**2. Terahertz-wave parametric generation**

and global environmental measurement, since they have higher directivity like infrared than microwaves and higher transmittances in the atmosphere and in soft materials like microwave than infrared. Therefore, high-peak-power, narrow-linewidth (high-brightness), and continuously tunable terahertz-wave sources that could be widely used in such applications are required. The terahertz (THz) region is relatively unexplored, because of the lack of the commercially available high-brightness and continuously tunable sources, high-sensitive and fast detectors, and optics, which has resulted in what is called the frequency gap [1–3]. Over the past two decades, there has been striking growth in the region of science and engineering, which has become a vibrant, international, cross disciplinary research activity [4]. Wavelength (frequency) conversion in nonlinear optical materials is an effective method for generating high-brightness and continuously tunable terahertz waves owing to the high conversion efficiency, bandwidth, wide tunability, and room temperature operation. A terahertz-wave

source using parametric wavelength conversion based on lithium niobate (LiNbO3

**Figure 1.** Development of parametric sources using LiNbO3

during 1–3 THz in each paper.

30 High Power Laser Systems

was first proposed in 1960s [5, 6] and realized in the mid-1990s with the terahertz-wave parametric oscillator [7]. At that time, the tuning range and the observed maximum peak output power of terahertz wave were from 1.1 to 1.6 THz (270–184 μm) and several milliwatts, respectively. By using the current injection-seeded terahertz-wave parametric generator (is-TPG), the tuning range expanding from 0.39 to 5.0 THz (750–60 μm) and the peak output power exceeding 55 kW [8–11] were observed, representing an increase by 10 times and seven orders of magnitude, as shown in **Figure 1**. **Table 1** lists the characteristics of three typical intense terahertz-wave sources: our injection-seeded terahertz-wave parametric generator (is-TPG), well-known intense terahertz-wave sources, a far-infrared free-electron laser (FIR-FEL) [12], and terahertz-wave pulse generation through optical rectification using a tilted-pulsefront

) crystals

in our group. Points represent the peak output power

When the intense laser beams pass through a nonlinear optical crystal, the transverse photon and phonon wave fields become coupled and behave as new mixed photon-phonon states called polaritons. Broadband terahertz-wave generation results from efficient parametric scattering of laser light via polaritons [5, 6]. The polaritons exhibit phonon-like behavior in the resonant frequency region (near the transverse optical (TO)-phonon frequency *ωTO*); however, they behave like photons in the nonresonant low-frequency region, as shown in **Figure 2**. Generation of narrowband terahertz waves can be achieved by applying an optical resonator (in the case of the terahertz-wave parametric oscillator (TPO)) or injecting a "seed" (in the case of the injection-seeded terahertz-wave parametric generator (is-TPG)) for the idler wave [14]. The wide tunability is accomplished simply by changing the angle between the incident pumping beam and the resonator axis (in the case of TPOs) or the wavelength and axis of the

**Figure 2.** (Left) Dispersion relation of the polariton. (Right) Noncollinear phase-matching condition.

seeding beam satisfying the phase-matching condition (in the case of is-TPGs). In the parametric wavelength conversion process, a terahertz-wave signal photon and a near-infrared idler photon are created parametrically from a near-infrared pumping photon, according to the energy conservation law *ω<sup>p</sup> = ωT + ω<sup>i</sup>* (where ω indicates frequency and p, T, and i denote the pumping, terahertz, and idler photons, respectively) and the momentum conservation law *k***<sup>p</sup>** *= k***<sup>i</sup>** *+ k***T** (noncollinear phase-matching condition). This condition leads to the angledispersive characteristics of the idler and terahertz waves. Thus, broadband terahertz waves can be generated depending on the phase-matching angle.

In this experiment, we used a magnesium oxide (MgO)-doped LiNbO3 crystal. The large figure of merit (FOM = *4deff 2 /nNIR 2 nTHz αTHz 2 ~ 10*, *deff*; the effective nonlinear coefficient, *nNIR* and *nTHz*; the refraction indices in the near infrared and terahertz range, *αTHz*; the absorption coefficient for the terahertz wave) [13] of LiNbO3 at room temperature makes this well-known nonlinear crystal ideal for such an application. The gain curve of the terahertz-wave parametric generation is determined by the parametric gain and absorption coefficients in the terahertz region. **Figure 3** shows the pumping intensity dependence (0.1, 0.2, 0.4, 0.8, 1.6, and 3.2 GW/cm2 ) of calculated gain curves [15]. As the pumping intensity increases, the gain coefficient also increases in whole frequency region, and the maximum value in the gain curve moves toward higher frequencies. All gain curves have a broad bandwidth, with a drop appearing at around 2.6 THz. This is because the low-frequency modes of doped MgO in the LiNbO3 work as crystal lattice defects. Under the noncollinear phase-matching condition, the effective gain curve depends on both the intensity and the beam diameter of the pumping beam. **Figure 4** shows the pumping beam diameter dependence of calculated effective gain curves. When an Nd:YAG laser

(λ = 1064 nm) is used to generate the pumping beam and an MgO:LiNbO3

nonlinear optical crystal, the effective gain coefficient is given [16–18] by

where *αcrystal* is the absorption coefficient of the terahertz wave in the MgO:LiNbO3

result, we can optimize the tuning curves by controlling these parameters.

*φ* is the phase-matching angle between the pumping beam and the terahertz wave, *g0*

and 5 mm) have enough gain coefficient over a broad range extending from less than 1 THz to more than 3 THz. As the pumping beam diameter becomes larger, the gain coefficient also increases, and the maximum value of the gain curve moves toward lower frequencies. As a

**Figure 4.** Pumping diameter dependence of effective calculated gain coefficient, when the pumping beam diameters

.

When a high-intensity laser beam propagates through a nonlinear crystal, a number of nonlinear processes occur, such as the following: second- or higher-harmonic generation (SHG or HHG); difference- or sum-frequency generation (DFG or SFG); optical parametric generation, amplification, or oscillation (OPG, OPA, or OPO); stimulated Raman or Brillouin scattering

) 1/2 –1]/2,

,

is the diameter of the pumping beam. When

, all gain curves (pumping beam diameter 0.5, 1, 2,

High-Brightness and Continuously Tunable Terahertz-Wave Generation

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33

*gT* = [(1 + 16 *cos* (*g*<sup>0</sup> /)<sup>2</sup>

were 0.5, 1, 2, and 5 mm. The pumping intensity was 1 GW/cm2

= *crystal* + *beam*,

*αbeam* ∝ *sin* /*rp*

parametric gain under the low-loss limit, and *rp*

the pumping beam intensity is 1 GW/cm2

crystal is used as the

crystal,

is the

**Figure 3.** Pumping intensity dependence of calculated gain coefficient using MgO:LiNbO3 pumped by Nd:YAG laser, when the pumping intensities were 0.1, 0.2, 0.4, 0.8, 1.6, and 3.2 GW/cm2 .

seeding beam satisfying the phase-matching condition (in the case of is-TPGs). In the parametric wavelength conversion process, a terahertz-wave signal photon and a near-infrared idler photon are created parametrically from a near-infrared pumping photon, according to

the pumping, terahertz, and idler photons, respectively) and the momentum conservation law *k***<sup>p</sup>** *= k***<sup>i</sup>** *+ k***T** (noncollinear phase-matching condition). This condition leads to the angledispersive characteristics of the idler and terahertz waves. Thus, broadband terahertz waves

the refraction indices in the near infrared and terahertz range, *αTHz*; the absorption coefficient

crystal ideal for such an application. The gain curve of the terahertz-wave parametric generation is determined by the parametric gain and absorption coefficients in the terahertz region.

culated gain curves [15]. As the pumping intensity increases, the gain coefficient also increases in whole frequency region, and the maximum value in the gain curve moves toward higher frequencies. All gain curves have a broad bandwidth, with a drop appearing at around 2.6 THz.

defects. Under the noncollinear phase-matching condition, the effective gain curve depends on both the intensity and the beam diameter of the pumping beam. **Figure 4** shows the pumping beam diameter dependence of calculated effective gain curves. When an Nd:YAG laser

**Figure 3** shows the pumping intensity dependence (0.1, 0.2, 0.4, 0.8, 1.6, and 3.2 GW/cm2

(where ω indicates frequency and p, T, and i denote

 *~ 10*, *deff*; the effective nonlinear coefficient, *nNIR* and *nTHz*;

at room temperature makes this well-known nonlinear

crystal. The large figure

work as crystal lattice

pumped by Nd:YAG laser,

) of cal-

 *= ωT + ω<sup>i</sup>*

In this experiment, we used a magnesium oxide (MgO)-doped LiNbO3

*2*

This is because the low-frequency modes of doped MgO in the LiNbO3

**Figure 3.** Pumping intensity dependence of calculated gain coefficient using MgO:LiNbO3

.

when the pumping intensities were 0.1, 0.2, 0.4, 0.8, 1.6, and 3.2 GW/cm2

can be generated depending on the phase-matching angle.

 *nTHz αTHz*

the energy conservation law *ω<sup>p</sup>*

*2 /nNIR 2*

for the terahertz wave) [13] of LiNbO3

of merit (FOM = *4deff*

32 High Power Laser Systems

**Figure 4.** Pumping diameter dependence of effective calculated gain coefficient, when the pumping beam diameters were 0.5, 1, 2, and 5 mm. The pumping intensity was 1 GW/cm2 .

(λ = 1064 nm) is used to generate the pumping beam and an MgO:LiNbO3 crystal is used as the nonlinear optical crystal, the effective gain coefficient is given [16–18] by

$$\begin{aligned} g\_r &= a \left[ \left( 1 + 16 \cos \varphi \left( g\_o / a \right)^2 \right)^{1/2} - 1 \right] / 2 \pi \\\\ a &= a\_{crystal} + a\_{beam} \\\\ \alpha\_{beam} &\propto \sin \varphi / r\_{p'} \end{aligned}$$

where *αcrystal* is the absorption coefficient of the terahertz wave in the MgO:LiNbO3 crystal, *φ* is the phase-matching angle between the pumping beam and the terahertz wave, *g0* is the parametric gain under the low-loss limit, and *rp* is the diameter of the pumping beam. When the pumping beam intensity is 1 GW/cm2 , all gain curves (pumping beam diameter 0.5, 1, 2, and 5 mm) have enough gain coefficient over a broad range extending from less than 1 THz to more than 3 THz. As the pumping beam diameter becomes larger, the gain coefficient also increases, and the maximum value of the gain curve moves toward lower frequencies. As a result, we can optimize the tuning curves by controlling these parameters.

When a high-intensity laser beam propagates through a nonlinear crystal, a number of nonlinear processes occur, such as the following: second- or higher-harmonic generation (SHG or HHG); difference- or sum-frequency generation (DFG or SFG); optical parametric generation, amplification, or oscillation (OPG, OPA, or OPO); stimulated Raman or Brillouin scattering (SRS or SBS); four-wave mixing; optical rectification (OR); multiphoton absorption; and the Kerr and Pockels effects. Of these, we revealed that the parametric wavelength conversion near the lattice resonance induced by SRS is significantly inhibited by SBS; however, this nonlinear process has long been ignored. In the previous research done by authors, the conversion efficiency in energy from an infrared pumping beam to a terahertz wave was less than 10−7. It has long been thought that this is the limit of the conversion efficiency using parametric wavelength conversion using LiNbO3 pumped by nanoseconds Nd:YAG lasers (duration, 10–25 ns) [14]. However, when a photon of the pumping beam (1064 nm) creates two photons (idler beam and terahertz wave (100–1000 μm), in principle, the conversion efficiency reaches 10−2–10−3 according to the Manley-Rowe relations because the wavelength of the terahertz wave is about 102 –103 times longer wavelength than that of the pumping beam. In our experiment, an infrared pumping beam excites acoustic phonons in LiNbO3 , and SRS of the pumping beam generates terahertz waves and an idler beams. We calculated both gain coefficient of the SRS and the SBS in the previous condition; the gain coefficient of SBS has 1000 times larger gain than that of the SRS [19–24]. Typically, the SBS gain reaches the steady state within 10 lifetimes of the acoustic phonon of crystal [25], within about 1.5 ns in LiNbO3 [24]. For efficient wavelength conversion, the pulse width of the pumping beam should be enough less than this, but the pulse width limits the linewidth of the generated terahertz waves. By applying a single-mode oscillated microchip Nd:YAG laser [26] with a sub-nanosecond (several hundreds of picoseconds) "pulse gap" pulse width [27] as a pumping source, a high-efficiency and narrow-linewidth wavelength conversion can be performed by the SRS without the SBS. Additionally, when the intensity of the pumping beam is too high, secondorder stoke (idler) beams can be generated, which do not contribute to the generation of terahertz waves as they undergo strong absorption. We thus precisely controlled both pumping and seeding intensity and diameter as well as the nonlinear crystal length.

crystal input surface. We used a 50-mm-long nonlinear MgO:LiNbO3

is more than 55 kW (BT ~ 1018 K, brightness ~ 0.2 GW/sr·cm2

tion coefficient of the MgO:LiNbO3

**Figure 5.** Experimental apparatus for an is-TPG.

**4. Result and discussion**

tion coating for a pumping beam. A prism made by high-resistivity silicon placed on the output surface of the nonlinear crystal works as an efficient output coupler only for the terahertz waves to avoid the total internal reflection of the terahertz waves on the crystal output side surface. For an optimization of terahertz-wave emission, the pumping region within the nonlinear crystal must be as close as possible to the output surface, because of the large absorp-

between the output surface and the beam center was precisely adjusted to obtain a maximum terahertz-wave output, and it was approximately equal to the pumping beam radius. The terahertz-wave output extracted through the Si-prism coupler was collimated, focused, attenuated, modulated, and then measured using a calibrated pyroelectric detector covered by thick black polyethylene sheet. The temporal waveform and linewidth of the terahertz wave were measured by a Schottky barrier diode (SBD) and a pair of scanning metal mesh plates.

**Figure 6** shows the tuning curves of two is-TPGs fabricated using our design obtained by scanning the wavelength of seeding beam. When the pumping beam diameter and energy are 1.5 mm and 20 mJ/pulse, and the seeding beam power is 800 mW (continuous wave), the tunable range of the terahertz wave is 0.7–3 THz (430–100 μm). The maximum output peak power

has a broad tuning range, with a flat region around 1.6–2.6 THz. The terahertz-wave output decreased in the low- and high-frequency regions (below 1.6 and above 2.6 THz) because of a low parametric gain and high absorption coefficient [29] in these regions, respectively. From the is-TPG, the pulsed terahertz waves are generated by 100 Hz (by 10 ms); however, the pyroelectric detector we used in the experiment only gives an average power. We therefore

crystal with antireflec-

) at around 1.8 THz. This source

crystal in the terahertz range (10–100 cm−1). The distance

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