peak fields of hundreds of kV/cm to about 1 MV/cm when tightly focused, strong enough for nonlinear terahertz spectroscopy. Organic crystals and two-colour air plasmas extend the bandwidth further.

Photomixing and difference-frequency generation

Two continuous-wave lasers offset by the target frequency produce an intensity beat that a fast photodetector converts into a terahertz current. Near 1550 nm, two lasers separated by 8.0 nm beat at 1.0 THz. Photomixers based on uni-traveling-carrier photodiodes or low-temperature-grown GaAs deliver microwatts near 1 THz, with a tunable, narrow-linewidth output useful for gas spectroscopy and wireless links above 100 GHz. With higher peak power, DFG between two nanosecond or picosecond pulses in a crystal such as GaSe, DAST or periodically poled material generates tunable narrow-band terahertz radiation; an optical parametric amplifier often supplies the two wavelengths.

Quantum cascade lasers

Terahertz quantum cascade lasers emit between roughly 1.2 and 5 THz from intersubband transitions in GaAs/AlGaAs heterostructures, with milliwatt-level continuous output and watt-level peak output in pulsed mode. They still require cooling: the highest reported operating temperature is about 261 K in pulsed mode (Khalatpour et al., 2023), within reach of thermoelectric coolers, although most practical devices still run with cryocoolers. Mid-infrared QCLs with an internal DFG process provide room-temperature terahertz output at microwatt to milliwatt levels.

Detection

Broadband pulses are usually detected coherently. In electro-optic sampling, the terahertz field induces birefringence in a ZnTe or GaP crystal through the electro-optic effect; a delayed femtosecond probe pulse reads that birefringence with a quarter-wave plate, Wollaston prism and balanced photodiodes. Scanning the delay maps the terahertz electric field, amplitude and sign, versus time, so a Fourier transform gives both amplitude and phase spectra and hence the complex refractive index of a sample without a Kramers-Kronig analysis. Photoconductive antennas can also act as gated detectors. Incoherent detection uses liquid-helium-cooled bolometers, Golay cells and pyroelectric detectors.

Where it matters

Terahertz radiation passes through paper, plastics, textiles and ceramics while being strongly absorbed by water and reflected by metals. Uses include inspection of coatings and packaged goods, spectroscopy of molecular crystals and pharmaceuticals, carrier dynamics in semiconductors, and wireless communication above 100 GHz.

Common questions

What is the most efficient terahertz source?

It depends on the regime. For high-energy single-cycle pulses, tilted-pulse-front optical rectification in LiNbO3 and organic crystals is the most widely used. For continuous-wave power above a few milliwatts, cryogenically cooled quantum cascade lasers are the main option. For compact broadband spectroscopy, photoconductive antennas are the standard.

Why is terahertz radiation described as non-ionizing?

A 1 THz photon carries 4.1 meV, roughly a thousand times less than the few electronvolts needed to break chemical bonds or ionize molecules. Biological effects at the power levels used are thermal.

References: Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009); J. Hebling, G. Almási, I. Z. Kozma and J. Kuhl, "Velocity matching by pulse front tilting for large-area THz-pulse generation," Opt. Express 10, 1161 (2002); B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26 (2002); R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008); A. Khalatpour et al., "Enhanced operating temperature in terahertz quantum cascade lasers," Appl. Phys. Lett. 122, 161101 (2023).