Vector measurement and performance tuning of a terahertz bottle beam-4
The properties of the THz bottle beam are also sensitively dependent on the base angle of the Teflon axicon. To check this point, the Teflon axicons with α = 15°, 20°, 25° and the silicon lens with f = 8 mm are selected to realize discrepant THz bottle beams. The Z-scan characterization method is operated to record the propagations of these THz bottle beams and their divergences are compared in detail. To acquire the complete optical barriers of these THz beams, the distances between the Teflon axicons with α = 15°, 20°, 25° and the silicon lens are carefully adjusted to 44 mm, 35 mm, 29 mm, respectively. Figure 7a exhibits the longitudinal amplitude patterns of Ex with α = 15°, 20°, 25° at 0.75 THz. For comparison, these images are normalized with respect to the amplitude maximum with α = 15°. Clearly, with increasing the base angle of the Teflon axicon, the intensity of the optical barrier is gradually attenuated and both of the transverse size and the longitudinal distance of the THz bottle beam are progressively magnified. To quantitively analyze characteristics differences between these THz beams, the amplitude curves with α = 15°, 20°, 25° are separately extracted from Fig. 7a along the lines of z = 0 mm and x = 0 mm, as shown in Fig. 7c,e. The measured results show that the radiuses of these THz annular amplitudes are 0.89 mm, 1.23 mm, 1.68 mm and the longitudinal distances of these THz bottle beams are 4.5 mm, 6.0 mm, 8.5 mm, respectively. According to Eqs (1–2) the calculated R and Δz are separately 0.93 mm, 1.29 mm, 1.70 mm as well as 4.45 mm, 6.30 mm, 8.49 mm, which are generally consistent with the measured results. To understand the phenomena, a Teflon axicon with a larger base angle can induce a bigger deflection angle between the z axis and the refracted THz beam. When these refracted THz beams emerge through the silicon lens, the superposition region of the converging or diverging THz beams is shrunk before or after the focal plane so that the intensity of the optical barrier is weakened and the central dark region of the THz bottle beam is enlarged. To further confirm this point, the longitudinal wrapped phase cross-sections of the Ex components with α = 15°, 20°, 25° are acquired, as shown in Fig. 7b. It can be seen that the spatial interval between the converging THz beams gradually increases at z = −4.5 mm and the superposition region between the diverging THz beams continuously reduces at z = 4.5 mm with increasing α. Specially, the part regions of the converging and diverging THz beams with α = 25° have gone beyond the view field of the imaging system. The reason may also results in the intensity attenuation of the optical barrier to a certain degree. The phase curves with α = 15°, 20°, 25° are extracted from Fig. 7b along the lines of z = 0 mm, as shown in Fig. 7d. The measured results manifest that the positions of the phase flat regions with α = 15°, 20°, 25° are approximately x = ±0.89 mm, ±1.23 mm, ±1.68 mm. In these phase patterns, the longitudinal phase curves are obtained on the corresponding amplitude maximal positions, as shown in Fig. 7f. For clarity, the original values of these curves at z = 0 mm are fixed as 0. Obviously, the phase evolutions with α = 15°, 20°, 25° manifest the almost same Gouy phase shifts, which are the phase differences of 0.5π between z = −4.5 mm and 4.5 mm. The reason can be explained that all of THz beams refracted by the Teflon axicons with various base angles are focused by the silicon lens with f = 8 mm. After the silicon lens, these out-going THz beams with different α undergo the similar converging process, so their longitudinal phase evolutions are almost identical. In addition, it can be seen that the Gouy phase shift of a bottle beam is only half of that of a converging Gaussian beam24. To understand the phenomenon, a transmitted THz Bessel beam from the silicon lens is only one-dimensionally focused on each radial cross-section along the propagation direction, so that a THz light ring on the focal plane and a Gouy phase shift of 0.5π are formed. Besides, there are some oscillations on the phase curve with α = 15°, which may be caused by the more significant interferences of the converging or diverging THz beams with a smaller α.
Variance of the THz bottle beam with adjusting the base angle of the Teflon axicon. (a,b)Present the longitudinal Ex amplitude and wrapped phase images when the silicon lens with the focal length of f = 8 mm and the Teflon axicons with the base angles of α = 15°, 20°, 25° are picked to form the THz bottle beams. (c,e) Give the amplitude curves with α = 15°, 20°, 25°. These curves are extracted along the lines of z = 0 mm and x = 0 mm in (a). (d) Shows the phase curves with α = 15°, 20°, 25°, which are extracted along the lines of z = 0 in (b). (f)Exhibits the longitudinal phase curves which are extracted from (b) on the amplitude maximal positions with α = 15°, 20°, 25°.
Finally, the influence of the focal length of the silicon lens to the THz bottle beam is also investigated. The Teflon axicon with α = 20° and the silicon lens with f = 11 mm are picked to generate the THz bottle beam. The distance between them is carefully adjusted to 39 mm for ensuring a complete optical barrier. The Z-scan characterization method is operated to reconstruct the propagation of the THz bottle beam. Herein, the scan range is from −6.5 mm to 6.5 mm and the scanning step is 0.5 mm. Figure 8b exhibits the longitudinal amplitude and wrapped phase cross-sections of Ex with 0.75 THz. For comparison, the corresponding longitudinal Ex amplitude and wrapped phase patterns of the THz bottle beam with α = 20° and f = 8 mm are also given in Fig. 8a. Comparing these amplitude images, the intensity of the optical barrier is attenuated and the scale of the central dark focus is magnified for the THz bottle beam formed by using a silicon lens with a longer focal length. From these phase images, it can be seen that the phase variation tendency of the THz bottle beam is slower with increasing f. The reason inducing these phenomena is easy to understand. When a silicon lens with a longer focal length is adopted, the THz beam experiences a smoother focusing process so that the weaker optical barrier is formed. To quantitively observe the variation of the THz bottle beam, the amplitude curves are acquired along the transverse (z = 0 mm) and longitudinal (x = 0 mm) directions, as shown in Fig. 8c,e. The radiuses of the THz light rings with f = 8 mm and 11 mm are 1.23 mm and 1.73 mm on their focal planes, respectively. The longitudinal distances of these central dark regions are 6.0 mm and 12.0 mm for the THz bottle beams with f = 8 mm and 11 mm. Utilizing Eqs (1–2), the calculated R and Δz with f = 8 mm and 11 mm are 1.29 mm, 6.30 mm as well as 1.78 mm, 12.24 mm, which are generally in accordance with the measured results. The transverse phase curves with f = 8 mm and 11 mm along the lines of z = 0 mm are obtained and shown in Fig. 8d. It can be observed that the positions of the phase flat regions with f = 8 mm and 11 mm are approximately x = ±1.23 mm and ±1.73 mm. Besides, the phase flat region with a larger f obviously exhibits a broader width. The phase flat regions with f = 8 mm and 11 mm separately possess the lateral scales of 0.67 mm and 1.06 mm. On the corresponding amplitude maximal positions, the longitudinal phase curves with f = 8 mm and 11 mm are also acquired and compared. In Fig. 8f, it can be observed that the phase difference with f = 11 mm between z = −6.5 mm and 6.5 mm also reaches 0.5π and shows a smoother variation tendency than the Gouy phase shift with f = 8 mm. The phenomena manifest that when a silicon lens with a longer focal length is chosen, the focusing THz beam possesses a longer focal depth, a larger focal spot, and a slower phase evolution, so that a bigger central dark focus, a thicker light ring, and a smoother Gouy phase shift are generated in the formed THz bottle beam. Actually, the characteristics are similar to the converging process of a THz Gaussian beam24. According to the discussion all above, it can be concluded that an axicon with a smaller base angle and a lens with a shorter focal length should be picked as the wave font modulators for forming a more compact optical barrier.
