PHOTONIC CRYSTALS

HIGHLY DIRECTIONAL RADIATION USING SOURCES EMBEDDED IN PHOTONIC CRYSTALS

_Photonic crystals (PCs) are artificial periodic structures, which strongly modify the dispersion properties of electromagnetic waves (EM) waves [1, 2].   Since PCs may control the propagation of EM waves in certain directions, they have recently attracted much attention. Many interesting phenomena _such   as enhancement and suppression of spontaneous emission, propagation of photons via hopping over coupled defects and localized donor and _acceptor   modes, have been suggested and observed. One of the major reasons behind this interest on PCs is the possibility of the control of emission _from   radiation sources by using PCs [3, 4, 5]. There are two main problems in the control of emission: enhancement or suppression of radiation and the   confinement of the emitted power to a narrow angular region.

Fig.1 Schematics of 3D layer-by-layer photonic crystal

Fig.2a Transmission from a 3D PC along the stacking direction between 10 GHz and 17 GHz.

Fig.2b Enhancement factor and delay from the PC at the band edge frequency.

  The photonic band gap edges are especially important for the study of the effect of PCs on the radiation properties of sources. The importance of the   band edge lies in the fact that radiative local density of states is strongly enhanced near the band edge frequencies. The radiative local density of states is   a measure of the coupling of the source to the electromagnetic modes of the photonic crystal structure.

  Delay time corresponds to the propagation time of the EM waves inside the PC. Hence, group velocity is inversely proportional to the delay time.   Delay time is an important quantity for the study of emission of radiation from sources because this quantity enters to the rate equations. For a PC it is   possible to find positions with high electric field amplitude and frequencies with low group velocity. Hence, at these positions there is a high enhancement   factor in certain frequencies. Enhancement factor is defined as the ratio of the intensity of the EM waves emitted from a source located inside the PC to   the intensity of the EM waves emitted from a source in free space.

  Measured transmission and delay times for the layer-by-layer PC are shown in Fig.2. The transmission measurement shows that the lower band-gap   edge along stacking direction is around 10.3 GHz and the upper edge is around 15 GHz. The delay time near the lower band edge (10.3 GHz) is 14.2   nsec. Hence, the time required for the EM waves to propagate along the structure which is 0.47 nsec. So, the PC reduces the group velocity of light at   this frequency by a factor of 30.

Fig.3 The measured and calculated radiation patterns of the monopole antenna inside the 3D photonic crystal for E and H planes.

  The modes at the band edges of a PC ae propagating modes and these modes are concentrated in low or high dielectric material region. Hence, the   surface of the PC can be regarded as a system of radiation sources all operating at the band edge frequency, having similar spatial and temporal   distribution of power with a uniform phase difference between the radiators. This system of radiators is similar to an array of antennas. Since all the   radiators of the system radiate in the same direction, we expect the emitted power from a source embedded inside the PC to be confined to a narrow   angular region.

  The measured half power beam widths along the E- plane and H-plane are presented in the Fig.3. 90degrees corresponds to the stacking direction.   The measured half power beam widths of 13degrees for both E and H planes. The directivity of the radiation source embedded inside 3D PC is   calculated as 245. Hence, radiation from a monopole source embedded inside a 3D PC is highly directional and enhanced at certain frequencies. These   results can be used to improve the efficiency of the PC based antennas, LEDs.

     References

  1. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987).

  2. E. Yablonovitch,“Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059 (1987).

  3. K. Busch, N. Vats, S. John, and B. C. Sanders, “Radiating dipoles in photonic crystals,” Phys. Rev. E 62, 4251-4260 (2000).

  4. S. Enoch, B. Gralak, and G. Tayeb, “Enhanced emission with angular confinement from photonic crystals,” App.Phys. Lett. 81 (9), 1588 (2002).

  5. S. Ogawa,M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Control of Light Emission by 3D Photonic Crystals,” Science 305, 227 (2004).

     Related Publications

  1. Irfan Bulu, Humeyra Caglayan, and Ekmel Ozbay, “Radiation properties of sources inside photonic crystals,” Physical Review B. 67, 205103 (2003).

  2. Irfan Bulu, Humeyra Caglayan, and Ekmel Ozbay, “Highly directive radiation from sources embedded inside photonic crystals,” App. Phys. Lett. 83,   3263 (2003).

  3. Humeyra Caglayan, Irfan Bulu, and Ekmel Ozbay “Highly directional enhanced radiation from sources embedded inside three-dimensional photonic   crystals,” Optics Express 13, 7645 (2005).

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