2000, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5 micron wavelength,” Opt

Highly efficient transmission of 1.5 {micro}m light in a two-dimensional (2D) photonic crystal slab waveguide is experimentally demonstrated. The light wave is shown to be guided along a triple-line defect formed within a 2D crystal and vertically by a strong index-guiding mechanism. At certain wavelength ranges, a complete transmission is observed, suggesting a lossless guiding along this photonic 1D conduction channel.

Compact, lossless, and broadband guiding of light is essential for building future large-scale optical integrated circuits. Photonic crystal waveguides offer a new guiding mechanism that is fundamentally different from that of a traditional waveguide based on total internal ref lection. A photonic crystal is a periodic dielectric structure that exhibits a photonic bandgap, a frequency range over which propagation of light is strictly forbidden. 1 The introduction of line defects into a photonic crystal structure creates an optical channel for propagation of light. 1 If the line defect is properly designed, the resulting guiding mode falls within a photonic bandgap and is highly confined. Because of its confining ability, a photonic bandgap material can be viewed as a compact mirror for light guiding and bending. The guiding mode can also be designed to be broadband and thus gives rise to a compact, broadband photonic crystal waveguide.
Early theoretical simulation suggested that lossless guiding and bending of electromagnetic waves is possible with a two-dimensional (2D) or a three-dimensional (3D) photonic crystal. 2 -5 Subsequently, a successful experimental demonstration of a 2D guide and bend was performed at millimeter wavelengths. 6 Guiding of optical light by a fiber conf iguration is also possible. 7 More recently, fabrication of a 1.5-mm 2D crystal waveguide was also reported. 8 However, to our knowledge there has been no successful experimental demonstration of perfect waveguiding at optical wavelengths by use of either 2D or 3D photonic crystals. The main diff iculty is that a pure 2D photonic crystal does not guide light well in the third direction, which leads to unavoidable leakage.
This Letter reports the experimental demonstration of eff icient guiding of light at the 1.5-mm wavelength by use of a 2D photonic crystal slab. Light is shown to be guided along a one-dimensional (1D) optical channel, def ined by a triple-line defect formed within a 2D crystal slab. At certain wavelength ranges, complete transmission is observed. This is to our knowledge the first experimental demonstration of lossless guiding in a photonic crystal at optical wavelengths.
The photonic crystal sample consists of a triangular array of 2D holes, lithographically etched through a thin slab of GaAs. The hole array has a lattice constant a 0 , and the hole diameter is d 0.6a 0 . This design gives a large photonic bandgap. 9 The GaAs slab has an underlying 2-mm-thick Al x O y layer and a thin SiO 2 layer on top; see Fig. 1(a). The straight waveguide is created by introduction of a triple-line defect along the GK symmetry direction. The diameters ͑d 0 0.8a 0 ͒ of the defect holes are wider than those of the regular holes.  means of electron-beam lithography and reactive-ion beam etching. 10,11 Our photonic crystal slab guide has three unique features: One is that, contrary to the guiding principle of a conventional waveguide, it steers light in the lower-index region. Second, the use of a slab design provides strong index guiding of light vertically, even within the photonic bandgap spectral region. 11 Third, it is made with a triple-instead of a single-line defect. Although a single-line defect also supports a guiding mode, its certer frequency is too close to the lower photonic band edge. 12 Any slight process variation may shift the guiding modes into the adjacent allowed band and cause the guide to become lossy. On the other hand, a triple-line defect structure has an effective index lower than that of a single-line defect, thus pushing the guided-mode frequency away from the lower band edge and more into the bandgap.
One potential drawback of the triple-line defect is that it is no longer single mode but instead has three guided modes. In Fig. 2, a theoretical calculation of the TE guided-mode dispersion is shown. The frequency v͑a 0 ͞l͒ and the wave vector k͑2p͞a 0 ͒ are plotted in reduced units. The filled circles represent the fundamental (first) even mode. The open and the f illed triangles represent the f irst odd and the second even modes, respectively. The conduction band, valence band, and light -cone regions are also indicated. The three guided bands extend from v͑a 0 ͞l͒ 0.273 to v͑a 0 ͞l͒ 0.30, covering ϳ36% of the bandgap. Experimentally, since the incoming laser light has an even symmetry, it cannot be coupled into an odd mode. Hence, at any given frequency in the guided band, there is only one even guided mode. A triple-line defect may then be treated as a single-mode waveguide.
To test the guiding efficiency and the bandwidth of our photonic crystal guide we carry out in-plane transmission measurement. The laser light is coupled laterally into the input ridge waveguide [see Fig. 1(b)], transmitted through the triple-line defect, and then coupled into the output ridge waveguide. The output light is then split and fed into a calibrated In-GaAs photodetector and an infrared camera. In the inset of Fig. 3 a modal prof ile image of the output light, obtained from a 16-period photonic crystal waveguide ͑a 410 nm͒ at l 1.550 mm, is shown. The observed image has a clean, round modal prof ile and is Gaussian-like. This prof ile indicates that the measured output signal is not derived from the undesired air mode or the substrate leaky mode. 11 Rather, it is a true measure of a well-conf ined photonic crystal guiding mode in the slab layer.
As the f irst step of the experiment, three spectra are taken from three different guiding samples: (i) a 2D hole array with a triple-line defect [see Fig. 1(b)], (ii) a 2D hole array with no defect, and (iii) no 2D hole array and no defect (the reference spectrum). By ratioing spectrum (i) to (iii), we obtain the absolute guiding eff iciency ͑h͒ of a triple-line defect. Similarly, by ratioing spectrum (ii) to (iii), we obtain the bulk transmittance ͑T ͒ of the 2D slab hole array. In Fig. 3, h is shown by f illed circles as a function of both l and v for a 16-period sample with a 0 410 nm. The guide has a high guiding efficiency and is broadband. Furthermore, at the fiber communication wavelength l ϳ 1540 1565 nm, perfect guiding efficiency is observed. This is believed to be the f irst demonstration of complete guiding of light by a photonic crystal, 2D or 3D, in the optical wavelengths. For l 1535 1575 nm, h . 70% is observed. The slightly higher than 100% efficiency at certain frequencies suggests that a photonic crystal guide confines light better than the reference guide.
To map the entire guiding-efficiency spectrum, i.e., h versus v͑ a 0 ͞l͒, we vary both a 0 and l experimentally. To achieve this goal we fabricate six samples with values of a 0 400, 410, 430, 450, 460, 470 nm. Also, three laser modules are used to tune l from 1290 to 1680 nm. This combination allows complete mapping of guiding eff iciency throughout the entire photonic bandgap regime. 13 In Fig. 4 the measured h and T are shown by the red triangles and the black circles, respectively. Also shown in Fig. 4 are the theoretically computed T (black curve) and h (red curve). The numerical simulation consisted of sending a Gaussian input pulse into the input waveguide, measuring the f lux in the output waveguide, and normalizing the f lux against the f lux of a straight waveguide for determination of absolute   transmittance. For T , the theory correctly predicts the transmission eff iciency at both the conduction band and the valence band to within Dv͑a 0 ͞l͒ 0.1. In the bandgap region, v͑ a 0 ͞l͒ ϳ 0.26 0.32, both the predicted line-shape spectrum and the intensity attenuation ͑T ϳ 10 23 10 24 ͒ agree with experimental data. For h, highly efficient guiding starts from the lower-frequency end ͓v͑a 0 ͞l͒ 0.26͔ and extends into the midgap at v ϳ 0.29, consistent with the prediction of Fig. 2. Moreover, although photonic bandgap attenuation is strong ͑T ϳ 4 3 10 24 ͒ at v͑a 0 ͞l͒ ϳ 0.265, a near-perfect h value of ϳ100% is observed. This correlation clearly demonstrates a strong guiding effect introduced by the formation of a triple-line defect and by the existence of a photonic bandgap. The observed h also agrees with the computed curve, except that it extends slightly into the midgap by Dv͑a 0 ͞l͒ ϳ 0.1. It is possible that the etched defect holes are slightly larger than the nominally designed d 0 0.8a 0 , and thus the guiding mode is pushed more into the bandgap.
To achieve an even-wider bandwidth we need to push the guided modes farther into the midgap. In principle, this can be done by a further increase in the defect hole size to d 0 . 0.8a 0 . In practice, however, nanofabrication difficulty prevents us from achieving this increase, as the nearest hole-to-hole spacing will be too small. One possible solution is to introduce a nonuniform triple-line defect, such that the middle line has a hole size d 0 0.8a 0 1 Dd and the outer lines have a hole size d 0 0.8a 0 2 Dd. As the guided-mode electric field intensity is concentrated mostly in the middle defect line, this arrangement effectively raises the guiding-mode energy while maintaining the hole-to-hole spacing.
In summary, the design, fabrication, and testing of a triple-line defect embedded in a 2D photonic crys-tal slab has been reported. This new class of photonic crystal waveguide guides light in the lower-index region, with a near perfect guiding eff iciency at the optical communication wavelength l ϳ 1.5 mm. Such lossless guiding of light in a lower-index region is a consequence of strong photonic confinement made possible by a photonic bandgap.