Enhancing THz wave generation in silica nanofibers with Zinc Telluride nonlinear coating

. This study investigates the use of Zinc Telluride (ZnTe) as a second-order nonlinear coating to enhance THz wave generation in silica nanofibers. Numerical simulations show that ZnTe coatings can significantly improve THz wave generation efficiency due to their large second-order nonlinear susceptibility and high transparency in the THz frequency range. Specifically, we observe a 2000-fold increase in THz wave generation efficiency with a 100nm thickness ZnTe coating compared to an uncoated silica nanofiber.


Introduction
Terahertz (THz) wave generation has potential applications in various fields, including medical imaging, non-destructive testing, and wireless communication [1,2].Silica nanofibers are attractive platforms for THz wave generation due to their compact dimensions and large surface-to-volume ratio, which can enhance nonlinear optical effects.However, their low secondorder nonlinear susceptibility limits their performance [3].
To improve the second-order nonlinear susceptibility of silica nanofibers and enhance THz wave generation efficiency, we propose a transparent second-order nonlinear coating for the THz region.Zinc Telluride (ZnTe) is a semiconductor material with a large secondorder nonlinear susceptibility and high transparency in the THz frequency range.In this study, we investigate the effect of the ZnTe coating on surface-emitted THz wave generation efficiency.

Theory and modeling
The proposed nonlinear structure consists of a silica tapered optical fiber with a thin layer of Zinc Telluride (ZnTe) nonlinear molecules.To simplify the study, we assume that these molecules are predominantly aligned radially, and that the second order susceptibility tensor is mainly determined by its radial components.The thickness of the nonlinear layer is on the order of tens of nanometers and is much smaller than the radius of the silica nanofiber, rendering it negligible in electromagnetic field calculations.As a result, the linear propagation of this structure behaves similarly to that of a silica tapered fiber in air. Figure 1 illustrates the proposed second-order nonlinear structure with a ZnTe coating.
In bare silica nanofibers, the THz wave generation efficiency is limited by the small mode area of the fiber and the mismatch between the wave vectors of the pump and generated THz waves.Modal phase matching can overcome this limitation by exploiting the mode dispersion of the nanofiber to achieve phase matching between the pump and THz waves at a specific frequency.Specifically, two pump pulses are launched into the silica nanofiber in two different modes, such that the modal dispersion of the two modes leads to phase matching of the Difference Frequency Generation (DFG) process at a specific frequency in the THz range.In this case of coated silica nanofibers, a second-order nonlinear material is coated onto the surface of the fiber to enhance the nonlinear susceptibility of the material.This can significantly increase the efficiency of THz wave generation by enhancing the local electric field and thus the nonlinear interactions.Modal phase matching in coated silica nanofibers involves selecting the appropriate modes of the fiber and optimizing the thickness and nonlinear properties of the coating to achieve phase matching between the pump and THz waves.
Figure 2 illustrates the energy conservation diagram and modal phase matching conditions for surface-emitted THz-wave generation.Due to the high absorption of silica

Introduction
Terahertz (THz) wave generation has potential applications in various fields, including medical imaging, non-destructive testing, and wireless communication [1,2].Silica nanofibers are attractive platforms for THz wave generation due to their compact dimensions and large surface-to-volume ratio, which can enhance nonlinear optical effects.However, their low secondorder nonlinear susceptibility limits their performance [3].
To improve the second-order nonlinear susceptibility of silica nanofibers and enhance THz wave generation efficiency, we propose a transparent second-order nonlinear coating for the THz region.Zinc Telluride (ZnTe) is a semiconductor material with a large secondorder nonlinear susceptibility and high transparency in the THz frequency range.ZnTe coating on silica nanofibers can be achieved through various deposition techniques, including chemical vapor deposition (CVD), atomic layer deposition (ALD), physical vapor deposition (PVD), or spin coating.In this study, we investigate the effect of the ZnTe coating on THz wave generation efficiency.

Theory and modeling
The proposed nonlinear structure consists of a silica tapered optical fiber with a thin layer of Zinc Telluride (ZnTe) nonlinear molecules.To simplify the study, we assume that these molecules are predominantly aligned radially, and that the second order susceptibility tensor is mainly determined by its radial components.The thickness of the nonlinear layer is on the order of tens of nanometers and is much smaller than the radius of the silica nanofiber, rendering it negligible in electromagnetic field calculations.As a result, the linear propagation of this structure behaves similarly to that of a silica tapered fiber in air. Figure 1 illustrates the proposed second-order nonlinear structure with a ZnTe coating.
In bare silica nanofibers, the THz wave generation efficiency is limited by the small mode area of the fiber and the mismatch between the wave vectors of the pump and generated THz waves.Modal phase matching can overcome this limitation by exploiting the mode dispersion of the nanofiber to achieve phase matching between the pump and THz waves at a specific frequency.Specifically, two pump pulses are launched into the silica nanofiber in two different modes, such that the modal dispersion of the two modes leads to phase matching of the Difference Frequency Generation (DFG) process at a specific frequency in the THz range.In this case of coated silica nanofibers, a second-order nonlinear material is coated onto the surface of the fiber to enhance the nonlinear susceptibility of the material.This can significantly increase the efficiency of THz wave generation by enhancing the local electric field and thus the nonlinear interactions.Modal phase matching in coated silica nanofibers involves selecting the appropriate modes of the fiber and optimizing the thickness and nonlinear properties of the coating to achieve phase matching between the pump and THz waves.As depicted in Fig. 2, in the surface-emitted configuration, the THz-wave is generated perpendicular to the direction of propagation of the optical waves.Equations (1,2) can be simplified as follows: The wavelength of the generated surface-emitted THzwave can be calculated using Eqs.( 3) and (4), where  is the wavelength and  is the refractive index.Modal phase matching is satisfied only by the optical waves (Eq.4), so the refractive index of the generated THz-wave is not needed.

Results and discussions
We consider a silica nanofiber that is excited by two pump pulses  $ and  % .Modal phase matching for surface emitted THz-wave generation in a silica nanofiber is verified for a nanofiber diameter  = 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm, as shown in Figure 3.The phase matching curve and the related THz frequency of the surface-emitted configuration are presented in Figure 4. We used an optical wave  $ of 760 nm and sought to calculate the optimum  % for THz-wave generation using energy conservation and modal phase matching conditions given by Equations (3,4).An optical wave  % near 760 nm can be used, high-power source in this region is easily available.The tuning range of  % between 763-782 nm results in a 1-12 THz range.
Our simulation results show that modal phase matching in silica nanofibers using DFG can achieve high conversion efficiency and tunability in the THz frequency range.We obtained a maximum conversion efficiency of 10 -5 with a  = 100nm thickness ZnTe coating, and could tune the THz frequency by adjusting the optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a 2000-fold increase in THz wave generation efficiency with a 100nm thickness ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.and modal phase matching conditions for surface-emitted THz-wave generation.Due to the high absorption of silica in the THz domain and the low efficiency of THz-wave generation, we do not consider the case of collinear wave generation.The relevant relationships are given below: ( $ − ( % = 0 (2) Where the angular frequency is denoted by !, and the propagation wave vector is denoted by (.The subscripts 1-2 indicate the optical waves (! $ > !% ), and the subscripts THz indicate the THz-wave.Equation (2) provides the modal phase-matching condition for the surface-emitted THz-wave.As depicted in Fig. 2, in the surface-emitted configuration, the THz-wave is generated perpendicular to the direction of propagation of the optical waves.Equations (1,2) can be simplified as follows: The wavelength of the generated surface-emitted THzwave can be calculated using Eqs.(3) and (4), where , is the wavelength and . is the refractive index.Modal phase matching is satisfied only by the optical waves (Eq.4), so the refractive index of the generated THz-wave is not needed.

Results and discussions
We consider a silica nanofiber that is excited by two pump pulses , $ and , % .Modal phase matching for surface emitted THz-wave generation in a silica nanofiber is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm, as shown in Figure 3.The phase matching curve and the related THz frequency of the surface-emitted configuration are presented in Figure 4. We used an optical wave , $ of 760 nm and sought to calculate the optimum , % for THz-wave generation using energy conservation and modal phase matching conditions given by Equations (3,4).An optical wave , % near 760 nm can be used, high-power source in this region is easily available.The tuning range of , % between 763-782 nm results in a 1-12 THz range.
Our simulation results show that modal phase matching in silica nanofibers using DFG can achieve high conversion efficiency and tunability in the THz frequency range.We obtained a maximum conversion efficiency of 10 -5 , and could tune the THz frequency by adjusting the optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a 2000-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.
THz-wave generation.Due to the high absorption of silica in the THz domain and the low efficiency of THz-wave generation, we do not consider the case of collinear wave generation.The relevant relationships are given below: Where the angular frequency is denoted by !, and the propagation wave vector is denoted by (.The subscripts 1-2 indicate the optical waves (! $ > !% ), and the subscripts THz indicate the THz-wave.Equation ( 2) provides the modal phase-matching condition for the surface-emitted THz-wave.As depicted in Fig. 2, in the surface-emitted configuration, the THz-wave is generated perpendicular to the direction of propagation of the optical waves.Equations (1,2) can be simplified as follows: The wavelength of the generated surface-emitted THzwave can be calculated using Eqs.( 3) and (4), where , is the wavelength and . is the refractive index.Modal phase matching is satisfied only by the optical waves (Eq.4), so the refractive index of the generated THz-wave is not needed.

Results and discussions
We consider a silica nanofiber that is excited by two pump pulses , $ and , % .Modal phase matching for surface emitted THz-wave generation in a silica nanofiber is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm, as shown in Figure 3.The phase matching curve and the related THz frequency of the surface-emitted configuration are presented in Figure 4. We used an optical wave , $ of 760 nm and sought to calculate the optimum , % for THz-wave generation using energy conservation and modal phase matching conditions given by Equations (3,4).An optical wave , % near 760 nm can be used, high-power source in this region is easily available.The tuning range of , % between 763-782 nm results in a 1-12 THz range.
Our simulation results show that modal phase matching in silica nanofibers using DFG can achieve high conversion efficiency and tunability in the THz frequency range.We obtained a maximum conversion efficiency of 10 -5 , and could tune the THz frequency by adjusting the optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a two-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.2, in the surface-emitted e is generated perpendicular ation of the optical waves.lified as follows: .
nerated surface-emitted THzg Eqs. ( 3) and ( 4), where , is refractive index.Modal phase the optical waves (Eq.4), so generated THz-wave is not ssions er that is excited by two pump phase matching for surface ion in a silica nanofiber is eter of 728 nm between two elength 773 nm and HE21 at wn in Figure 3.The phase lated THz frequency of the n are presented in Figure 4. , $ of 760 nm and sought to r THz-wave generation using modal phase matching ns (3,4).An optical wave , % h-power source in this region ng range of , % between 763z range.w that modal phase matching g DFG can achieve high nability in the THz frequency

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a two-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.As depicted in Fig. 2, in the surface-emitted configuration, the THz-wave is generated perpendicular to the direction of propagation of the optical waves.Equations (1,2) can be simplified as follows: The wavelength of the generated surface-emitted THzwave can be calculated using Eqs.( 3) and (4), where , is the wavelength and . is the refractive index.Modal phase matching is satisfied only by the optical waves (Eq.4), so the refractive index of the generated THz-wave is not needed.

Results and discussions
We consider a silica nanofiber that is excited by two pump pulses , $ and , % .Modal phase matching for surface emitted THz-wave generation in a silica nanofiber is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm, as shown in Figure 3.The phase matching curve and the related THz frequency of the surface-emitted configuration are presented in Figure 4. We used an optical wave , $ of 760 nm and sought to calculate the optimum , % for THz-wave generation using energy conservation and modal phase matching conditions given by Equations (3,4).An optical wave , % near 760 nm can be used, high-power source in this region is easily available.The tuning range of , % between 763-782 nm results in a 1-12 THz range.
Our simulation results show that modal phase matching in silica nanofibers using DFG can achieve high conversion efficiency and tunability in the THz frequency range.We obtained a maximum conversion efficiency of 10 -5 , and could tune the THz frequency by adjusting the optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a 2000-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.
THz-wave generation.Due to the high absorption of silica in the THz domain and the low efficiency of THz-wave generation, we do not consider the case of collinear wave generation.The relevant relationships are given below: ( $ − ( % = 0 (2) Where the angular frequency is denoted by !, and the propagation wave vector is denoted by (.The subscripts 1-2 indicate the optical waves (! $ > !% ), and the subscripts THz indicate the THz-wave.Equation ( 2) provides the modal phase-matching condition for the surface-emitted THz-wave.As depicted in Fig. 2, in the surface-emitted configuration, the THz-wave is generated perpendicular to the direction of propagation of the optical waves.Equations (1,2) can be simplified as follows: The wavelength of the generated surface-emitted THzwave can be calculated using Eqs.( 3) and (4), where , is the wavelength and . is the refractive index.Modal phase matching is satisfied only by the optical waves (Eq.4), so the refractive index of the generated THz-wave is not needed.

Results and discussions
We consider a silica nanofiber that is excited by two pump pulses , $ and , % .Modal phase matching for surface emitted THz-wave generation in a silica nanofiber is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm, as shown in Figure 3.The phase matching curve and the related THz frequency of the surface-emitted configuration are presented in Figure 4. We used an optical wave , $ of 760 nm and sought to calculate the optimum , % for THz-wave generation using energy conservation and modal phase matching conditions given by Equations (3,4).An optical wave , % near 760 nm can be used, high-power source in this region is easily available.The tuning range of , % between 763-782 nm results in a 1-12 THz range.
Our simulation results show that modal phase matching in silica nanofibers using DFG can achieve high conversion efficiency and tunability in the THz frequency range.We obtained a maximum conversion efficiency of 10 -5 , and could tune the THz frequency by adjusting the optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a two-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.n the surface-emitted generated perpendicular of the optical waves.as follows: (4) ed surface-emitted THzs.( 3) and ( 4), where , is tive index.Modal phase optical waves (Eq.4), so erated THz-wave is not ns t is excited by two pump e matching for surface in a silica nanofiber is of 728 nm between two gth 773 nm and HE21 at in Figure 3.The phase THz frequency of the e presented in Figure 4. f 760 nm and sought to z-wave generation using odal phase matching ,4).An optical wave , % wer source in this region nge of , % between 763ge.at modal phase matching FG can achieve high ity in the THz frequency

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a two-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.
THz-wave generation.Due to the high absorption of silica in the THz domain and the low efficiency of THz-wave generation, we do not consider the case of collinear wave generation.The relevant relationships are given below: Where the angular frequency is denoted by !, and the propagation wave vector is denoted by (.The subscripts 1-2 indicate the optical waves (! $ > !% ), and the subscripts THz indicate the THz-wave.Equation ( 2) provides the modal phase-matching condition for the surface-emitted THz-wave.As depicted in Fig. 2, in the surface-emitted configuration, the THz-wave is generated perpendicular to the direction of propagation of the optical waves.Equations (1,2) can be simplified as follows: The wavelength of the generated surface-emitted THzwave can be calculated using Eqs.( 3) and (4), where , is the wavelength and . is the refractive index.Modal phase matching is satisfied only by the optical waves (Eq.4), so the refractive index of the generated THz-wave is not needed.

Results and discussions
We consider a silica nanofiber that is excited by two pump pulses , $ and , % .Modal phase matching for surface emitted THz-wave generation in a silica nanofiber is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm, as shown in Figure 3.The phase matching curve and the related THz frequency of the surface-emitted configuration are presented in Figure 4. We used an optical wave , $ of 760 nm and sought to calculate the optimum , % for THz-wave generation using energy conservation and modal phase matching conditions given by Equations (3,4).An optical wave , % near 760 nm can be used, high-power source in this region is easily available.The tuning range of , % between 763-782 nm results in a 1-12 THz range.
Our simulation results show that modal phase matching in silica nanofibers using DFG can achieve high conversion efficiency and tunability in the THz frequency range.We obtained a maximum conversion efficiency of 10 -5 , and could tune the THz frequency by adjusting the optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a two-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.
enerated surface-emitted THzng Eqs. ( 3) and (4), where , is refractive index.Modal phase y the optical waves (Eq.4), so generated THz-wave is not ssions er that is excited by two pump phase matching for surface tion in a silica nanofiber is meter of 728 nm between two velength 773 nm and HE21 at own in Figure 3.The phase elated THz frequency of the ion are presented in Figure 4. , $ of 760 nm and sought to or THz-wave generation using d modal phase matching ons (3,4).An optical wave , % gh-power source in this region ing range of , % between 763z range.ow that modal phase matching g DFG can achieve high unability in the THz frequency of 10 -5 , and could tune the THz frequency optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a two-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.As depicted in Fig. 2, in the surface-emitted configuration, the THz-wave is generated perpendicular to the direction of propagation of the optical waves.Equations (1,2) can be simplified as follows: The wavelength of the generated surface-emitted THzwave can be calculated using Eqs.( 3) and (4), where , is the wavelength and . is the refractive index.Modal phase matching is satisfied only by the optical waves (Eq.4), so the refractive index of the generated THz-wave is not needed.

Results and discussions
We consider a silica nanofiber that is excited by two pump pulses , $ and , % .Modal phase matching for surface emitted THz-wave generation in a silica nanofiber is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm, as shown in Figure 3.The phase matching curve and the related THz frequency of the surface-emitted configuration are presented in Figure 4. We used an optical wave , $ of 760 nm and sought to calculate the optimum , % for THz-wave generation using energy conservation and modal phase matching conditions given by Equations (3,4).An optical wave , % near 760 nm can be used, high-power source in this region is easily available.The tuning range of , % between 763-782 nm results in a 1-12 THz range.
Our simulation results show that modal phase matching in silica nanofibers using DFG can achieve high conversion efficiency and tunability in the THz frequency range.We obtained a maximum conversion efficiency of 10 -5 , and could tune the THz frequency by adjusting the optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a 2000-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.
THz-wave generation.Due to the high absorption of silica in the THz domain and the low efficiency of THz-wave generation, we do not consider the case of collinear wave generation.The relevant relationships are given below: ( $ − ( % = 0 (2) Where the angular frequency is denoted by !, and the propagation wave vector is denoted by (.The subscripts 1-2 indicate the optical waves (! $ > !% ), and the subscripts THz indicate the THz-wave.Equation ( 2) provides the modal phase-matching condition for the surface-emitted THz-wave.As depicted in Fig. 2, in the surface-emitted configuration, the THz-wave is generated perpendicular to the direction of propagation of the optical waves.Equations (1,2) can be simplified as follows: The wavelength of the generated surface-emitted THzwave can be calculated using Eqs.( 3) and (4), where , is the wavelength and . is the refractive index.Modal phase matching is satisfied only by the optical waves (Eq.4), so the refractive index of the generated THz-wave is not needed.

Results and discussions
We consider a silica nanofiber that is excited by two pump pulses , $ and , % .Modal phase matching for surface emitted THz-wave generation in a silica nanofiber is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm, as shown in Figure 3.The phase matching curve and the related THz frequency of the surface-emitted configuration are presented in Figure 4. We used an optical wave , $ of 760 nm and sought to calculate the optimum , % for THz-wave generation using energy conservation and modal phase matching conditions given by Equations (3,4).An optical wave , % near 760 nm can be used, high-power source in this region is easily available.The tuning range of , % between 763-782 nm results in a 1-12 THz range.
Our simulation results show that modal phase matching in silica nanofibers using DFG can achieve high conversion efficiency and tunability in the THz frequency range.We obtained a maximum conversion efficiency of 10 -5 , and could tune the THz frequency by adjusting the optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a two-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.
% (4) ted surface-emitted THzs.( 3) and (4), where , is ctive index.Modal phase optical waves (Eq.4), so erated THz-wave is not ons at is excited by two pump se matching for surface in a silica nanofiber is r of 728 nm between two gth 773 nm and HE21 at in Figure 3.The phase d THz frequency of the re presented in Figure 4. f 760 nm and sought to z-wave generation using odal phase matching 3,4).An optical wave , % ower source in this region ange of , % between 763nge.at modal phase matching FG can achieve high lity in the THz frequency of 10 -5 optical wavelength.

Conclusion
Through our simulations, we have demonstrated that optimizing the nonlinear coatings of silica nanofibers, such as ZnTe, can significantly enhance the efficiency of THz wave generation by modal phase matching through DFG.Specifically, we have observed a two-fold increase in THz wave generation efficiency with a ZnTe coating compared to a bare silica nanofiber.To further improve THz wave generation efficiency in silica nanofibers, future research should investigate the use of other nonlinear coating materials, such as Lithium Niobate (LiNbO3) and Gallium Phosphide (GaP), which exhibit a large second-order nonlinear susceptibility and high transparency in the THz frequency range.

Figure 2
illustrates the energy conservation diagram and modal phase matching conditions for surface-emitted Silica Nonlinear molecules ZnTe !" in the THz domain and the low efficiency of THz-wave generation, we do not consider the case of collinear wave generation.The relevant relationships are given below:  !"# =  $ −  % (1)  $ −  % = 0 (2) Where the angular frequency is denoted by , and the propagation wave vector is denoted by .The subscripts 1-2 indicate the optical waves ( $ >  % ), and the subscripts THz indicate the THz-wave.Equation (2) provides the modal phase-matching condition for the surface-emitted THz-wave.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM 01 at wavelength 773 nm and HE 21 at wavelength 760 nm.
THz-wave generation.Due to the high absorption of silica in the THz domain and the low efficiency of THz-wave generation, we do not consider the case of collinear wave generation.The relevant relationships are given below:!!"# = !$ − !%(1)( $ − ( % = 0 (2) Where the angular frequency is denoted by !, and the propagation wave vector is denoted by (.The subscripts 1-2 indicate the optical waves (! $ > !% ), and the subscripts THz indicate the THz-wave.Equation (2) provides the modal phase-matching condition for the surface-emitted THz-wave.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM 01 at wavelength 773 nm and HE 21 at wavelength 760 nm.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM 01 at wavelength 773 nm and HE 21 at wavelength 760 nm.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm.
n and (b) phase matching THz-wave generation.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm.
THz-wave generation.Due to the high absorption of silica in the THz domain and the low efficiency of THz-wave generation, we do not consider the case of collinear wave generation.The relevant relationships are given below:!!"# = !$ − !%(1)( $ − ( % = 0 (2) Where the angular frequency is denoted by !, and the propagation wave vector is denoted by (.The subscripts 1-2 indicate the optical waves (! $ > !% ), and the subscripts THz indicate the THz-wave.Equation (2) provides the modal phase-matching condition for the surface-emitted THz-wave.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM01 at wavelength 773 nm and HE21 at wavelength 760 nm.

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM 01 at wavelength 773 nm and HE 21 at wavelength 760 nm.
the ted by (.The subscripts es (! $ > !% ), and the Hz-wave.Equation (2) ching condition for the (b) phase matching wave generation. in the surface-emitted generated perpendicular n of the optical waves.d as follows: % , $

Fig. 3 .
Fig. 3. Modal phase matching for surface emitted THz-wave generation in a silica nanofiber.It is verified for a nanofiber diameter of 728 nm between two guided modes, TM 01 at wavelength 773 nm and HE 21 at wavelength 760 nm.