A hybrid mode section is integrated into the end of the metal-metal (MM) waveguide of a terahertz (THz) frequency quantum cascade laser (QCL) by removing sub-wavelength portions of the top metal layer. This allows a hybrid mode to penetrate into the air, which reduces the effective index of the mode and improves the out-coupling performance at the facet. The transmission of the processed metal-metal hybrid section (MMHS) waveguide is further increased by ensuring its length fulfills the criterion for constructive interference. These simple modifications to a 2.5 THz MM QCL waveguide result in a significant increase in the output emission power. In addition, simulations show that further improvements in out-coupling efficiency can be achieved for lower frequencies with effective refractive indices close to the geometric mean of the indices of the MM waveguide and air

Davies, AG

Dean, P

Fobbe, T

Han, Y

Hekmat, N

Jukam, N

Li, L

Linfield, EH

Markmann, S

Nong, H

Pal, S

Schott, R

Wieck, AD

Zhu, J

White Rose Research Online

This is a repository copy of Metal-Metal Terahertz Quantum Cascade Laser with Hybrid Mode Section.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/90702/Version: Accepted VersionProceedings Paper:Fobbe, T, Nong, H, Schott, R et al. (11 more authors) (2015) Metal-Metal Terahertz Quantum Cascade Laser with Hybrid Mode Section. In: Infrared, Millimeter, and Terahertz waves (IRMMW-THz), 2015 40th International Conference. IRMMW 2015, 40th International Conference on Infrared, Millimeter, and Terahertz Waves, 23-28 Aug 2015, Hong Kong. IEEE . ISBN 978-1-4799-8272-1 https://doi.org/10.1109/IRMMW-THz.2015.7327687eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Abstract A hybrid mode section is integrated into the end of the metal-metal (MM) waveguide of a terahertz (THz) frequency quantum cascade laser (QCL) by removing sub-wavelength portions of the top metal layer. This allows a hybrid mode to penetrate into the air, which reduces the effective index of the mode and improves the out-coupling performance at the facet. The transmission of the processed metal-metal hybrid section (MMHS) waveguide is further increased by ensuring its length fulfills the criterion for constructive interference. These simple modifications to a 2.5 THz MM QCL waveguide result in a significant increase in the output emission power. In addition, simulations show that further improvements in out-coupling efficiency can be achieved for lower frequencies with effective refractive indices close to the geometric mean of the indices of the MM waveguide and air. I. INTRODUCTION Hz QCLs attain the highest temperature performance in MM waveguides, in which the laser mode is completely confined in the active region by two metal layers. However, the mode dimension in the growth direction is less than the wavelength. As a consequence, both a significant impedance mismatch at the laser facet and strong diffraction limit the out-coupling efficiency. Therefore several strategies have been employed to improve the out-coupling efficiency such as fabricating gratings for low divergence emission [1] and tapered horn antennas [2]. Recently, a hybrid waveguide [3] was formed by allowing the mode of a metal-metal waveguide to leak through a thin metal layer into a low index polymer. In this work, the out-coupling performance of a MM QCL is improved by reducing the effective refractive index at the facet via removing portions of the top metal layer. II. RESULTS A schematic diagram of the MMHS waveguide and the used experimental arrangement are presented in Fig. 1.  The hybrid section length is only 2.5% of the total waveguide which conserves the high confinement factor of the MM waveguide along the majority of the QCL. A significant improvement in the out-coupling efficiency is demonstrated from measurements on a QCL which is presented in Fig. 2. A MM waveguide is compared to the MMHS waveguide with respect to both total out-coupling performance and spectral emission. For a  current density of 720 A/cm2 the total power is increased by a factor of approximately 3 (Fig. 2(a)). The spectral emission at 2.5 THz is pronounced, since the hybrid section length l is optimized for constructive interference according to l=mc/(2fneff) (Fig. 2(b)).     Fig.1:  Schematic diagram of the experimental arrangement, showing relevant dimensions of the metal-metal hybrid section (MMHS) waveguide. The length of the hybrid section l is 38 µm. The distance between the metal lines d is 1 µm. A Michelson interferometer is used to detect the spectrum with a pyro-electric detector D.  Fig.2: (a) QCL output power and voltage as a function of current density for both the MMHS waveguide (black) with l=38 µm and the MM waveguide (red). The spectra from the MM (i - red) and MMHS (ii - black) QCL waveguides are shown for a current density of (b) 720 A/cm2. The MMHS waveguide QCL shows a pronounced emission at approximately 2.5 THz.     Here m is an integer, c the speed of light, f the frequency and neff  the effective refractive index of the mode. In order to investigate the out-coupling process in more detail and explore the full potential of the proposed concept, finite difference time domain (FDTD) simulations from a commercial software package were used. The constructive interference in the hybrid section is illustrated in Fig. 3 by  Tobias Fobbe 1,2 , Hanond Nong 1, Rüdiger Schott 2, Shovon Pal 1, 2, Sergej Markmann 1, Negar Hekmat 1, Jingxuan Zhu 3 ,Yingjun Han 3, Lianhe Li 3 , Paul Dean 3, Edmund H. Linfield 3, A. Giles Davies 3, Andreas D. Wieck 2 and Nathan Jukam 1 1 AG Terahertz Spektroskopie und Technologie, Ruhr-Universität Bochum, D-44780 Bochum, Germany 2 Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany 3 School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom. Metal-Metal Terahertz Quantum Cascade Laser  with Hybrid Mode Section  T Fig.3: Distribution of  |Ez| at a frequency of 1.7 THz for  (a) constructive and  (b)  destructive interference. Both MMHS waveguides differ only in the length of the hybrid section which is 88 µm in (a)  and 66 µm in (b).  Fig.4: (a) Frequency dependent total efficiency and neff for MM and MMHS waveguides. The peak in total efficiency at 1.7 THz is obtained by choosing neff close to the geometric mean of the indices of the MM waveguide and air. The mode distribution of |Ez| for (b) 1.45 THz and (c) 2.9 THz shows strong reflections at the corresponding interfaces.   plotting |Ez| for two hybrid sections whose satisfy the condition for constructive and destructive interference. In both cases the 1/e penetration depth of the mode into the air is the same. However the amplitude at the air-interface is much greater for constructive interference (Fig. 3(a)) than for destructive interference (Fig. 3(b)). The effective refractive index neff of the hybrid mode is investigated as a function of frequency in Fig. 4(a) (grey circles). The effective waveguide index can be defined as neff=くc/の, where の is the angular frequency, c is the speed of light in vacuum and く is the propagation constant of the mode. In Fig. 4(a) it becomes clear that neff decreases with decreasing frequency. For instance, at a frequency of 2.5 THz neff is slightly reduced with respect to the MM waveguide (3.1 vs 3.5). In addition to neff the total efficiency (defined as the total radiated power over the input power) is also shown as a function of frequency in Fig 4(a) (grey diamonds). The total efficiency is maximized for a frequency of 1.7 THz.  Interestingly, an optimum point of operation close to the geometric mean of the indices of the MM waveguide and air is observed. For this specific point of minimized reflections at both interfaces about 87 percent total efficiency are achieved at a frequency of 1.7 THz. Comparing this value to the MM waveguide (12 percent total efficiency, red diamonds) an improvement factor of about 7.25 is predicted (Fig. 4(a)).    For low neff the reflection at the hybrid  air interface is significantly reduced, whereas the reflection at the MM  hybrid interface is still decent (Fig. 4(b)). In contrast, at higher indices the reflections are high for the air  hybrid and low for the MM  hybrid interface (Fig. 4(d)). The decrease in neff is also accompanied by an increase of the penetration depth ݈݂݂݁ according to ݈݂݂݁ʹ = ɉʹ /(4ヾ2(݂݂݊݁2−1)). The increase in the spatial extent of the mode decreases the spatial mismatch between the waveguide mode and the air modes at the hybrid air interface which reduces its reflection coefficient. III. CONCLUSION In conclusion, by removing sub-wavelength portions of the top layer of a MM waveguide a hybrid section has been formed, where the lasing mode can penetrate into air. The hybrid section is found to improve significantly the out-coupling efficiency of the MM waveguide, and in contrast to other schemes, the approach presented here is straightforward to implement. In addition, FDTD simulations show that an almost ideal out-coupling performance of about 87 percent can be achieved, if a balanced reflection minimization is employed.  ACKNOWLEDGEMENT The work was financially supported by Referat 221 MIWF NRW, BMBF Quantum communication program - Q.com-H 16KIS0109 and BMBF-QUIMP 16BQ1062 as well as Mercur Pr-2013-0001. We are also grateful for support from the EPSRC (UK) the ERC TOSCA program, the Royal Society and the Wolfson Foundation. The authors would also like to acknowledge the DFH/UFA CDFA-05-06 Nice-Bochum and the RUB Research School. Additionally, T.F., S.P., N.J. and A.D.W. would like to acknowledge IMPRS-SurMat, MPIE Düsseldorf. S.M. and N.J. would like to acknowledge DFG GSC 98/3 RUB Research School PLUS. REFERENCES [1] M.I. Amanti et. al., Low divergence single-mode terahertz quantum cascade laser, Nat. Phot. 10, 586 (2009). [2] W. Maineult et al., Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna, Appl. Phys. Lett. 93, 183508 (2008). [3] R. Degllnnocenti et al., A hybrid plasmonic waveguide terahertz quantum cascade laser, Appl. P hys. Lett. 106, 082101 (2015).  

Metal-Metal Terahertz Quantum Cascade Laser with Hybrid Mode Section

Tobias Fobbe

Hanond Nong

Rudiger Schott

Shovon Pal

Sergej Markmann

Negar Hekmat

Jingxuan Zhu

Yingjun Han

Lianhe Li

Paul Dean

Edmund H. Linfield

A. Giles Davies

Andreas D. Wieck

Nathan Jukam

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Metal-metal terahertz quantum cascade laser with hybrid mode section

https://eprints.whiterose.ac.uk/90702/1/T1B3%20-%203135255%20-%20Metal-Metal%20Terahertz%20Quantum%20Cascade%20Laser%20With%20Hybrid....pdf

Metal-Metal Terahertz Quantum Cascade Laser with Hybrid Mode Section

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