The demand for compact terahertz (THz) components is continuously increasing due to emerged new applications of THz science and technology for art conservation, gas spectroscopy, astronomy, security screening, material research, medicine, etc. [1–3]. Only a limited kind of materials is suitable for the development of optical components for the upper THz band, namely above 1 THz [4]. On the other hand, either the available mechanical instruments or the multi-step photolithography-assisted ion etching and chemical treatment set the limits for new developments and prototyping [5–7]. On top of that, it requires high precision and skilled labor to ensure an accuracy better than one-tenth of the wavelength which makes developments expensive and slow. So far, THz lenses processed on silicon with a 25 mm focal length and 30 mm diameter for 1 THz have been demonstrated with a moderate focusing performance [8].

A huge variety of THz systems employs different THz lenses made of metal reflectors (reflection mode) or dielectric refractors (transmission mode) which are usually bulky and, therefore, require for alternative solutions. Diffractive lenses are more compact and provide an integration-ready solution which could be used to replace bulky optics in the THz systems. However, it is difficult and expensive to produce diffractive lenses and tiny corrugated horn antennas for the upper band of the THz range, counting on the usage of very precise milling machinery [6,7]. The silicon lens based on a dielectric metasurface with the overall efficiency of 24% has been recently demonstrated [9]. The efficiency for linearly polarized beams can be further increased employing a tri-layer metasurface [10]; however, the efficiency remains a major issue in many beamforming structures [11].

In this Letter, diffractive lenses of different materials were developed for the astronomically important frequency of 4.7 THz by employing a mask-less direct laser ablation (DLA) technology. On the one hand, the Soret zone plate lens (SZPL) composed of concentric Fresnel zone rings that were alternatively transparent (open) and reflecting (opaque) was studied. On the other hand, the multi-level phase-correcting Fresnel lens (MPFL) was considered and it was designed by replacing the opaque zones with transmitting phase-reversing rings in order to improve the focusing efficiency of the lens [12].

The diameter $D=25\mathrm{mm}$ and the focal depth $f=50\mathrm{mm}$, leading to an F-number of $\#/f=0.5$, were selected as the initial design parameters for the research employing the quantum cascade laser (QCL) operating at a frequency of 4.745 THz ($\lambda =63.18\mathrm{\mu m}$). The focal length was several hundred times the wavelength ($f/\lambda \approx 791$) and allowed us to apply analyses of focal region properties or far-field patterns [12]. From the theoretical point of view, the samples were designed to provide the numerical aperture of 0.243, an Airy disk diameter (minimum spot size) of 318 μm (308 μm), a Gaussian beam waist of 2 $w_0=164\mathrm{\mu m}$, a Rayleigh range of 1.1 mm, and a focusing gain of about 28 dB in the case of a SZPL sample. The focusing gain ($G$) was defined as the ratio of the focused beam intensity to the intensity at the focal plane without the lens [13].

The SZPL samples were fabricated of a $16.5\pm 2.2\mathrm{\mu m}$ thick molybdenum foil. The mechanical stability of the foil after DLA processing was found to be sufficient from our previous experiments [14]. This thickness of a free standing metal foil was also confirmed to be suitable for the development of efficient diffractive optics for the THz range. The samples were fabricated employing a second-harmonic beam of the femtosecond laser Pharos from Light Conversion (300 fs, 100 kHz, 515 nm) focused with a 10 mm focal length objective and scanned with a linear two-axis positioning stage from Aerotech. Smooth-cut lines were achieved by using a spot size of 5.6 μm, a pulse density of 40 000 pulses/mm, and a fluence of $17.9\mathrm{J}/{\mathrm{cm}}^2$, and by repeating each scan five times.

The MPFL samples were patterned on a $500\pm 25\mathrm{\mu m}$ thick and double-side polished high resistivity float zone silicon wafer with (100) orientation. It demonstrated a resistivity of 100 kΩ cm, a refractive index of 3.46, and a small absorption coefficient possessing an average transmission at the target wavelength of about 50%. In this case, a beam of the picosecond laser Atlantic-60 from Ekspla (13 ps, 100 kHz, 532 nm) focused with the telecentric 80 mm focal length objective was scanned using a hurrySCAN 14 scanner from SCANLAB. Exploring our previous experience, the MPFL with eight phase levels was considered as a good trade-off between fabrication time, design complexity, and the focusing performance [4]. The samples with eight (MPFL8) and two (MPFL2) phase levels were patterned with a beam spot size of about 28 and 13 μm, respectively. It is worth noting that the MPFL8 sample consisted of the largest amount of sub-zones equal to 200 from which the smallest size was about 32 μm. In order to achieve a 300 nm material layer removal rate in a single scan, the processing parameters were used as follows: $4\mathrm{J}/{\mathrm{cm}}^2$ fluence and 65% pulse overlap for the MPFL2 sample, and $1.6\mathrm{J}/{\mathrm{cm}}^2$ and 82% for the MPFL8 sample, respectively.

A stylus profiler (Dektak 150) and scanning electron microscope (SEM, JEOL JSM) were used to characterize the sample morphology. The SEM images of the sample and the step-profile scanned in the center are shown in Fig. 1. The surface roughness (Ra) after laser patterning of the silicon was below 500 nm, which is considerably smaller than the design wavelength of 63 μm.

 

Fig. 1. SEM image of the MPFL2 sample fabricated by the DLA technology. Insets: the depth profile and the surface morphology at different zones of the sample. The black and red lines present measured and calculated depth profiles.

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The focusing performance of the lens was measured using the experimental setup shown in Fig. 2. The QCL was operating in a laboratory version of the system used in the GREAT spectrometer on board of SOFIA [15] and, therefore, was very similar. At the current temperature setting used for lens characterization, the QCL emitted a single frequency of 4.745 THz. The iris diaphragm $P$ was employed for spatial filtering of the QCL emission. The transmitted THz radiation was measured with an uncooled real-time microbolometric camera (pixel size of 25 μm) and, alternatively, with a Golay cell detector, if the sensitivity of the camera was not sufficient. A pinhole of 1 mm diameter was used in front of the Golay in order to provide an appropriate spatial resolution for the measurements.

 

Fig. 2. Schematic illustration of the experimental setup for the performance measurements of the diffractive lens (L) which was facing toward the THz detector.

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The measured beam divergence (see Fig. 3) demonstrated the Gaussian distribution of the iris-shaped QCL beam where the intensity was inversely proportional to the squared distance, i.e., $I(z)\sim d^{-2}$. This result was used to estimate the focusing gain value of the samples. The change of the full width at half-maximum (FWHM) along the optical axis demonstrated an appropriate position for the samples at about $d=36\mathrm{cm}$ with $\mathrm{FWHM}\approx 14\mathrm{mm}$. Note that $d\gg f$.

 

Fig. 3. Beam intensity dependence on the distance after the pinhole (P). Inset: beam profile at selected distances to demonstrate a Gaussian radial symmetry.

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The measured focusing performance for all of the samples is shown in Fig. 4. As an example, a 2D beam profile in the focal xy-plane for the selected MPFL2 sample is shown in the inset of Fig. 4(b). The measured beam intensity distributions [Fig. 4(a)] allowed us to estimate the focusing gain values of 262 (24 dB), 348 (25 dB), and 804 (29 dB) for the SZPL, MPFL2, and MPFL8 samples, respectively. The results are summarized in Table 1. Those are measured results without a deduction of the optical losses in the laser-patterned Si wafer and blocking of THz radiation with opaque zones of the metal foil.

Table 1. Focusing Performance of the Laser-Processed Diffractive Lenses at 4.754 THz (Wavelength $\lambda =63.18\mathrm{\mu m}$)

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Fig. 4. (a) Beam intensity at the focal plane and (b) change of the waist in direction of the focal depth of different samples. Inset: the beam profile at the MPFL2 focal plane.

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The focusing gain of the SZPL sample can be described by the analytical formula $G_{\mathrm{SZPL}}=N_{\mathrm{OPEN}}^2$ which is valid for the case $f/\lambda \gg 1$ [12]. The largest number of all Fresnel zones in a zone plate with negligible axial spherical aberrations is defined as $n_a={(2F/\lambda )}^{1/2}$. The SZPL sample was possessed of $N_{\mathrm{OPEN}}=25$ and $n_a=40$ leading to $G_{\mathrm{SZPL}}=400$ (26 dB). The optical losses due to an axial spherical aberration of 2 dB were deduced resulting to the difference between theoretical and experimental values of about 2 dB.

The radii $b_s$ of the subzones, as well as other design parameters, for the samples were calculated as described in Ref. [4]. A close inspection of the SZPL zones under the microscope in different directions revealed that the fabricated radii deviated from the calculated values in average by $25\pm 9\mathrm{\mu m}$. Such a large difference between fabricated and theoretical radii values was more pronounced for the most outer zones leading to a reduction of the focusing gain by 2 dB. Nevertheless, this is the first demonstration of the SZPL developed from a free-standing metal foil for an upper band of the THz range.

Theoretically, the MPFL2 should possess four times higher focusing power at the primary focus, compared to that of the same diameter of SZPL [12]. The measured results are given in Table 1. A laser patterned Si wafer demonstrated the transmission values of about 0.4 measured independently at 4.7 and 3.1 THz frequency. The multiple THz beam reflections on the air/silicon interface contributed mainly to the total amount of optical losses which were found to be approximately 4.1 dB. These were deduced calculating the theoretical gain values for the MPFL samples. The difference between theoretical and experimental focusing gains was about 3 dB, independent from the MPFL sample. Furthermore, it was 1 dB larger in comparison to the findings for the SZPL sample. This difference might be attributed to the shadowing effect which occurs for the grooved zone plates [13]. The increase of phase quantization levels from two to eight leads to higher focusing gain values up to 29 dB, without a measurable change of optical losses in the laser-patterned silicon wafer. The $G_{\mathrm{MPFL}8}=29\mathrm{dB}$ is the largest experimental focusing gain value reported so far. The data demonstrated an improvement of about 10 dB in comparison to the MPFL fabricated of Si and TPX materials [4,6]. The main difference in our research was a higher number of the phase zones successfully laser-patterned on the silicon wafer. The absorption losses introduced during laser patterning of the silicon surface could be neglected at the first approach. In order to diminish the reflection losses, the anti-reflection coating on the back side of a Si wafer could also be patterned by the same DLA technology [16].

The samples with a binary-phase profile were able to focus the QCL to a beam waist diameter of 0.15 mm which is in agreement with the theory. However, a larger focused beam size for the MPFL8 sample was obtained at 4.745 THz, namely, $w_0=0.18\mathrm{mm}$. Note that the measured focal length was also different from the target value by about 20 mm.

The zone radii and depth profile for the MPFL2 sample were laser-processed in accordance to the calculated values, as shown in the inset of Fig. 1. The differences between the measurements and theory for the MPFL8 sample were also analyzed. The result is shown in Fig. 5. One can see that the depth profile of a hypothetical MPFL8 with 70 mm focal length and 5.5 THz frequency fits the measurements data better than that with the original design parameters. The focusing performance of the MPFL samples was also experimentally verified at 3.1 THz. The results (not shown) revealed the increase of the focused beam size for all of the samples being used at another than the design frequency.

 

Fig. 5. Depth profile for the MPFL8 sample measured (dots) and calculated at original (dotted line) and modified (solid line) design parameters.

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Aiming to demonstrate that, indeed, the laser-fabricated lenses are suitable for practical applications, the samples were placed on a rotation stage, and the focusing performance stability versus tilt angle with respect to the optical axis (off-axis aberrations) was measured. A maximum rotation angle of the sample was provided up to 15 deg in one direction in respect to the direction of the normal incidence. The results are shown in Fig. 6. The inset shows a peak intensity distribution along an optical axis in a vicinity of the focal plane for the MPFL8 sample.

 

Fig. 6. Normalized area under the curve obtained by measuring the intensity dependence along an optical axis (as shown in the inset). Inset: the dependence of the beam amplitude focused with the MPFL8 on the distance at different values of the incident angle.

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The intensity dropped by 40% relative to its maximum value within an angle change from 0 to 15 deg. Indeed, the positioning of the zone plate was minor sensitive to misalignments up to 10 deg. To evaluate the effect quantitatively, the measured intensity profile was integrated (i.e., the sum from the entire axial scan) and normalized to the result found at the case of normal incidence. The results are shown in Fig. 6. All of the samples were tolerant to misalignment as large as 10 deg with a reduction of the integrated focusing efficiency by not more than 10%, regardless of the type of zone plate and number of phase quantization levels. We noticed that it was very important which of the two sides of the diffractive lens was illuminated with THz radiation. Higher tolerance to the misalignments, including stability of the focused beam waist, was observed for a case when laser patterned silicon surface was facing toward the detector.

To conclude, the Soret zone plate and the multi-level phase-correcting Fresnel lenses for the target frequency of 4.7 THz have been developed by using a DLA technology. The samples fabricated of a metal foil and crystalline silicon at 4.745 THz have demonstrated the focusing gain values up to 24 and 29 dB, respectively. All of the lenses were tolerant to misalignment as large as 10 deg of oblique incidence with the focusing power drop no larger than 10%. Thus, a DLA technology provides an additional tool for further development of compact components and alignment-free spectroscopic imaging systems for the entire THz range.