Compact hollow-core photonic band gap resonator with optimised metallic cavity at microwave frequencies D. Fe ´rachou, G. Humbert, J.-M. Le Floch, M. Aubourg, J.-L. Auguste, M.E. Tobar, D. Cros and J.-M. Blondy A report is presented on the improvement by an optimised hexagonal metallic cavity of the electromagnetic field confinement in a hollow- core resonator based on out-of-plane two-dimensional photonic band-gap crystal cladding. A resonator was constructed with silica rods to prove the concept at frequencies around 30 GHz. It is shown that the technique can reduce the resonator size by 8.1 times without loss in quality. Introduction: High quality factor (Q-factor) resonators are of primary importance for applications in microwave and millimetre-wave domains. The development of dielectric resonators with high Q-factor is limited by dielectric losses of the material in super high frequency (SHF) and extremely high frequency (EHF) domains. One solution to beat the loss tangent limit in higher frequency domain is the confinement of the electromagnetic field in a hollow-core with an out-of-plane two- dimensional (2D) photonic band gap (PBG) crystal cladding that forbids field extension in the plane of the crystal [1]. The propagation of the wave is parallel to the invariance direction of photonic crystal. In con- trast with standard in-plane photonic crystal [2] where the invariance direction of the crystal is perpendicular to the propagation of the wave, the out-of-plane PBG crystal acts on the transverse component of the core mode leading to a crystal pitch longer than the wavelength and therefore to a weaker sensitivity of the confined field to fabrication imperfections. Recently, we reported the demonstration of a hollow-core resonator based on out-of-plane 2D PBG crystal cladding [3]. The PBG crystal is composed of an array of silica rods in air with a triangular lattice. The electromagnetic field is confined in a free space region, where one rod in the centre of the PBG crystal has been removed. Field con- finement efficiency was investigated by calculating the unloaded Q-factor of a resonator sandwiched by two perfect reflectors along the propagation axis (perpendicular to the crystal plane). It increases with the number of rod rings disposed around the hollow core, and a Q-factor as high as 5.1 × 10 5 can be obtained for four rings of silica rods, which is more than 26 times the loss tangent limit of a bulk silica resonator (with a complex permittivity of 3.78 2 j1.96 ×10 24 ), emphasising the potential of this out-of-plane 2D PBG crystal cladding for building high quality resonators at extremely high microwave fre- quencies. This is twice the best achievement using Bragg resonators [4, 5]. In contrast with standard in-plane PBG crystal, this out-of- plane crystal has a pitch 1.65 times longer than the wavelength, resulting in a large volume (61.23 cm 3 for a resonator operating at 40 GHz). However, this scaling factor allows high-Q resonators at millimetre- wave frequencies to have a reasonable size with easy to machine dielec- tric components. In this Letter, we report on an optimised hollow-core resonator based on a 2D PBG crystal composed of only one ring of silica rods inserted in a copper cavity. The new design improves the con- finement and means a similar Q-factor may be obtained with only one layer of rods, leading to a lower spurious mode density and more compact structure (fever dielectric components of similar size, resulting in a smaller cavity). Cavity design: Reducing the PBG crystal cladding from four rings of silica rods to one yields a weaker field confinement in the hollow core, which in turn causes a Q-factor reduction from 5.1 × 10 5 to 1.6 × 10 3 . To decrease the dominant metallic surface resistance losses, the radius of the hexagonal cavity needs to be optimised in order to maximise the reflection of the transverse component of the field at the air/metal interface [6]. In this work, we investigated the field confinement improvement for a PBG crystal cavity formed with one ring of silica rods of diameter 3.3 mm and a crystal pitch of 16.5 mm. The parameters of the crystal are chosen to allow the fundamental PBG to be centred around 30 GHz. The modes supported by the PBG crystal are simulated with the help of commercial software based on the finite element method. Allowed and forbidden photonic bands are formed within the mode spectrum of the crystal cladding (Fig. 1). Core modes with effective index below unity can be propagated into the hollow core within these band gaps [3]. The effective index against frequency curve inside the band gap (Fig. 1) corresponds to the fundamental core mode (hybrid mode HE 11 ) confined by the PBG effect. A computed intensity picture of this mode is shown in the inset of Fig. 1. 25 30 53 40 45 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04 n eff frequency, GHz photonic band gap z z z Fig. 1 Dispersion diagram of effective indices against frequency of modes supported in plan of opened ring PBG resonator Grey areas show domains where cladding array supports modes delimiting band gap Inset: computed intensity picture of fundamental mode confined in hollow core of out-of-plane 2D PBG crystal The Q-factor of the confined mode is then computed for a crystal enclosed in a hexagonal copper cavity assuming a conductivity of s ¼ 4.1 × 10 7 (V m) 21 . The evolution of the Q-factor against the radius of the cavity is plotted in Fig. 2. A maximum is reached for a radius of 23.76 mm corresponding to a Q-factor of 2.3 × 10 5 that is in the same order of the Q-factor obtained for a crystal cladding com- posed of four rings without metallic cavity. 20 22 24 26 28 30 32 0.5 1.0 1.5 2.0 2.5 quality factor (x10 5 ) radius of hexagon, mm r Z r r copper r Z Fig. 2 Evolution of Q-factor against radius of hexagonal copper cavity with one-rod PBG structure with s ¼ 4.1 × 10 7 (V m) 21 Inset: computed intensity picture of fundamental mode confined in cavity 29.50 29.55 29.60 29.65 29.70 –70 –65 –60 –55 –50 –45 –40 transmission, dBm frequency, GHz –35 –80 –70 –60 –50 –40 –30 transmission, dBm frequency, GHz 28 29 30 31 1 2 3 4 0 1000 2000 3000 4000 5000 Q-factor number of rings b a Fig. 3 Transmission spectra measured with vector network analyser of res- onant frequency in resonator Inset a: Q-factor measured against number of rings without cavity (black squares) compared to single one with hexagonal copper cavity cavity (star) Inset b: Wider transmission spectra measured of resonator Experiments: The optimised resonator with one ring of silica rods enclosed in a hexagonal 23.76 mm radius copper cavity was constructed (inset in Fig. 2). The confinement along the propagation axis (z) was achieved by a Fabry–Perot cavity composed of two copper plates, ELECTRONICS LETTERS 7th July 2011 Vol. 47 No. 14 Downloaded 06 Jul 2011 to 164.81.30.2. Redistribution subject to IET licence or copyright; see http://ietdl.org/copyright.jsp