Optical Terahertz Sources Based on Difference Frequency Generation in Nonlinear Crystals

Abstract

Terahertz (THz) sources, ranging from 0.1 THz to 10 THz, between microwaves and infrared waves, have important applications in spectral detection, medical imaging, communication, etc. Difference frequency generation (DFG) is an effective method for generating terahertz with the characteristics of low cost, simple structure, widely tunable range, no threshold, and room-temperature operation. This paper reviews various optical terahertz sources of difference frequency generation based on nonlinear crystals, including DFG with inorganic crystals, DFG with organic crystals, DFG with quasi-phase-matching (QPM) crystals, DFG in waveguides, cavity-enhanced DFG, and cascaded DFG. Their recent advances, as well as their advantages and disadvantages, are fully present and discussed. This review is expected to provide a comprehensive reference for researchers in this field and a quick understanding of optical THz sources of difference frequency generation with nonlinear crystals.

1. Introduction

The terahertz (THz) “gap” corresponding to the frequency range of 0.1–10 THz (3 mm to 30 μm in wavelength), between microwaves and infrared (IR) waves, was the last electromagnetic band to be exploited and utilized. Since the 1960s, optical methods to obtain THz radiation have also achieved breakthrough progress [1,2], and their related applications have become gradually commercialized and marketed with the leap in development of laser and material science. Due to the unique properties of low energy, water absorption, penetration, and fingerprint characteristics, terahertz waves have good prospects in high-resolution spectroscopy, radar, imaging, communication, and nondestructive inspection [3,4,5,6,7].

At present, the methods of terahertz generation are divided into electronic and photonic technology. The electronic methods usually generate relatively low-frequency terahertz radiation (below 1 THz), such as gyrotrons and Gunn diodes [8,9]. Although a free-electron laser with large size and high cost can realize broadband terahertz wave, it is difficult to apply widely [10,11]. In contrast, photonic technology can achieve a wider frequency range of terahertz radiation with a smaller and less expensive structure. Optical terahertz sources mainly include the optically pumped gas terahertz laser, the quantum cascade laser, photoconduction, and nonlinear optical frequency conversion. The optically pumped gas terahertz laser suffers from complicated operation and is bulky; thus, the size needs to be simplified and the efficiency and stability need to be improved for applications [12,13,14]. The quantum cascade laser is an important breakthrough for miniaturizing terahertz sources with the advantages of small size, low energy consumption, and easy integration, but it can only work in a low-temperature environment [15]. Moreover, terahertz waves generated by photoconductive antennas have higher power, but their frequencies are usually low [16,17,18].

The terahertz source of difference frequency generation (DFG) is a typical representative of nonlinear optical frequency conversion. There is no threshold in the DFG process, along with low cost, simple structure, and room-temperature operation. In addition, changing the pump wavelength or nonlinear crystal can achieve a widely tunable and narrow-linewidth terahertz wave output. In this review, the recent advances and developments of various DFG terahertz sources are fully presented, including DFG with inorganic crystals, DFG with organic crystals, DFG with quasi-phase-matching (QPM) crystals, DFG in waveguides, cavity-enhanced DFG, and cascaded DFG.

2. Theory of Difference Frequency Generation

DFG makes use of second-order (χ⁽²⁾) nonlinear materials for achieving THz waves under the condition of phase matching (PM). Two laser beams with similar frequencies ω₁ and ω₂ are used to generate coherent THz radiation (ω_T), whose frequency is the difference (ω₁ − ω₂ = ω_T) between the frequencies of the two lasers through a nonlinear medium. Ignoring the absorptions and reflections of the crystal, the DFG THz intensity in the small-signal approximation based on the plane-wave model can be expressed as

$$I_T=\frac{1}{2}{\left(\frac{{\mu }_0}{{\epsilon }_0}\right)}^{1/2}\frac{{\omega }_T^2{(2d)}^2{L}^2}{n_1{n}_2{n}_T{c}^2}{I}_1{I}_2\times \frac{{\sin }^2\left(\frac{1}{2}\Delta kL\right)}{{\left(\frac{1}{2}\Delta kL\right)}^2},$$

(1)

where I_T is the generated THz intensity, I₁ and I₂ are the incident laser intensity, ε₀ is the permittivity of free space, μ₀ is the magnetoconductivity, d is the efficient nonlinear coefficient, L is the crystal length, n₁, n₂, and n_T are the refractive indices of incident laser and THz frequencies, and Δk is the phase mismatch factor. The PM in the DFG process is Δk = k₁ − k₂ − k_T = 0. Figure 1 shows a schematic diagram of collinear PM and noncollinear PM. The condition of collinear PM can be written as

$$\Delta k=\frac{n_1{\omega }_1}{c}-\frac{n_2{\omega }_2}{c}-\frac{n_T{\omega }_T}{c},$$

(2)

while the PM condition (Δk = 0) of noncollinear DFG is as follows [19]:

$$\sin \frac{\theta }{2}={\left[\frac{n_3{({\omega }_T)}^2-{\left(n_1{\omega }_1-n_2{\omega }_2\right)}^2}{4n_1{n}_2{\omega }_1{\omega }_2}\right]}^{1/2},$$

(3)

$$\cos \phi =\left[1+2\frac{{\omega }_2}{{\omega }_T}{\sin }^2(\frac{\theta }{2})\right]\times {\left[1+4\frac{{\omega }_1{\omega }_2}{{({\omega }_T)}^2}{\sin }^2(\frac{\theta }{2})\right]}^{-1/2},$$

(4)

where θ is the angle between k₁ and k₂, and φ is the angle between k_T and k₁.

Inorganic crystals commonly utilize a birefringence effect or residual radiation band with dispersion compensation to achieve PM. According to the birefringence characteristics of anisotropic crystals, phase matching can be achieved by selecting appropriate k-vectors and polarization directions (o- or e-polarized) in the collinear interaction, such as GaSe, ZnGeP2 (ZGP), and LiNbO₃ crystals. Some isotropic nonlinear materials lack birefringence such as GaAs, GaP, and ZnTe, which can use a residual radiation band with abnormal dispersion to satisfy noncollinear PM. Figure 2 shows an example of the collinear PM angle with GaSe and the noncollinear PM angle with GaAs. The wavelengths of the pump lasers were λ₁ = 1.95 µm for both, while λ₂ ranged from 1.957 µm to 2.020 µm. Theoretically, a THz wave output of 0.55–5.33 THz can be generated.

According to the Manley–Rowe relation, a pump photon is divided into an idle photon and a terahertz photon in the process of DFG. The variation of power rate between three waves is expressed as

$$\frac{\Delta P_{{\omega }_T}}{{\omega }_T}=\frac{\Delta P_{{\omega }_2}}{{\omega }_2}=-\frac{\Delta P_{{\omega }_1}}{{\omega }_1},$$

(5)

where ΔP is the power rate variation with a frequency of ω. The maximum quantum efficiency in the DFG process is determined by

$${\eta }_{max}=\frac{{\omega }_T}{{\omega }_1}=\frac{{\lambda }_1}{{\lambda }_T},$$

(6)

where η_max is the maximum quantum efficiency. A longer pump wavelength has a higher power conversion efficiency when the terahertz wavelength is constant.

3. DFG Terahertz Sources with Inorganic Crystals

In addition to the quantum defect and the k-vector mismatch, the nonlinear coefficient and absorption coefficient of crystals also have a great influence on the DFG efficiency.

Table 1. Main pump bands of common inorganic crystals with various operating modes.

Operating Mode	Pump Wavelength	Inorganic Crystals
Femtosecond pulse	1–1.5 μm	GaSe
Picosecond pulse	1 μm	LiNbO3
	10 μm	GaAs
Nanosecond laser	1 μm	GaSe, ZGP, GaP, LiNbO3
	1.3–1.5 μm	GaSe, LiNbO3
	2 μm	GaSe
	10 μm	GaSe, GaAs
Continuous wave	1μm	GaP

shows main pump bands of common inorganic crystals with various operating modes. The GaAs crystal with a considerable nonlinear coefficient has strong two-photon absorption in the near-infrared band [20,21]. Generally, adopting mid-infrared lasers of about 10 μm generated by a bulky and complicated CO₂ laser can achieve a higher output power of terahertz in the DGF process. In 2011, Lu et al. reported that the average power of terahertz waves was about 10 μW, and the frequency range was 0.11–4.15 THz pumped with a nanosecond pulse and low-repetition frequency [22]. When a picosecond laser was used as the pump source, the peak power of THz waves could reach 2 MW [23]. In comparison, the absorption coefficient of the GaSe crystal is relatively smaller than various DFG crystals [24,25]. Flexible pump wavelengths have been employed to obtain the THz output. Leitenstorfer and Huber carried out collinear and noncollinear DFG with femtosecond pulses, where THz peak powers of 100 MW/cm were achieved [26]. High-repetition operation is required if some terahertz applications need to increase the sampling rate. Ding et al. reported a terahertz source with a frequency difference of 0.914 THz and average power of 260 μW using a high-repetition-frequency CO₂ laser [27]. Later, they realized terahertz output pumped by a compact Q-switched Nd:YLF dual-frequency laser at 1047 and 1053 nm, while the timing jitter of pulses was usually uncontrolled [28,29]. Recently, we proposed a flexible method to adjust the time interval and power ratio of dual-wavelength laser for THz generation based on the end-pumping configuration with two coaxially arranged Nd:YLF crystals [30], as shown in Figure 3, which could solve the problem of the timing jitter. Moreover, a tunable 2 μm optical parametric oscillator (OPO) for generating THz waves with a GaSe crystal was also investigated [31,32]. Degenerate 2 μm lasers with a short pulse duration are good for enhancing the DFG efficiency, as they are efficient, simple, and widely tunable. A microwatt output power and a range of 0.41–3.71 THz were enough to apply to imaging and spectroscopy. The tunable range was extended to 0.24–3.78 THz when the KTP was replaced with a type-II QPM PPLN crystal [33].

For LiNbO₃ crystals, serious absorption in the THz range limits the output power and tunability. An energy of about 1.58 nJ was achieved by using a 1 μm dual-wavelength pump laser at a low repetition frequency [34]. A ZnGeP₂ (ZGP) crystal with a large nonlinear coefficient and high damage threshold is commonly used for DFG with a THz output [35,36]. However, it has a higher absorption coefficient around 1 μm, restricting power scaling [37]. Creeden et al. realized an average power of 2 mW by using two all-fiber laser amplifiers, which is among the highest power recorded for DFG THz sources [38]. The GaP crystal has a very low two-photon absorption in the near-infrared region. A 1 μm dual-wavelength laser is usually used to improve the DFG efficiency. An average power of 27 nW at 6 kHz and a peak power of 40 W at the repetition frequency of 10 Hz were reported [39,40]. Furthermore, tunable THz sources were also achieved using GaP crystals [41,42,43].

In general, inorganic crystals have extremely large absorption coefficients above 5 THz limited by their lateral lattice vibrations. Therefore, the tuning range of THz sources is usually in the range of 0.1–5 THz, which is hard to cover the entire THz band.

4. DFG Terahertz Sources with Organic Crystals

Organic crystals have smaller absorption coefficients in the high-frequency THz band. Moreover, their dispersion characteristics are close and stable between the infrared band and the THz band, such that the type 0 collinear phase matching with loose condition can be met. On the basis of the D–π–A structure, an organic crystal with a larger nonlinear coefficient can easily achieve higher conversion efficiency. The DAST crystal is currently the most mature organic crystal, which has been proven to be an ideal nonlinear optical material in THz generation [44]. In 1999, Riken’s group used a DAST crystal pumped by a 800 nm dual-wavelength Ti–sapphire laser to achieve difference frequency generation with a THz wave output [45]. The DAST crystal had a greater coherence length in the ultrawideband THz frequency range when the wavelength of the pump laser was 1.3–1.5 μm. In 2004, Taniuchi et al. reported that the tuning range of a DFG terahertz source was extended to 2–30 THz with KTP-OPO by generating tunable dual-wavelength lasers around 1.3 μm [46]. Figure 4 shows a typical ultra-broadband tunable THz configuration with organic crystal. A double-pass OPO based on a reflective structure was carried out for improving the pump efficiency in 2007 [47].

Furthermore, a variety of high-performance dual-wavelength lasers and optimizing methods have been applied to DFG THz sources based on DAST crystals for high-efficiency terahertz output, including KTP-OPO intracavity pumping [48], CW dual-wavelength fiber laser [49], BBO-OPO [50], PPLN optical parametric generation (OPG) with seed injection [51], BBO-OPG [52], and dual-wavelength Nd:YAG laser [53].

Table 2. Performance of DFG THz radiation sources based on DAST crystal [45,46,47,48,49,50,51,52,53].

Year	Dual-Wavelength Lasers	Pump Intensity	THz Output	THz Wavelength
1991	Ti–sapphire laser	600 μJ	80 fJ	1.4 THz
2004	PPLN-OPO	0.75 mJ	180 nJ	2–30 THz
2007	KTP-OPO	21 mJ	μJ level	1–30 THz
2008	KTP-OPO intracavity pumping	168 MW/cm2	0.4 mW	2–4 THz
2011	CW fiber laser	0.8 W	-	0.5–2 THz
2012	BBO-OPO	2.5 mJ	-	1–30 THz
2015	Seed injection PPLN-OPG	80 μJ	14.7 nJ	1.5–27 THz
2017	BBO-OPG	0.44 mJ	80 pJ	0.3–4 THz
2017	1.3-μm Nd:YAG laser	1.68 MW/cm2	0.58 μW	3.28 THz

shows the performance of DFG THz radiation sources based on DAST crystals. In 2012, Uchida et al. used the annealing method to increase the damage threshold of DAST crystals to 1.1 GW/cm², which could effectively improve the output energy of THz waves [54]. Liu et al. specifically analyzed the optimal pumping conditions in various dual-wavelength pump sources [55]. He et al. realized a THz frequency-domain spectroscopy system based on an ultra-broadband tunable THz radiation source with a DAST crystal, which could be directly applied to material spectroscopy measurements [56].

With respect to DAST crystals, all kinds of DAST homologs including DSTMS, DASC, and other crystals have been successfully grown by replacing the anion group [57,58,59]. In 2014, Liu et al. reported an ultra-broadband tunable THz source with a tuning range of 0.88–19.27 THz from a DSTMS crystal [60]. It is worth noting that large organic crystals are difficult to grow, which limits their application. Furthermore, the output spectrum of THz waves based on DAST crystals and their homologs has a dip around 1.1 THz due to the intrinsic absorption characteristics [61]. Optimizing the crystal structure according to the needs with a short growth cycle can solve the problem of intrinsic absorption modes. Various types of organic crystals have been developed, such as OH1, BNA, HMQ-T, and HMQ-TMS crystals [62,63,64,65,66].

5. DFG Terahertz Sources with Quasi-Phase-Matching Crystals

Quasi-phase-matching technique is a flexible approach to meet PM without utilizing birefringence, which can use the entire transmission range and the largest nonlinear coefficient of the crystal. Thus, the nonlinear conversion efficiency is high, and the space walk-off effect can be avoided. The PM condition of the QPM crystal becomes Δk = k₁ − k₂ − k_T − k_Λ = 0, k_Λ = 2πm/Λ, where Λ is the QPM period, and m is the QPM order. The k_Λ designed into the required form is used to compensate for phase mismatch. Figure 5 shows schematic diagram of the principle of quasi-phase matching.

The methods for achieving QPM mainly include periodical poling (PP) [67], stacking crystal plates with periodical rotations of 180° [68], and orientation-patterned (OP) epitaxial growth [69]. Among the quasi-phase matching devices, the periodically polarized lithium niobate (PPLN) crystal is the most commonly applied to THz wave generation. In 2002, Sasaki et al. reported the THz wave surface radiation using the slant-stripe PPLN crystal [70]. Later, they achieved a 11.4 nW DFG terahertz source with a peak power of 0.1 mW pumped by a 1.5 μm dual-wavelength pulse laser (1 MHz,100 ps) [71]. An average power of about 2 mW was achieved using the 1 μm CW dual-wavelength laser [72]. Moreover, forward or backward DFG for terahertz generation could also be realized by using a multi-grating PPLN crystal [73]. Table 3 shows the performance of DFG THz radiation sources based on QPM crystals.

Adopting orientation-patterned epitaxial growth or the diffusion bonding technique based on QPM can solve the problem of isotropic crystals (such as GaAs and GaP) struggling to meet phase matching during the DGF process [74]. This gives full play to the advantages of large nonlinear coefficient and small THz absorption, effectively improving the generation efficiency of terahertz waves. Periodically inverted GaP has low absorption in the near-IR range, which enhances the conversion efficiency for terahertz generation [75]. In 2011, Petersen et al. achieved terahertz output with an average power of 339 μW and peak power of 212 mW pumped by a 1.5 μm pulse laser with a repetition frequency of 20 kHz [76]. Jiang et al. reported terahertz output with a peak power of 3.77 kW using a 1 μm pump laser at a low repetition frequency [77]. For QPM-GaAs, a DFG terahertz source with efficient optical-to-THz output pumped by a 2 μm picosecond dual-wavelength laser could be realized [78,79]. The maximum average output power of a tunable continuous-wave (CW) THz DFG source was beyond 1 mW when using QPM-GaAs [80].

Table 3. Performance of DFG THz radiation sources based on QPM crystals [71,72,76,79,80].

QPM Crystal	Dual-Wavelength Lasers	THz Output	THz Wavelength
PPLN	1.5 μm laser (1 MHz, 100 ps)	11.4 nW	1.5–1.8 THz
PPLN	1 μm CW laser	2 mW	1.9 THz
QPM GaP	1.5 μm pulse laser (20 KHz)	339 μW	1.5 THz
QPM-GaAs	2 μm laser (50 MHz, 7 ps)	1 mW	2.8 THz
OP-GaAs	2 μm CW laser	2 mW	1–4.5 THz

Table 3. Performance of DFG THz radiation sources based on QPM crystals [71,72,76,79,80].

QPM Crystal	Dual-Wavelength Lasers	THz Output	THz Wavelength
PPLN	1.5 μm laser (1 MHz, 100 ps)	11.4 nW	1.5–1.8 THz
PPLN	1 μm CW laser	2 mW	1.9 THz
QPM GaP	1.5 μm pulse laser (20 KHz)	339 μW	1.5 THz
QPM-GaAs	2 μm laser (50 MHz, 7 ps)	1 mW	2.8 THz
OP-GaAs	2 μm CW laser	2 mW	1–4.5 THz

6. DFG Terahertz Sources with Waveguides

Compared to bulk nonlinear crystals, waveguide structures provide better mode confinement to enhance the output intensity and DFG efficiency. Using waveguide structures with different dispersion can achieve various phase matching properties between different modes of light waves. Figure 6 shows a structure diagram of a ridge waveguide, which was used as an example to calculate the effective refractive index for phase matching, where w_r is the ridge width of the ridge waveguide, h is the ridge height, t and h are the thickness of the central coating and both sides, b is the thickness of the plate part, and the thickness of the waveguide base is infinite. Furthermore, n_a, n_c, n_r, and n_s represent the refractive index of air, surface coating, waveguide material, and substrate, respectively, while n₁ and n₂ are the effective refractive index of regions I and II. Here, the effective refractive index of a ridge waveguide was analyzed, according to the method proposed by Tyszkiewicz [81].

Both sides of the waveguide are assumed to be infinitely long. For the central region I, the dispersion equation is

$$\frac{2\pi }{{\lambda }_0}\left(b+h+t\right)\sqrt{n_r{}^2-n_1{}^2}={\tan }^{-1}\left[{\left(\frac{n_r}{n_s}\right)}^{2\rho }\sqrt{\frac{n_1{}^2-n_s{}^2}{n_r{}^2-n_1{}^2}}\right]+{\tan }^{-1}\left[\xi \frac{\psi \cosh \phi -\sinh \phi }{\psi \cosh \phi +\sinh \phi }\right],$$

(7)

where λ₀ is the wavelength in vacuum, ρ = 0 is the TE mode, and ρ = 1 is the TM mode. ξ, ψ, and φ can be expressed as

$$\xi ={\left(\frac{n_r}{n_c}\right)}^{2\rho }\sqrt{\frac{n_1{}^2-n_c{}^2}{n_r{}^2-n_1{}^2}}, \psi ={\left(\frac{n_c}{n_s}\right)}^{2\rho }\sqrt{\frac{n_1{}^2-n_a{}^2}{n_1{}^2-n_c{}^2}}, \phi =\frac{2\pi }{{\lambda }_0}t\sqrt{n_1{}^2-n_c{}^2},$$

(8)

and the above calculation process is based on the fundamental mode of TE and TM. For the region of both sides II, the dispersion equation is

$$\frac{2\pi }{{\lambda }_0}\left(b+h\right)\sqrt{n_r{}^2-n_2{}^2}={\tan }^{-1}\left[{\left(\frac{n_r}{n_s}\right)}^{2\rho }\sqrt{\frac{n_1{}^2-n_s{}^2}{n_r{}^2-n_2{}^2}}\right]+{\tan }^{-1}\left[\xi \frac{{\psi }^{\prime }\cosh {\phi }^{\prime }-\sinh {\phi }^{\prime }}{{\psi }^{\prime }\cosh {\phi }^{\prime }+\sinh {\phi }^{\prime }}\right],$$

(9)

where ξ′, ψ′, and φ′ can be expressed as

$${\xi }^{\prime }={\left(\frac{n_r}{n_c}\right)}^{2\rho }\sqrt{\frac{n_2{}^2-n_c{}^2}{n_r{}^2-n_2{}^2}}, {\psi }^{\prime }={\left(\frac{n_c}{n_s}\right)}^{2\rho }\sqrt{\frac{n_2{}^2-n_a{}^2}{n_2{}^2-n_c{}^2}}, {\phi }^{\prime }=\frac{2\pi }{{\lambda }_0}h\sqrt{n_2{}^2-n_c{}^2},$$

(10)

and the effective refractive index n₃ satisfies the following equation:

$$\frac{2\pi }{{\lambda }_0}\left(w_r\right)\sqrt{n_1{}^2-n_2{}^2}=2{\tan }^{-1}\left[{\left(\frac{n_1}{n_2}\right)}^{2\rho }\sqrt{\left(\frac{n_3{}^2-n_2{}^2}{n_1{}^2-n_2{}^2}\right)}\right],$$

(11)

where n₃ is the effective refractive index of the whole waveguide structure.

Thompson and Coleman first achieved THz output with nanowatt power from a planar GaAs waveguide using a CO₂ laser [82]. Later, various DFG THz sources based on GaAs waveguides were investigated [83,84]. Table 4 shows the performance of DFG THz radiation sources based on various waveguides. Using a 2 μm dual-wavelength laser and GaAs planar waveguides, the average power of terahertz waves at 2 THz could reach 1 μW [85]. By flexibly designing the waveguide structure of GaP, a high-power THz output with a wide tuning range could be realized [86,87,88]. When LiNbO₃ crystal was used as the waveguide medium, the output power of the THz wave was about 0.5 μW, and the frequency range covered 0.97–7.5 THz, pumped by a 1.5 μm CW dual-wavelength laser [89]. Suizu et al. reported that an average power of 400 pW and peak power of 4 μW were obtained using a PPLN waveguide [90].

A silicon waveguide was studied by strain-induced second-order nonlinearity, demonstrating promising potential for high-power THz generation [91]. Recently, Schulz et al. reported that the output power of terahertz waves was 10 μW with a tunable range of 1–10 THz based on an integrated nonlinear waveguide of silicon [92]. A metallic–dielectric hybrid (MDH) waveguide for THz parametric interactions was theoretically analyzed by Ding [93]. The strength of terahertz parametric converter was significantly enhanced by reducing the modal indices and eliminating the diffraction in forward or backward generation. Liu et al. proposed a high-power terahertz source with high brightness using nonlinear optical crystal fiber, which consisted of a GaAs core with periodical inversion [94]. Cherchi et al. thoroughly compared dielectric waveguides composed of zincblende semiconductors, exploiting the optical nonlinearity for guiding terahertz generation [95]. Recently, we theoretically investigated a category of ridge waveguides composed of GaAs and SiN in different sizes for efficient terahertz generation [96]. The output power and conversion efficiency based on integrated hybrid waveguides were much higher than those using bulk or micro-structured GaAs crystals, revealing their potential for on-chip terahertz systems.

Table 4. Performances of DFG THz radiation sources based on various waveguides [85,88,89,90,92].

Waveguide Type	Dual-Wavelength Lasers	THz Output	THz Wavelength
GaAs waveguide	2 μm laser (50 MHz, 7 ps)	1 μW	2 THz
GaP waveguide	OPO with 0.92–1.5 μm	56 pJ	0.48–4.3 THz
LiNbO3 waveguide	1.5 μm CW laser	0.5 μW	0.97–7.5 THz
PPLN waveguide	1.5 μm laser (1 MHz, 100 ps)	400 pW	1.48 THz
silicon waveguide	1.5 μm CW laser	10 μW	1–10 THz

Table 4. Performances of DFG THz radiation sources based on various waveguides [85,88,89,90,92].

Waveguide Type	Dual-Wavelength Lasers	THz Output	THz Wavelength
GaAs waveguide	2 μm laser (50 MHz, 7 ps)	1 μW	2 THz
GaP waveguide	OPO with 0.92–1.5 μm	56 pJ	0.48–4.3 THz
LiNbO3 waveguide	1.5 μm CW laser	0.5 μW	0.97–7.5 THz
PPLN waveguide	1.5 μm laser (1 MHz, 100 ps)	400 pW	1.48 THz
silicon waveguide	1.5 μm CW laser	10 μW	1–10 THz

In addition to the abovementioned DFG materials, the DFG medium based on quantum wells could also realize frequency conversion using the quantum confinement effect. A quantum well structure with the designed energy level based on GaAs/AlAs was used to produce THz waves [97,98,99].

7. Cavity-Enhanced DFG and Cascaded DFG

Although various DFG materials have been extended to increase the DFG efficiency, the THz conversion efficiency of a single-pass nonlinear crystal is usually low due to the limitation of pump intensity. Recycling the laser pulses is a practical approach to obtain high-power THz output through an external enhancement cavity. Figure 7 shows a typical external enhancement cavity with a bow-tie configuration. A piezoelectric transducer (PZT) is used to fine-tune the cavity length. The enhancement factor can be maximized by providing small cavity round trip losses (Δ) with the optimized enhancement cavity. The maximum enhancement factor A in the CW case is written as follows [100]:

$$A=\frac{1-R}{{\left[1-\sqrt{R\left(1-\Delta \right)}\right]}^2+4\sqrt{R\left(1-\Delta \right)}{\sin }^2(\frac{\delta }{2})},$$

(12)

where R is the cavity reflectivity, and δ is the difference of phase between two consecutive round trips.

Steady-state lasers with external cavity-enhanced nonlinear frequency conversions were investigated in CW, nanosecond, and femtosecond operation [101,102,103]. In 2010, Petersen et al. reported an enhanced terahertz generation with a resonant external cavity, which realized a sevenfold enhancement compared with a single-pass orientation [104]. Later, they greatly improved the enhancement factor by 250 times using QPM GaP [76]. In terms of narrow linewidth, Paul et al. proposed a single-frequency terahertz source exceeding 100 μW using an external enhancement cavity for DFG [105].

Due to the barrier of inherent quantum defects, the conversion ratio between near-IR and THz ranges was also restricted (see Equation (6)). The cascade DFG generates multiple terahertz photons from the depletion of a single pump photon, which provides a feasible approach to break the constraint of the Manley–Rowe relation. The basic concept of cascaded DFG terahertz radiation is shown in Figure 8. A terahertz photon with frequency of ω_T is generated by the interaction between a high-frequency pump photon with a frequency of ω_m and a low-frequency pump photon with a frequency of ω_m+1, while the low-frequency pump photon is amplified. If the gain is high in the DFG process, the amplified pump photon as a new high-frequency pump photon interacts with the terahertz wave to generate a new low-frequency pump photon with a frequency of ω_m+2. Meanwhile, the THz photon with a frequency of ω_T is amplified. The repeated conversion of energy between high-frequency pump light and low-frequency light continuously generates a series of THz photons under the condition of phase matching.

A birefringent crystal with anisotropy cannot satisfy the cascade conditions limited by polarization and parameters. Isotropic crystals such as GaP, GaAs, and ZnTe are usually applicable for the cascade DFG. In 2004, Cronin-Golomb first predicted cascaded DFG for enhanced THz generation from ZnTe using a 800 nm laser [106]. In 2008, Schaar et al. used a GaAs crystal based on quasi-phase matching technology to generate terahertz waves and detected both Stokes light and anti-Stokes light in the experiment, confirming the cascade process [107]. Later, the dynamic process of cascaded DFG in QPM crystals and isotropic crystals for optimal designing parameters was theoretically analyzed [108,109]. In 2016, Ravi et al. proposed a high-energy terahertz generation technology based on spectrally cascaded optical parametric amplification from PPLN under low-temperature cooling cycles [110]. The light waves with different order were formed by the repeated energy conversion from the first-order high-frequency pump light to the low-frequency light in the cascade process. Therefore, cascading DFG for terahertz output can be further enhanced by increasing the order and improving the period variation of the crystal.

8. Conclusions

This paper provided a review of optical terahertz sources of difference frequency generation, including DFG with inorganic crystals, DFG with organic crystals, DFG with quasi-phase-matching crystals, DFG in waveguides, cavity-enhanced DFG, and cascaded DFG. Various kinds of operating modes involved in Q-switching, CW, single frequency, or tunability were covered. The terahertz radiation generated by the DFG method can meet the needs of many applications, such as spectroscopy and imaging. Optimizing the DFG THz source based on nonlinear crystals is of great significance to the development and application of terahertz technology. This review is expected to provide a comprehensive reference for researchers and help to push the progress of optical THz sources based on difference frequency generation with nonlinear crystals.