Multichannel Optical Add-Drop Processes in Symmetrical Waveguide-Resonator Systems Wei Jiang and Ray T. Chen Department of Electrical and Computer Engineering and Microelectronic Research Center, University of Texas, Austin, Texas 78758, USA (Received 7 October 2002; published 17 November 2003) Multichannel optical add-drop processes are studied in a class of symmetric waveguide-resonator systems. With insight gained from group theory, we analyze these systems and show that they can add or drop multiple wavelengths simultaneously, with 100% efficiency. A new mechanism is presented to reduce the remnant light at the dropped wavelengths in the pass-through port. High-order Butterworth filters can also be achieved in these systems. Built upon conventional or photonic-crystal based structures, these systems can be used in optical communication applications. DOI: 10.1103/PhysRevLett.91.213901 PACS numbers: 42.82.Et, 42.70.Qs, 42.79.Sz, 42.82.Bq In today’s fiber-optic networks, light of multiple wave- lengths propagates along a single optical fiber. Each wave- length of light transmits its own information undisturbed by the other wavelengths. A single-channel optical add- drop multiplexer (OADM) is a device that can add or remove a specific wavelength of light from a fiber. Recently, more and more applications demand OADMs that are able to add and remove multiple wavelengths. Filters based on photonic crystals (PC) have been dis- cussed for single-channel OADM applications. Fan et al. first proposed a structure of two parallel waveguides in a photonic crystal, with two resonators in between [1]. Light of multiple wavelengths comes into one waveguide from a fiber. With a proper design of the resonators, light of a specific wavelength will be completely transferred to the other waveguide, while light of the other wavelengths passes through the original waveguide and is coupled into another fiber. Quantum Green’s functions have been used to analyze the light transfer process in this structure. Additionally, simulations are performed to study PC- based single-channel OADMs [2] and demultiplexers [3]. A problem encountered in current simulations is that for many ports the light transfer efficiencies are fairly low. This also results in much light remaining in the pass-through port. Clearly, an analytic theory is needed to explore the characteristics and ultimate per- formance of PC-based multichannel OADMs and to give direction to the simulation efforts. New system architec- ture may be needed to overcome the limitations of the old systems. In this Letter, we propose a class of new structures which can add or drop multiple wavelengths simulta- neously. In such a structure that has n-fold symmetry, n pairs of resonators and n waveguides are arranged in a symmetrical manner. An n-fold structure can achieve 100% add and drop of light at n  1 different wave- lengths. These structures also provide a way of suppress- ing the remnant light intensity at the pass-through port for the bands of dropped frequencies. Such an improve- ment in optical isolation is ideal for many applications. Consider a system having n waveguides on the edges of a regular n-polygon. Inside the polygon, near the middle of each edge, there is a pair of identical cavities each having a single resonant mode. Their modes can be com- bined to form one even and one odd mode with respect to the mirror plane between them.With the resonators placed symmetrically, the system possesses a symmetry of point group C nv . Figure 1 illustrates the case n  3. An n-fold system is described by a Hamiltonian [1] H  H 0  V; H 0  X n1 m0 X k ! k jmkihmkj X n1 m0 X c ! mc jmcihmcj; V  X m;m 0 X c;c 0 1   m;m 0  c;c 0 V mc;m 0 c 0 jmcihm 0 c 0 j X m;m 0 X k;c V mc;m 0 k jmcihm 0 kj V m 0 k;mc jm 0 kihmcj; (1) where jmki is a propagating mode with wave vector k and frequency ! k in waveguide m. The mode jmci is a local- ized mode of the resonator pair next to waveguide m, c  e;o for the even and odd modes, respectively; ! mc is its frequency. The coefficients V mc;m 0 c 0 and V mc;m 0 k measure the coupling between the corresponding modes. We have neglected the coupling between the propagating modes of different waveguides as discussed by Xu et al. [4]. For n> 2, the symmetry operations of the group C nv do not commute with each other; therefore, irreducible represen- tations of dimensions higher than unity appear [5]. In simple words, a set of basis functions that are the eigen- states of all symmetry operations does not exist. Compared to the standard basis functions of irreducible representations, the eigenfunctions of C n operations are found to offer more convenience to analysis. One can readily show that, constructed from jmki, the modes PHYSICAL REVIEW LETTERS week ending 21 NOVEMBER 2003 VOLUME 91, NUMBER 21 213901-1 0031-9007= 03=91(21)=213901(4)$20.00  2003 The American Physical Society 213901-1