The terahertz (THz) radiation spectrum, lying between the infrared and microwave regimes, encompasses a wide range of energy levels of lattice vibrations and molecular rotations in matter. Hence, THz radiation has potential applications in fields including matter manipulation, nondestructive testing, and biomedical imaging. However, a key challenge hindering the application of THz radiation is the need to further improve its energy and intensity. Therefore, exploring techniques for producing high-energy THz radiation remains a major focus and hot topic.

One method for generating intense THz radiation involves the nonlinear interaction between high-energy, ultrafast laser pulses and gases, resulting in a remarkably wide bandwidth of approximately 200 THz. This exceeds other commonly used THz radiation sources, such as optical-conductive antennas or optical rectification crystals, which are usually limited to a bandwidth below 5 THz. Furthermore, air-based THz sources offer advantages over solid-state sources, including immunity to laser damage and renewable properties, making them a pivotal for generating powerful and wide-ranging THz radiation.

An early study involving air plasma-based THz sources employed a one-color femtosecond laser pulse (usually with a wavelength near 800 nm from a Ti∶Sapphire laser) for THz generation. A two-color scheme, combining the fundamental laser field and its second harmonic, has also been intensively studied over the past 20 years. For the two-color scheme, it was revealed that the asymmetry of the two-color optical field plays a crucial role in generating high-intensity THz radiation. Nevertheless, the asymmetry of the optical field provided by the two-color field remains limited. Hence, there is a strong incentive to utilize multi-color laser fields to optimize the conversion efficiency of THz radiation, while also enabling manipulation of its properties.

This paper provides a comprehensive review of THz generation techniques based on air plasma, with an emphasis on the evolution from one-color field excitation to an advanced excitation scheme with a multi-color optical field. The development and progression of these methodologies are discussed in detail. In 1993, Hamster et al. focused a one-color femtosecond laser onto a gas target and observed THz radiation emitted from the gaseous plasma. However, the energy conversion efficiency of THz radiation produced by one-color laser fields was low, of the order of 10^-7‒10^-5, limiting the further applications of this THz source.

In 2000, Cook et al. first employed a two-color laser field to produce THz waves from air plasma. Their findings demonstrated that the amplitude of the resulting THz waves was much stronger than that generated using a one-color field. In the two-color field experiments, a BBO crystal used to generate a second harmonic pulse was installed before the laser focus in the beam path. By adjusting the distance between the BBO crystal and the focal point, the relative phase of the two-color fields could be finely controlled. Later, K. Y. Kim et al. proposed a local current model to explain the underlying physical mechanism. With the two-color field, the breaking of the symmetry of the electron motion effectively produces a net transverse electron current in the plasma, resulting in THz electromagnetic radiation (Fig. 4).

Cleric et al. explored the impact of the pump-laser wavelength on THz generation in the near-IR to far-IR regime. Their research showed that the yield of THz radiation increases with the wavelength of the pump laser field (Fig.6). In the latest reported two-color field scheme with a pump laser in the mid-infrared regime, the strength of the THz radiation field reaches up to 100 MV/cm, with a corresponding energy conversion efficiency of 2.36%. Moreover, Vvedenskii’s group discovered that non-harmonic two-color lasers can also be used to generate THz radiation (Fig.8).

To further improve the conversion efficiency, the exploration of multi-color fields was proposed in a theoretical perspective. L. Bergé et al. proposed a multi-color field scheme with a sawtooth wave shape to generate THz radiation. The multi-color sawtooth field maximizes the electron drift velocity at the ionization instants, which increases the THz efficiency by up to 1 order of magnitude compared to a standard two-color field (Fig.9). However, the construction of the sawtooth wave requires many harmonic laser pulses, and its synthesis is currently challenging.

Experiments frequently exploit a three-color field to mimic a sawtooth-wave excitation. Jeremy A. Johnson’s group utilized a three-color field from an optical parametric amplifier (OPA), composed of a fundamental frequency, the variable IR signal, and idler outputs from the OPA. They achieved higher THz radiation intensities compared to a two-color laser field (Fig.12). With the three-color pulse from the OPA, the relative phases of the optical fields were not controlled, and the temporal waveform of the multi-color optical field was therefore random.

Recently, an inline setup for three-color field synthesis for THz excitation was demonstrated. This setup allows the relative phases between the three optical fields to be controlled independently with attosecond precision. It was found that both photoionization and THz emission can be controlled coherently. THz enhancement, relative to the widely used two-color scheme, was also confirmed.

Employing a multi-color laser field to excite air plasma for THz generation can improve conversion efficiency significantly. Furthermore, the properties of THz emission, such as its polarization and polarity, can be controlled precisely by manipulating the optical phase. Due to its high intensity and wide bandwidth, the air-based THz source holds potential for applications in the manipulation of matter, electron acceleration, and biomedicine. Moreover, utilizing phase-controlled multi-color optical fields enables coherent control of the nonlinear interaction between powerful ultrafast lasers and gases, offering potential benefits for various high-field physics studies, such as high-order harmonic generation, attosecond pulse generation, and laser micro- and nano-machining. This article reviews the progress in research on THz generation with multi-color laser fields, with emphasis on the evolution of the experimental methods from one-color excitation to two- and three-color schemes, the relevant theoretical models, as well as the effects of the laser parameters on THz energy enhancement.