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Abstract
This study experimentally demonstrates and theoretically analyzes the enhancement of terahertz (THz) waves from two-color laser-field (consisting of a near-infrared femtosecond laser and its second-harmonic wave) induced air plasma using an additional 800 nm femtosecond laser. The experiments revealed that the additional 800 nm laser increased the THz energy up to 22 times. To understand the enhancement mechanism and reveal the maximum enhancement conditions, the effects of the 800 nm beam’s polarization and energy variations of both beams on the THz amplification were studied. With the increase in the 800 nm pulse energy, the THz yield initially increases, and then decreases after reaching an inflection point. The THz increase rate continues to increase with the decrease in energy of the near-infrared two-color fields. The 800 nm beam could efficiently modulate the THz spectral energy distribution by increasing the high-frequency components, while decreasing the low-frequency components.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) sources generated using an air-excited plasma have been extensively studied because of their high performance and extensive applications in THz spectroscopy and imaging and THz–matter interactions [1–3]. In 2000, Cook et al. demonstrated strong THz waves generated from air plasma excited using two-color pulses of fundamental and its second harmonic (SH) waves and presented a four-wave mixing model to explain the generation [4]. Since then, extensive studies have been carried out on the physical mechanism and approaches for an enhancement of the THz generation from two-color fields by manipulating the transverse asymmetry of the electric field in the plasma to obtain an advanced and practical method to produce intense THz waves [5–9]. Among the models, the photocurrent model proposed by Kim et al. has been widely applied and further developed [10–12].
Compared to the two-color scheme, a THz source with a higher conversion efficiency and wider spectrum can be obtained from three-color or multi-color pulsed air plasma. Various methods have been analyzed to generate THz radiation using multi-beam or multi-frequency laser hybrid focusing [13–15]. The aim is to increase the intensity of the THz radiation by constructing multiple beams in particular manners. Martinez et al. have reported that the free-electron trajectory could be optimized using a sawtooth shape laser field to obtain the maximum electron drift velocity. This could increase the THz conversion efficiency to 2%, compared to the value ${10^{ - 4}}$ obtained using a two-color laser plasma [16]. They have theoretically proposed the ideal combination of multi-color fields for the best THz yield. However, such precise experiments are tedious to carry out in practice. The generation of THz radiation has been demonstrated by focusing ultrafast laser pulses having three incommensurate wavelengths, including signal and idler beams, from an optical parametric amplifier (OPA) and an 800 nm beam from a Ti:sapphire laser amplifier into a plasma. THz radiation can be generated only when all the three beams are present. The polarization characteristics of the generated THz radiation cannot be comprehensively explained using the plasma current model [17]. The effect of the energy ratio of the three beams on the THz yield was not analyzed in this study. In addition, the combined effect of the three lasers for the THz generation and the unusual behaviors of their polarizations have not yet been elucidated. Recently, the THz emission of the plasma induced using the two-color laser pulses could be enhanced by adding a residual 800 nm pulse from an OPA; the THz electric field could be enhanced up to 30 times [18]. The variations in polarization and spectrum were not considered in this study. Upon excitation using a three-color pulse in ambient air, the output THz pulse has exhibited a spectrum range of up to 50 THz [19]. These studies show the potentials of the air plasma to generate high-power THz waves with wider spectra, which are more adaptable for experimental and practical use.
In this study, we propose a THz emission system using three-color lasers with adjustable near-infrared wavelengths obtained using an OPA, its SH, and an additional 800 nm ultrafast pulse. We demonstrate a large stable THz enhancement of the near-infrared two-color fields after the addition of the 800 nm laser. Moreover, we obtained the variation trends of the THz strengthening effect with important parameters in the system such as the polarizations and energies of the lasers, and then analyzed the optimal conditions for the maximum THz enhancement. The modulation of the THz spectral energy distribution and central frequency shifting after the addition of an 800 nm pulse could provide valuable insights for the generation of THz radiations with specific frequency distributions for certain purposes.
2. Experimental setup
Figure 1 shows a schematic of the experimental setup. A regenerative Ti:sapphire laser amplifier (Spitfire, Spectra Physics) was employed to emit horizontally polarized 50-fs 1-kHz 800 nm laser pulses. The laser beam was split into two beams. One portion was injected into the OPA (TOPAS), which provided a vertically polarized laser with a wavelength tunable in the range of 1200–1600 nm. Combining the various properties of the laser amplifier, the laser wavelength was set at the optimal value of 1550 nm. It was incident through a lens with a focal length of 125 mm and a 90 $\mathrm{\mu }$m thick type-I BBO crystal into a hole behind the first off-axis parabolic mirror (PM1). The other part of the 800 nm pulse was focused using PM1 with a focal length of 50.8 mm after a temporal delay stage and half-wave plate, and then coaxially co-focused with the near-infrared two-color pulses. The THz wave was excited forward using the plasma at the focal point; then collected, collimated, and refocused using a pair of off-axis parabolic mirrors (PM2 and PM3). It was then detected through electro-optic sampling with a 3-mm-thick ZnTe crystal after passing through a silicon wafer, which blocked the residual pump lasers, and THz filter (Tydex).
Fig. 1. Schematic of the experiment; BBO: type-I β-barium borate crystal, PM1, PM2, PM3: off-axis parabolic mirrors.
3. Results and discussion
3.1 Experimental result and overall analysis of terahertz enhancement in three-color laser-field scheme
The 800 nm pulse was added collinearly along the light propagation direction of the near-infrared two-color field lasers, which excited the air plasma to generate the THz waves. The THz signal produced by the single 800 nm laser plasma was very weak and could not be easily detected using our electro-optic sampling system. Therefore, the THz enhancement was obtained using the 800 nm laser acting on the near-infrared two-color fields, rather than using a simple superposition or interference of the two THz signals generated by the two laser sources. We used the temporal delay stage to control the relative time delay between the 800 nm laser and the near-infrared two-color fields. When the 800 nm pulse arrives in advance, the intensity of the THz radiation generated by the near-infrared two-color fields is suppressed owing to the pre-ionization of the ambient air by the 800 nm beam, which consumes air molecules at the focus [20]. In addition, the carrier recombination time was considerably larger than the time delay between the near-infrared two-color pulses and the 800 nm pulse, which excludes the possibility of any electron-ion recombination [21] and restrains the THz output. An 800 nm pulse closer to the near-infrared two-color pulses provides a larger THz attenuation effect. When the optical path difference between them two is approximately zero, the three pulses arrive simultaneously and the three-color field lasers act together, which significantly increases the THz intensity, as shown in Fig. 2(a). The near-infrared two-color field energy was 80 µJ, while the 800 nm pulse energy was 100 µJ. The x-coordinate is the phase delay between the near-infrared two-color fields and the 800 nm pulse. The initial part of −0.3–0 ps is the region where the 800 nm pulse arrives before the near-infrared two-color pulses. The THz intensity then increased rapidly. After increasing until a peak point, the THz signal decreased for several ps, wherein the THz intensity was essentially equal to that produced by the near-infrared two-color fields. The enhancement range was approximately 0.2 ps at a low near-infrared two-color field strength, which was narrowed when the energy was increased (Figs. 2(a) and 2(b)). Figure 2(b) shows the THz signal scanned as in Fig. 2(a) when the near-infrared two-color field energy was 60 µJ and the 800 nm pulse energy was 100 µJ. The THz enhancement effect in Fig. 2(b) is larger than that in Fig. 2(a). Figure 2(c) shows the THz time-domain signals with and without the 100-µJ 800 nm pulse when the near-infrared two-color field energy was 60 µJ. The x-coordinate is the phase delay between the three-color pulses and the probe light. The red curve was scanned at Point A in Fig. 2(b).
Fig. 2. THz enhancement curves. (a) Peak THz electric field intensity as a function of the relative delay between the near-infrared two-color fields (80 uJ) and the 800 nm pulse (100 uJ). (b) Peak THz electric field intensity at 60-µJ near-infrared two-color field energy with relative delay to additional 800 nm pulse (100 uJ). (c) THz temporal waveforms in the absence and presence (point A) of the 800 nm pulse (100 uJ) at the near-infrared two-color field energy of 60 µJ.
The photocurrent model [6,10,11,22,23] was employed to explain the THz increase. The generation of THz radiation includes three steps, laser-induced ionization of gas molecules, electron transversal movement driven by the optical field, and THz wave radiation outward by the transverse net current. The velocity of the electrons ionized at the extrema of the pump electric field periodically varies. By analyzing the average velocity in a pulse, we can obtain the direction in which the electrons move overall. The changing transverse net current generates THz waves. Thus, the plasma current generated because of photoionization can be expressed as
where where $\textrm{d}{N_e}(t^{\prime})$ is the electron density produced in the range $t^{\prime}$ to $t^{\prime} + \textrm{d}t^{\prime}$. At this point, the electric field of the generated THz wave is proportional to the first time derivative of the plasma current, which can be expressed asTo maximize ${E_{\textrm{THz}}}$, we may increase the free-electron velocity ${v_d}(t)$, in addition to the ionization rate $w(t)$. According to the simulation, the air at the focal point was not completely ionized when the near-infrared two-color fields had low energy. Therefore, when the 800 nm beam was added, its energy completely ionized the electrons in the region of the superposition of the two plasmas. This increased the number of electrons under the effect of asymmetric near-infrared two-color fields, and thus increased the transverse quasi-direct current, which largely enhanced the THz radiation. In theoretical simulation, with the same beam diameters and focal lengths of the two beams as the experiment, the THz generated by the three-color fields in ideal situation of complete overlap of two plasmas is much larger than that generated by the two-color fields with the same energy. This can be inferred from Eq. (7). The electric field intensity of each component of the light waves at the plasma focus was obtained using
where, P is the single-pulse energy of the laser, a is the focal radius of each laser, ${T_0}$ is the effective laser width, c is the speed of light, and ${\varepsilon _0}$ is the vacuum dielectric constant. the laser wavelength of 800 nm is shorter than 1550 nm laser, the laser beam diameter is bigger than 1550 nm (determined by laser amplifier and OPA), so that the electric field intensity of 800 nm at the focus is stronger than 1550 nm with equal energy. Hence, more free electrons can be obtained using a three-color field rather than a two-color scheme under equal energy. Under the action of two-color asymmetric electric fields, the larger free electrons can generate more transverse net current, thus producing more THz radiation. Figure 3(a) is simulation result of THz signal when near-infrared two-color fields (160 µJ) and three-color fields (two-color field energy is 60 µJ; 800 nm pulse energy is 100 µJ) have equal total pump energy of 160 µJ. It is obtained under the ideal condition of complete overlap of two plasmas. Because the Ti:sapphire laser amplifier and OPA are not phase-stable, the phase is random when the third field is superimposed on the near-infrared two-color fields. Thus we set the initial phase of the 800 nm pulse from $- \pi \sim \pi $ with the phase step of $\pi /4$ and get the THz temporal waveforms. Then the average value of the nine signals was taken as the THz intensity signal of the three-color fields.Fig. 3. (a) THz temporal waveforms in ideal situation, when the two plasmas are completely superimposable. (b) THz temporal waveforms in actual situation, when the two plasmas are not completely superimposable.
However, in experiments, we found the THz yield of the three-color fields is not as high as that of the two-color fields with the same energy. We believe the reason for the deviation between theory and practice is that, in practice, the 1550 nm filament and the 800 nm spot-like plasma do not overlap completely because of their respective focal lengths, and the overlap area only accounts for a small part of the two-color field filament. Thus the range in which 800 nm laser can play a role is relatively small, leading to our practical measurements. The relevant simulation proof is shown in Fig. 3(b), where we control the proportion of the three-color field area to get a simulation result consistent with the experiment. The proportion of the overlapping area is estimated by experimental observations. The total energy of it is equal to Fig. 3(a). We will continue to improve the system in order to achieve the ideal performance of the three-color fields.
3.2 Effect of 800 nm laser’s polarization on terahertz enhancement
The enhancement effect of polarization of the 800 nm laser beam on the THz intensity was investigated. Initially the THz signal generated using the air plasma excited by the near-infrared two-color fields was optimized. Here, the 1550 nm fundamental wave was vertically polarized and the SH wave was oriented at approximately 45° clockwise from the vertical direction controlled using BBO. The observation plane was the incident plane of light. Then, the 800 nm laser was added and the superposition of the two plasmas and the retardation between the two pulses was adjusted to maximize the THz intensity increase. In this system, polarization of the 800 nm laser could be freely controlled using a half-wave plate. In Fig. 4, the x-coordinate is the degree of clockwise rotation of the 800 nm laser from the horizontal polarization. The largest THz enhancement was achieved when the 800 nm laser was oriented at approximately 45°, similar to the SH. When the polarization of the 800 nm beam was approximately perpendicular to that of the SH, almost no increase was observed.
Fig. 4. Enhancement effect on the 800 nm laser THz intensity; solid line is the sine fit of the experiment data.
According to the photocurrent model and the sawtooth wave shape theory [6,10,11,16,22,23], when the three beams are polarized in the same direction, the maximum excitation electric field can be obtained by matching their powers and phases. Similarly, a large transverse current is obtained and an intense THz wave can be generated. However, owing to the experimental realization limitation, we can only balance between the conversion efficiency of the SH and its polarization direction in the two-color field scheme [12]. This would inevitably lead to a deviation between the polarization direction of the fundamental wave and that of the SH. The fundamental wave was orthogonally decomposed along the SH direction and its vertical direction. The component of the fundamental wave in the direction of the SH interacts with the SH to produce the THz waves. It was assumed that the other fundamental wave component along the vertical direction of the SH ionizes electrons accelerated by the SH. The resulting THz radiation was oriented along the SH [11], however, this part contributes slightly to the THz radiation. After the addition of the 800 nm laser, the enhancement trend could be exactly fitted by a sine curve. At the point where the THz enhancement was maximized, the 800 nm pulse was exactly aligned along the polarization direction of the SH, as shown in Fig. 4. The sine curve indicates that only the 800 nm laser in the SH direction had an effect on the THz wave enhancement and that the near-infrared fundamental wave and the 800 nm laser in all other polarization directions except for the orientation parallel to the SH could not act together to produce the THz radiation. This demonstrates that the THz enhancement signal can be generated only when all the three beams are present and when the polarization directions of the SH and the 800 nm pulse are identical. This result is of significance for future experimental studies to obtain a higher THz yield by adjusting the laser polarizations.
3.3 Effect of relative energy of three-color laser-field on terahertz enhancement
To further investigate the effects of the additional 800 nm beam on the THz intensity and spectrum, the polarization of the 800 nm pulse was set in the optimal direction (at an angle of approximately 45° from the near-infrared fundamental wave), energy of the near-infrared two-color field laser was fixed at 40 $\mathrm{\mu}$J, the 800 nm laser energy was changed, and the THz energy changes with the 800 nm beam energy were observed. At this incident laser power, the THz radiation generated by the near-infrared two-color fields was significantly weak, reaching the low limit of the THz signal that could be sensed by the detector. In addition, the electrons in the filament could not be completely ionized. When the energy of the near-infrared two-color fields exceeded 80 $\mathrm{\mu}$J, the THz enhancement after the addition of the 800 nm beam was not considerable. Therefore, three values were chosen in this range for measurements, 40 $\mathrm{\mu}$J, 60 $\mathrm{\mu}$J, and 80 $\mathrm{\mu}$J. The THz energy was obtained by integrating over the square of the whole THz time-domain waveform, as shown in Fig. 2(c).
When the energy of the 800 nm beam was relatively low, the THz energy exponentially increased with the 800 nm laser energy, as shown in Fig. 5(a) and Fig. 5(b) obtained using the results in Fig. 5(a). The THz output then slowly increased. After reaching the maximum enhancement point, the THz energy saturated and gradually decreased with the increase in the 800 nm wave energy. When the energy of the near-infrared two-color fields was 60 $\mathrm{\mu}$J or 80 µJ, two sets of data were measured. These were consistent with the trend of the curve in Fig. 5(a), except for a more gradual increase in the first half. The THz enhancement below the inflection point can be justified. One important factor was the considerably larger step-like jumps of electron ionization by the higher 800 nm pulse energy and the electron acceleration under the three-color fields. As shown in Fig. 6(a), at higher energies of the 800 nm beam, the ionization rate and electron drift velocity increased. In addition, the THz signal with a spectrum cut-off < 3 THz (obtained in the experiment) scaled up, as shown in Fig. 6(b). Notably, the three-color fields in the simulation had the same pulse width and the electric fields exactly superimposed. Thus, in the experiment, the enhancement would be smaller. In addition to the THz enhancement by the larger 800 nm laser power, the increase in overlapped area of the 800 nm pulse plasma with the near-infrared two-color field filament by the increase in 800 nm laser plasma volume was also an influencing factor. The increasing volume of the three-color field interaction led to the continuous THz enhancement by the electric fields. When the 800 nm pulse was increased to a specific extent, the plasma induced by the 800 nm pulse became larger (volume), which led to a larger phase difference between the near-infrared fundamental wave and the SH when they passed through the plasma. It severely affected the generation of THz radiation and hence reduced the enhancement efficiency. However, it was still stronger than the near-infrared two-color-field THz radiation as a whole.
Fig. 5. (a) dependence of the THz energy increase on the 800 nm pulse energy at the fixed near-infrared two-color field energy of 40 µJ (solid line is a visual guide). (b) exponential curve fitting of the first six data points in (a).
Fig. 6. Simulation results. (a) normalized electron density, electron velocity, and ionization rate under 40-uJ near-infrared two-color fields when the additional 800 nm pulse energy was 200 or 300 µJ. (b) Red curve is the normalized THz temporal waveform with a 300-µJ 800 nm pulse; blue curve shows the values with a 200-uJ 800 nm pulse.
After the analysis of the variation in THz enhancement with the 800 nm pulse energy, the THz yield changes with the near-infrared two-color field energy were analyzed. With the energy of the 800 nm laser fixed at 100 µJ, the energy of the near-infrared two-color fields was changed, the time-domain waveforms scanned, and then the variation curve of the THz energy was recorded.
Figure 7(a) shows the THz energy dependences on the near-infrared two-color field pulse energy with (red curve) and without (blue curve) the 800 nm beam. Figure 7(b) shows the amplification ratios of the 800 nm-pulse scheme to the non-800 nm-pulse scheme for the four data points in Fig. 7(a). The y-coordinate is the energy amplification. With the increase in energy of the near-infrared two-color fields, the THz enhancement effect of the addition of the 800 nm pulse gradually weakened. After the energy of the near-infrared two-color fields exceeded a certain value, the additional laser could not enhance the THz signal. In addition to the effect of the energy ratio of the 800 nm laser to the near-infrared two-color field, this experimental result can be explained by the coincidence region of the two plasmas. In the experiment, the diameter of the dot plasma of the 800 nm laser was larger than that of the cross section of the filament from the two-color field. When the energy of the near-infrared two-color field decreased, the filament became thinner and shorter. The superposed volume of the two plasmas in proportion to the near-infrared two-color field filament gradually increased. This led to a constant increase in the THz enhancement factor. Based on this characteristic of the method, to expand the ranges of use and practicality, the power density can be reduced by increasing the focusing spot diameter, so that the power of the near-infrared two-color fields can enter the increasing range and achieve the THz enhancement effect.
Fig. 7. (a) THz energy dependences on the near-infrared two-color field energy in the presence and absence of the 800 nm beam at a fixed energy of the 800 nm laser of 100 µJ (solid lines are the visual guides). (b) amplification ratios of the 800 nm pulse scheme to the non-800 nm-pulse scheme for the four data points in (a).
3.4 Terahertz spectrum distribution changing and central frequency shifting
Further, with the 800 nm beam energy fixed at 100 $\mathrm{\mu}$J and the near-infrared two-color field laser energy fixed at 80 $\mathrm{\mu}$J, the THz time-domain waveforms were scanned in the presence or absence of the 800 nm pulse, as shown in Fig. 8(a). They were then Fourier-transformed to obtain the spectrum diagrams, as shown in Fig. 8(b). The normalized spectrum diagram suggests that the low-frequency THz component decreased while the high-frequency component increased upon the addition of the 800 nm laser. Moreover, with the increase in the incident energy of the 800 nm laser, the high-frequency component further increased, even though the THz energy already passed the enhancement peak point. Therefore, the additional 800 nm laser beam could contribute to the high-frequency THz component proportion, in addition to increasing the THz intensity. This is of significance for the generation of THz waves with specified frequency component requirements. For example, in THz detection, a THz wave with a specific central frequency or specific spectral distribution is required for a certain substance. Thus, this system can be used to generate the required THz wave and realize a rapid spectrum adjustment through a pump laser frequency switch, so that various substances can be flexibly tested. The spectrum cut-off beyond 3 THz is attributed to the cut-off frequency of the detection crystal ZnTe. We believe that our scheme can additionally provide a good frequency modulation effect in a higher-frequency range, which will be investigated in following studies.
Fig. 8. (a) THz time-domain waveforms in the presence and absence of the 100-µJ 800 nm pulse when the near-infrared two-color field laser energy was 80 µJ. (b) normalized spectrum diagrams of the waveforms in (a) obtained by Fourier transform.
4. Conclusion
The experiments revealed that the THz waves generated using the near-infrared two-color-field-excited air plasma could be considerably enhanced by the additional 800 nm laser up to 22 times. The enhancement was optimized when the polarization of the 800 nm laser was approximately parallel to the SH laser (775 nm). The polarization curve of the 800 nm pulse showed that the THz increase could be obtained only when all three-color fields existed and when the polarization directions of the SH and the 800 nm pulse were identical. At the same 800 nm laser energy, the lower energy of the near-infrared two-color field yielded a higher THz enhancement factor. In addition, when the power of the near-infrared two-color fields was fixed, with the increase in power of the 800 nm pulse, the THz output initially rapidly increased, and then gradually decreased after reaching the peak. Therefore, to obtain the maximum THz enhancement, the energy of the additional 800 nm laser should be adjusted flexibly according to the energy of the near-infrared two-color field to ensure peak amplification. In addition, the experiment showed that the additional laser beam could increase the high-frequency components of the THz radiation. Thus, a suitable manipulation can provide THz waves with specified frequency distributions for specific requirements.
Our experimental results can provide better understanding of the generation mechanism and improved method for THz generation by a three-color-field-excited air plasma. A good approach to control the THz spectrum distribution was obtained to provide strong THz waves with required spectral characteristics. Our experimental system is effective for diverse THz emission experiments and applications as the frequency of the near-infrared laser can be switched as required. We demonstrated similar enhancement ability at other laser frequencies. It is a simple tabletop-scale THz emission system with tunable THz frequency-domain signals. The pumped laser frequency can be flexibly adjusted, suitable for applications requiring multiple diverse THz spectrum signals and intensity enhancement. The system has numerous adjustable factors to change the THz characteristics to provide THz sources for various purposes. Changes to our system to control the individual polarization precisely, the phase delay, and power of the three femtosecond laser beams could increase the THz generation efficiency, change the THz spectral characteristics, and have crucial impacts on the generation, detection, and application of THz waves. The limitations of the energy increase range and enhancement intensity of the third beam on the near-infrared two-color fields may be attributed to the energy waste of the incident pump lasers caused by the failure of the two plasmas to completely coincide, which could be improved in following studies.
Funding
Natural Science Foundation of Beijing Municipality (JQ18015); National Natural Science Foundation of China (61935001, 61905271); Guangdong Basic and Applied Basic Research Foundation (2020A1515011083).
Disclosures
The authors declare no conflicts of interest.
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