**1. Introduction**

96 Photonic Crystals – Innovative Systems, Lasers and Waveguides

Wang, K., Z. Zheng, Y. L. Su, Y. M. Wang, Z. Y. Wang, L. S. Song, J. Diamond, and J. S. Zhu.

Sensors. *Sensor Letters* 8 (2):370-374.

2010. High-Sensitivity Electro-Optic-Modulated Surface Plasmon Resonance Measurement Using Multilayer Waveguide-Coupled Surface Plasmon Resonance

> The most common 2D geometrical arrangements of photonic crystals (PhC) are square and triangular (hexagonal) lattices as shown in Fig.1. Assuming that a PhC structure is expanded to infinity along the x-axis, the problem belongs to a so-called vector 2D class (Gwarek et al., 1993). However, it may frequently be simplified even further to a scalar 2D class, restricting a wave vector *k* to a PhC plane (yz-plane in Fig.1). In such a case, any electromagnetic field propagating in the PhC plane can be decomposed into two orthogonal modes, usually denoted as transverse magnetic (TM) and transverse electric (TE) with respect to the x-axis.

> Although performance of PhC-based devices relies, in most cases, on the confinement of light within a photonic bandgap (PBG), photonic crystals also exhibit remarkable dispersion properties in their transmission bands, thus opening the perspective for new optical functionalities.

> A lot of research activities have been undertaken in the development of planar PhC passive optical devices, like waveguides (Loncar et al., 2000; Chow et al., 2001), filters (Ren et al., 2006; Fan et al., 1998), couplers (Yamamoto et al., 2005; Tanaka et al., 2005), power splitters (Park et al., 2004; Liu et al., 2004) or, recently, active devices for laser beam generation operating as a surface-emitting microcavity laser (Srinivasan et al., 2004), a photonic bandedge laser (Vecchi et al., 2007) or an edge-emitting laser (Shih et al., 2006; Lu et al., 2009). However, PhC devices in practical realizations are of a finite thickness (see Fig.2), thus, limiting applicability of the approximate 2D modelling approach to those scenarios where the PhC's thickness is large enough with respect to wavelength. Otherwise, the problem becomes 3D and a complete full-wave EM approach is essential.

> Similarly to 2D waveguiding slabs, optical confinement of light in thin membranes depends primarily on a contrast between the membrane's and cladding's refractive indices. Most of all, a propagating mode has to be located beyond a light cone of the cladding, if energy leakage wants to be suppressed. Secondly, the mode has to be confined within a channel processed between the surrounding photonic crystal boundaries. The photonic bandgap exists only for those modes that are totally internally reflected at the interface between the channel and the photonic crystal. Furthermore, if the membrane is deposited on a low-index dielectric film, instead of being symmetrically surrounded with air, additional complications of a design process are introduced.

On the Applicability of Photonic Crystal Membranes to Multi-Channel Propagation 99

results in significantly different near field envelope patterns of the fundamental and higherorder supermodes, in contrast to the case of uniform arrays (Kapon et al., 1984a). In such arrays, higher order supermodes can be suppressed by employing a proper gain

a) b) c)

Fig. 3. Near-field patterns of the supermodes in a five-element a) uniform array b) inverted-

Next, in an inverted-V chirped array (Fig.3b), the power of the fundamental supermode is concentrated in central channels, whereas the higher order supermodes are more localized in the outermost channels. Since gain in the active region is larger when the laser channels are wider, the fundamental supermode is expected to have a higher modal gain (near

In (Kapon et al., 1986), a buried ridge array has been proposed. In such arrays, a small refractive index contrast between the channels and inter-channel regions is applied. That soft index profile ensures effective coupling between the adjacent array laser channels via their evanescent optical fields. Since the channels in those arrays are defined by a built-in distribution of the refractive index, it is possible to achieve a uniform gain distribution across the array, while maintaining the channel definition. Such an approach makes the buried ridge arrays different from the gain guided arrays, in which inter-channel regions are inherently more lossy. Moreover, buried ridge arrays operate mainly with the fundamental

threshold) and, in consequence, is more likely to oscillate (Kapon et al., 1984b).

V chirped array, c) linearly chirped array (Kapon et al., 1984a).

supermode, thus, producing a single-lobe radiation beam.

distribution.

Fig. 1. The definition of square (left) and triangular (right) air-hole lattices.

Fig. 2. A perspective view of dielectric membranes with square (left) and triangular (right) PhC air-hole lattices.

In the next Section, a brief overview of the developments of mutli-channel laser generation techniques is given, especially in the context of so-called supermode multi-channel propagation.
