Kamers-Kronig关系在反射太赫兹时域光谱测量中的应用

太赫兹时域光谱技术是材料介电参数测量的重要方法，是材料研究、鉴别和分析的重要工具。太赫兹时域光谱技术是一种太赫兹频段的相干探测技术，可以同时获得太赫兹波的幅度和相位信息，通过透射测量、反射测量可获得材料的复透射率或复反射率来反演材料的电磁参数。在实际中，大多数被测材料太赫兹波无法穿透，或者不满足透射材料参数反演需要的弱吸收近似，因此反射测量更具应用价值。在已发表的研究结果中，研究人员仍普遍采用透射测量的方案，很少见使用反射测量方案获取材料参数。究其原因，在反射测量时，由于样品和参考板位置的放置误差很难消除，从而导致无法准确提取反射相位。将光学领域广泛使用的Kamers-Kronig关系应用于太赫兹时域光谱系统反射测量中，以解决反射测量中无法准确获得相位信息从而无法提取介电参数的问题。为了验证Kamers-Kronig关系的准确性，一方面，通过透射、反射方法分别测量硅材料的复透射率、复反射率并反演了其材料参数，两者的反演结果一致性较好。另一方面，利用同一组硅的反射测量数据分别用Kamers-Kronig关系和最大熵法对其材料参数进行反演，两种处理方法也可以实现相互印证，进一步确保了提取数据的可靠性。对Kamers-Kronig关系和最大熵方法所取得的结果进行了对比讨论，通过Kamers-Kriong关系和最大熵法获得的折射率、消光系数以及复介电参数结果一致性较好，且基于Kamers-Kriong反演了一种精神药物的吸收谱，与透射结果做了比对。结果表明，Kamers-Kronig关系非常适合提取材料光学参数和吸收谱，且相比最大熵法其普适性更强，甚至对于无法获取相位信息的非相干测量系统依然适用，但该方法需要整个频段的反射率幅度信息，对于没有测量的频率需要进行外推，对于反射率随频率变化不大的物质更加适用。该研究成果对于利用反射式太赫兹时域光谱系统获取材料太赫兹波段的光学参数提供了一种有效方法，可解决绝大数情况下反射测量参数提取问题，对太赫兹时域光谱技术的实际应用具有重要意义。

The Application of Kamers-Kronig Relation in Time Domain Spectral Measurement of Reflection Terahertz

Terahertz timedomain spectroscopy(THzTDS)technology is extremely significant in measuring the dielectric parameters of materials in the Terahertz band,and it is also important for analyzation and identification of these materials.The THzTDS technology is based on coherent detection,which can measure the amplitude and phase of terahertz wave simultaneously.The electromagnetic parameters of materials can be retrieved from the complex transmittance or complex reflectivity which measured by transmission or reflection of the materials.In most practical application,the refractive index and extinction coefficient cannot be obtained when materials are hard to penetrated by THz wave,and the weak absorption approximation condition cannot be met in the measurement.Therefore,reflection measurement has more application value in this field.However,in the published research results,researchers still generally use the transmission measurement scheme and rarely use the reflection scheme to obtain the material parameters.The reason is that the position error of the sample in the reflection measurement is difficult to eliminate,so it is impossible to extract the reflection phase accurately.In this paper,the Kamers-Kronig relation,which is widely used in the field of optics,is applied to the reflection measurement of terahertz timedomain spectral system to solve the problem that the phase information cannot be obtained accurately and the dielectric parameters cannot be extracted correctly.In order to verify the accuracy of the Kamers-Kronig relationship,on the one hand,the complex transmittance and reflectivity of silicon materials are measured by transmission detection and reflection detection respectively,and then the material parameters are inversed.The results indicated that they have a good consistency.On the other hand,Kamers-Kronig relation and maximum entropy method(MEM)are used to inverse the material parameters of the silicon reflection measurement data,and these two methods can also agree with each other,which ensuring the reliability of the extracted data.Finally,the results obtained by the Kamers-Kronig relation and the maximum entropy method are compared and discussed in this paper,respectively.Compared with the maximum entropy method,The Kamers-Kronig relation is more applicable in the extraction of material parameters and absorption spectrum.Therefore,the Kamers-Kronig relation is not only suitable for the coherent measurement,but also for the incoherent measurement in which the phase information cannot obtain.However,the method needs the reflectivity amplitude information of the whole frequency band,the frequency which we can’t measure needs to be extrapolated,so it is more suitable for the matter whose reflectivity changes little with the frequency.This paper provides an effective method for obtaining the terahertz optical parameters of materials by using the reflection THzTDS system,which can solve the problem of extracting the reflection measurement parameters in the vast number of cases.It is of great significance to the application of Terahertz Technology.