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Abstract
In this work we demonstrate a frequency-tunable terahertz (THz) Bessel beam with zero- and first- order modes and orbital angular momentum, by utilizing a Tsurupica Axicon lens in combination with a picosecond difference frequency generation laser. This system enabled the selective generation of zero- or first-order THz Bessel beams with frequency-tunability across the range 3–7 THz.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Studies of electromagnetic waves in the frequency range (0.1–30 THz), i.e. terahertz (THz) waves are ever-advancing and with the development of new, novel THz sources and detectors, a wide variety of exotic, fundamental phenomena and advanced technologies have emerged. These include breaking of optical selection rules [1], high harmonic generation based on nonlinear optical responses [2,3], THz biotechnologies [4,5], ultrahigh data capacity telecommunications beyond 5G [6,7], coherence tomography [8], and quantum sensing [9]. Many of these new insights and applications are enabled by the fact that THz waves are capable of driving vibrations and stretching modes of molecular aggregations and lattice oscillations in solids.
Structured light beams, such as Laguerre-Gaussian (LG) modes [10,11], Bessel beams [12,13] and Airy beams [14], have been intensely studied and applied across a myriad of applications in the visible and a near-infrared wavelength regions. For instance, LG modes, possessing an annular intensity profile and orbital angular momentum (OAM) (characterized by a topological charge ℓ) owing to their spiral wavefront, provide advanced optical manipulation with the freedom of orbital motion [15], space division multiplexing optical communications [16], high spatial resolution microscopy which exceeds the diffraction limit [17], chiral material formation [18,19], and optical sorting of metallic and dielectric nanoparticles [20]. Also, Bessel beams exhibit non-diffraction properties and self-healing effects, enabling the creation of super-resolution focused spots with a long penetration depth [21]. Such spots have been applied to the development of high-resolution three-dimensional imaging (light-sheet imaging) [22], micro-fabrication of through-holes with high aspect ratio [23], optical coherence tomography with a long penetration depth (OCT) [24], and centimeter-scale self-written fibers based on photo-polymerization [25].
Similar to the innovations developed in the visible and near-infrared wavelength ranges, the application of structured light beams in the THz region (THz structured light beams), should also open the door towards advanced THz technologies. Here innovations, such as three-dimensional THz spectroscopy with deep-focal imaging, THz coherent tomography with a long penetration depth, and long distance THz communications [26], may be realized.
To date, we have successfully applied a Tsurupica spiral phase plate (SPP) to the generation of THz optical vortex beams [27] and we have demonstrated “super-resolution” THz imaging [28] in bilayer graphene through the application of an intense THz vortex pulse. Furthermore, we have also developed frequency-tunable THz optical vortex sources with high beam quality which operate in the frequency range of 2–6 THz [29].
The most common method of generating a Bessel beam is through the use of an axicon conical lens, however, there are few practical THz axicon lenses due to strong absorption and large dispersion of many optical materials in the THz frequency region [30–33]. While silicon binary phase axicons [34,35] and axicon lenses formed from Teflon [36] have been reported, they are designed for specific THz frequencies, and do not operate efficiently across a broad THz frequency range. Plasmonic metasurfaces and planar structures are alternative methods of generating THz Bessel beams [26,37], however, they are also designed for specific frequencies.
In this paper, we propose a new THz axicon lens formed from Tsurupica polymer which features high transmission and low frequency dispersion across the entire THz frequency region, and thereby facilitates the generation of frequency-tunable THz Bessel beams. We also detail the generation of higher-order Bessel beams with OAM.
2. Principle of operation and optical design of the Tsurupica axicon lens
Bessel beams which are eigen functions of variables separation in the Helmholtz equation, possesses unique properties, such as non-diffraction, and self-healing [12,13]. Figures 1(a) and 1(b) illustrate a schematic and a photograph of the Tsurupica axicon lens designed and fabricated in this work. The depth of focus (DOF) and central bright spot radius ${r_\ell }$ of the Bessel beam generated by the axicon lens are defined as follows:
where D is the diameter of the beam incident on the axicon lens, $\alpha $ is axicon angle, ${J_\ell }$ is the first zero point of the ℓth order Bessel function, and n is the refractive index of the lens medium. Figure 1(c) shows the optical properties of Tsurupica (thickness: 2 mm) and Teflon (which is the material used to fabricate conventional THz axicon lenses). As mentioned in our previous publications [27,28], Tsurupica exhibits high transmission (>50%) and a constant refractive index (∼1.52) with extremely low frequency dispersion (dn/dν = −5.1×10−4 / THz), thereby enabling the generation of THz Bessel beams in the entire THz frequency region.
Fig. 1. (a) Schematic diagram; and (b) photograph of a fabricated Tsurupica axicon lens.
(c) Optical transmittance of Tsurupica and Teflon substrates of 2 mm thickness, measured using Fourier transform infrared spectroscopy. (d) False-color image showing the spatial intensity profile of a 532 nm Bessel beam generated using a fabricated Tsurupica axicon lens.
A range of Tsurupica axicon lenses with axicon angles of 10, 15, 20, and 25 degrees were fabricated using mechanical polishing. The polishing process was refined to ensure that the incident surface roughnesses were small compared to THz wave wavelength (they were measured to be less than 0.05 µm and 0.3 µm respectively). The optical quality of the fabricated lenses were so high as to enable the generation of Bessel beams using a green laser diode (Fig. 1(d)), hence ensuring that the fabricated lenses will also work well for the generation of THz Bessel beams.
3. Experiments
The experimental setup of our THz Bessel beam source, comprising a 1.5 µm band dual-wavelength picosecond laser pumped 4’-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) difference frequency generator (DAST-DFG) in combination with a Tsurupica axicon lens, is shown in Fig. 2. The THz laser beam generated by the DAST-DFG had a Gaussian spatial profile and was tunable across a frequency range of 0.1 - 13.5 THz. This beam was collimated by a parabolic gold mirror (f = 25.4 mm) or plano-convex Tsurupica lens (f = 30 mm), and it was then converted into a Bessel beam using a fabricated Tsurupica axicon lens. Generation of a THz LG mode with high mode purity (estimated mode purity of >90%) was allowed by employing a difference frequency generator with soft aperture effects owing to the spatial overlap between Gaussian and optical vortex pump beams, as mentioned in our previous report [29]. The spatial form and output power of the generated Bessel beam were measured using a THz camera (NEC: IRV-T0831) and a room-temperature detector (Gentec: THZ5B-BL), respectively.
Fig. 2. Experimental setup for the generation of frequency-tunable zero- and high-order THz Bessel beams via a Tsurupica axicon lens.
Figure 3 (a-d) shows the spatial form of the generated THz Bessel beams at 4 THz by using axicon lenses with axicon angles of $\alpha = $ 10°, 15°, 20°, and 25°. The experimentally observed bright spot radius ${r_0}$ of the generated Bessel beam with multiple-rings was inversely proportional to the axicon angle, and followed a fit calculated using Eq. (2); both the experimental data and calculated fit are shown in Fig. 3(e). The intensity spatial profile of 4 THz Bessel beam is plotted as shown in Fig. 3(f). The experimental plots are well fitted by the 0-order Bessel function, ensuring that the Tsurupica axicon lens works well to generate a THz Bessel beam. The maximum average power of the generated Bessel beam was measured to be 3 µW at 4 THz.
Fig. 3. (a-d) Spatial intensity profile of zero-order THz Bessel beams generated using Tsurupica axicon lenses with axicon angles of 10, 15, 20 and 25 degrees. (e) Plot of the experimentally measured and theoretically calculated THz Bessel beam diameters for different axicon angles. (f) Intensity spatial profile of 4 THz Bessel beam at Fig. 3 (b).
It should be noted that the generated THz Bessel beams possessed excellent non-diffraction characteristics with a depth-of-field extending beyond 15 mm, which is approximately 10 times longer than that of the THz Gaussian beam. Images of the beam propagation of both the generated Bessel and Gaussian beams are shown in Fig. 4. Zemanek et al. pointed out on-axis intensity oscillation effects of the Bessel beam in the visible region owing to diffraction effects on a round tip-shape of an axicon lens [38]. The fabrication error (0.3 µm) of the THz axicon lens used in the experiments was only less than one-hundredth of the THz wavelength, thus, such effects were negligible.
Fig. 4. Measurements of the beam propagation characteristics of (a) a Gaussian beam; and (b) a Bessel beam at 4 THz. The normalized beam power is plotted as a function of transverse dimension (x-axis) and propagation distance (z-axis).
The spatial forms of THz Bessel beams produced at a range of THz frequencies are summarized in Fig. 5. In this case, an axicon with a fixed axicon angle of α = 15° was used. The system enabled the THz Bessel beam generation within the frequency range of 3–7 THz, its tunability was limited to the output spectrum of DAST-DFG. It is worth mentioning that our proposed Tsurupica axicon lens itself is available in the entire THz range from 0.1 to 12 THz.
Fig. 5. (a) Spatial intensity profiles of Bessel beams at different THz frequencies (in the range 3–7 THz), generated using a fabricated Tsurupica axicon lens with α =15°. (b) Comparison of the experimentally measured and theoretically calculated beam diameters of the generated THz Bessel beams as a function of the laser frequency.
The experimentally measured beam diameter, along with the beam diameter calculated using Eq. (2), are plotted in Fig. 5(b). Here, excellent correlation is observed between the experimental and calculated results. These results show that as the frequency of the incident THz laser beam increases, the diameter of the generated Bessel beam decreases. Such a characteristic must be kept in mind when pursuing applications of such Bessel beams in conjunction with frequency-tunability.
It should be noted that all of the Bessel beams presented and discussed above are zero-order and possess a topological charge of ℓ = 0. To generate a first-order Bessel beam with a topological charge of ℓ = 1, it is necessary to utilize a THz vortex beam which carries a topological charge of ℓ = 1. To this end, we applied our THz vortex source based on a soft-aperture difference frequency generator to generate the desired THz vortex beam [29]. This system is capable of generating a high-quality vortex beam, which is frequency-tunable across the range 3–6 THz. The vortex beam generated from this system was collimated using a plano-convex Tsurupica lens, instead of the gold parabolic mirror, to avoid breaking of the cylindrical symmetry of the beam, which may arise from astigmatic aberration. The fabricated Tsurupica axicon lenses were then used to convert the THz vortex beam into a first-order Bessel beam. Figure 6 shows the spatial forms of both the incident THz vortex beams and the resulting THz Bessel beams generated at a range of THz frequencies. The spatial profile of the generated first-order Bessel beams exhibit a central dark core with multiple rings. These generated beams also exhibit a strong non-diffractive property, as evidenced by a long depth-of-focus which was ∼10 times longer than that of the original vortex beams. A comparison of the DOF of the incident vortex beam and generated Bessel beam at a THz frequency of 4 THz is shown in Fig. 7.
Fig. 6. Images showing spatial beam profiles of THz vortex beams (upper images) and corresponding Bessel beams (lower images) generated using a Tsurupica axicon lens (axicon angle α = 15°). Images are shown for beams with topological charge ℓ = 1 and for frequencies in the range 3–6 THz.
Fig. 7. Measurements of the beam propagation characteristics of (a) a vortex beam; and (b) a Bessel beam at 4 THz. The normalized beam power is plotted as a function of transverse dimension (x-axis) and propagation distance (z-axis).
The application of a Tsurupica spiral phase plate (SPP) and Tsurupica axicon lens for the generation of a first-order Bessel beam with a topological charge of ℓ = 1 was also investigated. While this approach worked, it was extremely sensitive to off-axis misalignment which would result in breaking of the beam cylindrical symmetry. The THz Bessel beams generated using this approach also exhibited only a few rings, a characteristic which indicates a degradation of the Bessel beams non-diffraction property. A comparison of the spatial profile of the THz Bessel beam at 4 THz generated using this approach, in comparison to the combination of the vortex THz beam and Tsurupica axicon lens as discussed in the previous paragraph is shown in Fig. 8. Here, it is clear that the latter approach produces a Bessel beam with far greater uniformity and fidelity.
Fig. 8. Spatial intensity profile of first-order Bessel beams at 4 THz generated by (a) a combination of a Tsurupica SPP and a Tsurupica axicon lens; and (b) a THz vortex DAST-DFG beam with a Tsurupica axicon lens. [Note that the image in (b) is the same as that presented in Fig. 6]
4. Conclusion
We have successfully developed and applied a Tsurupica axicon lens to the generation of THz Bessel beams. The Tsurupica axicon lens features low dispersion and high transmission in the THz region has enabled the generation of both zero- and high- order THz Bessel beams with frequency-tunability across the range 3–7 THz. The maximum average power of the generated Bessel beam was measured to be ∼3 µW at 4 THz. The generated Bessel beams exhibited high beam quality and a very long depth-of-focus, far exceeding that of the original beams incident on the axicon lens. We anticipate that such frequency-tunable Bessel beams with OAM will be an enabling technology for novel, advanced investigations into THz-based fundamental science and technologies, such as OAM spectroscopy [39], OAM dichroism [40,41], ultrahigh capacity communications beyond 5G, and high-resolution three-dimensional multi-spectroscopy. We also believe that this THz Bessel beam source is ideal for the generation of so-called “perfect vortex beams” using Fourier optics [42–44].
Funding
Core Research for Evolutional Science and Technology (JPMJCR1903); Japan Society for the Promotion of Science (JP18H03884, JP19K05299).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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