Photonic-crystal lasers operating on Γ-point band-edge states of a photonic structure naturally exploit the so-called "nonradiative" modes. As the surface output coupling efficiency of these modes is low, they have relatively high Q factors, which favor lasing. We propose a new 2D photonic-crystal design that is capable of reversing this mode competition and achieving lasing on the radiative modes instead. Previously, this has only been shown in 1D structures, where the central idea is to introduce anisotropy into the system, both at unit-cell and resonator scales. By applying this concept to 2D photonic-crystal patterned terahertz frequency quantum cascade lasers, surfaceemitting devices with diffraction-limited beams are demonstrated, with 17 mW peak output power. In the terahertz (THz) frequency range of the electromagnetic spectrum, several PhC design strategies have been applied to quantum cascade laser (QCL) technologies in recent years [5,6]. The goal has been to improve the shape and quality of the strongly divergent emission [5,6] and the power efficiency of the devices by using the confinement and/or the dispersion properties of periodically patterned (in 1D or 2D) metal-semiconductor-metal structures. To date, a coherent single-lobed emission with reduced divergence has been obtained in edgeemitting devices, using third-order distributed feedback (DFB) gratings [7,8], and in surface-emitting devices, using 2D PhCs [9,10] and second-order DFBs [11,12]. However, efficient power extraction and, hence, wallplug efficiency (WPE) from DFB-or PhC-patterned QCLs has been elusive. WPEs for these devices fall well below the current state-of-the-art for THz QCLs exploiting unpatterned single-plasmon waveguides, where values in the 0.5%-1% range are currently achieved at 10 K [5].The problem in achieving high WPE has a fundamental origin. 1D and 2D PhCs support two classes of modes at the high symmetry points in the band structure where PhC lasers usually operate. These modes are associated with either symmetric or antisymmetric electric field profiles on the scale of the unit cell. When located above the light line, both modes will give rise to emission but will result in constructive or destructive interference. THz frequency QCLs (and indeed all QCLs) are TM polarized, i.e., the electric field is aligned parallel to the growth (z) axis. Since surface emission originates from the in-plane components of the field in the holes/slits of 2D/1D PhCs, it is only the magnetic field component that sources the radiation [13]. As a general rule, antisymmetric modes with respect to E z are symmetric with respect to the in-plane H field in the slits/holes of the DFB/PhC and are, hence, labeled "radiative." Conversely, symmetric E z modes are antisymmetric with respect to the in-plane H field and are, hence, termed "nonradiative." In fact, radiative modes at the Γ point (k in-plane 0) naturally exhibit an emission maximum in the direction normal to the device surface. As a consequence, the following relation is always true:...