Discussion

Herein, we still want to simply discuss similarities and differences between THz special beams carrying orbital angular momentum (OAM) and the THz bottle beam. Currently, various THz beams carrying OAM have been paid more and more attentions due to their important application potentials in THz imaging and communications, such as Bessel, Laguerre-Gaussian, and Airy beams with high-order topological charges. Analogous to the THz bottle beam, these THz beams also have a hollow-core intensity25. However, the discrepancy between these THz beams and the THz bottle beam is that the central intensity nulls of these THz beams are originated from their phase singularities, so their central zero-amplitude zones are in two dimensions. Meanwhile, the dark focus of the THz bottle beam is due to the interference effect of converging or diverging THz beams so that the THz optical capsule is formed in three dimensions. Therefore, researchers prefer to classify these THz beams carrying OAM as the THz hollow beam. Actually, the optical bottle beam carrying OAM has been also investigated in 2015. Interestingly, the radius of the central annular amplitude is fixed with varying the topological charge for an optical bottle beam carrying OAM, so this kind of optical beam is called as “perfect vortex beam”21. To be honest, diffraction characteristics of these special THz beams have been underutilized, which leaves much room for the development of the future THz technology.

In conclusion, the THz bottle beam is generated by utilizing a Teflon axicon and a silicon lens. The complex field of the THz bottle beam are coherently characterized by applying the THz imaging system with a focal-plane array and the evolution process of the THz field is detailedly recorded by implementing the Z-scan measurement. For a linearly polarized THz bottle beam, Ex exhibits the amplitude distribution of a Bessel-like beam and the doughnut-shaped optical barrier on the two terminals and the intermediate section of the optical bottle. Besides, the Ex phase pattern shows the converging as well as diverging processes of the THz beam refracted by the Teflon axicon after passing through the silicon lens and manifests the formation origin of the THz bottle beam. Besides, the Ez component of the THz bottle beam is measured and analyzed by applying the vector measurement function of the THz imaging system. The Ez component with a linear or a circular polarization separately shows a double-lobe characteristics or a vortex pattern. By adopting the vectorial diffraction algorithm, the complex field characteristics of the Ex and Ez components are exactly simulated. Finally, performance tuning of the THz bottle beam is achieved by adjusting the parameters of the Teflon axicon and the silicon lens. The switch of the optical barrier can be easily controlled by varying distance the between the Teflon axicon and the silicon lens. With decreasing the base angle of the Teflon axicon or the focal length of the silicon lens, the THz bottle beam shows a stronger optical barrier and a smaller central dark focus. In a nutshell, this work describes the vector characteristics of the THz bottle beam in detail and achieves the modulations to the features of the THz beam. We consider that the work is helpful for the application and development of the THz technology in particle manipulation and microscopy. In addition, these experimental laws and theoretical discussions can be readily transferred to the infrared, visible, and other frequency ranges.

Methods

To observe the characteristics of a THz bottle beam, a THz imaging system with a focal-plane array is utilized to acquire the complex field of the THz beam, including amplitude and phase information. Figure 1apresents the schematics of the experimental setup. The light source is a Spectra-Physics femtosecond laser amplifier with a central wavelength of 800 nm, a pulse duration of 50 fs, a repetition ratio of 1 kHz, and an average power of 700 mW. The incoming laser is divided into the exciting and detecting beams for the generation and detection of the THz radiation. The average powers of the exciting and detecting beams are 690 mW and 10 mW, respectively. Firstly, a concave lens (L1) with a focal length of 50 mm is used to expand the exciting beam and a <110> ZnTe crystal with a thickness of 3 mm is chosen as the THz source. After the exciting beam passing through the ZnTe crystal, a THz beam with an x-linear polarization is generated by the optical rectification26. Then, the THz beam is collimated by a parabolic mirror (PM) with a focal length of 100 mm for forming a THz quasi-plane wave. The collimated THz beam possesses a diameter of 14 mm. A Teflon axicon and a silicon lens are used as the wave front modulators for generating a THz bottle beam, as shown in Fig. 1b. The incident THz beam successively passes through them to form the peculiar THz field. The out-going THz field illuminates a sensor crystal for detecting the complex THz field. In the path of the detecting beam, a polarizer (P) is used to ensure the probe polarization. The detecting beam is reflected onto the sensor crystal by a non-polarization beam splitter with a 50/50 ratio. In the sensor crystal, the probe polarization is modulated by the THz field to carry the two-dimensional THz information due to the Pockels effect27. Then, an imaging module is adopted to receive the reflected detecting beam, which is composed of a lens (L2), a quarter wave plate (QWP), a Wollaston prism (PBS), a lens (L3), and a CCD camera. A mechanical chopper is used to modulate the output frequency of the exciting beam. A balanced detection method28 and a dynamics subtraction technique29 are utilized to remove the background intensity of the detecting beam. A series of THz temporal images are acquired by adjusting the relative delay between the THz and detecting beams and the THz images in the frequency domain are extracted by operating the Fourier transformation.

To reconstruct the evolution process of a THz bottle beam, the Teflon axicon and the silicon lens are mounted on a motorized translation stage to fulfill a Z-scan measurement. The focal point of the silicon lens is viewed as the base point. The diffraction process of the THz beam is recorded from z = −4.5 mm to z = 4.5 mm and the scanning step is set as 0.5 mm. The advantage of the measurement scheme is that the optical path of the THz beam is fixed, so the linear phase term exp(jkz) of the THz wave is negligible. Besides, a quartz TQWP with a central wavelength of 385 μm and a bandwidth of 200 μm is utilized to adjust the THz polarization for observing the discrepancies between the linearly and circularly polarized THz bottle beams.

To comprehensively observe the vector characteristics of a THz bottle beam, the different polarization components need to be separately measured, including the transverse (Ex) and longitudinal (Ez) components. In the experiment, a ZnTe crystal with a <110> crystalline orientation and a 1 mm thickness is picked up as the sensor crystal to measure Ex. The angle between the <001> axis of the crystal and the polarization direction of the detecting beam and is fixed as 0° to maximize the detection efficiency30. To acquire the Ez component, a ZnTe crystal with a <100> crystalline orientation and a 1 mm thickness is chosen as the sensor crystal. The angle between the <010> axis of the crystal and the polarization direction of the detecting beam is adjusted as 45° for optimizing the detection efficiency31. Herein, it should be noted that both of <110> and <100> ZnTe crystals have the identical detection sensitivities to the THz field32.