Universal traveling-wave antenna model for terahertz radiation from laser-plasma interactions

1-Thanks for the reviewer’s advice. “universal” will be removed or replaced all over the revised manuscript.

2-According to Ref. [17] cited in Table IV, the THz intensity after the water film absorption is given by $I_{THz} = I_0exp[-\alpha d/2cos\theta_t]$, where $\alpha = 100 cm^{-1}$ is the power absorption coefficient [DOI: 10.1109/ICIMW.2009.5325641], d = 120 $\mu$m is the thickness of the water film, and $\theta_t$ is the THz incidence angle on the water-to-air interface, as described in Table IV. On this interface, THz waves can’t be coupled out if its total internal reflection occurs, and the critical angle can be easily calculated as 25 degree ($n_{THz}$ = 2.33 in water). Thus $\theta_t$ varies between -25 and +25 degree, and $I_{THz}$ is between 0.51$I_0$ and 0.54$I_0$.

Due to this little change of $I_{THz}(\theta_t)$, the water absorption is not considered in our work when profiling the THz radiation distribution from the water film (Table IV) for the sake of convenience.

3-The reviewer is correct that $\omega_p$, $\omega_p/\sqrt2$ and $\omega_p/\sqrt3$ are all characteristic frequencies related with the plasma. Normally, they correspond to the plasma frequencies of the plasma line, cylinder and sphere, respectively. In our case, we considered mostly the plasma as a filament, whose length is longer than 10 mm (e.g., in Table I) while its column diameter is much smaller as about 50 $\mu$m. Thus we chose $\omega_p$ in the derivation of the model (Section 3).

On the other hand, if the plasma cylinder and $\omega_p/\sqrt2$ were allowed, the main conclusion of this work (THz radiation profiles induced by the TWA model and THz-plasma resonance) won’t be changed, because $\omega_p/\sqrt2$ is still in THz band, and the THz-plasma interaction remains.

At last, $\omega_p/\sqrt3$ is not our case since neither our laser beam is tightly focused, nor a micro-plasma-sphere [Optica 2(4) 366-369 (2015)] is studied in this work.

1-Thank the reviewer for pointing this issue out. As shown in Fig. S1 of our manuscript, towards low frequencies such as 0.1 THz, the spectral current $j_{ex}$ (green dot and dash line) excited by the external electric field $E_{ex}$ is about two orders of magnitude larger than the original one $j_{w}$ (black line) given by the laser wakefield. For this reason, $j_{w}$ was not included in our calculations at 0.1 THz, and the THz yield is solely proportional to |$j_{ex}$| (also |$E_{ex}$|, see Eq. S9). Thus we stated that the direction of $E_{ex}$ (i.e., ±$E_{ex}$) won’t change the radiated THz intensity.

However, if larger THz frequency (>0.1 THz) is considered, one can also see in Fig. S1 that, $j_{w}$ rapidly increased and even exceeded $j_{ex}$ at around 2 THz. This time, $j_{w}$ is no longer negligible and the total THz yield is decided by Eq. S8 as [$j_{w}$+$j_{ex}$($E_{ex}$)], which is now influenced by the sign of $E_{ex}$. From Eq. S8, we can further predicted that the minimum THz yield is obtained at a negative $E_{ex}$ (=-$j_{w}$/$j_{ex}$), thus in agreement with Fig. 2(a) of Ref. [Phys. Rev. E 102, 063211 (2020)].

2-Thanks for the reviewer’s information. As put in Ref. [Phys. Rev. Lett. 71(17), 2725 (1993)], strong resonant enhancement of the THz radiation was observed if the plasma frequency $(\omega_p/2\pi)$ was close to the inverse pulse length of the pumping laser ($t_0$ = 120~140 fs, thus 1/$t_0$ is in THz band). Although the concept of plasma-THz resonance was not directly raised in this work, the above relationship showed the clue.

Furthermore, the PRL work indicates that (i) the frequency of the THz emission varies with gas density (by changing the ambient gas pressure) and is close to the bulk plasma frequency as shown in its Fig. 3, and (ii) the THz signal was attributed to the nonlinear current in its Eq. (1), whose denominator contains the item of $[1-(\omega_p/\omega)^2]$. Both (i) and (ii) reveal that maximum THz signals could be achieved at $\omega_p=\omega_{THz}$ (i.e., resonance effect).

Hence, we think the PRL work might share several phenomenological conclusions with our Section 3 (e.g., Fig. 2b$_1$), while the plasma filament is studied in quite different ways. For us, the THz resonant radiation is mainly investigated by its longitudinal evolution along the filament (Fig. 3-5), rather than collecting the signal from the whole filament. This is a new view in the community, to the best of our knowledge.

3-The reviewer is right that Section B and C of the Supplemental Material are informative, since they formed the gain coefficient ($n$) and the rotation angle factor ($\phi$) from the microscopic point of view, respectively, which were then used in the macroscopic TWA model (Section 2.2 and 2.3).

Following the reviewer’s suggestion, we are going to emphasize this point in the first part of Section 3 to strength its link with Section 2.