Extremely Efficient Terahertz Second-Harmonic Generation from Organic Crystals

. Achieving efficient and intense second harmonic generation (SHG) in the terahertz (THz) spectrum holds great potential for a wide range of technical applications, including compact tunable THz sources THz nonlinear functional device, wireless communications, and data processing and storage. However, the current researches on THz harmonic emission primarily focus on inorganic materials, which often face challenges in achieving both efficient and broadband SHG. Herein, the remarkable efficiency of organic materials in producing THz harmonics is studied and demonstrated, thereby opening up a new avenue for searching candidates for frequency-doubling devices in the THz band. By utilizing DAST, DSTMS, and OH1 crystals, we showcase their superior frequency conversion capabilities when pumped over a broadband THz range by the narrowband THz pulse centered at 2.4 THz, 1.6 THz and 0.8 THz. The SHG spanned a high-frequency THz domain of 4.8 THz, achieving an unprecedented conversion efficiency of approximately 1.21% while maintaining a perturbative nonlinear response. The highly efficient SHG of these materials is theoretically analyzed by considering the combined effects of dispersion, phonon absorption, polarization, and the nonlinear susceptibility of organic crystals. This work presents a promising platform for efficient THz frequency conversion and generation across a wide range of frequencies, offering new opportunities for novel nonlinear THz applications in next-generation electronics and optics.


Introduction
2][3][4][5] The spectral boundary between electrons and optics, once known as the "THz gap", appears to be a missing component in the well-established field of nonlinear optics.][8][9][10][11] However, studies on frequency up-conversion using second harmonic generation (SHG) or high-order harmonic radiation to bridge optoelectronics and THz technology are relatively scarce.][8][9][10][11][12][13][14][15][16][17] The carriers in the majority of such materials are accelerated symmetrically with respect to the direction of an incident THz field, which leads to nonlinear optical responses that can be described by odd-order electrical susceptibility, where THz odd-order harmonic generation has recently been demonstrated 12,19,20 .In contrast On the other hand, the second-order nonlinear processes related to second-order susceptibility, such as optical parametric oscillation and second harmonic generation (SHG), theoretically offer higher efficiencies and more promising potential for exploitation, also have development potential and are expected to advance various technologies such as compact tunable THz sources THz nonlinear functional device, wireless communications, data processing and storage, and radar-based systems. 18-23 21-26Unfortunately, the scarcity of suitable second-order nonlinear materials for the THz spectrum hindered the exploration of THz nonlinear processes.
Very few pioneering studies on THz SHG have primarily focused on inorganic materials.In earlier studies, researchers have demonstrated that the THz SHG process can arise from the inherent second-order susceptibility of lattice resonance in gallium arsenide (GaAs) and lithium tantalate (LiTaO 3 ), 24 27 or from the asymmetric electronic response caused by the artificial quantum wells. 25 28However, due to the weak inherent nonlinearity of crystal materials 24 and the limited operating frequency band, 25 their conversion efficiencies are too low to be applied.due to the weak inherent nonlinearities of materials, the conversion efficiency of these works is generally low 27,28 In recent years, superconductors and metamaterials have been explored for their feasibility in achieving efficient SHG. 26,27Superconductors have shown promise promising prospects in achieving efficient SHG due to the dynamical symmetry breaking caused by lightwave acceleration of supercurrent at cryogenic temperature. 29But this solution imposes strict temperature requirements, and the operating frequency band is also limited to a narrowband by the energy gap of the material. 29The latest research indicates that metamaterials Metamaterials leverage artificially designed resonant structures to enhance nonlinear Thomson scattering, generating SHG at room temperature. 30Nevertheless, due to limitations such as extremely thin effective thickness in nanometers and low saturation threshold, the conversion efficiency of this metamaterial scheme is difficult to further improve. 30However, both the pioneering studies and those advanced platforms based on inorganic materials are severely restricted in improving the conversion efficiency due to essential constraints such as inherently weak nonlinear responses, 24 very thin effective thickness in nanometers, 26,27 and low saturation thresholds. 27Additionally, for advanced platforms of superconductors and metamaterials, 29,30 their operations are limited at several specific frequencies, typically below 1 THz, [25][26][27] which are also unfavored by most potential applications.In fact, nonlinear materials capable of achieving highly efficient THz SHG over a wide range of frequencies remain challenging.In fact, achieving highly efficient SHG for THz waves over a wider frequency range remains challenging.
In this study, we demonstrate THz SHG in organic materials with record-breaking conversion efficiency and broad bandwidth.We directly excited three organic crystals, namely DAST, DSTMS, and OH1, using THz pulses with frequencies of 0.8 2.4 THz, 1.6 THz, and 2.4 0.8 THz, respectively.Remarkably, we achieved highly efficient SHG over a wide frequency range at room temperature.8][29][30] Importantly, unlike semiconductors, we observed no electric field saturation of SHG as the energy of the THz pump pulse fundamental energy increased, indicating that organic crystals are expected to produce extremely strong harmonic pulses.To evaluate the frequency-doubling capability of these materials, we further investigated the SHG process from the perspectives of dispersion, photon absorption, polarization, and second-order nonlinear susceptibility.Our findings suggest that organic crystals hold great prospects as THz frequency-doubling devices.The proposed THz SHG scheme offers several advantages, including a convenient experimental setup, a wide operating frequency range, and high conversion efficiency.This research provides an excellent platform for the development of THz nonlinear functional devices.

THz SHG from organic crystals
Our experiment, depicted in Fig. 1(a), is designed to observe THz harmonics in crystals using strong-field THz time-domain spectroscopy (see Appendix A.1 and Supplementary Material for detailed information about the experimental system).Narrow-band, multi-cycle quasimonochromatic pulses with specific fundamental frequencies of 0.8 2.4 THz, 1.6 THz, or 2.4 0.8 THz are used to excite substrate-free organic crystals DAST, DSTMS, and OH1.Second harmonics are generated due to the strong second-order nonlinearities and are then filtered at a frequency of 1.6 4.8 THz, 3.2 THz, or 4.8 1.6 THz and measured using an electro-optical sampling (EOS) device. 3639All measurements are performed at room temperature in a nitrogen atmosphere.
The bottom panels of Figs.1(b)-1(d) display the measured incident THz time-domain waveforms, along with the corresponding peak electric field strengths of 210.3 kV/cm, 78.6 kV/cm, and 23.5 kV/cm, for frequencies of 2.4 THz, 1.6 THz, and 0.8 THz.We pumped DAST, DSTMS, and OH1 crystals with thicknesses of 300 μm, 300 μm, and 500 μm, respectively, using pulses of these three frequencies and measured the generated second harmonic time-domain signals, as shown in Fig. S3 in the Supplementary Material.The corresponding THz second-order harmonic spectra are shown in Figs.1(e)-1(g).It is evident that all three crystals are capable of efficiently generating second-harmonic radiation, although the optimal operating frequency differs for each crystal.
Specifically, for THz pulses with pump frequencies of 2.4 THz, 1.6 THz, and 0.8 THz, the DAST, DSTMS, and OH1 crystals exhibit strong harmonic generation capabilities, with clear and visible second harmonic waveforms and maximum electric fields of 2545 V/cm, 405 V/cm, and 11.4 V/cm, respectively, as shown in the upper panels of Figs.1(b)-1(d).The stability measurement and error evaluation of SHG signals is described in Section IV of the Supplementary Material.

The dependence of SHG on the incident electric field
We examined the relationship between the electric field strength of SHG of different crystals and the fundamental electric field of 2.4 THz, 1.6 THz, and 0.8 THz, as depicted in Figs.2(a)-2(c).
The dependence of SHG on field strength can be accurately described by a power law of with respect to the fundamental field strength, indicating a second-order nonlinear  (c)), we provide a small number of valid measurements for subsequent mechanism analysis.Importantly, saturation of SHG is not observed within the range of the incident electric field, suggesting that there is still significant room for improvement in conversion efficiency.It is worth noting that prior to this study, only a few efforts had achieved conversion efficiencies of a similar magnitude based on the second-order nonlinearity of the material, and the operating frequency bands were all for low-frequency THz pump pulses below ~1 THz.For example, previous studies achieved a SHG field conversion efficiency ( ) of ~0.035% for SHG in metamaterials excited by a 0.68 THz pulse with a 2 / f f E E maximum peak field of ~98.9 kV/cm, 27 30 and of ~0.3% in a superconductor pumped by a 0.5 THz pulse with a maximum peak field of ~21.7 kV/cm at a low temperature of ~4.2 K. 26 29 THz.

The influence of dispersion and phonon absorption on SHG and evaluation of second-order nonlinear susceptibility
To gain a deeper understanding of the physical mechanism behind strong SHG from organic crystals across a wide THz frequency range, we conducted a detailed analysis of various factors that affect SHG.The DAST, DSTMS, and OH1 crystals used in this study, which are commonly mentioned as THz sources in previous reports, exhibit absorption characteristics in the THz range that can significantly impact the spectra. 32,33 9,35These absorption characteristics of the crystals in the THz range as well as the dispersion associated with refractive index perturbations mainly arise from phonon resonance, resulting in different frequency sensitivities of the three crystals to THz SHG.To analyze this complex process, we use the concept of effective distance (L eff , refer to Eq. (3) in the Appendix A. Furthermore, the simulations conducted in this study also provide guidance for the design and selection of frequency-doubling crystals.The simulated results show that DSTMS crystals in the thickness range of 100~300 μm have a high effective distance for THz pump pulses of these three frequencies.However, due to the difficult manufacturing process of organic crystal materials, the thickness of the thinnest DSTMS crystal we have commercially obtained is 300 μm.We further measured the electric field of SHG from DSTMS crystals with thickness of 300 μm, 400 μm and 500 μm at three fundamental frequencies, as indicated by the red dots in Fig. 3(d).The results demonstrate that the measured electric field of SHG aligns with the trend of the effective distance curve, implying that the evaluation of effective distance can directly reflect the THz electric strength of SHG.This information is valuable in selecting the optimal crystal thickness for SHG at a specific pump frequency.Based on the above series of theoretical analysis and experimental measurements, we further calculated the second-order nonlinear susceptibility of the crystal at different THz


THz are 1036 pm/V, 1265 pm/V, and 522 pm/V, respectively.Similarly, the measured of the (2)

Polarization dependence of SHG in crystals
Taking DAST crystal as an example, the polarization dependence of SHG related to material anisotropy is further discussed.Assuming that the polarization direction of the fundamental pulse is in the x-direction and is incident perpendicular to the crystal.(2 ) 2 cos sin cos . Similarly, the electric field measured along the y-direction can be expressed as , where represents the nonlinear optical (2 ) 2 cos sin sin coefficients for THz SHG of the crystal. 37,43 40,46crystal, the latter due to the structural properties of the a-cut of the OH1 crystal. 31,44-46 34,47-49Our findings suggest that when DAST/DSTMS and OH1 crystals are used as THz frequency doubling materials, the a-polarized pump and c-polarized pump of the respective crystals are preferred.

Discussion and Conclusion
Based on the theoretical simulations and experimental measurements discussed above, it can be concluded that the strong THz SHG observed in organic crystals can primarily be attributed to their high nonlinear polarization and low dispersion loss properties.The second-order nonlinear polarization in organic crystals is primarily derived from the π-electron system, 30,31 where the electrons form an extended π-electron cloud due to the presence of conjugated bonds.This allows the electrons to move freely within this system, enabling more effective responses to changes in the external electric field and promoting asymmetric responses.The asymmetry of molecular structures in organic crystals, coupled with the uneven electron distribution caused by the presence of strong electron donors and acceptors, provides the conditions necessary for these organic crystals to exhibit strong second-order nonlinear coefficients.Moreover, the specific molecular structures and bonding patterns in these organic crystals form complex π-electron conjugated systems.The π-electrons in this conjugated system are not confined to a specific atom but are distributed across the atoms of the entire conjugated system, 33,34 supporting a broader distribution and movement of electrons, and a more sensitive response to electric fields, and the second-order nonlinear susceptibility be further enhanced.The π-electron system also possesses small energy gaps in its electronic energy levels, making it capable of absorbing and emitting photons in the THz frequency range.Notably, the three advanced crystals used in our study are designed as chromophores packed with their main charge transfer axis, leading to a high diagonal acentric order parameter, which is closely optimized for THz photonics applications, 30,35 33,37 thus resulting in enhanced second-order nonlinear effects.
Another significant factor contributing to the efficient SHG of organic crystals is their low dispersion losses in specific THz frequency ranges.For instance, DAST and DSTMS crystals exhibit refractive index differences of less than 0.1 within the 2~6 THz range, while OH1 crystal has a refractive index difference of less than 0.1 below 2 THz.This characteristic ensures that there is an adequate effective distance for SHG within the crystal.These characteristics enable organic crystals to achieve coherence length ( ) for SHG of over several hundred micrometers within the c l corresponding frequency band (>300 μm in DAST, >500 μm in DSTMS, and >1 mm in OH1), indicating that the THz fundamental and second harmonic pulses are phase-matched during propagation through the selected crystal, while also establishing favorable conditions (refer to Eq. ( )) for effective distances required to generate second harmonics.Additionally, it is possible that there exists a coupling relationship between the phonon mode and the electronic state within the crystal, further enhancing the nonlinear polarization derived from the π-electron system.For example, DAST and DSTMS exhibit similar optical properties, with their nonlinear susceptibility and frequency doubling ability being almost identical when pumped at 2.4 THz, where both crystals are free from weak phonon interference.However, at a pump frequency of 1.6 THz, the presence of weak phonon vibrations near 3.1 THz in DAST leads to a slight increase in nonlinear polarizability but significantly reduces the effective distance for SHG, resulting in a relatively low radiated electric field of 3.2 THz.This highlights the importance of avoiding the impact of phonon vibrations for achieving efficient SHG.This is further supported by the SHG results of OH1 crystal and DAST/DSTMS crystal, which respectively exhibit advantages in the low-frequency (<1 THz) and high-frequency (>1 THz) pump regions.Furthermore, we believe that phonon vibration has an effect on both the nonlinear polarizability and the effective distance of the SHG process in organic crystals, and the two effects show a competitive relationship.On the one hand, phonon vibration is an energy transfer process in the crystal structure, which indicates that organic crystals have a strong lattice effect at the THz scale, and also enhances the sensitivity of π-electrons in conjugated system to changes in the incident electric field, resulting in large second-order nonlinear susceptibility of organic crystals.On the other hand, phonon vibration causes dispersion and absorption of the crystal, which affects the effective distance for SHG.For example, the DAST crystal has a phonon mode near 3.1 THz, resulting in a larger second-order nonlinear susceptibility than the DSTMS crystal for SHG at 3.2 THz, but at the same time, this phonon vibration also leads to stronger dispersion and absorption, making the effective distance of the DAST crystal small.
Under the above comprehensive influence, the SHG of DAST at 3.2 THz is weaker than that of DSTMS crystal.Therefore, we suggest that in future applications, the operating frequency range of organic crystals used as THz SHG devices should moderately avoid resonant sharp peaks of phonons.These findings can be extrapolated to various types of organic crystals in the THz field, including N-Benzyl-2-methyl-4-nitroaniline (BNA), 4750  polarization dependence, we further analyze the physical mechanism of SHG in these crystals, and predict that DSTMS and DAST are suitable for higher frequency bands beyond the measured range.
Overall, the proposed THz SHG scheme based on organic materials is convenient, efficient, and has a wide operating frequency range, making it advantageous for material selection in artificial structure design and the development of small integrated devices.Furthermore, it opens up new opportunities for future nonlinear applications at THz frequencies.

A.2 The calculation of second-order nonlinear susceptibility and effective distance of crystal for SHG
In the case of negligible absorption coefficient and near-perfect phase matching, the classical expression for the intensity of SHG in nonlinear media can be derived as follows: 37,38,49 40,41,52 (1) is the second-order nonlinear susceptibility, and is the sample thickness. (2)

 l
In our experiment, the crystal has a certain thickness, and the influence of dispersion and absorption on SHG cannot be ignored.Taking into account parameters such as the refractive index and absorption coefficient of the crystal, the amplitude of the electric field for THz SHG in the crystal can be expressed as: 37,38,49 40,41,52 (2) where is the optical group index of a fundamental THz pulse propagating within the sample.fundamental and second harmonic pulse, which can be expressed as: (3) where represent the coherence length for SHG within the sample.Based 2 ( , 2 ) on the absorption coefficient and refractive index for THz fundamental pulse and second harmonic pulses (as shown in Fig. S4 of the Supplementary Material), the effective distance can be eff L determined.By integrating the measurement of the harmonic electric field with the aforementioned equations, the second-order nonlinear susceptibility can be calculated. (2)

A.3 The measurement of nonlinear optical coefficients of DAST crystal for THz SHG
In this experiment, the polarization direction of the fundamental pulse is assumed to be in the xdirection.The linearly-polarized pump pulse propagates along the z-direction (i.e., ), ' 0 and it is incident on the sample perpendicularly.is the angle of crystal rotation relative to the So the second-order electric field component in the crystal can be written as: (5)

Fig. 1
Fig. 1 The THz SHG from organic crystals.(a) Schematic of the experiment.(b) The time-domain waveform of THz SHG from a DAST crystal (upper panel) and the corresponding THz pump waveform with a fundamental frequency of 2.4 THz (lower panel).(c) The time-domain waveform of THz SHG from a DSTMS crystal (upper panel) and the corresponding THz pump waveform with a fundamental frequency of 1.6 THz (lower panel).(d) The timedomain waveform of THz SHG from an OH1 crystal (upper panel) and the corresponding THz pump waveform with a fundamental frequency of 0.8 THz (lower panel).(e)-(g) The frequency spectra of THz SHG from different crystals with incident THz waves at fundamental frequencies of 2.4 THz, 1.6 THz, and 0.8 THz.
anticipated.3740Notably, this study extends the range of SHG to a high-frequency THz range of 4.8 THz, as shown in Fig.2(a).The DAST crystal exhibits a high nonlinear field conversion efficiency ( ) of 1.21% (The corresponding intensity conversion efficiency .46× 10 -4 ), while the DSTMS crystal has a conversion efficiency of 1.08% (The 2 /f f I Icorresponding intensity conversion efficiency is 1.17 × 10 -4 ), both substantially higher than previous THz SHG studies.Similarly, the DSTMS crystal shows strong SHG at ~3.2 THz, as shown in Fig. 2(b), with a maximum conversion efficiency of 0.515% (The corresponding intensity conversion efficiency is 2.65×10 -5 ), which is unprecedented for this operating band.For lowfrequency pump pulses of 0.8 THz, as shown in Fig. 2(c), the OH1 crystal demonstrates effective SHG with a maximum conversion efficiency of 0.049% (The corresponding intensity conversion efficiency is 2.40×10 -7 ), limited by the small pump electric field strength of 23.5 kV/cm.The resolution of the electric field strength of the second harmonics is affected by the background noise (refer to Section IV of Supplementary Material).Due to the weak second harmonics of 4.8 THz and 3.2 THz produced by OH1 crystal (as shown in Figs.2(a), (b)) and 1.6 THz produced by DAST and DSTMS crystals (as shown in Figs. 2

Fig. 2
Fig. 2 The dependence of the generated second harmonic field strength on the pump field strength.(a)-(c) The field strength of SHG from different crystals with the incident fundamental frequency of 2.4 THz, 1.6 THz, and 0.8 2), which takes into account both dispersion and phonon absorption.The key parameters such as the refractive index and absorption coefficient of DAST, DSTMS, and OH1 crystals are depicted in Fig.S4(Supplementary Material), where they are simulated using the Lorentz model by considering the numerous resonant features of the different crystals.35,38-42   37,41- The simulated effective distances L eff for SHG at different fundamental frequencies in DAST, DSTMS, and OH1 crystals of varying thicknesses are shown in Figs.3(a)-3(c).The fundamental pulses of 2.4 THz, 1.6 THz, and 0.8 THz selected in this study achieve optimal SHG conversion efficiency in different crystals, as shown in Figs.2(a)-2(c), providing the necessary data for analyzing the influence of crystal phonon resonance on SHG.Specifically, DAST and DSTMS exhibit a pronounced phonon vibration near 1 THz, which is evident in the dip in the effective distance around ~1 THz in Figs.3(a) and 3(b).This results in a low SHG when pumped by 0.8 THz, as shown in Fig. 2(c).However, DAST and DSTMS have weak phonon vibrations in the range of 1.5~4.5 THz, enabling them to have a significant effective distance in the highfrequency region of 1.5~4.5 THz, leading to the strong SHG observed in Figs.2(a) and 2(b).Moreover, the presence of a weak phonon vibration at ~3.1 THz in the DAST crystal directly inhibits SHG at 3.2 THz, distinguishing its frequency-doubling ability from that of DSTMS under 1.6 THz pumping conditions, as shown in Fig.2(b).On the other hand, OH1 exhibits strong phonon vibrations at ~2.85 THz and ~4.5 THz, with high amplitude and damping.These vibrations strongly interfere with the dispersion and absorption of the crystal above 2 THz, resulting in difficulties in achieving SHG in the high-frequency range, as depicted in Figs.2(a) and 2(b).This corresponds to a rapid decrease in the effective distance for the fundamental pulse above 1 THz, as shown in Fig.3(c).

Figure 3 (
d) visually presents the effective distance curves of DSTMS crystals with different thicknesses at fundamental frequencies of 0.8 THz, 1.6 THz, and 2.4 THz.Additionally, the red dots in Fig. 3(d) represent the measured electric field of SHG from DSTMS crystals with thicknesses of 300 μm, 400 μm, and 500 μm at the three fundamental frequencies.the thickness of DAST, DSTMS, and OH1 crystals selected in Figs.1-2 are 300 μm, 300 μm, and 500 μm, respectively.Compared with the actual crystal thickness, the effective distance of organic crystals in the SHG process is limited by factors such as phase matching and absorption, and is shown as a function of the operating frequency and crystal thickness (refer to Eq. (3) and Fig.3).Therefore, the simulations performed in Figs.3(a)-(c) also provide guidance for the thickness design and selection of crystal for SHG.Taking the DSTMS crystal as an example, the blue curves in Fig.3(d) visually presents the theoretical simulation of the effective distance with different crystal thicknesses at fundamental frequencies of 2.4 THz, 1.6 THz and 0.8 THz.

Fig. 3
Fig. 3 The effective distance for SHG in crystals.(a)-(c) The effective distance for SHG in DAST, DSTMS, and OH1 crystals with varying thicknesses under different fundamental frequencies pumping.(d) The blue curves depict the simulated effective distance for SHG in DSTMS crystals of varying thicknesses under fundamental frequencies of 0.8 2.4 THz, 1.6 THz, and 2.4 0.8 THz, and the red dots represent the measured electric field of SHG from DSTMS crystals with thicknesses of 300 μm, 400 μm, and 500 μm under the three fundamental frequencies.


fundamental frequencies.The detailed calculation method is provided in the Appendix A.2.The relationship between the measured electric field of the second harmonics and the second-order nonlinear susceptibility can be described by Eq. (2), which takes into consideration various(2) factors such as dispersion, absorption, and the effective distance discussed earlier.As a result, we determine that the of the DAST crystal pumped at frequencies of 2.4 THz, 1.6 THz, and 0.8(2) represents the rotation angle of  the a-axis of the DAST crystal relative to the polarization direction of the fundamental wave (as shown in Fig. S1 of the Supplementary Material).We rotate the organic crystal DAST and measure the electric field components of SHG along the x-and y-directions using a GaP crystal, and obtain the time-domain waveform of SHG with different rotation angles, as shown in Figs.4(a) and 4(b).The bottom panels of the figure depict the maximum electric field strength of SHG from the crystal with a time delay of t=2 ps, and the rotation angle of 0 degrees represents the polarization direction of the incident pulse along the a-axis of the DAST crystal.Based on the calculation of the polarizability tensor element in the crystal (see Appendix A.3 for more details), the electric field measured along the x-direction can be expressed as

Fig. 4 11 d 11 d 11 d 33 d
Fig. 4 Polarization dependence of SHG from DAST crystal at a pump frequency of 2.4 THz.(a)-(b) The timedomain waveform of SHG measured in the x-and y-direction with the DAST rotation angle of .The color  information represents the measured electric field strength of SHG.The bottom panels of the figure represent the variation of the peak electric field of the SHG with the rotation angle of . 2-(4-hydroxy-3-methoxystyryl)-1methylquinolinium 2,4,6-trimethylbenzenesulfonate (HMQ-TMS),4851  and potential future nonlinear optical crystals, thereby offering valuable theoretical guidance for selecting suitable crystal samples based on the desired operating frequency and the distribution of phonon resonance within the sample.In summary, we introduced organic crystals as a novel category in the field of SHG over a wide THz range.By directly exciting the second-order nonlinear response in DAST, DSTMS, and OH1 crystals with three THz fundamental pulses at different frequencies, we observed effective SHG performance across a wide range of THz frequencies.Based on our findings, we recommend OH1 crystal and DAST/DSTMS crystal as high-quality candidate materials for SHG with lowand high-frequency THz pulse pumping respectively.Especially for high-frequency incident pulses of 2.4 THz, the conversion efficiency of the pumping-harmonic field in DAST and DSTMS can exceed ~1%, marking a significant achievement.Similarly, for low-frequency pump pulses of 0.8 THz, the conversion efficiency can reach ~0.049%, which can be further optimized by increasing the thickness of the OH1 crystal and the strength of the pump electric field.Importantly, our results indicate that the SHG of three crystals does not saturate as the pump energy increases, suggesting that organic crystals have potential application prospects for generating extremely strong harmonics.Taking into account factors such as dispersion, phonon absorption, and

A. 1
Experimental setupThe THz time-domain spectroscopy employed in this experiment is based on the organic crystal pumped by a femtosecond laser with a repetitive frequency of 1 kHz for generating a strong-field THz wave.The setup of the experiment is illustrated in Fig.S1(Supplementary Material).The pump fundamental pulses of 0.8 2.4 THz, 1.6 THz, and 2.4 0.8 THz are selected by the specific type of THz bandpass filters and are vertically incident on the c-cut DAST crystal, c-cut DSTMS crystal and a-cut OH1 crystal (Swiss Terahertz) respectively.A set of THz wire-grid polarizers are used to modulate the fundamental pump energy.The generated harmonics of 1.6 4.8 THz, 3.2 THz, and 4.8 1.6 THz are selected through the corresponding THz bandpass filters, and then measured using the EOS technique with a 1 mm thick ZnTe crystal or a 0.2 mm thick GaP crystal.The transmittance of different types of THz bandpass filters, as well as the response functions of ZnTe and GaP crystals to frequency, can be found in Fig. S2 (Supplementary Material), which are used to correct the THz electric field values at different frequencies.Dry nitrogen gas is used to purge the system, eliminating the absorption of water vapor.More detailed information regarding the experimental setup can be found in the Supplementary Material.
coefficients of the sample for THz fundamental and second 2    harmonic pulses.denotes the refractive index of the sample to the THz second harmonic 2 n  pulses.c denotes the vacuum speed of light.denotes the effective distance between the eff L


x-direction.The electric field components of the crystal can be expressed as , order nonlinear polarizability tensors, and consequently, the relationship between the second-order polarization tensor matrix and the electric field component for SHG in DAST can be expressed as:

Fig. 2
Fig.2The dependence of the generated second harmonic field strength on the pump field

Fig. 3
Fig. 3 The effective distance for SHG in crystals.(a)-(c) The effective distance for SHG in

Fig. 4
Fig. 4 Polarization dependence of SHG from DAST crystal at a pump frequency of 2.4 THz.
If the above electric field is projected onto the laboratory coordinates, the measured electric