Design of Low-loss THz Waveguides and Guided-wave Devices by using the Finite Element Method

B. M. A. Rahman, C. Themistos, A. Quadir, C. Markides, H. Tanvir and K. T. V. Grattan

City University London, Northampton Square, London EV1V 0HB, UK

BIOGRAPHY B M A Rahman: In 1982, B. M. Azizur Rahman received his PhD degree in Electronics from University College London and joined UCL as a Postdoctoral Research Fellow. In 1988, he joined City University, London, as a lecturer, where he is now a Professor. At City University, he leads the research group on Photonics Modelling, specialised in the use of rigorous and full-vectorial numerical approaches to design, analyse and optimise a wide range of photonic devices. He has published over 400 journal and conference papers, and his journal papers have been cited more than 1900 times. Prof. Rahman is a Senior Member of IEEE (USA), and members of the SPIE, Optical Society of America, and IET (UK), and a Chartered Engineer. He is also the Assistant Dean (Internationalization) for the School of Engineering and Mathematical Sciences.

TECHNICAL ABSTRACT THz technology is quickly becoming a major enabling technology with many applications in imaging and sensing,

however, due to lack of low-loss waveguides most of the systems are free-space based. Design of low-loss waveguides suitable for this frequency band is presented here. Design of simple power splitters and narrow band filter are also shown along with the optimization of active region of a quantum cascade laser to stabilize mode to prevent beam instability.

Key words: THz, waveguides, QCL, finite element method

SUMMARY Over the last 4 decades a range of optical waveguides have been developed, including silica fibers, which are

extremely low-loss waveguides, to cover the high frequency optical bands. On the other hand, for lower microwave and mm-wave frequencies metal waveguides and microstrips are being successfully used, respectively, but these waveguides become very lossy as the frequency increases further. In the THz band, most of the dielectric materials or metallic regions have high dielectric or conductive losses, which restrict the opportunity to design low-loss waveguides for this THz frequency band. With limited materials availability for this frequency band the waveguide engineering becomes a major challenge. Our earlier work on the design [1] of low-loss air-core circular waveguides were fabricated at Rutgers University and measured at Bell Labs. In our recent work [2], we have shown that similarly a polarization maintaining rectangular core air-core dielectric-clad metal-coated waveguide can also be less lossy. A thin metal coating would support plasmonic modes, but these are relatively lossy. However, a Teflon coating on the gold layer can draws field away from the lossy conducting layer and loss may reduce considerably. Figure 1 shows the variation of the loss value with the Teflon thickness for the Hx

12 mode in an air-core 1mm x 0.6 mm rectangular waveguide with 0.7 μm gold coating at 2.5 THz. It can be seen that at the optimum 21 μm Teflon thickness, the loss value can be 3.5 dB/m, one of the lowest reported so far [2]. The evolution of third order mode for no Teflon coating to a near Gaussian profile for 18 µm Teflon coating are shown as insets.

Similar to the VLSI, MMIC or PIC technology as used for semiconductors, microwave or optical frequencies, if we want to develop compact guided-wave THz systems, it would also be necessary to design and fabricate such integrated components. The MMI principle has been widely used to design compact optical power splitters and a similar approach is shown here. The evolution of field at the center of the waveguide along the axial direction is shown in Fig. 2 for a 1.0 mm by 3.0 mm metal-coated dielectric clad hollow-core multimoded THz waveguide, similar as reported earlier [2]. It can be observed here that at a distance of 37.2 mm, a neat 1 x 2 power splitting can be achieved. Similarly, THz filters can be used for on-chip signal processing and sensing. The variation of the Insertion Loss with the operating frequency for a microstrip-based THz filter is shown in Fig.3, which clearly illustrate the fundamental resonating frequencies of two 192 μm and 82 μm long filter stubs with 5 μm width.

During the last decade, Quantum Cascade Lasers (QCL) have emerged as one of the best compact sources for the generation of useful amount of power in this frequency band. To confine T-rays in a sub-wavelength thick core plasmonic confinement is essential. The gain threshold and mode confinement of several higher order lateral modes were studied [3]. Although, it was observed that a wider QCL yields a lower threshold, but the differential gain-threshold with higher order modes are small, which may cause mode hoping during any environmental variations. We have considered to engineer the upper metal layer and the gain threshold for 4 lower modes for etched and slotted electrodes are shown in Fig.4. This figure clearly shows the differential gain threshold can be substantially increased for a slotted electrode which will prevent mode hopping. All these simulations shown here have been carried out by using numerically efficient finite element based mode solver [4] and beam propagation methods [5].

REFERENCES [1] C. Themistos, B. M. A. Rahman, M. Rajarajan, K. T. V. Grattan, B. Bowden, and J. Harrington, “Characterization of Silver/Polystyrene (PS)-

coated hollow glass waveguides at THz frequency,” J. Lightw. Technol., vol. 25, no. 9, pp. 2456–2462, 2007 [2] B. M. A. Rahman, A. Quadir, H. Tanvir, and K. T. V. Grattan, Characterization of Plasmonic Modes in a Low-Loss Dielectric-Coated Hollow

Core Rectangular Waveguide at Terahertz Frequency,” IEEE Photonics J., vol.3, No.6, pp.1054,, 2011 [3] H. Tanvir, B.M.A. Rahman, N. Kejalakshmy, A. Agrawal and K.T.V. Grattan, “Evolution of Highly Confined Surface Plasmon modes in

Terahertz Quantum Cascade Laser Waveguides,” IEEE/OSA J. Lightwave Technol., vol. 29, no. 14, pp. 2116-2125, 2011. [4] B.M.A. Rahman and J.B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. 2, pp. 682-688, 1984. [5] S. S. A. Obayya, B. M. A. Rahman and H. A. El-Mikati, “New Full-Vectorial Numerically Efficient Propagation Algorithm Based on the Finite

Element Method,” J. Lightwave Technol., vol.18, no.3, pp.409-415, 2000

Fig.1 Effective index and loss with the Teflon thickness for the Hx

12 mode. Fig.2 BPM Simulation of the MM-based THz 3dB coupler.

Fig.3 Insertion Loss with frequency for the microstrip filter.

Fig.4 Gain Threshold of the lasing modes for different electrode arrangements.