VOLUME 67, NUMBER 24 PHYSICAL REVIEW LETTERS 9 DECEMBER 1991 Donor and Acceptor Modes in Photonic Band Structure E. Yablonovitch and T. J. Gmitter Navesink Research Center, Bell Communications Research, Red Bank, Ne~ Jersey 07701-7040 R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Received 11 March 1991) Three-dimensionally periodic dielectric structures, photonic crystals, possessing a forbidden gap for electromagnetic wave propagation, a photonic band gap, are now known. If the perfect 30 periodicity is broken by a local defect, local electromagnetic modes can occur within the forbidden band gap. Addi- tion of extra dielectric material locally, inside the photonic crystal, produces "donor" modes. Converse- ly, removal of dielectric material from the crystal produces "acceptor" modes. It is now possible to make high-Q electromagnetic cavities of — 1 cubic wavelength, for short wavelengths at which metallic cavi- ties are useless. These new dielectric cavities can cover the range from mm waves to uv wavelengths. PACS numbers: 42. 50. — p, 41. 10.Hv, 71. 25. Cx, 84. 90.+a There has been great progress recently in the creation of artificial three-dimensionally periodic dielectric struc- tures which are to photon waves as semiconductor crys- tals are to electron waves. That is, these photonic crys- tals have a photonic band gap, a band of frequencies in which electromagnetic waves are forbidden [1], irrespec- tive of propagation direction in space. Both face-cen- tered-cubic lattice [2] and diamond symmetry [3] dielec- tric structures have now been shown to produce a photon- ic band gap. The photonic band gap is very interesting in its own right. It is an energy band in which optical modes, spon- taneous emission, and zero-point Auctuations are all ab- sent. Nevertheless, the photonic band gap might actually be at its most interesting when the perfect translational symmetry is disrupted in a controlled manner. For exam- ple, by introducing a known degree of disorder, mobility edges and the Anderson localization transition [4] can be investigated. Lasers, perhaps the most important application, also require that the 3D translational symmetry should be broken. Even while spontaneous emission into all 4z sr would be inhibited, a local electromagnetic mode is still necessary to accept the stimulated emission. In eAect the local defect-induced structure resembles a Fabry-Perot cavity, except that it rejects radiation back upon itself in all 4tr spatial directions. Independently, Meade et al. [5] have proposed that this could be accomplished by intro- ducing a simple defect into the system. The perfect three-dimensional translational symmetry of a dielectric structure can be lifted in either one of two ways: (1) Extra dielectric material may be added to one of the unit cells. We find that such a defect behaves very much like a donor atom in a semiconductor. It gives rise to donor modes which have their origin at the bottom of the conduction band. (2) Conversely, translational sym- metry can be broken by removing some dielectric materi- al from one of the unit cells. Such defects resemble ac- ceptor atoms in semiconductors. The associated acceptor modes have their origin at the top of the valence band. We will find that acceptor modes are particularly well- suited to act as laser microresonator cavities. Indeed it appears that photonic crystals made of sapphire or other low-loss dielectrics will make the highest-Q single-mode cavities (of volume — lk, ) covering all electromagnetic frequencies above the useful working range of supercon- ducting metallic cavities. The short-wavelength limit in the ultraviolet is set by the availability of optical materi- als with refractive index ~ 2, the threshold index [2, 3] for the existence of a photonic band gap. For these experiments, we have chosen a face-cen- tered-cubic (fcc) photonic crystal [2] employing non- spherical atoms. This fcc structure lends itself readily to microfabrication since it consists of intersecting drill holes [2] which can be made by reactive ion etching. While such microstructures have already been fabricated [6] in GaAs, we have chosen initially to investigate local defect modes in larger structures on the scale of 1 cm wavelengths. We selected a refractive index n = 3.6 for the microwave material, matching that of the common semiconductors Si and GaAs. Experiment is supplement- ed by theoretical calculations of the photonic bound states. Photonic crystals generally consist of a continuous three-dimensional web of dielectric material, made up of interconnecting ribs. The Wigner-Seitz unit cell of our photonic crystal [2] is the standard fcc rhombic dode- cahedron [2] with "air atoms" created by drill holes cen- tered on the top three faces, which exit through the bot- tom three faces. Figure 1 is a (1 10) cross section of our photonic crystal cutting through the center of a unit cube. Shading represents dielectric material. The large dots are centered on the air atoms and the rectangular dashed line is a face-diagonal cross section of the unit cube. Such structures are made simply by drilling three sets of holes 35.26 off vertical into the (111)top face. Since we could design the structure at will, donor de- fects were chosen to consist of a single dielectric sphere 3380 1991 The American Physical Society