**5. Conclusion**

Multiple examples can be given to demonstrate that a combination of different physical phenomena can create a possibility of substantial extension of the variety of the obtainable regimes and new ideas for low-cost and/or compact designs. Thus, hybridization is a rather general approach in modern optics and physics. In this chapter, it has been shown how the effects, which are well known for the gratings, on the one hand, and those for the PCs, on the other hand, can be combined in the nonsymmetric PCGs composed of dielectric rods in such a way that new operation regimes can be obtained, which are not realizable in dielectric gratings or noncorrugated PCs. The most interesting transmission and reflection regimes of PCGs originate from the nonsymmetry, i.e., from the broken spatial inversion symmetry. The studied mechanism is characterized by absence of polarization conversion, while the extreme redistribution of the incident wave energy into that of of higher orders plays a key role. In particular, PCGs promise new solutions for unidirectional diode-like devices, splitters, deflectors, mirrors, and nano- and microwave antennas. From the point of view of the theory of PCs, introduction of corrugations while dispersion is known enables new coupling scenarios owing to diffractions. From the point of view of the grating theory, using a PC with the alternating pass and stop bands and substantially different properties of various Floquet-Bloch modes, instead of a homogeneous linear material, enables new diffraction scenarios as compared to those typical for dielectric gratings. Finally, from the point of view of the asymmetric and unidirectional transmission, PCGs demonstrate a high potential in obtaining of strong directional selectivity without breaking time reversal symmetry and, hence, without using anisotropic or nonlinear materials. A new direction in the studies of PCGs concerns asymmetric transmission for defect modes that might appear in chains of the cavity defects or/and line defects, which are parallel to the interfaces.

## **6. Acknowledgment**

The author thanks the Deutsche Forschunsgemeinschaft for partial support of this work under Project Nos. SE1409-2/1 and SE1409-2/2, and Prof. E. Ozbay and members of his research group for fruitful discussions.

#### **7. References**

42 Photonic Crystals – Introduction, Applications and Theory

and *kL*=8.29 in Fig. 18(b). Tilting can be an efficient tool of tuning in the reflection regime.

0.2

, and cyan dotted line - *R* .

Multiple examples can be given to demonstrate that a combination of different physical phenomena can create a possibility of substantial extension of the variety of the obtainable regimes and new ideas for low-cost and/or compact designs. Thus, hybridization is a rather general approach in modern optics and physics. In this chapter, it has been shown how the effects, which are well known for the gratings, on the one hand, and those for the PCs, on the other hand, can be combined in the nonsymmetric PCGs composed of dielectric rods in such a way that new operation regimes can be obtained, which are not realizable in dielectric gratings or noncorrugated PCs. The most interesting transmission and reflection regimes of PCGs originate from the nonsymmetry, i.e., from the broken spatial inversion symmetry. The studied mechanism is characterized by absence of polarization conversion, while the extreme redistribution of the incident wave energy into that of of higher orders plays a key role. In particular, PCGs promise new solutions for unidirectional diode-like devices, splitters, deflectors, mirrors, and nano- and microwave antennas. From the point of view of the theory of PCs, introduction of corrugations while dispersion is known enables new coupling scenarios owing to diffractions. From the point of view of the grating theory, using a PC with the alternating pass and stop bands and substantially different properties of various Floquet-Bloch modes, instead of a homogeneous linear material, enables new diffraction scenarios as compared to those typical for dielectric gratings. Finally, from the point of view of the asymmetric and unidirectional transmission, PCGs demonstrate a high potential in obtaining of strong directional selectivity without breaking time reversal symmetry and, hence, without using anisotropic or nonlinear materials. A new direction in the studies of PCGs concerns asymmetric transmission for defect modes that might appear in chains of the cavity defects

0.4

0.6

Reflectance

0.8

1

**(b)**

=20 degrees; corrugated-side illumination; blue solid line - *r*<sup>0</sup> , violet

at *kL*=5.57 in Fig. 18(a), and at *kL*=5.66

<sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>0</sup>

kL

=45 degrees, and (b) for the same

for the entire, or a desired part of

Two examples are shown in Fig. 18. Here, *r r* 0 1

**stop**

**(a) band**

<sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>0</sup>

kL

Fig. 18. Reflectance (a) for the same PCG as in Fig. 9(a) at

, dark green line - *r* <sup>2</sup>

or/and line defects, which are parallel to the interfaces.

, one can change *k*1 and, hence, obtain *r* <sup>1</sup> 0

Varying

0.2

0.4

0.6

Reflectance

0.8

1

the lowest stop band.

PCG as in Fig. 9(b) at

dashed line - *r* <sup>1</sup>

**5. Conclusion** 

Born, M. & Wolf, E. (1970). *Principles of Optics*, Pergamon Press, Oxford


**3** 

*USA* 

**Resonant Guided Wave Networks** 

*Thomas J. Watson Laboratory of Applied Physics California Institute of Technology Pasadena, CA* 

Eyal Feigenbaum, Stanley P. Burgos and Harry A. Atwater

In the last two decades, the development of new photonic material design paradigms has opened up new avenues for designing photonic properties based on different underlying physics. For example, photonic crystals, as described elaborately throughout this book, are based on dispersive Bloch wave modes that arise in periodic index structures. Different in operation than photonic crystals, metamaterials (Smith 2004, Shalaev 2007) are based on subwavelength resonant elements (or "meta-atoms") that interact with incident radiation to give rise to complex refractive indices. In this chapter, we introduce a new approach to optical dispersion control based on resonant guided wave networks (RGWNs) in which power-splitting elements are arranged in two- and three-dimensional waveguide networks. A possible framework for comparing and classifying photonic design paradigms is according to their basic resonating elements with which light interacts to give the desired artificial dispersion. Under this classification scheme, we can think of materials that operate based on the local interaction of waves with sub-wavelength resonating elements (i.e. metamaterials), structures based on the nonlocal interference of Bragg periodic waves (i.e. photonic crystals), and arrays of coupled resonator optical waveguides (CROWs) where adjacent resonators are evanescently coupled (Yariv 1999). Different from these existing concepts, the dispersion that arises in RGWNs is a result of the multiple closed-path loops that localized guided waves form as they propagate through a network of waveguides connected by wave splitting elements. The resulting multiple resonances within the network give rise to wave dispersion that is tunable according to the network layout. These distinctive properties, that will be described here, allow us to formulate a new method for

A RGWN is comprised of power splitting elements connected by isolated waveguides. The function of the splitting element is to distribute a wave entering any of its terminals between all of its terminals, as illustrated in Fig. 1a. The waves are then propagated in isolated waveguides between the splitting elements, where the local waves from different waveguides are coupled together. For example, four splitting elements arranged in a rectangular network layout form a 2x2 RGWN (see Fig. 1b). When one of the terminals is excited, the multiple splitting occurrences of the incident wave within the network form closed path resonances that reshape the dispersion of the emerging waves according to the network layout and is different from the dispersion of the individual waveguides. Properly

designing photonic components and artificial photonic materials.

**1. Introduction** 

