Metal–metal waveguide quantum cascade lasers (QCLs) are attractive for applications because of their low-power dissipation and good c.w. operation properties, especially at lower operation frequencies. Although these lasers typically emit high output powers up to the milliwatt range [1–3], the application of these lasers is limited because of the poor beam quality [4]. The subwavelength size of the laser facet is responsible for the poor far field, as well as for its high reflectivity ($R\approx 0.7–0.9$). A lens combined with an anti-reflection coating [5], active leaky-wave antennas [6], an on-chip horn antenna [7,8], or integration to a rectangular waveguide [9,10] was used to improve the far-field and/or the power extraction. Unfortunately, those solutions often imply complex manufacturing and integration work. Narrow third-order distributed feedback lasers [11] and antenna-coupled photonic wire lasers [12] show a narrow far field and have an intrinsically single-mode emission, but the beam may not be entirely linearly polarized, and the lasers may be prone to frequency detuning due to residual gas deposition [13].

To overcome the high facet reflectivity, a metal–metal QCL with a linear patch antenna array was developed [14] based on a BCB polymer layer planarization process described in [15]. This approach demonstrates improved power extraction by an increased threshold current, slope efficiency, and emitted power. In our new approach, we change to a vertically emitting, two-dimensional patch antenna array to improve the far field. Furthermore, we add a partially transmitting reflector to assure lasing in the antenna’s operation band. The patch antenna array is fabricated by structuring a gold layer on top of the BCB substrate which is planarized to the height of the laser ridge with $h=13.6\mathrm{\mu m}$. The high thickness of the BCB substrate, together with the low dielectric constant ${ϵ}_r=2.45$ [16], entirely governs the design of the power distribution network because under these conditions, ($h\approx 0.091{\lambda }_0$) the field is only loosely confined to the microstrip line. All microstrip bends, microstrip T-junctions, and other discontinuities will radiate power into the substrate and into free space. This power is lost for the actual antenna beam. Thus, it is imperative to minimize microstrip bending angles. Therefore, it is impossible to use complex power distribution and phase balance microstrip networks to feed every patch antenna with the correct power fraction and phase, as is usually done in patch array designs for instance in radar applications. On the other hand, the substrate properties enable a wide patch antenna bandwidth of 15%–20% [17,18].

Two power distribution networks which minimize radiative losses are proposed. The first is a parallel fed $2\times 2$ patch array, where all patches are directly connected to the distribution network [Figs. 1(a) and 1(b)]. The second is a serial fed $3\times 3$ patch array, where the patches are arranged in three branches [Figs. 1(c) and 1(d)], similar to the serial fed patch array structure in [19]. In both structures, all patches are fed in phase by designing the electrical path differences between the patches to be multiples of $2\pi$ at the design center frequency of 1.9 THz. We use elliptic instead of rectangular patches because simulations reveal a 1%–3% increase of antenna efficiency over the antenna bandwidth from 1.7 to 2.1 THz. Furthermore, elliptic patches allow smaller bending angles in the central feed of the $2\times 2$ parallel feeding network.

 

Fig. 1. (a) and (b) show a microscope image and a drawing of the parallel fed $2\times 2$ patch array, while (c) and (d) describe the $3\times 3$ serial fed array. All dimensions in μm for a design frequency ${\nu }_0=1.9\mathrm{THz}$ (${\lambda }_0=158\mathrm{\mu m}$). Dimensions L1, L2, and L3 refer to the dimensions of the partially transmitting reflector. For the reflector with transmission $T\approx 50\%$, we use $\mathrm{L}1=7\mathrm{\mu m}$, $\mathrm{L}2=16\mathrm{\mu m}$, and $\mathrm{L}3=37\mathrm{\mu m}$. In (d), the beam waist radius $w_0=129\mathrm{\mu m}\pm 6\mathrm{\mu m}$, which can be calculated from the beam divergence, is added to the antenna structure.

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Simulations with CST Microwave Studio [20] allow us to estimate the total efficiency of the antenna to $\approx 70\%$ for the $3\times 3$ patch array. The input reflection of the bare antenna structure is about $-13$ to $-20\mathrm{dB}$ over the 1.7–2.1 THz bandwidth [compare Fig. 2(d)], accounting for $\approx 3\%–5\%$ loss. Losses due to surface wave generation in the substrate are comparatively low ($\approx 6\%$) due to the low dielectric constant and due to the in-phase (even mode) excitation of the patches [17]. The high conductivity of the gold film at cryogenic temperatures contributes only a small fraction of $\approx 4\%$, whereas the lossy BCB substrate ($\tan (\delta )=0.01$) [16] dissipates $\approx 16\%$ of the available power. The antenna efficiency of the $2\times 2$ array is higher ($\approx 76\%$), mainly due to the shorter path lengths in the structure.

 

Fig. 2. (a) and (b) show power patterns of the $2\times 2$ and $3\times 3$ patch arrays calculated with CST. (The normalized radiated power density is proportional to the distance from origin.) The main lobe of the arrays has a FWHM of 49° and 35°. In (c), the E-field vectors are extracted from the simulation results. The spherical coordinates are projected as direction cosines in the xy-plane for improved presentability. The main lobe is linearly polarized. The side lobes show polarization with opposite signs. In (d), the S-parameters of the $3\times 3$ antenna and the antenna combined with reflectors with partial transmission $T\approx 33\%$ and $T\approx 50\%$ is shown. The E-field polarization and S-parameters for the $2\times 2$ patch array look similar.

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Figures 2(a) and 2(b) show the far-field properties of both antenna structures. As expected, the $2\times 2$ array has a broader beam lobe. For the $3\times 3$ array, the E-field distribution has been extracted from the simulation, as shown in Fig. 2(c). The main lobe shows polarization along the x-axis. The far-field simulation yields E-field vectors in spherical coordinates with full phase information. This vector field is fitted to a Gaussian field distribution. For the $3\times 3$ array, the FWHM angle of the Gaussian beam is 35°, corresponding to a beam waist radius of $w_0=129\mathrm{\mu m}\pm 6\mathrm{\mu m}$. $w_0$ is in the order of the overall antenna dimensions [compare Fig. 1(d); blue, dashed circle].

The maximum power coupling to a Gaussian beam (Gaussicity) is calculated by evaluating the normalized overlap integral of the simulated E-field data with the fitted Gaussian field distribution following [21]. For the $3\times 3$ array, the coupling yields 87%–93% in the 1.7–2.1 THz range. For the $2\times 2$ array, the coupling is slightly higher, $\approx 98\%$, due to the smaller side lobes [compare Figs. 2(a) and 2(b)].

Because the electrical lengths of the feeding network change with frequency, the beam steers with $\partial \theta /\partial \nu =0.064\mathrm{°}/\mathrm{GHz}$ toward the QCL ridge [compare Fig. 2(b)].

Since the patch array itself has a very low input reflection of $⪅-13\mathrm{dB}$ [Fig. 2(d)], we introduce a reflector between the antenna and the QCL ridge consisting of a short BCB section with length L1, followed by a section of active medium with length L2. The dimensions L1 and L2 are chosen to center the maximum reflection in the operation band of the antenna. In addition, the amount of power transmitted to the antenna can be chosen with L1 and L2 in a wide range. If very low reflection coefficients are desired, a quarter wave transformer or a taper section as published in [14] can be used. To equalize the reflected power over the band, it is important to choose length L3 accordingly.

We fabricated QCLs with both antenna structures and partial reflectors with $\approx 50\%$ transmission. In Figs. 3(a) and 3(b) the beam shape of the antenna structures is presented. A solid circle marks the FWHM of a Gaussian beam shape, fitted to the actual power measurements, while a dashed circle marks the FWHM of the calculated E-field distribution of the corresponding CST model.

 

Fig. 3. (a) Beam shape of a $2\times 2$ parallel fed device (maximum output power 808 μW). (b) Beam shape of a $3\times 3$ serial fed device (maximum output power of 620 μW), together with one-dimensional cuts through the peak. The powers have been measured with a 20% duty cycle, 200 ns pulses with 1 μs repetition time at 10 K. The solid circles mark the FWHM of a Gaussian fit to the measured power density distribution. For comparison, the dashed circles mark the FWHM of a Gaussian fitted to the simulated E-field pattern, as described above. The dotted circle is obtained when the simulated E-field distribution is converted to a scalar power pattern, where phase and vector information has been omitted to emulate the power detector measurement. (c) LIV curves of two 1.9 THz QCLs with 2D patch array antennas.

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To evaluate the Gaussicity for the measured beam shapes, we calculate the magnitude of the E-field by taking the square root of the measured power. The measurements with a wire grid polarizer show that the main lobe is entirely linearly polarized. Only the phase of the wavefront cannot be accessed. Since the power was measured in the far-field distance $z\gg z_c$, where $z_c\approx 0.35\mathrm{mm}$ is the confocal distance, the assumption of a spherical phase front is justified. Thus, we can again calculate the power coupling of the main beam by evaluating the overlap integral [21] with the fitted Gaussian beams which yields 98% for the $2\times 2$ array and 96% for the $3\times 3$ array. The actual power coupling to a Gaussian beam is less because the beam scan does not cover the full side lobe pattern, and the power detector does not see the actual polarization and phase of the side lobes.

In conclusion, both patch array variants enable metal–metal QCLs to emit linearly polarized beams with high efficiency and over 90% coupling to a Gaussian beam. The integrated reflector allows us to optimize the output reflectivity according to the given application.