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Abstract
Frequency upconversion technology with good performance including high sensitivity, fast response, and room-temperature operation is a promising method for terahertz-wave detection. The sum-frequency conversion and difference-frequency conversion jointly affect the detection ability for upconversion detection using organic crystals as nonlinear media. The concurrence of both processes has been ignored in past studies, which results in discrepancies between theoretical simulations and experimental results. In this paper, four-wave interaction equations involving two nonlinear conversion processes are proposed, and the effect of the sum-frequency process is analyzed in upconversion terahertz-wave detection via a 4-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) crystal. The ratio of the sum-frequency signal to the difference-frequency signal varies for different terahertz frequencies and crystal thicknesses. Experiments suggest that theoretical simulations are good at predicting physical processes. Under certain conditions, the detection efficiency can be improved by simultaneously utilizing the two signals. The total signal photon number is not sensitive to the crystal thickness. Furthermore, the theoretical exploration of terahertz single-photon detection provides a noteworthy reference for future experiments.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz waves, which are also called submillimeter radiation, T-rays, T-waves, or THz waves, are located between microwave and infrared spectral bands in the electromagnetic spectrum in the frequency range of 0.1–30 THz [1,2]. Possessing unique properties for the penetrability and spectroscopy of materials, terahertz waves show promising applications in various fields, such as wireless communications [3], medical imaging [4], molecular structure analysis [5], and security inspection [6]. As a result of the vigorous development of terahertz technology, room-temperature terahertz-wave detection with high sensitivity and fast response has received considerable attention.
By identifying terahertz radiation according to different physical properties, terahertz detectors can be conventionally categorized into thermal detectors, electrical detectors, quantum detectors, and optical detectors [7,8]. As typical representatives for thermal detectors, the bolometer, Golay cell, and pyroelectric detectors are extensively used in research [9]. They are advantageous for broadband detection but have a relatively long response time [10]. Electrical detection has two types: direct detection and heterodyne coherent detection. Both amplitude and phase information can be obtained from coherent detection with fast response, which is beneficial to spectroscopic applications [11]. However, the operative range is limited to low terahertz frequency due to the influence of the electron transit time and stray capacitance [12]. Quantum detectors are notably sensitive but often need cryogenic cooling [13,14].
These detectors cover only a limited terahertz range or particular frequencies, while optical detectors based on nonlinear optical crystals are of particular interest because they can efficiently achieve broadband terahertz-wave detection [15]. Except for electro-optic sampling in which femtosecond laser is required [16], terahertz-wave detection based on a frequency upconversion process using nanosecond laser is also a promising method due to its high sensitivity, fast response, and room-temperature operation. In comparison with conventional inorganic crystals (e.g., LiNbO3 [17], GaSe [18], and ZnGeP2 [19]), organic crystals (e.g., DAST [20], DSTMS [21], HMQ-TMS [22], OH1 [23], and BNA [24]) exhibit a larger second-order nonlinear coefficient and satisfactory phase matching over a broader terahertz frequency range, which further enhances the performance of terahertz-wave detection.
The difference-frequency process and sum-frequency process, which are significant second-order nonlinear behaviors in light-matter interactions, have been studied in upconversion terahertz-wave detection in previous works [25,26]. However, previous studies only focused on one of these processes individually. In fact, both difference-frequency process and sum-frequency process can satisfy the collinear phase matching condition over a wide terahertz spectrum, i.e., the two frequency conversions simultaneously occur when a pumping laser is incident in the nonlinear crystal. For example, when a pumping laser (νP) and terahertz wave (νT) are collinearly incident onto a DAST crystal, a sum-frequency signal (νSF=νP+νT) and a difference-frequency signal (νDF=νP−νT) are generated. The two conversions are coupled together, and the detection results are actually determined by their combined effects. Previous studies have only considered the difference-frequency process, which results in a substantial difference between theoretical results and experimental simulations. To better explain the laws of physical action, further research on upconversion terahertz-wave detection is necessary, with both nonlinear conversions accounted for in theoretical analysis. We have performed preliminary analysis [27] and theoretically indicated that the interactions were different from those of a single difference-frequency process.
In this study, we investigate the influence of the sum-frequency process on the detection results in depth and verify the correctness of the theoretical simulations through experiments. Both theoretical calculations and experimental studies are based on DAST crystals. First, the corresponding theoretical coupled equations that involve four-wave interactions are proposed and numerically simulated. The nonlinear optical evolution processes of terahertz-wave detection are studied, and the parameter of crystal thickness is analyzed in detail to achieve optimization. The influence of the sum-frequency signal on the detection outcomes for different terahertz frequencies and crystal thicknesses is further discussed. Second, terahertz frequency upconversion detection with high sensitivity has been experimentally demonstrated. The signals of difference-frequency and sum-frequency progresses are measured and compared in different situations. The simulated results are consistent with the experimental values. Finally, by applying the theoretical model, terahertz single-photon detection is explored to provide further guidance on experimental design.
2. Theoretical simulation and analysis
Difference-frequency conversion is the most common method for upconversion terahertz-wave detection due to the terahertz-wave generation in the process. In contrast, terahertz waves are consumed in the sum-frequency process. However, the two processes usually occur simultaneously. The near-infrared (NIR) laser and terahertz wave can have good phase matching over a wide range. The typical coherence length (lc) across the terahertz band is calculated as follows:
For our simulations, the terahertz-wave detection of pumping polarization along the a-axis of the DAST crystal is studied as an example. The related refractive index (n) parameters are from Ref. [28,29]. Figure 1(a) and Fig. 1(b) represent the difference-frequency process and sum-frequency process, respectively. When a certain pumping laser in a specified wavelength range is incident in a DAST crystal, both processes can satisfy collinear phase matching to some extent. Therefore, the difference-frequency conversion and sum-frequency conversion are usually coupled together and interact with each other.
Fig. 1. The phase matching condition across the terahertz band for the (a) difference-frequency process and (b) sum-frequency process.
Upconversion terahertz-wave detection, which contains both the difference-frequency process and sum-frequency process, is determined by the four-wave interactions. Deduced from the familiar three-wave coupling equations [30], the four-wave interaction equations with two coupled nonlinear processes are as follows:
Subsequently, relevant numerical analyses of four-wave interaction equations are taken in the main part, where calculations and simulations are performed in MATLAB. First, to learn the laws of interaction, the absorption and coherence lengths are temporarily omitted during the four-wave nonlinear interaction process of terahertz-wave detection. The interactions are compared with those that have only one process, as shown in Fig. 2. The difference-frequency signal and sum-frequency signal simultaneously exponentially increase. The terahertz wave has a slight variation due to the combined effect of two nonlinear processes. Because there is a sum-frequency process, terahertz photons do not rise like those in the sole difference-frequency process. Simultaneously, terahertz photons do not decline as rapidly as those considered by only the sum-frequency process due to the influence of the difference-frequency process. More detailed descriptions can be found in a previous work [27].
Fig. 2. The evolution of all lights within a DAST crystal in a simplified condition. (a) Coupled difference-frequency conversion and sum-frequency conversion; (b) only difference-frequency conversion considered; (c) only sum-frequency conversion considered.
To make the theoretical simulations more instructive and consistent with the experimental results, the influence of the absorption and coherence length is accounted for. We mainly focus on weak light detection in consideration of the relatively high sensitivity of upconversion terahertz-wave detection. The terahertz-wave average power is set as 18.2 nW (near the minimum detectable power of the Golay cell). The pumping intensity is set as 42 MW/cm2. For the pumping wavelength, we choose the phase-matching wavelength of the difference-frequency process according to Fig. 1. The effect of the sum-frequency conversion is analyzed in upconversion terahertz-wave detection with phase-matching difference-frequency process. Based on numerical simulations of the coupling equations, the dynamic process in the DAST crystal can be obtained under certain conditions. The difference-frequency signal photons and sum-frequency signal photons vary with the terahertz frequency (3–21 THz) and crystal thickness (0.1–0.7 mm), as shown in Fig. 3. It shows that in the low terahertz frequency range (3–8 THz), the sum-frequency process has basically equal efficiency to the difference-frequency process, and the signal generated from the sum-frequency process cannot be ignored in terahertz-wave detection. In the high terahertz frequency range (14–21 THz), there are very few sum-frequency signal photons compared to difference-frequency signal photons. The sum-frequency process is negligible to some extent. Between these two terahertz regions (8–14 THz), the influence of the sum-frequency signal varies for different crystal thicknesses depending on the circumstances.
Fig. 3. The (a) difference-frequency signal and (b) sum-frequency signal photons as functions of terahertz frequency and crystal thickness.
These different trends of the two signals originate from different interactions and phase-matching conditions of the two processes. When the difference-frequency conversion or the sum-frequency conversion is separately considered, the upconverted signal output with respective phase-matched wavelengths is obtained, as shown in Fig. 4. It is significant that the difference-frequency conversion has a higher efficiency (more upconverted photons) than the sum-frequency conversion. The graphic also illustrates how the crystal thickness responds to the detection efficiency. Unlike the higher conversion efficiency that corresponds to a larger crystal thickness (∼mm) in the sole difference-frequency conversion, there is an optimal crystal thickness for sum-frequency conversion at one terahertz frequency. Similarly, these two signals are different within various crystal thicknesses in the interaction of coupled difference-frequency and sum-frequency processes. Meanwhile, the higher terahertz frequency indicates a larger phase mismatch for the sum-frequency process when one applies the phase-matching pumping wavelength of the difference-frequency conversion, which further declines the sum-frequency signal.
Fig. 4. The upconverted signal photons of two situations being considered separately: (a) difference-frequency conversion and (b) sum-frequency conversion.
Furthermore, specific light conversions of terahertz-wave detection are studied considering two coupled nonlinear optical processes. Taking 11.8 THz as an example, the simulation results are exhibited in Fig. 5. It shows the photon number of the pumping laser, terahertz wave and two signal lights at different positions in a DAST crystal. The major contributing factors for the photon number are the absorption in the DAST crystal and optical wavelength conversion. The small reduction in pumping photons is mainly caused by crystal absorption. Terahertz photons first quickly fall (interaction length below 0.2 mm) and subsequently level off. At the beginning of the interaction, the difference-frequency process has comparable conversion efficiency to the sum-frequency process. Thus, the different effects on terahertz photons almost cancel out each other. The rapid decline in terahertz photons is due to the greater absorption in the DAST crystal. After the terahertz wave expands over a distance, its residual and the addition generated from the difference-frequency process cannot maintain the sum-frequency conversion. This leads to the reversion of the sum-frequency process, and the photon number of the sum-frequency signal begins to drop. For the difference-frequency process, the pumping laser is sufficiently strong to maintain the forward conversion, and the corresponding photons still slowly increase. Meanwhile, the combination of absorption and optical conversion makes the terahertz photon number slightly fluctuate. Figure 5(b) also shows that a better method to improve the detection efficiency is to simultaneously utilize the two signals. More importantly, crystals within a certain thickness range (0.2–0.6 mm) can achieve a relatively large total output. Thus, the total signal photon number is not sensitive to the crystal thickness, which provides us with a wide range of optional crystal thicknesses.
Fig. 5. The evolution of different lights in a DAST crystal based on coupled difference-frequency conversion and sum-frequency conversion.
3. Experiment setup and results
The coupling effects of sum-frequency and difference-frequency processes on upconversion terahertz-wave detection were also experimentally investigated via the DAST crystal.
The terahertz-wave detection system based on the nonlinear frequency upconversion process is illustrated in Fig. 6. A NIR pumping laser and a terahertz wave were collinearly focused in a DAST crystal through a parabolic mirror to generate the signal light by a second-order nonlinear effect. The pumping laser was generated from an optical parametric oscillator (OPO) with an angle-tunable potassium titanium oxide phosphate (KTP) to achieve pumping wavelength tuning. Four bandpass filters (Edmund Optics) with a bandwidth of 50 nm and an optical density (OD) value of 4 were employed to filter out the pumping laser. A focusing lens was used to collect the frequency upconverted signal into a positive-intrinsic-negative (PIN) diode detector (Thorlabs PDA10CF-EC). The detection results were displayed in waveform on an oscilloscope (Teledyne LeCroy HDO6104, 1 GHz). Thus, high-sensitivity detection of terahertz waves were indirectly realized by detecting the signal light with available high-sensitivity detectors in the NIR region.
The inset of Fig. 6 exhibits the terahertz difference-frequency generation part. A DAST crystal was pumped by two focused NIR lasers generated from a dual-KTP OPO. The generated terahertz wave was detected by a Golay cell (Tydex GC-1D). A 100-µm-thick germanium wafer with a 2-inch diameter was placed in front of the detector to block the residual NIR pumping laser. We scanned all detectable terahertz peaks using the current experimental system, as shown in Fig. 7(a). Continuously tunable terahertz waves from 3 to 21 THz were generated with representative peak frequencies of 4.3, 11.8, and 16.3 THz. The terahertz peaks are attributed to the absorption and nonlinear conversion in the DAST crystal. Figure 7(b) shows a typical Golay cell signal of 4.3 THz with the chopper frequency of 5 Hz in the experiment. The sub-pulses underneath the signal correspond to the laser frequency of 100 Hz.
Fig. 7. (a) The measured signal amplitude as a function of terahertz frequency. (b) The terahertz signal measured by a Golay cell.
To explore the influence of the sum-frequency signal on the detection consequences, the terahertz frequency and crystal thickness are two necessary factors to consider. To obtain better detection results, we chose three typical terahertz emission peaks of 4.3, 11.8, and 16.3 THz for experimental research. Two DAST crystals of different thicknesses (0.2 mm and 0.4 mm) were employed to study the effect of the crystal thickness. Weak light detection was performed when the terahertz power decayed to the minimum detectable power of the Golay cell (18.2 nW). The pumping intensity was adjusted to 42 MW/cm2. The relevant experimental wavelength parameters are provided in Table 1. To measure different sum-frequency signals and difference-frequency signals, the corresponding filters of appropriate central wavelengths were employed.
Table 1. Wavelength parameters of terahertz-wave detection
The experimental results in Fig. 8 demonstrate the changes in sum-frequency signals and difference-frequency signals with the terahertz frequency and crystal thickness. For terahertz-wave detection with 0.2-mm-DAST, the sum-frequency signal cannot be omitted regardless of the terahertz frequency. The two signals were not significantly different. For the 0.4-mm-DAST, the results are different. The detection frequencies of 4.3 and 11.8 THz must account for both signals. However, for 16.3 THz, the sum-frequency signal is obviously too small in comparison with the difference-frequency signal, so it has little overall effect on the detection results. In addition, regarding the same terahertz frequency, a thicker crystal leads to a larger difference-frequency signal. However, for the sum-frequency signal, the crystal thickness has different implications for different terahertz frequencies. In other words, a larger thickness corresponds to a higher signal for 4.3 and 11.8 THz, while 16.3 THz has exactly the opposite effect. The principles have been specifically analyzed and explained in Section 2. Meanwhile, the terahertz frequency upconversion detection is more sensitive than the Golay cell, considering the large detectable voltage and much higher signal-to-noise ratio (SNR) of the upconverted signal. At 4.3 THz, frequency upconversion detection with a PIN detector is at least three orders of magnitude more sensitive than that of the Golay cell.
Fig. 8. Various signal voltages of the difference-frequency signal and sum-frequency signal for terahertz-wave detection of different frequencies within 0.2 mm-DAST and 0.4 mm-DAST.
To clearly compare with the simulated results, Table 2 shows the concrete values and ratios of the two signals in the experiment. The theoretical simulations are basically consistent with the experimental results, considering inevitable measuring errors in the experiment.
Table 2. Experimental and simulated results of different upconverted signals
4. Theoretical analysis of terahertz single-photon detection
As mentioned above, the theory and experimentation have suggested that the model of four-wave interaction equations is correct. Combining the difference-frequency and sum-frequency signals is a good solution to improve the detection efficiency. For weak light detection and even terahertz single-photon detection, the pumping wavelength can be further optimized to maximize the combined signal and improve the detection efficiency. The optimal pumping wavelength for the combined signal photons is calculated and analyzed, as shown in Fig. 9. The pumping intensity is set to 280 MW/cm2 (one tenth of the damage threshold of 2.8 GW/cm2 [32]), the incident terahertz photon is set to a single photon, and a DAST crystal of 0.5 mm is used in the simulation. Different terahertz frequencies have different dependencies on the pumping wavelength, and a high terahertz frequency is more sensitive to the selection of the pumping wavelength. Figure 9 also shows that a higher terahertz frequency is more likely to produce more signal photons because a higher photon energy corresponds to a higher conversion efficiency.
Fig. 9. The total signal photons vary with the terahertz frequency and pumping wavelength for terahertz single-photon detection.
Finally, the possibility of terahertz single-photon detection is explored using the calculated optimal pumping wavelength. Similarly, we take 11.8 THz as an example. Figure 10 presents the variations of the total signal photons with different crystal thicknesses and pumping intensities. The required experimental conditions for one output signal photon are clearly marked. We can draw a conclusion from the figure that terahertz single-photon detection using both signals can theoretically be achieved with the help of single-photon detectors (SPDs). Additionally, a large pumping intensity and crystal thickness are more helpful.
Fig. 10. The total signal photons vary with the crystal thickness and pumping intensity for terahertz single-photon detection.
5. Conclusion
In summary, we have systematically investigated terahertz-wave detection via a DAST crystal based on coupled difference-frequency and sum-frequency processes. In terms of theory, four-wave interaction equations are proposed, including two nonlinear conversion processes. The evolution of all waves within a DAST crystal in simplified conditions and actual experimental settings are analyzed in detail. The detection efficiency can be improved by simultaneously utilizing the two signals, and the total signal photon number is not sensitive to the crystal thickness. The difference-frequency signal and sum-frequency signal for different terahertz frequencies and crystal thicknesses are further explored. For low terahertz frequencies and small-thickness crystals, the sum-frequency signal is nearly identical to the difference-frequency signal. However, it can be ignored in higher frequencies and thicker crystals to a certain extent. From an experimental perspective, terahertz frequency upconversion detection with high sensitivity has been demonstrated, and it performs nearly three orders better than the Golay cell at 4.3 THz. In addition, the signals of difference-frequency and sum-frequency processes are measured and compared, which indicates diverse effects on the detection results for different terahertz frequencies and crystal thicknesses. The theoretical calculation results fit well with those of the experiment. Finally, a theoretical exploration of terahertz single-photon detection is conducted, which will provide some guidance for experiments.
Funding
National Natural Science Foundation of China (61775122, 12074222); Key Technology Research and Development Program of Shandong (2019JMRH0111); Natural Science Foundation of Shandong Province (ZR2017MF038).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Dataset 1, Ref. [33].
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