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Traceable Measurement of Terahertz Wavelength Using Terahertz Interferometry
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摘要: 频率是太赫兹辐射的关键参数，太赫兹频率测量和溯源是太赫兹技术研究和应用的关键。为实现太赫兹激光波长的准确测量和量值溯源，研制了太赫兹干涉仪对太赫兹辐射源波长和频率进行测量。搭建了法布里—珀罗干涉仪和迈克尔逊干涉仪测量太赫兹辐射源的波长和频率，对返波管振荡器太赫兹辐射源和太赫兹倍频器分别进行了波长测量。提出采用高阻硅片作为太赫兹分束器，不仅结构简单，而且实现了宽频段范围的波长和频率测量。使用单个硅片作为分束器，实现了90～800 GHz宽频段范围内太赫兹辐射源的测量并获得了理想的测量结果。通过对测量的太赫兹干涉作Fourier变换，获得太赫兹频率信息。采用太赫兹频率梳对两种太赫兹干涉仪在100 GHz和300 GHz频率进行了标定校准，实现了太赫兹干涉仪对太赫兹辐射波长的准确测量和结果校正，从而实现了太赫兹干涉仪测量结果量值溯源至国际单位制，并对测量结果进行了不确定度分析。太赫兹干涉法测量波长结构简单，使用方便，将在太赫兹波长测量中获得广泛应用。Abstract: Frequency is one of the key parameters of terahertz radiation, and accurate and traceable measurement of terahertz frequency is crucial for research and applications of terahertz technology. In order to achieve accurate measurement and traceability of terahertz laser wavelength, we have developed a terahertz interferometer to measure the wavelength and frequency of terahertz radiation sources. We constructed Fabry-Perot and Michelson interferometers to measure the wavelength and frequency of terahertz radiation sources, including backward wave oscillator terahertz sources and terahertz frequency multipliers. We propose using high-resistivity silicon plates as terahertz beam splitters, which not only have a simple structure, but also enable wide-band wavelength and frequency measurements. Using a single silicon plate as the beam splitter, we achieved ideal measurement results across a wide frequency range from 90 GHz to 800 GHz. By performing Fourier transforms on the measured terahertz interference patterns, we obtained terahertz frequency information. We calibrated the two terahertz interferometers at frequencies of 100 GHz and 300 GHz using terahertz frequency combs, enabling accurate measurement and correction of the radiation wavelength from the terahertz sources. This allowed traceability of the interferometer measurement results to the International System of Units (SI). We also performed uncertainty analysis on the measurements. Terahertz interferometry provides a simple and convenient approach to measuring terahertz wavelengths, and will find wide applications in terahertz metrology.
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图 1 法布里—珀罗干涉仪装置图
注：SP1、SP2：硅片；TS：移动平台；C：斩波器；D：热释电探测器；Lock in：锁相放大器。
Figure 1. Schematic of the terahertz Fabry-Perot interferometer
图 2 迈克尔逊干涉仪装置图
注：M1、M2：平面金属反射镜；C：斩波器；BS：分束器；D：热释电探测器；Lock in：锁相放大器。
Figure 2. Schematic of the Michelson interferometer
图 3 法布里——珀罗干涉仪测量返波管振荡器辐射频率结果
注：(a) 4372 V；(b) 4447 V；(c) 4658 V；(d) 4661 V。
Figure 3. Measurement results of the backward-wave oscillator radiation frequency using the Fabry-Perot interferometer
图 4 法布里——珀罗干涉仪对高频信号发生器倍频辐射频率测量结果
Figure 4. Measurement results of frequency multiplier radiation frequency using the Fabry-Perot interferometer
图 5 迈克尔逊干涉仪测量返波管振荡器辐射频率结果
注：(a) 4372 V；(b) 4447 V；(c) 4658 V；(d) 4661 V。
Figure 5. Measurement results of the backward-wave oscillator radiation frequency using the Michelson interferometer
图 6 迈克尔逊干涉仪对高频信号发生器倍频辐射频率测量结果
Figure 6. Measurement results of frequency multiplier radiation frequency using the Michelson interferometer
图 7 法布里——珀罗干涉仪与迈克尔逊干涉仪测量结果比较
Figure 7. Comparison of measurement results between the Fabry-Perot interferometer and the Michelson interferometer
表 1 法布里——珀罗干涉仪测量返波管振荡器频率结果
Table 1. Measurement results of the backward-wave oscillator frequency using the Fabry-Perot interferometer
Voltage/V Frequency/GHz 4372 758.0 4447 766.5 4658 777.5 4661 778.5 
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表 2 法布里——珀罗干涉仪频率测量溯源结果
Table 2. Traceable frequency measurement results using the Fabry-Perot interferometer
Frequency comb
measurement
results/GHzFabry-Perot
interferometer measurement
results/GHzCorrection factor 100.0752 99.50 1.0058 300.2256 298.0 1.0075
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表 3 法布里——珀罗干涉仪校准后的返波管振荡器频率测量结果
Table 3. Corrected frequency measurement results of the backward-wave oscillator using the Fabry-Perot interferometer
Voltage/V Measured Frequency/GHz Corrected Frequency/GHz 4372 758.0 763.0 4447 766.5 771.5 4658 777.5 782.6 4661 778.5 783.6
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表 4 迈克尔逊干涉仪测量返波管振荡器频率结果
Table 4. Measurement results of the backward-wave oscillator frequency using the Michelson interferometer
Voltage/V Frequency/GHz 4372 758.0 4447 764.5 4658 777.5 4661 778.0
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表 5 迈克尔逊干涉仪频率测量溯源结果
Table 5. Traceable frequency measurement results using the Michelson interferometer
Frequency comb measurement results/GHz Fabry-Perot interferometer measurement results/GHz Correction factor 100.0752 99.0 1.011 300.2256 297.5 1.009
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表 6 迈克尔逊干涉仪校准后的返波管振荡器频率测量结果
Table 6. Corrected frequency measurement results of the backward-wave oscillator using the Michelson interferometer
Voltage/V Measured Frequency/GHz Corrected Frequency/GHz 4372 758.0 765.6 4447 764.5 772.1 4658 777.5 785.3 4661 778.0 785.8
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表 7 太赫兹干涉仪测量波长和频率的不确定度评定表
Table 7. Uncertainty assessment table for terahertz wavelength and frequency measurements using a terahertz interferometer
Source Type Uncertainty Traceable standard B 0.10% Source stability B 0.05% Measurement repeatability A 0.05% Frequency resolution B 0.08% Stage nonlinearity B 0.05% Optical path B 0.10% Surrounding B 0.05% Combined uncertainty (k=1) B 0.19% Expanded uncertainty (k=2) B 0.38%
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