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Abstract
A widely tunable regenerative terahertz parametric amplifier is proposed based on degenerate four-wave mixing in an asynchronously pumped highly nonlinear medium. To enhance the Kerr nonlinearity, a hybrid structure of cyclic olefin co/polymer (COC/P) TOPAS integrated by a graphene oxide film is utilized as the gain medium and embedded into a cavity. A low-power terahertz seed wave is injected inside the cavity and sequentially pumped by four asynchronous coupled beams of identical powers. Our results reveal that the output power, the tuning frequency range and the power conversion efficiency of terahertz waves could be considerably improved in the proposed design. Terahertz waves with maximum peak power of 641 W, the accumulated conversion efficiency of 3.8% and amplification gain of 320.5 are obtained at a frequency of 9.61 THz, which could be tuned over a range of 1.17 − 19.736 THz.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Efficient and powerful terahertz sources are in high demand to realize the potential applications of terahertz waves that are expanding in many areas including noninvasive sensing, medical and pharmaceutical science, and security inspection [1–14]. Meanwhile, broadband and tunable radiation generation at high-frequency range of terahertz waves ($>$3THz) are of great importance for spectroscopy studies in some specific areas such as intermolecular inspection and semiconductor industry [15,16]. Among various laser-based terahertz sources, and particularly those established on nonlinear processes, the terahertz parametric oscillation (TPO) has been recognized as a versatile technique [17–19], which is suitable for producing tunable, broadband, and high power terahertz wave radiation [20–24]. Virtual energy levels of nonlinear gain media along with the phase matching and velocity matching conditions provide the TPO process with great spectral flexibility that is controlled not only by the frequency of interacting waves but also by the intensity, pulse duration, and spot size of the input beams [25]. Therefore, various TPO’s schemes have been proposed to improve the features of the generated terahertz waves [26–28] including high-energy and broadly tunable terahertz source based on difference frequency generation in DAST crystal [29], surface-emitting enhanced of injection-seeded terahertz wave parametric generator [30], and engineered quasi-phase-matching TPO in a PPLN crystal without cavity [20]. Although third-order nonlinear effects provide relatively more accessible phase-matching conditions without inversion symmetry considerations, less attention has been paid to TPO based on third-order nonlinear effects. So far, third-order nonlinear TPO has been demonstrated in conventional optical fibers by neglecting the pump depletion [31], silicon photonic crystal fiber with conversion efficiency restricted due to the high absorption of silicon [32], and recently within silicon nitride with various features compatible for terahertz generation [33]. Comparing the various TPO schemes proposed so far, it is evident that the power of the generated terahertz waves is typically low. Thus, one could expect more efficient and tunable TPO designs based on degenerate four-wave mixing (FWM) in nonlinear media with high third-order nonlinearity.
The attainable output power in TPO is limited mainly due to the maximum quantum efficiency, restricted interaction length of the gain medium, and upper limit of the input pump power. The quantum efficiency is determined by the frequency ratio of the terahertz wave to the input pump beam and is unavoidably small. Moreover, the longitudinal separation of terahertz and pump waves due to their velocity mismatch along the gain medium suppresses the output power enhancement in longer gain media. Besides, since the nonlinear contribution of the phase-matching conditions strongly depends on the power of the pump beam, the pump power has to be kept close to its optimum value and, consequently, it would impose upper limitations on the achievable terahertz power and even the bandwidth and efficiency. It should be also noted that during the TPO process, the power of the pump beam would gradually get away from its optimal value i.e., phase matching condition, not only as a result of pump depletion along the gain medium but also due to the spatial spreading of its transverse intensity distribution. Therefore, bypassing the restrictions caused by power-dependent phase-matching conditions should be included in the solutions toward TPO designs with higher efficiency and power, utilizing higher pump powers.
Multiple pumping as a technique for improving the gain and the bandwidth of the amplification process has been well-developed in optical parametric amplification schemes [34–36]. Such an idea could be extended to TPO setups to improve the gain of terahertz generation, provided that the pump beams are separated both temporally and spatially to ensure that phase-matching conditions are fulfilled. This is the idea that is elaborated in the present work. We propose a regenerative terahertz parametric amplifier (TPA) design based on the nonlinear FWM process in a hybrid gain medium pumped by asynchronously coupled pump beams with powers adjusted at optimum value.
The gain medium is a hybrid structure composed of a thin layer of graphene oxide (GO) integrated on cyclic olefin co/polymer (COC/P) TOPAS which is embedded in a designed Fabry–Pérot cavity to improve the conversion efficiency. TOPAS is a well-known third-order nonlinear material commonly used for the generation, propagation, and detection of terahertz waves, 3D printed lenses, and transmission gratings [37–40]. The negligible power absorption, as well as the low dispersion of TOPAS, makes it a suitable choice as a third-order nonlinear gain medium [39,41,42]. However, since the higher-order dispersion of TOPAS at our desired wavelengths is almost positive, it accumulates a considerable linear phase mismatch, which could be compensated only by a comparable value of nonlinear phase mismatch. This could not be obtained in TOPAS at pump powers around the estimated optimal value. Therefore, we provide TOPAS with a thin layer of another nonlinear material through a hybrid structure in a manner that the linear phase mismatch is suppressed and total phase-matching conditions are satisfied. Among various materials with high nonlinear coefficient, GO as a 2D dielectric film with a bandgap of 2.1- 2.4 eV and a superior Kerr nonlinearity [43–52], and without two-photon absorption in the terahertz band [53–58] would be a good candidate for such a purpose. It is worthy to mention that despite the high nonlinearity, GO could not be considered as a suitable main nonlinear material in the parametric process, because of its high absorption coefficient in a bulk multilayer structure. Therefore, we use GO film as an auxiliary layer to increase the effective Kerr coefficient and improve the phase-matching conditions.
The power and path of the pump beam branches, the geometry of the interaction and the cavity, the size of TOPAS and the thickness of GO film, and finally the phase matching and velocity matching conditions are simultaneously optimized in order to provide the asynchronous coherent amplification of the terahertz wave at each round trip inside the cavity. Our simulation results reveal that the design proposed for a regenerative TPA with four asynchronous pumping along with the TOPAS-GO hybrid cavity can significantly improve the power, frequency tunability, and the power conversion efficiency of the output terahertz waves. It is shown that terahertz waves with maximum peak power of 641 W, the accumulated conversion efficiency of $3.8 \%$ and amplification gain of 320.5 could be obtained at a frequency of 9.61 THz, which could be tuned over a range of $1.17-19.736$ THz.
2. Theory and design
The layout of the proposed regenerative TPA setup is schematically illustrated in Fig. 1. The layout has been designed to provide an asynchronous four pumping sequence at identical powers. The pump beam is divided into four branches of equal powers by utilizing three beam splitters of BS1, BS2, and BS3 with reflectance/transmittance ratios of 50/50, $\mathrm {\sim }$38/62, and $\mathrm {\sim }$38/62, respectively. The pump beam branches are sequentially coupled into the Fabry–Pérot cavity to support the amplification of a low-power terahertz seed wave through four sequential single passes i.e., two round trips. The front and end surfaces of the gain medium are provided with partial (50$\%$) and perfect (100$\%$) reflection coating at terahertz frequency, respectively. Both surfaces are transparent for the pump beam with an anti-reflection coating at pump frequency. ITO material as a good reflector for terahertz radiation and transparent at pump wavelength [59] could be utilized as a coating on the end surface. Therefore, the pump beams could enter the cavity from both sides and each pump branch drives only a single pass amplification through the gain medium. The power of the pump beams is equally set at an optimal value satisfying the nonlinear phase-matching conditions. Four separate pump beams are steered through different optical paths of different lengths that are controlled by using three delay lines. The delay time between each sequential pump beam is adjusted according to the optical path of the gain medium at THz frequency so that four pump beams could support four-pass amplification of the terahertz wave. The terahertz wave is initially inserted from the front surface, makes round trips inside the cavity and is accompanied by a new pump pulse in each passage through the gain medium. The terahertz wave is amplified in each round trip inside the cavity based on FWM process and exits from the partially reflective surface (front) of the gain medium. We employ cyclic olefin co/polymer (COC/P) TOPAS as the gain medium, which provides a Fabry–Pérot cavity with the described end coatings. A thin auxiliary layer of highly nonlinear GO film is embedded on TOPAS to improve the phase-matching conditions.
Fig. 1. Schematic of the proposed regenerative TPA setup, based on four-wave mixing within TOPAS with an auxiliary layer of GO film embedded in Fabry–Pérot cavity.
The pump beam with optimal power at the frequency ${\omega }_p$ is introduced into the cavity along with a low energy terahertz seed wave at THz frequency ${\omega }_T$. Terahertz wave is amplified through the FWM process and a signal pulse is simultaneously generated at the frequency ${\omega }_s$. The phase-matching conditions in this nonlinear process can be written as
The amplification gain in terms of the total non-linear coefficient, $\ \gamma ={\gamma }_{sp}+{\gamma }_{tp}-{\gamma }_p$, can be given by
The variation of group velocity dispersion versus pump wavelength has been compared with higher-order dispersion of $\beta _{4p}$ and $\beta _{6p}$ in Fig. 2. It is clear from this figure that ${\Delta k}_L$ would be positive over the desired wavelength range, which results in a nonzero contribution according to Eq. (2) and considering that the frequency detuning ${\Omega }_{sp}$ is greater than 0. Therefore, to establish the phase-matching condition, Eq. (1), a negative nonlinear mismatch contribution with comparable value would be required. This is obtained by embedding a thin auxiliary layer of highly nonlinear GO film on TOPAS. Our simulation reveals that the presence of GO film would not pronouncedly change the linear effective refractive index of the hybrid structure and, consequently, cannot pronouncedly disturb the linear phase-matching conditions over the studied wavelength range. We establish the phase-matching conditions for the case that an ultrashort intense femtosecond laser pulse with the wavelength of 1560 nm is used as pump pulse, aiming to amplify seed terahertz waves with the wavelength of 31.2 $\mu$m. Therefore, the frequency detuning would be ${\Omega }_{sp}=182.69\ THz$ and the linear part of phase matching is obtained as ${\Delta k}_L=0.010$ ${1}/{\mu m}$.
Fig. 2. Second (GVD), fourth and sixth orders of dispersion in TOPAS as a function of pump wavelength.
Moreover, we consider the Kerr coefficient of TOPAS as $2 \times 10{}^{-}{}^{20}$ m${}^{2}$/W in the optical frequency range [60,61] and $1\times 10{}^{-20}$ m${}^{2}$/W in the terahertz range, based on the reasoning provided in [27]. The Kerr coefficients of GO are also considered as $4.5\times 10{}^{-15}$ m${}^{2}$/W and $20\times 10{}^{-12}$ m${}^{2}$/W in optical frequency [62] and terahertz range [63], respectively. Thus, by assuming that the pump and terahertz seed waves are tightly focused inside the cavity with spot sizes of $\sim \lambda _p$ and ${\sim 5\lambda }_{THz}$, respectively, and using a GO film with the thickness of 2$\mathrm {\ }\mathrm {\mu }\mathrm {m}$, the total non-linear coefficient, $\ \gamma ={\gamma }_{sp}+{\gamma }_{tp}-{\gamma }_p$, would be obtained as $-1.2054$ 1/Wm. The absorption of pump beam by the GO film is also negligible and it has been ignored in our simulation [47]. In order to adjust the nonlinear contribution to phase mismatch and, consequently, suppress the linear phase mismatch, the peak power of the pump pulse should be tuned as described in Eq. (1). Our calculations show that the total phase mismatch would be negligible ($\mathrm {\Delta }k\mathrm {=654}{1}/{m}$), using a pump beam with an optimized peak power of 4200 W. This is 15 times smaller than the phase mismatch obtained in the case without utilizing the GO film layer. The obtained phase mismatch could be used to determine the coherence length as $L_c={2\pi }/{\Delta k}=9.595\ \mathrm {mm,}$ required for minimizing the velocity mismatch of the pump and terahertz waves.
To provide coherent amplification conditions at each pass inside the cavity, we adjust the total interaction length to be comparable with the coherence length and, consequently, the length of the gain medium to be $\sim 2.4\ mm\approx \frac {1}{4}L_c$. This length is obtained by assuming that pump power, and consequently the mismatch, is constant during the amplification. However, the peak power of the pump beam would decrease during the amplification not only due to the energy conversion process but also due to the spatial broadening during the propagation inside the cavity, as shown in Fig. 3. This figure represents how the spatial distribution of the pump beam varies inside the cavity and its power deviates from its optimal value. Thus, one may conclude that neither employing longer gain media nor increasing the pump power could improve the amplification gain. It can be also seen in Fig. 3 that the intensity at GO film position (x,y= $\pm 25 \mu m$ ) is in the order of that at the axis (x,y=0) and could provide considerable nonlinear contribution in phase matching conditions. However, asynchronous multi-pumping could be considered as an alternative scheme in which the pump power deviation from its optimal value is relatively lower. Indeed, asynchronous multi-pumping at powers close to the optimal value results in gain and conversion efficiency higher than that in the case of single pumping at powers much higher than the optimal value.
Fig. 3. Spatial distribution of the pump intensity at three different cross sections of the gain medium: (a) at the beginning (z=0), (b) at z=50$\mu m$ and (c) end of the cavity with a length of $2.4 \ mm$.
On the other hand, the time delay between sequential pump beams in such an asynchronous multi-pumping would be a key parameter which is determined by the length of the gain medium, the optical path differences, and the refractive indices at THz frequencies. Although shorter gain medium, at least equivalent to the pump pulse duration, could be also considered, the delay times between the sequential pump branches in such a case would be too small to be practically feasible. It should be noted that for a gain length in the order of a few millimeters, a time delay of the order of a few picoseconds would be required. Therefore, to provide each round trip with a refresh pump pulse, a repetition rate as high as $\mathrm {\sim }$ 86 GHz would be required. However, such required conditions could be provided by using the delay lines as presented in Fig.1.
The spatial distribution of the pump beam presented in Fig. 3 could also determine the minimum transverse dimensions of the cavity. Here we utilize a gain medium with an effective cross section of $50\times 50 {\mathrm {\mu }\mathrm {m}}^{\mathrm {2}}$ integrated with an additional layer of GO film with a thickness of 2 ${\mathrm {\mu }\mathrm {m}}$. These dimensions have been chosen to be larger than the wavelength of the seed terahertz wave so that both beams could reach the GO layer and provide an acceptable nonlinear refractive index contribution. Figure 4 shows the nonlinear part of the refractive index multiplied by the pump intensity at the transverse edge of the gain medium at a cross section with 10 ${\mathrm {\mu }\mathrm {m}}$ distance from the cavity edge. As it can be seen, the nonlinearity is dramatically larger at GO film position, which can play an important role in amplifying the terahertz wave.
Fig. 4. Variation of the nonlinear refractive index multiplied by the pump intensity at the upper edge of TOPAS integrated by the GO layer with 2 $\mu \mathrm {m}$ thickness.
To obtain terahertz output at any desired frequency, the peak power of the pump beam should be adjusted according to the phase-matching condition. Figure 5(a) shows the variation of the optimal pump power versus the desired terahertz central frequency. It can be seen that higher pump powers would be required for terahertz wave generation at lower frequencies. By using Eqs. (1)–(5), we compare the parametric gain variations versus the pump beam wavelength for the cases with and without the auxiliary GO layer in Fig. 5(b). It is clear from this figure that the presence of the GO layer considerably enhances the parametric gain over a pump wavelength range of 1.52-1.595 $\mu$m (colored region). This range of pump wavelengths could generate and amplify terahertz waves with frequency in the range of $1.17- 19.736$ THz, according to the phase-matching conditions. Among which, we adjust the wavelength at 1.56 $\mu$m, considering the commercially available ultrashort laser systems. Besides, the modification of the nonlinear properties of the structure in the presence of GO film strongly depends on the power of the pump beam as well as the film thickness. Thus, we further investigate the variation of the parametric gain versus the peak power of pump pulse and GO thickness, as shown in Fig. 6. This figure shows that the parametric gain (G) is maximized at certain thicknesses of GO film (Fig. 6(a)) among them, we have chosen the thickness of 2$\mathrm {\ }\mathrm {\mu }\mathrm {m}$ that is thick enough comparing with the wavelength of the pump beam, and thin enough to ensure that the wave is completely consumed and evinced inside the layer. Consequently, the linear and non-linear parts of the phase mismatch are balanced for optimal terahertz generation at the tuning frequency. Figure 6(b) reveals that although the parametric gain (G) slowly increases at higher pump powers, it is also maximized at certain values of pump powers that satisfy the phase-matching conditions. Owing to this small difference, one may prefer to adjust the pump power at the lower possible optimum values.
Fig. 5. (a) Optimal required pump power versus the desired terahertz frequency. (b) Parametric terahertz amplification gain of FWM process versus the pump wavelength within TOPAS with and without GO auxiliary layer.
In order to simulate the regenerative amplification of terahertz seed in GO-coated Olefin embedded in a Fabry–Pérot hybrid cavity, we use the FWM theory in third-order nonlinear media [33,64,65] as follows:
3. Results and discussion
By numerically solving Eqs. (6)–(8), and taking into account the initial conditions according to Eqs. (1)–(5), the temporal evolution of the peak power of the interacting waves through the regenerative process is obtained as presented in Fig. 7. In these simulations, we use pump pulses with a wavelength of 1.56 $\mu$m to amplify the terahertz wave seed at the wavelength of 31.2 $\mu$m. The pump wavelength has been chosen among the existing commercial ultrashort laser systems. For the first pass, a pump pulse with a peak power of $4200 W$ amplifies the terahertz wave with a peak power of $2 W$. The pulse duration has been chosen short enough to provide the intensity required for the nonlinear process. It can be seen in Fig. 7(a) that by consuming the pump energy, the terahertz wave is amplified up to a peak power of $\mathrm {\sim }$8.46 W, and a very weak signal wave with wavelength 800 nm is also generated. In fact, pump to signal conversion is diminished by inserting a terahertz seed into the cavity, which stimulates and dominates photon conversion at the seed frequency. Moreover, we adjust all the parameters affecting $\gamma$ coefficients in a way that provides much higher conversion rate for terahertz wave compared with that for the signal wave. Figure 7(a) also illustrate that the amplification process takes place in a time interval below $\mathrm {\sim }$3 ps that is much shorter than a single pass cavity optical path $({n}_{t}L/c\approx$ 12 ps). Therefore, by moving along the gain medium, the pump beam becomes too weak to drive additional nonlinear processes and its power deviates from the optimal value of phase-matching conditions.
Fig. 7. (a) Temporal evolution of the peak power of the interacting waves through the regenerative process. (b) Conversion efficiency and peak power of amplified terahertz waves obtained at different input pump powers.
As discussed in relation to Fig. 6, increasing the pump power could not necessarily improve the parametric amplification gain. To investigate this result for terahertz amplification inside the proposed cavity, we compare the single-pass amplification process with different pump powers in Fig. 7(b). This figure compares the output terahertz power as well as the single-pass conversion efficiency obtained by various pump powers. The peak power of the terahertz seed is kept the same at 2 W for all cases. The conversion efficiency is defined as the ratio of the terahertz power amplified via a single pass, to the input pump power. It is clear from Fig. 7(b) that single-pass conversion efficiency for the case with an input pump power of 4200 W is even higher ($\sim$ four times) than that with an input pump power of 16800 W. It can be also seen that the terahertz conversion efficiency in single pass amplification gradually decreases at higher pump powers, while the peak power of the output terahertz wave would not considerably change when the power of the pump beam increases. This figure also reveals that single pass amplification with a pump power of 16800 W would result in a terahertz wave with an output power of 8.4 W, comparable with that obtained at much less pump powers. We also investigate the single-pass terahertz amplification gain, $\frac {{P}_{t}(L)}{{P}_{t}(0)}$, versus pump power. As shown in Fig. 8(a), the single-pass amplification gain of the terahertz waves is consistent with that presented in Fig. 6, which implies the sensitivity of phase-matching conditions to the input power. By taking into consideration the results of Figs. 7(b) and 8(a), it is clear that increasing the pump power could not significantly improve the amplification gain.
Fig. 8. (a) Single pass terahertz amplification gain at various pump powers. (b)-(d) Temporal evolution of the peak power of the interacting waves in second, third and fourth passes through the gain medium.
However, the situation would change when the asynchronous pumping layout presented in Fig. 1 is employed. In this case, a pump power of 16800 W is divided into four branches with equal powers of 4200 W and asynchronously applied to the gain medium to provide a four sequential amplification process. Each amplification pass is supplied by a fresh pump beam and the terahertz wave circulates inside the cavity synchronously with the pump beam. Figures 8(b)–8(d) presents the temporal evolution of the peak power of the interacting waves through the regenerative process in second, third, and fourth passes, respectively. It can be seen in Fig. 8(b) that the terahertz wave is further amplified by applying the same pump power in the second pass, comparing to that in the first pass (Fig. 7(a)) and reaches a peak power of 35.79 W. Similarly, the third and fourth passages of the terahertz wave inside the cavity could result in additional terahertz amplification up to peak powers of 151.4 W and 640 W, as presented in Figs. 8(c) and 8(d), respectively. Comparing the results with that presented in Fig. 7(b), it is clear that two orders of magnitude improvement in terahertz output power would be expected by employing the same pump power (16800 W) in the asynchronous pumping layout. This comparison emphasizes how the multiple pumping enhances the amplification process at the same input pump power.
Our investigation reveals that the terahertz power would not be further amplified by increasing the number of multiple asynchronous pump beams, because the nonlinear effects caused by high power terahertz wave and the divergence of the terahertz wave in such multi-pass amplification become considerable. Moreover, multiple asynchronous pumping at higher pump powers also would not necessarily improve the amplification features. To show this behavior, we compare the terahertz output power and the conversion efficiency in asynchronous pumping schemes with different pump powers, as presented in Fig. 9. The power conversion efficiency from pump input to terahertz wave is defined as $\eta =\frac {{P}^{out}_{THz}}{{P}^{in}_{Pump}}$ [66], in which ${P}^{in}_{Pump}$ denotes the total pump peak power that is applied to the four branches, and ${P}^{out}_{THz}$ is the peak power of the Terahertz wave obtained after four passes. It can be seen that applying higher pump powers in the proposed asynchronous pumping layout could not necessarily improve the amplification features. Figure 9 also indicates that amplified terahertz wave with a peak power of 641 W and conversion efficiency of 3.8% could be obtained at a frequency of 9.61 THz by adjusting the pump peak power at 4200 W. It is noteworthy to confirm that the single-pass conversion efficiency in our work is obtained as 0.05% in the 9.61 THz and pump power of 4200 W, which is smaller than the maximum possible value of ${\mathrm {\eta }}_{\mathrm {max}}\mathrm {=1.16\%}$, that is obtained as ${\mathrm {\eta }}_{\mathrm {max}}\mathrm {=}{\mathrm {2}{\mathrm {\omega }}_{\mathrm {t}}{\mathrm {\tau }}_{\mathrm {ep}}{\mathrm {\tau }}_{\mathrm {et}}}/{{\mathrm {\omega }}_{\mathrm {p}}{\mathrm {\tau }}_{\mathrm {lp}}{\mathrm {\tau }}_{\mathrm {lt}}}$. Moreover, the terahertz amplification gain $\frac {{P}_{t}(L)}{{P}_{t}(0)}$ obtained in the four-pumped layout (with the power of 4$\mathrm {\times }$4200 W) is $\mathrm {320.5}$, which is much higher than that in a single-pumped setup with a total power of 16800 W.
Fig. 9. Power conversion efficiency and final peak power of Terahertz wave output versus peak power of the pump.
In addition, we compare the peak power and the spectrum of terahertz waves obtained at various pump wavelengths. As illustrated in Fig. 10, the frequency of the amplified terahertz wave could be tuned over a relatively wide range of $1.17- 19.736$ THz by adjusting the central pump wavelength from $1.52- 1.595$ according to the phase-matching conditions. It can be seen that the terahertz wave peak power is maximized by using the pump wavelength of 1.56 $\mu$m corresponding to the optimal phase-matching condition.
Fig. 10. a) Output power and b) the spectrum of amplified Terahertz pulses obtained at different pump wavelengths.
Furthuremore, the hybrid structure of the proposed gain medium could be considered to work as an asymmetric planar step-index dielectric waveguide for terahertz waves. The waveguide structure can affect the terahertz waves in two different approaches: (1) affecting the output power efficiency and (2) changing the phase matching condition as well as the parametric amplification gain. To take into account the efficiency effects, it should be noted that each mode in such dielectric waveguide has its own cutoff wavelength, which represents the frequency at which the waveguide could switch between single mode and multimode operation. Therefore, one could expect the different transverse distributions at both lower and higher parts of the output spectrum to contribute in overall integrated power. Regarding the waveguide effects on the parametric amplification gain, we confirmed that the presence of GO film could not considerably change the effective refractive index and, consequently, the phase matching conditions.
4. Conclusion
We proposed a regenerative terahertz parametric amplification scheme based on degenerate four-wave mixing in GO-TOPAS that is embedded Fabry–Pérot cavity and pumped by multiple sequential coupled beams. The hybrid structure of the gain medium, TOPAS integrated with a thin layer of 2D GO film, could enhance the Kerr nonlinearity and provide the optimal phase-matching conditions. GO-TOPAS has been pumped by four asynchronous beams with identical powers to provide a multipass amplification of the terahertz seed in a spatiotemporally controlled amplification process. The structure of the gain medium, the cavity geometry, and pump beam powers have been designed and optimized by taking into account the linear and nonlinear contributions of the phase matching and velocity matching conditions. The optimal terahertz output power and conversion efficiency could be attained using pump beams with the wavelength of 1.56 $\mu$m and peak power of 4200 W. Our results revealed that the conversion efficiency, as well as the terahertz output power, could be significantly improved by the proposed scheme. Terahertz wave with maximum peak power of 641 W, amplification gain of 320.5, and accumulated conversion efficiency of 3.8% have been obtained at a frequency of 9.61 THz. By using the proposed hybrid structure, we would be able to tune the frequency of the amplified terahertz waves in a range of $1.17- 19.736$ THz by varying the pump wavelength from $1.52$ to $1.595\;\mu$m. By introducing GO-TOPAS as a potential highly nonlinear gain medium and employing a multi-pumping layout, our results present a promising way toward realizing robust, reasonable, and easy-to-use terahertz amplifiers. It should be noted that the obtained results are valid at room temperature conditions without applying external electrical and magnetic fields.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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