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Tunable photonic metamaterials. (English) Zbl 1170.82417
Summary: We illustrate a mechanism based on coherent optical nonlinearities to realize optically tunable photonic crystals built from media supporting electromagnetically induced transparency. These exhibit specific periodic patterns where a light probe can experience a fully developed photonic band-gap with negligible absorption. An analytical method based on a two-mode approximation is developed to study the optical response of such a periodically modulated medium driven into a regime of standing-wave electromagnetically induced transparency. A comparison with a transfer matrix approach and with techniques based on the coupled Maxwell-Liouville equations shows that our method is very accurate to describe the optical properties of such photonic metamaterials in the frequency region of interest. Nearly perfect reflectivities may be attained for ultracold $$^{87}$$Rb atoms samples which are seen to reflect with little loss and deformation light pulses whose frequency components are contained within the gap. When the same mechanism is implemented for inhomogeneously broadened optical transitions of nitrogen-vacancy centers in diamond, which is more amenable to device applications, fully developed photonic band-gap structures with negligible absorption, reflectivities very close to unity and sufficiently large bandwidths may also be attained. We further examine more flexible schemes based on four level systems under double driving conditions showing more accurate and efficient coherent optical control of the photonic band-gap. The remarkable experimental simplicity of the schemes that we presented is set to ease quantum nonlinear optics applications.

##### MSC:
 82D25 Statistical mechanical studies of crystals 78A60 Lasers, masers, optical bistability, nonlinear optics
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##### References:
 [1] DOI: 10.1007/978-3-662-14324-7 · doi:10.1007/978-3-662-14324-7 [2] DOI: 10.1070/PU1968v010n04ABEH003699 · doi:10.1070/PU1968v010n04ABEH003699 [3] DOI: 10.1038/nmat1588 · doi:10.1038/nmat1588 [4] DOI: 10.1364/JOSAB.19.002046 · doi:10.1364/JOSAB.19.002046 [5] DOI: 10.1038/nature02176 · doi:10.1038/nature02176 [6] DOI: 10.1007/BF02749417 · doi:10.1007/BF02749417 [7] DOI: 10.1016/S0079-6638(08)70531-6 · doi:10.1016/S0079-6638(08)70531-6 [8] DOI: 10.1016/S0030-4018(96)00483-X · doi:10.1016/S0030-4018(96)00483-X [9] DOI: 10.1103/PhysRevLett.89.143602 · doi:10.1103/PhysRevLett.89.143602 [10] DOI: 10.1103/PhysRevA.71.013821 · doi:10.1103/PhysRevA.71.013821 [11] DOI: 10.1103/PhysRevLett.96.073905 · doi:10.1103/PhysRevLett.96.073905 [12] He Q-Y, Phys. Rev. B 73 pp 195124-1– (2006) [13] Bassani F, Electronic States and Optical Transitions in Solids (1975) [14] DOI: 10.1103/PhysRevA.52.1394 · doi:10.1103/PhysRevA.52.1394 [15] Artoni M, Phys. Rev. E 72 pp 046604-1– (2006) [16] DOI: 10.1016/j.optcom.2006.03.075 · doi:10.1016/j.optcom.2006.03.075 [17] Born M, Principles of Optics, 6. ed. (1980) [18] DOI: 10.1364/OL.22.001138 · doi:10.1364/OL.22.001138 [19] DOI: 10.1103/PhysRevLett.88.023602 · doi:10.1103/PhysRevLett.88.023602 [20] DOI: 10.1103/PhysRevA.60.2540 · doi:10.1103/PhysRevA.60.2540 [21] DOI: 10.1364/OL.26.000361 · doi:10.1364/OL.26.000361 [22] DOI: 10.1103/PhysRevLett.85.290 · doi:10.1103/PhysRevLett.85.290 [23] DOI: 10.1103/PhysRevLett.96.070504 · doi:10.1103/PhysRevLett.96.070504 [24] DOI: 10.1364/OE.14.007986 · doi:10.1364/OE.14.007986 [25] DOI: 10.1098/rspa.1976.0039 · doi:10.1098/rspa.1976.0039 [26] DOI: 10.1016/S0030-4018(03)01134-9 · doi:10.1016/S0030-4018(03)01134-9
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