Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations

Abstract

We fabricate three-dimensional photoresist templates by means of laser holography. In particular, fcc structures are achieved by placing a specially designed ''prism'' onto the photoresist surface. This solves the problem of previous work, in which the refraction at the air-photoresist interface made it impossible to obtain the required angles of the light wave vectors inside the photoresist. The photoresist templates are characterized by scanning electron microscopy as well as by optical transmission spectroscopy, which agree well with numerical band-structure calculations. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1557328͔Large-area, three-dimensional ͑3D͒ photonic crystals 1,2 incorporating cavities and waveguides would not only offer interesting perspectives in high-density integrated optics for telecommunications applications, but would also be interesting for fundamental studies, for instance on the quantum optical properties of nanoresonators. 3,4 Different approaches towards this goal are currently being followed, such as inverse opals, 5 stacked two-dimensional structures fabricated by electron-beam lithography, 6,7 and holographically generated photoresist templates [8][9][10][11] with the potential to be infiltrated by appropriate materials.In the latter holographic approach, N collimated coherent laser beams are sent onto a photoresist. The resulting multiple-beam interference pattern exposes the photoresist. In the developer, the more exposed and less exposed parts have different solubilities, leading to a porous photoresist structure. To obtain a 3D intensity pattern I(r), which exposes the photoresist, N needs to be four or larger ͓Fig. 1͑a͔͒. The light intensity for Nϭ4 can be written asHere, the reciprocal lattice vectors G nm ϭk n Ϫk m are determined by the differences of the wave vectors k n of the incident plane waves and the ͑generally complex͒ form factors a nm ϭE n 0•E m 0* , resulting from the relative amplitudes and polarizations of the incident laser beams. Three of the reciprocal lattice vectors G nm , for instance G 12 , G 13 , and G 14 , are linearly independent and form a basis of reciprocal space. The terms with nϭm lead to a constant background. Therefore, the reciprocal lattice vectors G nm determine the lattice of the crystal structure, whereas the form factors a nm determine the internal structure of the unit cell. While Ref. 8 used linear polarizations only, choosing different linear, circular, or generally elliptical polarizations results in more design freedom via the form factors a nm .In order to achieve a complete 3D photonic band gap, it is known that symmetric structures are advantageous as compared to more asymmetric structures. 12 An interesting candidate might be the fcc crystal structure ͑analogous to the inverse opals or diamond structures͒. In the pioneering work of Ref. 8, a bcc reciprocal lattice ͑equivalent to a fcc real-space lattice͒ was demonstrated in air.However, it is important to note that this fcc lattice in air translates into a non-fcc, st...

Introducing Defects in 3D Photonic Crystals: State of the Art

“…The optical properties of 3D PhCs formed via holography are weaker than expected for reasons that are not obvious. There are only limited reports on the optical response of these structures [89] and although a direct comparison is difficult, to date, it appears that colloidal crystals (CCs) present better optical properties. The optical response of holographic structures could be improved by better lasers, photoresists, and processing param- eters, but these improvements are not trivial.…”

Holographic fabrication of photonic crystals using multidimensional phase masks

“…Holographic lithography based on multibeam interference has recently been employed to fabricate 3D photonic crystals by exposing a photoresist or polymerizable resin to interference patterns of laser beams. [7][8][9][10][11][12][13][14][15][16][17][18][19][20] This multibeam interference technique has produced submicron-scale structures over large substrate areas. 8,9 A diamondlike structure is desirable due to a larger photonic bandgap when compared to a simple face-centered-cubic ͑fcc͒ structure and its bandgap robustness to deviations of the structural parameters from their optimum values.…”

Holographic fabrication of three-dimensional orthorhombic and tetragonal photonic crystal templates using a diffractive optical element

“…Recently, a number of groups have demonstrated the construction of multibeam interference using a single diffractive or deflective optical element. [10][11][12][13] The holographic lithography based on multiple diffractive elements on one glass mask 10 and a single flat-top prism 11 was demonstrated for the fabrication of photonic crystal template. By employing two-layer orthogonally aligned phase masks, photonic crystals with woodpile structures have been recently demonstrated through one or two laser exposures.…”

“…[12][13][14] The utilization of single optical element can effectively reduce complexity of the optical setup and its vulnerability to the thermal and mechanical variations. 10,11 When the multibeam interference is constructed by bulk optical elements, the interference laser beams can be directed from all spaces ͑360°͒. 4 However, the interference pattern generated through a single optical element can only comes from the same half-space, which leads to elongated 3D structures in the z direction.…”

“…3,4 Intrigued by their vast potential in photonics engineering, tremendous efforts have been invested into the fabrication of defect-free three-dimensional ͑3D͒ photonic crystal structures with complete band gaps around the visible and near infrared telecommunication windows. [5][6][7][8] So far, a number of fabrication techniques such as conventional multilayer stacking of woodpile structures using semiconductor fabrication processes, 5 colloidal self-assembly, 6 multiphoton direct laser writing, 7 and multibeam holographic lithography 4,[8][9][10][11][12][13][14] have been employed to produced submicron 3D photonic crystals or templates. With appropriate infiltration and inversion processes, 15 these 3D templates can be converted into 3D photonic crystal structures with complete band gaps in the visible and the near infrared regions.…”