1. Introduction

Bessel-Gauss beams, also called cylindrical vector beams, are solutions of Maxwell’s equation in paraxial approximation [1, 2]. Their lowest-order modes exhibit a donut-like intensity distribution and radial or azimuthal polarization. The radially polarized beams possess interesting fundamental properties such as smaller beam waists in the focus as compared to linearly polarized Gaussian beams, and strong longitudinal field components in the focus [3–5]. Most experiments on radially polarized beams have been carried out for visible or near infrared radiation [6–8]. For terahertz (THz) radiation radially polarized beams have been studied as plasmonically guided modes on metal wires, so called Sommerfeld modes [9, 10]. An increase in coupling efficiency to the wire by two orders of magnitude has been predicted for radially polarized beams as compared to converted linearly polarized modes [11]. Photoconductive emitters consisting of a ring electrode have been modeled in detail [12, 13] and realized experimentally to generate radially polarized modes directly coupled to wire waveguides [10 , 11]. Recently also free-space propagation of radially polarized THz beams has been reported [14]. The radiation was generated via velocity mismatched optical rectification in (001) oriented ZnTe and detected with photoconductive antennas for linearly polarized radiation [14]. To our knowledge azimuthally polarized THz beams have not been realized so far.

In this paper we present a concept for microstructured photoconductive emitters and detectors for generation and optimized detection of any desired THz mode. The concept is demonstrated for the lowest order Bessel-Gauss beams, namely radially and azimuthally polarized beams. Beam profiles are measured for the divergent beams behind the emitters and for refocused beams and a quantitative analysis of the beam propagation is provided.

2. Principle and experimental setup

Patterned large-area photoconductive antennas can be used to generate THz beams of various field patterns. Hereby the field pattern is inverse to the electrode geometry. This principle is sketched in Figs. 1(a)–1(f) for antennas for radially and azimuthally polarized beams. However, the change of the bias field direction for neighboring electrode gaps would result in destructive interference of the emitted THz wavelets in the far field. This can be prevented by a second metallization covering every second gap, as shown in Fig. 1(b) and 1(e). Antennas of this principal layout have been fabricated with diameters of 2 mm. The second metallization is insulated from the first one by a layer of Si₃N₄. The antenna for radially polarized THz beams consists of 100 gaps between the electrodes, each of them having a width of 5 μm. The antenna for azimuthally polarized beams contains 92 gaps. For comparison, also periodic antennas for linearly polarized radiation [15] are produced. They consist of interdigitated electrodes with an electrode width of 5 μm, an electrode spacing of 5 μm and an active area of 1 mm². The advantages of these antennas, namely large active areas combined with high bias fields resulting in strong THz fields [16, 17], apply also to the antennas for radially and azimuthally polarized radiation. In contrast to the antennas with one ring electrode, as described in [10–13], the periodic microstructured antenna for radial polarized radiation described here provides electric bias fields of similar strength throughout the whole structure. While the bias field pattern of a single-ring antenna is well suited for matching Sommerfeld modes, the emitter periodic microstructured antenna allows exploiting the maximum excitation field strength over a large area. Additionally the bias field is forced in radial direction by the small spacing of the ring electrodes. This is expected to reduce the effect of the breaking of radial symmetry by the metallization lines, which connect all parts of the electrodes of similar polarity. The emitter antennas for all polarization modes are based on semi-insulating GaAs. For detection, antennas with the electrode geometries for linear, radial and azimuthal polarization are prepared on semi-insulating GaAs substrates implanted with N⁺. Ion implantation (dual energy implantation, 0.4 MeV, dose 1 × 10¹³ cm^-2 and 0.9 MeV, dose 3 × 10¹³ cm^-2) results in a carrier lifetime of 0.7 ps which is well suited for photoconductive detection [18, 19].

 

Fig. 1. Sketch of electrode geometry (a, d), full emitter structure (b, e) with second metallization layer (orange) and resulting mode pattern (c, f) for radial (a-c) and azimuthal (d-f) polarization. The arrows in the mode patterns indicate the electric field, the shade the intensity distribution. The rectangles in the mode patterns mark the cross section of the pattern that is studied in the experiments.

Download Full Size | PDF

A titanium-sapphire laser (wavelength 805 nm, repetition rate 832 MHz, pulse duration 40 fs) provides near-infrared pulses for excitation of the emitters and gating of the photoconductive antennas. The power and spot size (full width at half maximum, FWHM) at the antennas are 470 mW and 400 μm for the excitation beam and 80 mW and 350 μm for the gating beam, respectively. A rectangular voltage of 15 V, a duty cycle of 50 % and a frequency of 5 kHz serves as a bias for the emitters. The photocurrent induced in the detector antennas is amplified by a transimpedance amplifier and detected with a lock-in amplifier, where the bias voltage of the emitter serves as a reference. The detector can be scanned in the x direction, which denotes the horizontal direction perpendicular to the propagation direction. All scans are performed at the height of the propagation axis in order to measure cross sections of the beam profiles as indicated in Fig. 1(c) and Fig. 1(f). For one set of experiments the detector is placed in the divergent THz beam 25 mm behind the emitter. For a second set of experiments the THz beam is refocused on the detector by a set of two off-axis parabolic mirrors. The effective focal length of the mirrors is 190.5 mm and 76.2 mm for the mirror behind the emitter and in front of the detector, respectively. A mechanical delay stage is employed to adjust the time delay between the THz pulse and the gating pulse.

3. Results and discussion

Polarization sensitive detection is studied for a beam generated with an emitter of radially polarized radiation. In this experiment the beam is refocused on the detectors. THz traces measured with detectors for radial and azimuthal polarization are presented in Fig. 2(a). The detector signal from the antenna matched to the radial polarization of the beam is seven times larger than the signal detected with the antenna for azimuthal polarization. This serves as a proof of principle that the antennas are advantageous in systems for detection of changes in the mode pattern. This is an extension of the polarization sensitive THz detection, which so far has been demonstrated only for orthogonal components of linearly polarized radiation [20].

 

Fig. 2. THz transients emitted from an antenna for radially polarized beams detected with an antenna optimized for this mode (red solid) and detected with an antenna optimized for azimuthal polarization (blue dots) (a). Experimental data (dots) for detection of linearly polarized beams with respect to the azimuthal angle α of the detector for linear polarization (b). The solid line in (b) represents a cos(α) function.

Download Full Size | PDF

 

Fig 3. THz transients of the horizontally polarized component emitted by the emitter for radially polarized beams. The traces are shifted both horizontally and vertically for clarity.

Download Full Size | PDF

In the following, beam profiles are studied and a linear polarization component is measured. To this end, a microstructured detector with an electrode geometry as described in [18] is used. The polarization sensitivity of this measuring device is studied by placing the detector 25 mm behind a microstructured emitter of linearly polarized radiation and rotating the detector azimuthally along the propagation axis. In Fig. 2(b) the detected peak-to-peak THz signal is plotted against the detector angle α, where α = 0 corresponds to the electrodes of the detector being parallel to the electrodes of the emitter. The detected signal is proportional to cos(α), indicating that the detector is sensitive only for the linearly polarized component perpendicular to the direction of the electrodes.

Replacing the emitter by an antenna for radially polarized radiation, THz transients were recorded at different positions x from the propagation axis (Fig. 3). Here, x = 0 denotes the position of the propagation axis. The detector was sensitive to the horizontally polarized component of the field. The THz transients show a change in sign as the detector is moved from negative to positive values of x. Signals measured with the detector rotated by 90° (not shown) are negligible compared to the signals presented in Fig. 3. This, together with the change in sign, is in qualitative agreement with a radially polarized Bessel-Gauss mode (cf. Fig. 1(c)).

 

Fig. 4. Beam profiles for divergent beams (a) and refocused beams (b) of linear (black squares and solid lines), radial (red circles and dashed lines) and azimuthal (blue triangles and short dashed lines) polarization. The dots represent experimental data, the lines are calculated. The calculated curves are fits based on Eq. (1) for the radially and azimuthally polarized beams and fits using a Gaussian function for the linearly polarized beams. Both experimental and calculated data for the radially and azimuthally polarized focused beams are scaled vertically by a factor of 4 and 2, respectively, for clarity reasons.

Download Full Size | PDF

In Figs. 4(a) and 4(b) beam profiles for the three types of emitters are shown for the divergent beam and for the refocused beam. In all cases the detector is sensitive for linear polarization. For the emitters of linear and radial polarization the horizontal component of the field is detected, while for the emitter of azimuthal polarization the vertical component is detected. Plotted are the peak-to-peak values of the photocurrent of the THz transients. They can be well described by Gaussian functions in case of the linearly polarized beam. The electric field of the lowest order Bessel-Gauss beams for a cross-section at the height of the propagation axis has the form [1]

where E⃗₀ is a constant value for the field, J ₁ the Bessel function of the first kind of order one, d ₁ a characteristic scale for the lateral extension of the Bessel function, d ₂ the FWHM of the Gaussian function. The direction of E⃗₀ is along the x-direction for the radial polarization and perpendicular to both the x-direction and the propagation direction in case of the azimuthal polarization. The measured beam profiles for the radially and azimuthally polarized beams can be described well by these lowest order Bessel-Gauss modes (Fig. 4(a) and 4(b)). Furthermore free-space propagation and refocusing does not distort the profiles of these THz beams. The deviation of the measured beam profiles from perfect inversion symmetry with respect to x = 0 is attributed to the imperfect symmetry of the near infrared excitation beam and imperfect alignment of the excitation beam on the antennas. Hence, a hybrid mode consisting of a Bessel-Gauss mode and small contribution of a Gaussian mode is excited.

For a more quantitative description of the propagation of the beams, the THz transients are Fourier transformed and beam profiles for the divergent beam are plotted in Fig. 5(a)–5(c) for three different frequencies. For all THz modes the lower frequency components are more divergent than the higher-frequency components. The data for the beam of linear polarization are fitted with Gaussian curves with FWHM of 19.6 mm, 10.4 mm and 5.4 mm for the frequencies 0.5 THz, 1 THz and 2 THz, respectively. The data for radially and azimuthally polarized radiation are fitted using Eq. (1). For the radially polarized beam all frequency components can be well described taking the same values for d ₂ as for the fits of the linearly polarized beam and d ₁ = 1.25 d ₂ (dashed lines in Figs. 5(a)–5(c)). The curves for the azimuthally polarized beam are calculated for the same values of d ₁ as for the radially polarized beam for all frequencies. However, the profiles of the azimuthally polarized beam are somewhat wider compared to the radially polarized beam. Good agreement is found for d ₂ being 1.2 times larger than for the linearly and radially polarized beams for the frequencies 0.5 THz and 1 THz (short dashed lines in Figs. 5(a) and 5(b)). For 2 THz a good fit is obtained with a 1.5 times larger value of d ₂ (short dashed line in Fig 5(c)). The larger divergence of the azimuthally polarized beams can be explained by the different bias field distribution. In contrast to the emitters for linearly and radially polarized radiation, the strength of the electric bias field is not constant for the emitter of azimuthally polarized radiation. Instead the strength of the bias field decreases proportionally to 1/x. Hence, the THz generation is more efficient in the center of the emitter, resulting in a smaller value of the THz beam waist at the emitter. This in turn leads to more divergent beams and therefore larger values of d ₂ for the detected profiles. For higher frequencies this effect is even more pronounced, since these frequency components are enhanced for higher bias fields [15].

 

Fig. 5. Measured (dots) and calculated (lines) beam profiles for 0.5 THz (a), 1 THz (b) and 2 THz (c). Black rectangles and solid lines correspond to linear polarization, red circles and dashed lines to the radial polarization, blue triangles and dotted lines to azimuthal polarization.

Download Full Size | PDF

4. Conclusion

In conclusion, large-area microstructured emitter and detector antennas for radial and azimuthal polarization have been demonstrated. Nearly distortion-free propagation and refocusing is evidenced. The beams can be described well as lowest-order Bessel-Gauss beams with a divergence similar to linearly polarized Gaussian beams in case of radial polarization, and a slightly larger divergence in case of azimuthal polarization. The emitters and detectors, which are scalable in size, open new possibilities to study interesting properties such as longitudinal fields in the focus of freely propagating beams of radial polarization as well as optimized coupling to guided THz modes.