We demonstrate that azimuthally polarized surface emitting Terahertz quantum cascade lasers fabricated in a micro-ring resonator geometry can be coupled to cylindrical hollow aluminum waveguides reaching efficiencies as high ≈98%, when a collimating lens is used. By placing the waveguide in close contact with the QCL in a simple back-to-back geometry, the laser mode can be perfectly matched with the low loss TE01 waveguide mode showing attenuation losses as low as ≈2.3-2.7 dB/m at 3.2 THz.
© 2011 OSA
The far infrared or Terahertz (THz) region of the electromagnetic spectrum bridges the gap between the microwave and optical regimes, offering a great potential in many scientific, technological and industrial fields.
Efficient and miniaturized quantum cascade (QC) sources operating in the THz range have been successfully developed in the last few years and implemented in heterodyne [1,2] or imaging systems [3,4] for spectroscopy and security applications. Despite their cryogenic operation temperatures in the Terahertz , quantum cascade lasers have indeed attracted considerable attention thanks to the high output power, spectral purity, stability, compactness and reliability.
Terahertz QCL resonators are conventionally based on surface-plasmon waveguides, either in single metal , or double-metal configuration . Low divergence, high power double-metal devices working in the range 2-4 THz have been recently realized by employing horn antennas [7,8], hyperhemispherical silicon lenses , photonic crystals  3rd-order  or 2rd-order distributed feedback gratings [12–14] as well as micro-disk  or micro-ring [16,17] resonators for vertical emission. The latter approach is particularly appealing since surface emitting devices are easy to fabricate, show regular beam profiles and high output power also in an array configuration and allow two-dimensional integration and on-chip testing.
Despite the considerable advances in the development of compact and efficient THz sources, detectors and systems, the realization of optical components to control THz waves in this intermediate spectral region still remains a challenge. Specifically, to move THz technology toward component integration, more effort is required to improve the mechanisms to confine light in specified areas (resonant cavities), filter certain frequencies (optical filters) and, in particular, to direct the propagation of terahertz light (optical waveguides).
Neither conventional metal waveguides for microwave radiation, nor dielectric fibers for visible and near-infrared radiation can be used to guide terahertz waves over a long distance owing to the high Ohmic losses in metals or the high absorption coefficient in most dielectric materials in this spectral range. Terahertz waveguides with low transmission losses and small group velocity dispersion have been recently demonstrated in several geometries including photonic crystal waveguides , single  or double metal  wires transmitting a surface wave, and hollow waveguides including metal tubes , dielectric tubes , and plastic tubing with an inner metal coating and/or dielectric coating [23,24].
In a hollow waveguide the wave energy is mostly distributed in the air region and only a small fraction propagates inside the absorbing medium. Because the terahertz waves are strongly confined within their core, hollow waveguides can be inserted in cables, and this will be an advantage especially in medical endoscopic applications.
Losses in the hollow metallic waveguides arise from the non-vanishing electric field component at the metallic surface that penetrates and is absorbed in the waveguide wall. As a result, transmission losses of pure metallic waveguides are in general limited to 8-10 dB/m in the THz range . In a hollow cylindrical metallic waveguide two modes have low loss characteristics, i.e. the linearly polarized TE11 mode and the lowest losses azimuthally polarized TE01 mode that however is not easily excited by linearly polarized THz sources . The losses for the linearly polarized mode can be reduced by adding a thin (~λ/10) dielectric coating to the inner core via liquid flow coating processes. The waveguide dominant mode structure in the dielectric-lined waveguide will change from TE11 to the hybrid HE11 mode that exhibits minimal penetration into the absorbing metallic wall, assuring transmission losses lower than 1 dB/m . For the pure metallic waveguide however propagation in the TE01 mode offers a significant loss reduction compared to the TE11 mode, especially at high frequencies (ν > 2 THz).
The selection of a preferential waveguide mode is a crucial issue for a complete loss and dispersion analysis of waveguides. The conventional procedure employed for the optical characterization of a THz waveguide is based on the measurement of the waveguide transmission spectra by THz time domain spectroscopy (TDS). THz TDS, however, doesn’t facilitate mode selection and, as a result, experimental spectra often contain periodic patterns caused by waveguide mode interference.
In the present work, we demonstrate that the THz light of an azimuthally polarized micro-ring QCL can be coupled with a simple hollow metallic waveguide exhibiting a very high efficiency (> 96%) when the waveguide diameter is twice as large as the QCL ring diameter. We demonstrate a simple experimental approach that allows studying the mode-specific dispersion characteristics in THz hollow waveguides, by alternatively focusing a coherent THz beam at the waveguide entrance or shining the unfocused QCL beam in a waveguide mounted in close contact with it. Specifically, we analyze the TE01 and TE11 mode profiles and the corresponding transmission losses in cylindrical aluminum waveguides and show that by using a back-to-back configuration the propagation losses can be reduced to values < 3dB/m even in the 3-4 THz range.
2. Fabrication and experimental set-up
Aluminum cylinders having lengths in the range 1 cm-7 cm and bore diameters d >> λ and d ≈λ have been employed to couple in the THz beam of both edge emitting and surface emitting THz QC sources operating in the range 3.2 – 3.9 THz.
Sample (a) is an azimuthally polarized micro-ring distributed feedback QCL operating at 3.2 THz based on a double metal optical waveguide. The active region design features a 200 stage resonant-phonon structure; details on the fabrication procedure are described in Ref. 16. After substrate thinning, micro-ring devices, having a diameter dr = 990 μm, were soldered to copper bars with an In/Ag alloy and wire bonded taking care to distribute uniformly 6 bonding wires along the ring. The latter procedure allows having single mode operation and constant polarization along the whole QCL ring. Sample (b) has the same active region and waveguide configuration of sample (a) and has been processed with an identical photolithographic procedure. However, in the latter case, the outcoming light is not uniform along the ring and shows a more pronounced linear polarization component, likely owing to the slight misalignment of the top metallic layer with the semiconductor ring . Sample (c) is a linearly polarized edge emitting QCL operating at 3.9 THz and fabricated in a single-plasmon optical waveguide. The active region design and the fabrication procedure of the latter device are reported in Ref. 26.
The lasers were mounted on the cold finger of a continuous-flow liquid-helium cryostat for the measurements. Lasing spectra were recorded by focusing the QCL beam with an f/1 Picarin lens in a Fourier transform infrared spectrometer working in rapid scan mode and collected with a DTGS detector at the maximum resolution of 0.125 cm−1. Figure 1a shows the laser spectra of sample (a) and (b) collected by driving the devices with 200 ns pulses at 5 kHz repetition rate at a current of 2.04 A (sample a) and 2.14 A (sample b), respectively. Figure 1b shows the multimode pulsed emission spectra of sample (c) driven at a current of 1.62A under the same experimental conditions.
To couple the QCL beam into the hollow waveguide we follow two distinct experimental approaches, schematically sketched in Fig. 2a and 2b, respectively. In a first run of measurements we coupled the QCL beam into the waveguide with a 5 cm focal length Picarin lens, which focuses the laser beam into a ≈1 mm spot at the waveguide input (Fig. 2a). A calibrated pyroelectric detector, having a sensitive area of about 3 mm, has been mounted on a XY translational stage, driven by stepper motors with a spatial resolution of about 0.2 μm to scan across the waveguide end and image the mode profile at the output (≈2 cm from the edge). The total transmitted power at the waveguide end is therefore recorded in the far-field for each scanning position.
A second run of experiments has been performed in a so called back-to-back configuration i.e. by placing the hollow waveguide at ≈ 4 mm from the QCL (Fig. 2b). The unfocused QCL beam couples into the waveguide through a pinhole in a thin stainless steel circle positioned in contact with the waveguide input. The pinhole diameter has been kept identical to the waveguide hollow core. After propagating through the waveguide, the THz wave is detected and imaged in the far field at about 2 cm from the waveguide output.
3. Results and discussion
Figures 3a-c show the far field spatial intensity distribution of sample (a), (b) and (c), measured by keeping the pyroelectric detector 2 cm away from the QCL, and without any focusing optics.
The doughnut-shape of the intensity distribution measured in sample (a) agrees with theoretical predictions based on the Stratton-Chu formula , and is expected to be in a perfect match to the TE01 mode of the hollow waveguide. The beam profile of sample (b) is more divergent and shows an asymmetric, partly linear, polarization along the ring diameter. As for sample (c), the mode profile is made up almost entirely of linearly polarized radiation, as expected for edge-emitting QCLs.
Figures 4 show the far field spatial intensity distribution of sample (a) upon exiting a 2 cm long, 2 mm (panels a,d) or 1 mm (panels b,e) bore diameter aluminum waveguide, measured by focusing the incoming THz beam on the waveguide entrance by means of an f/1 Picarin lens. When the waveguide bore diameter d ≈ 2 dr or d ≈ dr two optical modes can be identified in the beam profile. The intensity distribution at the waveguide entrance is extremely focused and gradually decays to zero at the waveguide walls. In this case, the wave is mostly coupled to the TE11 mode. However, there is also a weak “ring” in the same image, which is likely caused by the TE01 mode, particularly visible in the 3D plot of Fig. 4d. Despite the presence of this low intensity ring, the mode profile obtained guarantees good coupling efficiency to and from free space. Finally, in panels c) and f) we show the 2D and 3D spatial intensity distribution of sample (a) upon exiting a tapered metallic waveguide having an entrance internal diameter of about 1mm and an internal diameter of 90 μm at the waveguide exit. The latter has been measured by keeping the pyroelectric detector at a distance of ≈ 300 μm from the 90 μm waveguide core.
Under these experimental conditions the highly confined TE11 mode is predominant. Moreover, it is worth noticing that extremely thin, wavelength sized hollow core diameters still give a reasonably good coupling between the THz QCL wave and the metallic waveguide
The TE01 mode can be easily excited without beam focusing by positioning the micro-ring QCL 4 mm distant from the entrance of a waveguide having a bore diameter d ≈ 2 dr or d ≈ dr. The measured far field patterns are shown in Figs. 5a and 5b, respectively.
The doughnut shape of the electric field profile is characteristic of the low loss TE01 mode that has the best coupling efficiency when the QC source is placed back-to-back to the waveguide entrance. Under this configuration the micro-ring QCL mode is perfectly matched with the waveguide mode, and ensures an almost total coupling efficiency with the waveguide when d ≈ 2 dr.
For the sake of comparison we also show in Fig. 6 the far field spatial intensity distribution of a linearly polarized QCL (sample c) upon exiting a 2 cm long, 2 mm (a), 1 mm (b), 90 μm (c) bore diameter waveguide, measured in a back-to-back configuration, under the same experimental conditions of Fig. 4. The mode profile, in this case, has an elliptical shape and the wave diverges more rapidly for smaller core waveguides as expected for the TE11 mode. No evidence of the TE01 mode is now present in the measured beam profile, in agreement with the expected waveguide mode symmetry. Finally, when the hole diameter approaches the wavelength of the impinging linearly polarized optical beam, the light can be still guided by the metal cylinder in the single-mode regime.
By measuring the input/output power values at the waveguide entrance/exit we extracted the coupling efficiency of the waveguide with the investigated QCL THz sources. The results obtained by focusing the QCL beam at the waveguide entrance, are plotted in Fig. 7 . Under this experimental condition the azimuthally polarized QCL (sample a) shows a very good matching with the waveguide TE11 mode. We get a coupling efficiency in the range 96% - 78% when dr ≤ d ≤ 2 dr. It is worth noticing that when d ≈ λ we still coupled the QCL beam with an efficiency of ≈14%. The mentioned efficiency values are reduced by almost one half when the polarization of the incoming beam is not uniform along the ring (sample b) or linear (sample c), keeping values in the range 35%-60% and 25%-52% for sample (b) and (c) respectively, when the ring diameter is dr ≤ d ≤ 2 dr. With a wavelength sized hollow core we still coupled radiation in the waveguide with ≈1.5% efficiency. Note that the coupling efficiency values plotted in Fig. 7 include the contribution of the transmission losses along the 2 cm long waveguides and therefore have to be considered as a lower limit of the effective coupling efficiency. A more detailed estimate of the above values can be extrapolated from the plots of the total losses as a function of the waveguide length.
Figure 8a shows the total transmission losses in the hollow waveguide, when the THz beam of sample (a) is either focused on the waveguide or coupled back-to-back, plotted as a function of the waveguide length. From the intercept of the linear fit to the data we extracted coupling efficiency values as high as 98% and 81% for a d ≈ 2 dr and d ≈ dr waveguide. Transmission losses of 4.6-5.1 dB/m and 2.3-2.7 dB/m have been found using the lens or in the back-to-back configuration, respectively, when the hollow diameter is d = 2 dr or even smaller (d ≈ dr).
Our results prove that in the back-to-back configuration coupling takes place mostly with the TE01 mode, while presumably a significant fraction of the THz beam is instead coupled to the TE11 mode when using the focusing lens. Note that the larger value of the optical losses when d ≈ dr is due to the worst coupling efficiency of the THz beam at the waveguide entrance.
Previous reports of the transmission losses in hollow metallic waveguides irradiated by a broadband THz wave in a lower frequency range (≤ 2.5 THz), give values of about 4-5 dB/m  and theoretical calculations at high frequencies (≥ 3.2 THz) predict losses as high as 12-15 dB/m for the TE11 mode . Taking into account that the atmospheric absorption at 3.2 THz is ≈ 0.6 dB/m, our results demonstrate that coupling a micro-ring surface emitting QCL with a hollow waveguide in close contact with it (back-to-back configuration), allows the propagation of very low loss modes with excellent coupling efficiency.
4. Conclusions and perspectives
We have demonstrated a promising new scheme to couple surface emitting QCL sources fabricated in a micro-ring resonator with a simple Terahertz hollow metallic waveguide. By focusing the QCL beam at the waveguide entrance the TE11 mode is preferentially excited resulting in propagation losses of about 4.6-5.1 dB/m with a coupling efficiency > 96% with the azimuthally polarized QCL beam. By coupling the laser source directly with the hollow cylinder in a simple back-to-back configuration, the QCL mode can be perfectly matched with the low loss TE01 waveguide mode, giving an almost unitary coupling efficiency and transmission losses as low as ≈ 2.3-2.7 dB/m up to 4 THz.
This very simple experimental approach combining a coherent, powerful source well matched to the waveguide propagation mode design is particularly attractive for practical applications owing to the low loss, the complete radiation confinement inside the waveguide, the efficient coupling to free-space propagating beams, and the simplicity of the waveguide scheme, that requires neither sophisticated fabrication procedure nor growth of dielectric layers for the selection of a preferential low loss mode. This is really appealing for the realization of THz sensors and systems requiring compact and efficient sources integrated with small and low-cost optical components.
We would like to acknowledge Lukas Mahler for the contribution in the device fabrication. This work was partly supported by the FIRB project NG-Lab of the Italian Ministry of Research and by the Fondazione Monte dei Paschi di Siena.
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