This paper chronicles the leaky-mode leakages in a corner-fed square patch. First, the measured peak RPA (relative power absorbed, 1-|S11|2-|S21|2) values of the two-port corner-fed square patch (two-port test circuit) are reported. These are 21.1%, 52.3%, 89.8% and 81.3% at 5.68 GHz, 11.76 GHz, 16.68 GHz and 22.29 GHz, respectively. Such periodicity of frequencies and the phenomenon of increasing losses at higher frequencies enable us to link these peak frequencies to leaky-mode excitations. The modal spectra of the higher-order leaky modes with a strip width of 630 mil, equal to the side length of the square patch, are obtained by the well-known space-domain integral equation method. The maximum available power gain (GA,max), obtained by simultaneously complex conjugate matched impedance at the referenced two ports of the test circuit, depicts that (1) nearly loss-free transmission parameter outside the leaky-mode regions and (2) substantial losses inside the leaky-mode regions. This result suggests that the leaky modes are the main sources causing losses for the two-port test circuit. Furthermore, the valley points of the measured and theoretical GA,max are about -7.5 dB, -9.7 dB and -12.0 dB at 10.13 GHz, 16.68 GHz and 22.29 GHz, respectively, and all are in the leaky-mode regions of the modal spectra. The one-port properties of the two-port patch with the second port opened are then investigated. The degenerated (0,N) and (N,0) modes (N=1, 2, 3 and 4), calculated by the cavity model method, fall into the strong leakage regions from the first to the fourth higher-order leaky modes. The well-known leaky line's frequency-scanning characteristics also appear in the one-port test circuit, with the angle of the main beam moving from θ=30 to θ=40 as the operating frequency is increased from 22.50 GHz to 23.75 GHz. Lastly, a two-dimensional (2-D) transmission-line model of the one-port test circuit is proposed. This model uses two orthogonal modal currents as excitations to stimulate the corner-fed square patch. At 22.60 GHz, in the fourth higher-order leaky mode (EH4) region, the current distributions obtained by the 2-D transmission-line model closely agree with those of the full-wave simulation. This consistency shows that the damped-oscillation current distributions of the corner-fed square patch at 22.60 GHz are caused significantly by the multiple reflections of the leaky mode. Furthermore, at the resonant frequencies of the patch, the tangled bound-mode resonance of the EH0 mode can enhance the leaky-mode leakages.

An asymmetric left-handed coupled-line is presented to implement the tight forward coupler. Two left-handed transmission lines are coupled through its shunt inductors. The numerical procedures based on the generalized four-port scattering parameters combined with the periodical boundary conditions are applied to extract the modal characteristics of the asymmetric coupled-line, and theoretically predict that the proposed coupled-line can make a normalized phase constant of c mode 1.57 times larger than π mode for the forward coupler miniaturization. The design curves based on different overlapping length of the shunt inductors are reported for the coupler design. The procedures, so-called the port-reduction-method (PRM), are applied to experimentally characterize the coupler prototype using the two-port instruments. The measured results confirm that prototype uses 0.21 λg at 430 GHz to achieve -4.55 dB forward coupling with 13% 1-dB operating bandwidth.