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This work presents the successful fabrication of 1D photonic crystals (PCs) with two defects using the glancing angle deposition (GLAD) technique. We study the coupling behavior of the two PC defects and demonstrate the ability to control the defect interaction. GLAD allows engineering of film nanostructure to produce PCs with sinusoidal refractive index variation through control of film nanostructure and porosity. Two phase-shift defects are introduced into the refractive index profile of the film. The observed defect-defect coupling is explained by a coupled-oscillator model and the interaction strength is found to decrease exponentially with increasing defect separation. Furthermore, the results demonstrate the promise of GLAD as a platform technology for PC research and device fabrication.
©2010 Optical Society of America
1. Introduction
Glancing angle deposition (GLAD) is a micro- and nanostructure fabrication technique based on oblique thin film deposition and controlled substrate rotation [1,2]. Ballistic shadowing and limited surface diffusion during film growth produce a porous film with a separated columnar microstructure. Among the many applications being studied [2], there is significant GLAD research on one-dimensional photonic crystal (PC) fabrication. Multiple PC architectures have been realized using GLAD: Bragg multilayers [3–5], helically-sculpted columns [6–8], and inhomogeneous films with sinusoidal index variation [9,10]. GLAD is compatible with many materials, provides precise control over optical anisotropy, and produces high surface area porous materials. These advantages make GLAD-fabricated PCs promising candidates for polarization filters [11,12] and optical sensors [13–16] operating in various spectral regions.
While incorporating a single defect in GLAD-fabricated PCs has been demonstrated [17–19], multi-defect PCs have not been realized in GLAD PC research. A PC defect acts as an optical microresonator, supporting a field confined to the defect location [20]. Positioning two PC defects sufficiently close together permits energy exchange between the localized fields, leading to defect mode splitting [21] and Rabi oscillation [22]. These phenomena are entirely absent in single-defect PCs. Energy coupling between defects creates novel device capabilities and coupled-defect PCs are being actively studied for integrated optical devices [23,24], slow-light optics [25,26], and intriguing experiments in quantum optical systems [27].
In this work, we used GLAD to fabricate PCs with sinusoidally-varying index profiles containing two defects and examined their optical properties. The presence of defect mode splitting and the observed exponential dependence of the defect interaction confirm that we have successfully fabricated coupled-defect PCs. Furthermore, the realization of complex optical PC systems in this research demonstrates the precision of GLAD and its suitability as a platform technology for optical PC research.
2. Properties of coupled PC defects
Coupled PC defects are commonly examined using analytic formalisms based on the tight-binding approximation [21,28], coupled-mode theory [29], or coupled-harmonic-oscillators [30]. We employ the coupled-harmonic-oscillator approach because of its relative simplicity and connection with mechanical and electrical systems. In a system of two harmonic oscillators (with natural oscillation energies Ea and Eb), coupling causes a periodic energy exchange between the oscillators. The coupled system will exhibit two oscillating supermodes with energies E+ and E-, as given by
where g quantifies the coupling strength between the two oscillators [30–32]. For the present case of PC defects, the harmonic oscillators represent the optical resonances. The interaction between the two defects is determined by the overlap of the localized defect eigenmodes. The evanescent tails of these modes mediate the field coupling and g falls off exponentially with increasing defect separation [29,33]. Maximizing the energy coupling efficiency requires minimizing the resonance detuning (Ea−Eb). Experimental realization of coupled-defect PCs requires sufficiently accurate fabrication, especially for visible wavelength operation. The development and verification of this level of precision is an important test of GLAD PC fabrication.3. PC fabrication
Fabricating 1D PCs with GLAD is accomplished through precise nanostructure control. The refractive index of the deposited layer depends on the film density (ratio of column material to interstitial void) as well as the microgeometry [34]. These parameters are determined by the film’s columnar structure which is, in turn, determined by the deposition angle [35]. Consequently, refractive index variation along the film thickness can be realized via appropriate deposition angle changes during film fabrication.
We consider PCs with the following sinusoidal refractive index profile,
where z is the film thickness, na is the average refractive index of the film, np is the peak-to-peak index variation, λ0 is the photonic bandgap center wavelength, and ϕ0 is the phase term. The physical period P of the film is P = λ0/2na. PCs with sinusoidal index variation are commonly referred to as rugate filters [36]. Defects are introduced via index profile discontinuities [19]; in this work, π rad phase-shift defects were introduced to the film at z = (L ± Δz)/2, where L is the total film thickness and Δz is the separation between defects. An example of this index profile is shown in Fig. 1 (a) .
Fig. 1 (a) The sinusoidal refractive index profile with two phase-shift defects separated by Δz = 2P. (b) Scanning electron micrograph (35 000 X magnification) of a nanostructured 1D PC fabricated with TiO2 using the GLAD technique. The film smoothly alternates between a high and low density structure for 16 periods. (c) Zoomed in view of the phase shift defects from (b). Shifting the periodic structural variation by π rad creates a PC defect. Two defects are present in this image separated by two periods.
Films were deposited by electron-beam evaporation of TiO2 starting material (Cerac, Inc., rutile phase 99.9% purity) in a vacuum system specifically modified for GLAD use. For every deposition, the chamber was evacuated to a pressure below 133 μPa. O2(g) was added to the system, increasing the chamber pressure to 12.0 ± 1.3 mPa, to promote the formation of stoichiometric TiO2 at the substrate. Films were deposited onto both Si (100) and glass (Schott, B270) substrates and no substrate heating or cooling was employed. Typical deposition rates were 0.7 ± 0.1 nm/s, measured using a quartz crystal microbalance. To place film spectral features in the visible spectrum, λ0 was chosen to be 550 nm. During deposition, the deposition angle was cycled between 30° and 80° to create the density gradient and the required sinusoidal index variation. Based on previous measurements of GLAD-fabricated TiO2 films [20], this produces index parameters of na = 1.87 and np = 0.46 at a wavelength of 550 nm. A total of eight 16-period (L = 16P) films were deposited, each having two π rad phase-shift defects and a starting phase ϕ0 = 0. Defects were introduced by phase-shifting the deposition angle cycling by π rad at the desired points of film growth. In each film, the defects were separated by an integer multiple of periods (Δz = NP, where N = 1 through 8).
Films deposited on Si wafers were cleaved and the exposed edge was imaged using a scanning electron microscope (SEM; Hitachi S-4800). The normal incidence transmittance spectra of films deposited on glass were measured (Perkin Elmer 900 UV-VIS-NIR) at wavelengths between 320 nm and 800 nm, at 2 nm intervals. To precisely measure the defect-modes, spectra were converted to energy units (E = hc/λ) and a line shape function was numerically fit to the transmittance peaks using the Levenberg-Marquart algorithm [37]. The line shape used was a sum of two Lorentzian functions, given by
where E is the energy (in eV), Ii, Ei, and γi are, respectively, the amplitude, location, and width of the ith peak. Fitting Eq. (3) measures both defect modes simultaneously and the defect mode splitting is calculated as ΔE = E1−E2. Quoted with the results are one standard deviation confidence intervals estimated from the covariance matrix of the fit.4. Experimental results
Figure 1(b) shows a cross-sectional SEM image of the film with defect separation Δz = 2P. All 16 periods are shown at this magnification (35000X). The grayscale contrast in the image is created by structural topography, allowing observation of the columnar structure and density variation. Over one period, the microstructure smoothly alternates between densely packed columns (corresponding to high refractive index) and separated, sparsely packed columns (low refractive index). Introducing a defect causes a subtle change in the PC structure. Defects are detected by following the periodic structural variation through the film thickness until a phase change is observed. Figure 1(c) shows an enlarged section of the image in Fig. 1(b) in the vicinity of the defects, highlighting the phase changes.
Figure 2 shows the transmittance spectra measured for the film with Δz = 4P. This graph is representative of the other measurements, and we show it to highlight the important spectral features of the coupled defect system. Note the presence of the photonic bandgap, spanning the wavelength interval from 451 nm to 628 nm (measured between points of 40% transmittance). The mean bandgap center wavelength of all 8 samples is λmean = 555 nm ± 15 nm. This result shows good agreement with the design value of 550 nm and the observed variation is attributed to process fluctuations. We expect that more sophisticated control and monitoring techniques will improve fabrication tolerances. Outside the bandgap we see interference fringes typical of optical thin films. Each film examined in this study showed similar bandgap formation and interference fringes. Labeled in this figure are two defect modes, located at 547.3 nm and 512.0 nm with Q-factors of 114 ± 2 and 133 ± 1, respectively.
Fig. 2 The optical transmittance spectra of a film with two defects separated by Δz = 4P. Inside the photonic bandgap, two defect modes are observed. These modes are created by coupling between the fields localized at the phase-shift defects.
Figures 3(a)-(d) show the measured transmittance in the vicinity of the defect modes for defect separations of Δz = 2P, 3P, 5P, and 8P periods, respectively. The spectra are plotted in energy units (eV) and the fitted lineshapes have been included. The other four spectra are omitted for brevity. In all cases, two well-defined defect modes are observed and the Lorentzian function accurately reproduces the defect mode lineshapes.
Fig. 3 Measured transmittance (data points) in the vicinity of the resonant transmittance peaks inside the bandgap. The spectra correspond to defect separations of (a) two periods, (b) three periods, (c) five periods, and (d) eight periods. Also shown on the spectra are Lorentzian lineshapes fit to the measured data.
Figure 4 shows the measured relationship between peak separation and defect separation in the film. Also shown on this plot is the function
after curve-fitting to the data via the constants A, B, and C. Equation (4) is derived from the third term in Eq. (1) and separates the mode splitting into contributions from defect detuning and coupling. The curve fitting yields parameters of A = (0.08 ± 0.02) eV, B = (0.25 ± 0.02) eV, and C = (−0.32 ± 0.05) P −1. The agreement between the measured data and Eq. (4) is excellent, supporting the validity of the coupled oscillator model for this system.Fig. 4 The measured defect mode separation is plotted as a function of deparation between defects in the PC. The theoretical curve plotted is Eq. (4) in the text after fitting to the data set.
The appearance of two peaks in the measured transmittance can be created by the coupling interaction and/or a mismatch between defect resonances [30,32]. However, the exponential behavior confirms that defect coupling contributes significantly to the mode splitting in addition to resonance detuning. This indicates that we have successfully fabricated coupled defect PCs using the GLAD technique and can accurately control the defect coupling through the defect spacing.
The parameter A = (0.08 ± 0.02) eV found for Eq. (4) provides an estimate of the average defect mode detuning across all eight samples. Detuning can be attributed to multiple sources. First, random fabrication errors will detune the resonances. However, this can be mitigated by improved fabrication control. A second source comes from the PC boundaries. Because the PCs are finite, the defect modes leak into freespace at the system boundaries. Since the boundaries are different (one being air/film and the other film/substrate) they introduce different losses and detune the resonances. By increasing the number of periods in the film the defects can be moved further from the film edges, decreasing the boundary influence. Alternatively, the defect resonances could be intentionally detuned at the design stage to compensate.
5. Summary
We have successfully used the GLAD technique to fabricate PCs with two defects and demonstrated control over the defect interaction. The properties of our coupled-defect PCs are well-explained by an analytic, coupled-harmonic-oscillator model. GLAD is a promising, simple, one-step technique for bottom-up nanofabrication and our results further highlight the utility of GLAD in PC research. GLAD is a precise and repeatable technique, able to successfully conduct experiments on visible wavelength PCs and is a viable approach for PC device fabrication. GLAD-fabricated coupled-defect PCs may find use as optical delay filters and filters with engineered dispersion characteristics. By leveraging properties unique to GLAD PCs, including tunable porosity, wide material compatibility, and optical anisotropy, novel devices could be realized. Our results provide the foundation for developing coupled-defect GLAD PCs into improved optical sensors, tunable liquid-crystal/film hybrids, and polarization-sensitive optical devices.
Acknowledgments
The authors would like to thank the Natural Sciences and Engineering Research Council of Canada, the Alberta Informatics Circle of Research Excellence, and Micralyne Inc. for financial support. The University of Alberta Micromachining and Nanofabrication Facility is thanked for providing equipment access.
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