This work was partially supported by the Research Corporation for Science Advancement (Grant 10626), National Science Foundation (DMR-1308084), and the San Francisco State University internal award to W. M. We thank our collaborator Paul M. Chaikin from NYU for helpful discussions in experimental design and for providing the VNA system for us to use on site at SFSU. We thank our theoretical collaborators, the inventor of the HD PBG materials, Marian Florescu, Paul M. Steinhardt, and Sal Torquato for various discussions and for providing us the design of the HD point pattern and continuous discussions.

1. Design a 2D Hyperuniform Disordered Dielectric Structure11
<ol>
	<li>Chose a subclass of 2D hyperuniform disorder point pattern (blue circles in Figure 2) and partition it (blue lines in Figure 2) using Delaunay tessellation. A 2D Delaunay tessellation is a triangulation that maximizes the minimum angle for each triangle formed and guarantees there are no other points inside the circumcircle of each triangle11.</li>
	<li>Locate the centroids of each triangle (solid black circles in Figure 2); these centroids are the locations of the dielectric rods of radius r11.</li>
	<li>Connect the centroids of the neighboring triangles (thick red lines in Figure 2) to generate cells around each point11.</li>
	<li>Create the CAD design file for the 2 cm tall HD base template with holes and slots on which the rods and walls will be assembled14. Use an HD pattern with the average inner-rod spacing of a=1.33 cm and set the hole-radius to be 2.5 mm and slot-width to be 0.38 mm. Set the depth for holes and slots to be 1 cm deep to stabilize the inserted rods and walls.</li>
	<li>Create a similar CAD design file for the crystalline base template (a square lattice) for comparison14. Use the same lattice constant as the HD structure (1.33 cm) and the same hole-radius (2.5 mm) and slot-width (0.38 mm).</li>
</ol>
2. Sample Construction and Preparation
<ol>
	<li>Fabricate the template. Manufacture the HD and Square lattice plastic bases by using a stereolithography machine that produces a solid plastic model by ultraviolet laser photo-polymerization. Use a clear resin, for example polycarbonate-like plastic. The resolution is 0.1 mm in both lateral and vertical directions. (See Figure 3, center panel).</li>
	<li>Prepare the building blocks: Order commercially available Alumina rods and thin walls cut to precise dimensions (see Figure 3, left panel). Set the height to be no less than a few wavelengths, for example 10.0 cm. The diameter of all rods is 5.0 mm. Wall thickness is always 0.38 mm and widths vary from 1.0 mm to 5.3 mm, with 0.2 mm increments. &#160;&#160;</li>
	<li>Construct the defect-free test structure for bandgap measurements. Insert rods and walls into the base for the desired structure architecture. The side view of the constructed network of both rods and walls on the polymer base is shown in Figure 3, right panel.</li>
	<li>Design a waveguide or a cavity defect: Create various waveguides through the samples by directly removing or modifying rods and walls along the designed path, as shown in Figures 9A and 9C. The modular design of the samples allows fast and easy modification of point and line or curve defects.&#160;</li>
</ol>
3. Major Instruments
<ol>
	<li>Use a synthesized sweeper (microwave generator) to provide microwaves with frequency coverage of 45 MHz to 50 GHz with precise 1 Hz frequency resolution. Connect the generator to an S-parameter test set to measure transmission parameters between the two ports (terminals). Use General Purpose Interface Bus (GPIB) links and cables for communications between the sweeper and the test-set.</li>
	<li>Use a Microwave Vector Network analyzer (VNA) to process the signal received from the S-parameter test-set and to measure the signal&#8217;s magnitude and the phase. Set the S-parameter test set to S21 mode so that the VNA outputs a data file containing the real and imaginary components of the detected E-field at port 1 with respect to the source signal from port 2 as a function of frequency</li>
</ol>
4. Instrument Setup
<ol>
	<li>Start/End Frequency.&#160; Select the appropriate start and end values of the frequency range for the measurement using the VNA user menu. The relevant frequency range associated with PBG depends on the dielectric index of lattice spacing of the samples. Use 7 GHz to 15 GHz microwaves for the Alumina samples with lattice spacing a=1.33 cm.</li>
	<li>Averaging Factor. Vector analyzer computes each data point based on the average of multiple measurements to reduce random noise. Select an averaging factor from 512 to 4,096 by inputting the desired multiple on the VNA keypad. Choose a higher averaging factor to minimize noise and chose a lower averaging factor for a quicker scan.</li>
	<li>Number of Points. For measurements in the 7 GHz to 15 GHz range, chose the maximum number of data points (801), on the VNA on-screen menu, to achieving a frequency resolution of 10 MHz.</li>
	<li>Calibration. Calibrate the system by directly measuring the relative transmission ratio, and normalize it against the transmission of a pre-calibrated setting with the same background and without the sample between the horn antennas. By doing this, all the background loss due to the cables, adaptors, waveguides, and antennas can be eliminated, and the relative transmission ratio with and without the tested sample is directly recorded.&#160;&#160;
	<ol>
		<li>For bandgap measurements, measure the microwave transmission through free space between the horns facing each other at the distance of 28a and save the results as a calibration set in the VNA. Before taking data for the actual experiment with a structure between the horns, turn on the calibration set by selecting &#8220;CALIBRATION ON&#8221; on the VNA monitor. Data calculated by the VNA will be automatically normalized against the calibration set and return the ratio of transmission power with and without the sample in place.</li>
		<li>For waveguide measurements, a meaningful calibration is not well-defined, since the transmission through the sample waveguides can easily exceed the calibrated transmission between the two horns in free space. Turn off calibration on the VNA monitor and record the raw transmission, which is the detected signal over the source signal. Place the horns right next to the waveguide channel openings to achieve the best coupling efficiency.</li>
	</ol>
	</li>
</ol>
5. Experimental Setup
<ol>
	<li>Configure the experimental setup shown in Figure 4. Use high quality semi-flexible coaxial cables to connect the S-parameter test-set ports with input/output waveguides. Connect pyramidal horn antennas with the ports through rectangular single mode waveguides and adaptors to ensure the radiation to be linearly polarized, The E-field of the radiation from the horn is parallel to the short edge of the horn.</li>
	<li>For bandgap measurements: Adhere to the following steps to measure the transmission through the defect-free samples to characterize the PBG of the defect free samples.
	<ol>
		<li>Align the horns vertically and horizontally to face each other. Arrange the horns at a far enough distance, such as 20 times of the average wavelength, so that the far-field radiation reaching the sample can be approximated to plane waves. Calibrate the transmission between the facing horns in free space without the testing sample and store it in calibration memory.</li>
		<li>Place defect-free structures made of rods and walls on the rotating stage in between the two facing horns. Turn on the calibration set recorded into VNA memory during step 5.2.1. The system is now ready to measure the relative transmission ratio through the sample normalized against the transmission power of the calibrated memory.</li>
	</ol>
	</li>
	<li>For waveguides and cavity defects measurements: Adhere to the following steps to setup the experiments:
	<ol>
		<li>Construct various waveguides and cavities by removing or replacing rods and walls in the defect-free structures, as shown in Figures 9A and 9C.&#160;&#160;&#160;&#160;</li>
		<li>Arrange the horns as close to the channel openings as possible to ensure good coupling into the channel. For curved and bent channels center the horns in the middle of the channel with the edge parallel to the opening.</li>
		<li>Turn off calibration. Now the VNA system is ready to measure and record the raw transmission ratio of the detected power at port 2 over the source power at port 1.</li>
	</ol>
	</li>
</ol>
6. Data Acquisition and Analysis
<ol>
	<li>Characterize the angular dependence of the photonic properties of the samples:
	<ol>
		<li>Place structures made of rods and walls with a nearly circular boundary on a rotating stage in between the two facing horns.</li>
		<li>Make sure that the calibration saved in the VNA memory is turned on in step 5.2.2. Zero the angle scale on the rotating stage and measure transmission through the structure. After the initial measurement at zero incident angle, rotate the sample and measure the transmission in equal angle increments, such as every 2&#176;&#160;until 180&#176;&#160;rotation is reached.</li>
	</ol>
	</li>
	<li>Characterize the polarization dependence of the photonic properties for the samples: 
	Perform all measurements described above in two different polarizations respectively, by changing the horn opening orientations. For TM polarization, set the horns&#8217; short edge (the E-field direction) perpendicular to the horizontal plane of the sample base and parallel to the rods. For TE polarization, rotate the horns 90 degrees, so that their short edges (the E-field direction) are in the horizontal plane.</li>
	<li>Characterize various waveguides channels: Make sure that the calibration is turned off in step 5.3.3. Place the horns next to the sample for best coupling. Measure the transmission through various channels constructed by removing and/or replacing rods and walls along the channel path. While monitoring the transmission signal on the VNA in real time, modify the channel path by adding and removing extra rods and walls for optimized transmission power or desired filtering bandwidth.</li>
	<li>Perform analogous measurements similar to what are described above on a square lattice photonic crystal for comparison.</li>
	<li>Data analysis. Analyze and graph the data using a computer program, such as MATLAB.&#160; Plot measured transmission as a function frequency (line plot), such as Figure 5, Figure 2, and Figure 9B and 9D to study the stopgap through the samples or transmission pass though the waveguide channels.&#160; Plot transmission as a function of frequency and angle (color contour plot) to analyze the stop bands characteristics of the structures and their angular dependence, as shown in Figure 6 and Figure 7.</li>
	<li>This protocol suggests presenting the measured transmission through the samples as a function of frequency and incident angle in polar coordinates12, in order to directly visualize the rotational symmetries and angular dependence of photonic properties. Generate the polar-coordinate plots to directly show the Brillouin zone boundaries of crystalline structures and reveal the relationship between PBG formation and Bragg scattering planes (Brillouin zone boundaries) in crystals and quasicrystals.</li>
</ol>

<ol>
	<li>Strut, J. W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> The propagation of waves through a Medium Endowed with a Periodic structure. Philosophical magazine. XXIV, 145-159 (1887).</li><li>Yablonovitch, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Inhibited+spontaneous+emission+in+solid-state+physics+and+electronics.">Inhibited spontaneous emission in solid-state physics and electronics.</a> Phys. Rev. Lett. 58, 2059-2062 (1987).</li><li>Yablonovitch, E., Gmitter, T. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photonic+band+structure:+The+face-centered-cubic+case.">Photonic band structure: The face-centered-cubic case.</a> Phys. Rev. Lett. 63, 1950-1953 (1989).</li><li>Sajeev, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Strong+localization+of+photons+in+Certain+Disordered+Dielectric+super+lattices.">Strong localization of photons in Certain Disordered Dielectric super lattices.</a> Phys. Rev. Lett. 58, 2486-2489 (1987).</li><li>Joannopoulos, J., Johnson, S. G., Winn, J. N., Mead, R. D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Photonic Crystals: Molding the Flow of Light. , 243-248 (2008).</li><li>Noda, S., Chutinan, A., Trappin Imada, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=emission+of+photons+by+a+single+defect+in+a+photonic+bandgap+structure.">emission of photons by a single defect in a photonic bandgap structure.</a> Nature. 407, 608-610 (2000).</li><li>Cao, H., Zhao, Y. G., Ho, S. T., Seeling, E. W., Wang, Q. H., Chang, R. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Random+laser+action+in+semiconductor+powder.">Random laser action in semiconductor powder.</a> Phys. Rev. Lett. 82, 2278-2281 (1999).</li><li>Chutinan, A., John, S., Toader, O. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Diffractionless+flow+of+light+in+all-optical+microchips.">Diffractionless flow of light in all-optical microchips.</a> Phys. Rev. Lett. 90, 123901 (2003).</li><li>Vynck, K., Burresi, M., Riboli, F., Wiersma, D. S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photon+management+in+two-dimensional+disordered+media.">Photon management in two-dimensional disordered media.</a> Nature Mater. 11, 1017-1022 (2012).</li><li>Ishizaki, K., Koumura, M., Suzuki, K., Gondaira, K., Noda, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Realization+of+three-dimensional+guiding+of+photons+in+photonic+crystals.">Realization of three-dimensional guiding of photons in photonic crystals.</a> Nature Photon. 7, 133-137 (2013).</li><li>Florescu, M., Torquato, S., Steinhardt, P. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Designer+disordered+materials+with+large,+complete+PBGs.">Designer disordered materials with large, complete PBGs.</a> Proc. Natl. Acad. Sci. 106, 20658-20663 (2009).</li><li>Man, W., Megens, M., Steinhardt, P. J., Chaikin, P. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Experimental+measurement+of+the+photonic+properties+of+icosahedral+quasicrystals.">Experimental measurement of the photonic properties of icosahedral quasicrystals.</a> Nature. 436, 993-996 (2005).</li><li>Torquato, S., Stillinger, F. H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Local+density+fluctuations,+hyperuniformity,+and+order+metrics.">Local density fluctuations, hyperuniformity, and order metrics.</a> Phys. Rev. E. 68, 041113 (2003).</li><li>Man, W., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Isotropic+band+gaps+and+freeform+waveguides+observed+in+hyperuniform+disordered+photonic+solids.">Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids.</a> Proc. Natl. Acad. Sci. 110, 15886-15891 (2013).</li><li>Freeform wave-guiding and tunable frequency splitting in isotropic disordered photonic band gap materials. Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) Available from: <a target="_blank" href="https://www.osapublishing.org/abstract.cfm?uri=FiO-2012-FTh2G.5">https://www.osapublishing.org/abstract.cfm?uri=FiO-2012-FTh2G.5</a> (2012)</li><li>Cavity Modes Study in Hyperuniform Disordered Photonic Bandgap Materials. Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) Available from: <a target="_blank" href="https://www.osapublishing.org/abstract.cfm?uri=FiO-2012-FTh3F.4">https://www.osapublishing.org/abstract.cfm?uri=FiO-2012-FTh3F.4</a> (2012)</li><li>Man, W., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photonic+band+gap+in+isotropic+hyperuniform+disordered+solids+with+low+dielectric+contrast.">Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast.</a> Opt. Express. 21, 19972-19981 (2013).</li><li>Man, W., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Experimental+observation+of+photonic+bandgaps+in+Hyperuniform+disordered+materials.">Experimental observation of photonic bandgaps in Hyperuniform disordered materials.</a> , (2010).</li><li>Schelew, E., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Characterization+of+integrated+planar+photonic+circuits+fabricated+by+a+CMOS+foundry.">Characterization of integrated planar photonic circuits fabricated by a CMOS foundry.</a> Journal of Lightwave Technology. 31 (2), 239 (2013).</li><li>Guo, Y. B., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Sensitive+molecular+binding+assay+using+a+photonic+crystal+structure+in+total+internal+reflection.">Sensitive molecular binding assay using a photonic crystal structure in total internal reflection.</a> Opt. Express. 16, 11741-11749 (2008).</li></ol>

The authors have nothing to disclose.

Starting from a hyperuniform disordered point pattern, 2D HD structures consisting rods and/or wall network can be designed to obtain a complete PBG for all polarization11. Based on the design, we constructed a template with holes and slots for assembling 2D Alumina rods and walls structures at cm-scale which could be tested with microwaves. We chose to work with microwaves, because cm-scale building blocks, such as Alumina rods and walls, are inexpensive, and easily handled. We have experimentally demonstrate...

The existence of a bandgap for photons has been the focus of many scientific works, starting from the earlier studies done by Lord Rayleigh on the one-dimensional stop-band, a range of frequencies that are forbidden from propagation through a periodic medium1. Research into electromagnetic wave (EM) propagation in periodic structures has really flourished in the last two decades after the seminal publications of E. Yablonovitch2,3 and S. John4. The term &#8220;photonic crystal&#8221; was coined by Yablonovitch to describe the periodic dielectric structures that possessed a photonic bandgap (PBG). &#160;

Photonic crystals are periodic dielectric structures possessing discrete translational symmetries, rendering them invariant under translations in directions of periodicity. When this periodicity is matched with the wavelengths of incoming electromagnetic (EM) waves, a band of frequencies becomes highly attenuated and may stop propagating. If wide enough, the ranges of the forbidden frequencies, also called stop bands, may overlap in all directions to create a PBG, forbidding the existence of photons of certain frequencies.

Conceptually, EM wave propagation in photonic crystals is similar to electron wave propagation in semiconductor materials, which have a forbidden region of electron energies, also known as a bandgap. Similar to the way engineers have employed semiconductors to control and modify the flow of electrons through semiconductors, PBG materials can be used for various applications requiring optical control. For example, PBG materials can confine light of certain frequencies in wavelength size cavities, and guide or filter light along line defects in them5. PBG materials are suggested to be used for controlling the flow of light for applications in telecommunication6, lasers7, optical circuits and optical computing8, and solar energy harvesting9.

A two-dimensional (2D) square lattice photonic crystal has 4-fold rotational symmetry. EM waves entering the crystal at different angles of incidence (for example, 0&#176; and 45&#176; with respect to the lattice planes) will face different periodicities. Bragg scattering in different directions leads to stop bands of different wavelengths that may not overlap in all directions to form a PBG, without very high refractive-index contrast of the materials. In addition, in 2D structures, two different EM wave polarizations, Transverse Electric (TE) and Transverse Magnetic (TM), often form bandgaps at differing frequencies, making it even harder to form a complete PBG in all directions for all polarizations5. In periodic structures, the limited choices of rotational symmetry lead to intrinsic anisotropy (angular dependence), which not only makes it hard to form a complete PBG, but also greatly limits the design freedom of functional defects. For example, waveguide designs are proven to be restricted along very limited choices of major symmetry directions in photonic crystals10.

Inspired to surpass these limitations due to periodicity, much research has been done in the past 20 years on unconventional PBG materials. Recently a new class of disordered materials was proposed to possess an isotropic complete PBG in the absence of periodicity or quasiperiodicity: the hyperuniform Disorder (HD) PBG structure11. The photonic bands do not have exact analytical solution in disorder structures. Theoretical study of the photonic properties of the disordered structures is limited to time&#8211;consuming numerical simulations. To calculate the bands, the simulation needs to employ a super-cell approximation method and the available computational power may limit the finite size of the super-cell. To calculate transmission through these structures, computer simulations often assume ideal conditions and thus neglect real world problems like the coupling between the source and detector, the actual incident EM wave profile, and alignment imperfections12. Furthermore, any modification (defect design) of the simulated structure would require another round of simulation. Due to the large size of the minimum meaning for super-cell, it is very tedious and impractical to systematically explore various defect design architectures for these disordered materials.

We can avert these computational problems by studying the disordered photonic structures experimentally. Through our experiments we are able to verify the existence of the complete PBG in HD structures. Using microwave experiments, we can also obtain phase information and reveal the field distribution and dispersion properties of existing photonic states in them. Using an easily modifiable and modular sample at cm-scale, we can test various waveguide and cavity (defect) designs in the disordered systems and analyze the robustness of the PBGs. This kind of analysis of complex disordered photonic structures is either impractical or impossible to obtain through numerical or theoretical studies.

The design process begins by selecting a &#8220;stealthy&#8221; hyperuniform point pattern13. Hyperuniform point patterns are systems in which the number variance of the points within a &#8220;spherical&#8221; sampling window of radius R, grows more slowly than the window volume for large R, that is, more slowly than Rd in d-dimensions. For example, in a 2D Poisson random distribution of point pattern, the variance of the number of points in domain R is proportional to R2. However, in a hyperuniform disorder point pattern, the variance of the points in a window of radius R, is proportional to R. Figure 1&#160;shows a comparison between a hyperuniform disordered point pattern and a Poisson point pattern11. We use a subclass of hyperuniform disordered point patterns called &#8220;stealthy&#8221;11.

Using the design protocol described in Florescu&#160;et al11, we construct a network of dielectric walls and rods, creating a 2D hyperuniform dielectric structure similar to a crystal, but without the limitations inherent to periodicity and isotropy. The wall networks are favorable for TE-polarization bandgap, while the rods are preferable for forming band gaps with TM-polarization.&#160; A modular design was developed, so that the samples can be easily modified for use with different polarizations and for introducing freeform waveguides and cavity defects. Due to the scale invariance of Maxwell&#8217;s equations, the electromagnetic properties observed in the microwave regime are directly applicable to the infrared and optical regimes, where the samples would be scaled to micron and submicron sizes.

<table border="0" cellpadding="0" cellspacing="0" width="599">
	<tbody>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">stereolithography machine</td>
			<td style="width:97px;">3D Systems</td>
			<td style="width:119px;">SLA-7000</td>
			<td style="width:167px;"></td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">resin for base</td>
			<td style="width:97px;">3D Systems</td>
			<td style="width:119px;">Accura 60</td>
			<td></td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Alumina rods</td>
			<td style="width:97px;"></td>
			<td style="width:119px;"></td>
			<td>r=2.5mm, cut to 10.0cm height</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Alumina sheets</td>
			<td style="width:97px;"></td>
			<td style="width:119px;"></td>
			<td>thickness 0.38mm, various width: from 1.0mm to 5.3mm with 0.2mm incerments</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Microwave Generator</td>
			<td style="width:97px;">Agilent/HP</td>
			<td style="width:119px;">83651B</td>
			<td></td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">S-Parameter Test set</td>
			<td style="width:97px;">Agilent/HP</td>
			<td style="width:119px;">8517B</td>
			<td></td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:216px;">Microwave Vector Network Analyzer</td>
			<td style="width:97px;">Agilent/HP</td>
			<td style="width:119px;">8510C</td>
			<td></td>
		</tr>
	</tbody>
</table>

using microwave and macroscopic samples of dielectric solids to study the photonic properties of disordered photonic bandgap materials

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). In this article we will describe the methods for constructing and characterizing macroscopic disordered photonic structures using microwaves. The microwave regime offers the most convenient experimental sample size to build and test PBG media. Easily manipulated dielectric lattice components extend flexibility in building various 2D structures on top of pre-printed plastic templates. Once built, the structures could be quickly modified with point and line defects to make freeform waveguides and filters. Testing is done using a widely available Vector Network Analyzer and pairs of microwave horn antennas. Due to the scale invariance property of electromagnetic fields, the results we obtained in the microwave region can be directly applied to infrared and optical regions. Our approach is simple but delivers exciting new insight into the nature of light and disordered matter interaction.

Our representative results include the first experimental demonstration of the existence of a complete and isotropic PBG in a two-dimensional (2D) hyperuniform disordered dielectric structure. Additionally we demonstrate experimentally the ability of this novel photonic structure to guide electromagnetic waves (EM) through freeform waveguides of arbitrary shape.

We have achieved the first confirmation ever of an isotropic complete PBG present in hyperuniform disorder dielectric structures. Here, we present our HD structure results and compare them to that of a periodic square lattice photonic crystal.
Figure 5 shows a semi-log plot of TE polarization transmission (dB) vs. frequency (GHz) for a hyperuniform disorder structure at one incident angle. This plot shows that the stop band region is located approximately between 8.5 and 9.5 G...

Watch this Scientific Journal Video about Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials at JoVE.com

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Disordered structures offer new mechanisms for forming photonic bandgaps and unprecedented freedom in functional-defect designs. To circumvent the computational challenges of disordered systems, we construct modular macroscopic samples of the new class of PBG materials and use microwaves to characterize their scale-invariant photonic properties, in an easy and inexpensive manner.

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). ...

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12.2K Views.  San Francisco State University. Disordered structures offer new mechanisms for forming photonic bandgaps and unprecedented freedom in functional-defect designs. To circumvent the computational challenges of disordered systems, we construct modular macroscopic samples of the new class of PBG materials and use microwaves to characterize their scale-invariant photonic properties, in an easy and inexpensive manner.

Video: Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Harvesting Solar Energy by Means of Charge-Separating Nanocrystals and Their Solids

Conjoining different semiconductor materials in a single nano-composite provides synthetic means for the development of novel optoelectronic materials offering a superior control over the spatial distribution of charge carriers across material interfaces. As this study demonstrates, a combination of donor-acceptor nanocrystal (NC) domains in a single nanoparticle can lead to the realization of efficient photocatalytic1-5 materials, while a layered assembly of donor- and acceptor-like nanocrystals films gives rise to photovoltaic materials.
Initially the paper focuses on the synthesis of composite inorganic nanocrystals, comprising linearly stacked ZnSe, CdS, and Pt domains, which jointly promote photoinduced charge separation. These structures are used in aqueous solutions for the photocatalysis of water under solar radiation, resulting in the production of H2 gas. To enhance the photoinduced separation of charges, a nanorod morphology with a linear gradient originating from an intrinsic electric field is used5. The inter-domain energetics are then optimized to drive photogenerated electrons toward the Pt catalytic site while expelling the holes to the surface of ZnSe domains for sacrificial regeneration (via methanol). Here we show that the only efficient way to produce hydrogen is to use electron-donating ligands to passivate the surface states by tuning the energy level alignment at the semiconductor-ligand interface. Stable and efficient reduction of water is allowed by these ligands due to the fact that they fill vacancies in the valence band of the semiconductor domain, preventing energetic holes from degrading it. Specifically, we show that the energy of the hole is transferred to the ligand moiety, leaving the semiconductor domain functional. This enables us to return the entire nanocrystal-ligand system to a functional state, when the ligands are degraded, by simply adding fresh ligands to the system4.
To promote a photovoltaic charge separation, we use a composite two-layer solid of PbS and TiO2 films. In this configuration, photoinduced electrons are injected into TiO2 and are subsequently picked up by an FTO electrode, while holes are channeled to a Au electrode via PbS layer6. To develop the latter we introduce a Semiconductor Matrix Encapsulated Nanocrystal Arrays (SMENA) strategy, which allows bonding PbS NCs into the surrounding matrix of CdS semiconductor. As a result, fabricated solids exhibit excellent thermal stability, attributed to the heteroepitaxial structure of nanocrystal-matrix interfaces, and show compelling light-harvesting performance in prototype solar cells7.

A general strategy for the development of charge-separating semiconductor nanocrystal composites deployable for solar energy production is presented. We show that assembly of donor-acceptor nanocrystal domains in a single nanoparticle geometry gives rise to a photocatalytic function, while bulk-heterojunctions of donor-acceptor nanocrystal films can be used for photovoltaic energy conversion.

Conjoining different semiconductor materials in a single nano-composite provides synthetic means for the development of novel optoelectronic materials ...

Micro 3D Printing Using a Digital Projector and its Application in the Study of Soft Materials Mechanics

Buckling is a classical topic in mechanics. While buckling has long been studied as one of the major structural failure modes1, it has recently drawn new attention as a unique mechanism for pattern transformation. Nature is full of such examples where a wealth of exotic patterns are formed through mechanical instability2-5. Inspired by this elegant mechanism, many studies have demonstrated creation and transformation of patterns using soft materials such as elastomers and hydrogels6-11. Swelling gels are of particular interest because they can spontaneously trigger mechanical instability to create various patterns without the need of external force6-10. Recently, we have reported demonstration of full control over buckling pattern of micro-scaled tubular gels using projection micro-stereolithography (P&mu;SL), a three-dimensional (3D) manufacturing technology capable of rapidly converting computer generated 3D models into physical objects at high resolution12,13. Here we present a simple method to build up a simplified P&mu;SL system using a commercially available digital data projector to study swelling-induced buckling instability for controlled pattern transformation.
A simple desktop 3D printer is built using an off-the-shelf digital data projector and simple optical components such as a convex lens and a mirror14. Cross-sectional images extracted from a 3D solid model is projected on the photosensitive resin surface in sequence, polymerizing liquid resin into a desired 3D solid structure in a layer-by-layer fashion. Even with this simple configuration and easy process, arbitrary 3D objects can be readily fabricated with sub-100 &mu;m resolution.
This desktop 3D printer holds potential in the study of soft material mechanics by offering a great opportunity to explore various 3D geometries. We use this system to fabricate tubular shaped hydrogel structure with different dimensions. Fixed on the bottom to the substrate, the tubular gel develops inhomogeneous stress during swelling, which gives rise to buckling instability. Various wavy patterns appear along the circumference of the tube when the gel structures undergo buckling. Experiment shows that circumferential buckling of desired mode can be created in a controlled manner. Pattern transformation of three-dimensionally structured tubular gels has significant implication not only in mechanics and material science, but also in many other emerging fields such as tunable matamaterials.

We demonstrate controlled pattern transformation of swelling gel tubes by elastic instability. A simple projection micro stereo-lithography setup is built using an off-the-shelf digital data projector to fabricate three-dimensional polymeric structures in a layer-by-layer fashion. Swelling hydrogel tubes under mechanical constraint display various circumferential buckling modes depending on dimension.

Buckling is a classical topic in mechanics. While buckling has long been studied as one of the major structural failure modes1, it has recently drawn new ...

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view and for its considerable potential for practical applications. Slow light photonic crystal waveguides, in particular, have played a major part and have been successfully employed for delaying optical signals1-4 and the enhancement of both linear5-7 and nonlinear devices.8-11
Photonic crystal cavities achieve similar effects to that of slow light waveguides, but over a reduced band-width. These cavities offer high Q-factor/volume ratio, for the realization of optically12 and electrically13 pumped ultra-low threshold lasers and the enhancement of nonlinear effects.14-16 Furthermore, passive filters17 and modulators18-19 have been demonstrated, exhibiting ultra-narrow line-width, high free-spectral range and record values of low energy consumption.
To attain these exciting results, a robust repeatable fabrication protocol must be developed. In this paper we take an in-depth look at our fabrication protocol which employs electron-beam lithography for the definition of photonic crystal patterns and uses wet and dry etching techniques. Our optimised fabrication recipe results in photonic crystals that do not suffer from vertical asymmetry and exhibit very good edge-wall roughness. We discuss the results of varying the etching parameters and the detrimental effects that they can have on a device, leading to a diagnostic route that can be taken to identify and eliminate similar issues.
The key to evaluating slow light waveguides is the passive characterization of transmission and group index spectra. Various methods have been reported, most notably resolving the Fabry-Perot fringes of the transmission spectrum20-21 and interferometric techniques.22-25 Here, we describe a direct, broadband measurement technique combining spectral interferometry with Fourier transform analysis.26 Our method stands out for its simplicity and power, as we can characterise a bare photonic crystal with access waveguides, without need for on-chip interference components, and the setup only consists of a Mach-Zehnder interferometer, with no need for moving parts and delay scans.
When characterising photonic crystal cavities, techniques involving internal sources21 or external waveguides directly coupled to the cavity27 impact on the performance of the cavity itself, thereby distorting the measurement. Here, we describe a novel and non-intrusive technique that makes use of a cross-polarised probe beam and is known as resonant scattering (RS), where the probe is coupled out-of plane into the cavity through an objective. The technique was first demonstrated by McCutcheon et al.28 and further developed by Galli et al.29

Use of photonic crystal slow light waveguides and cavities has been widely adopted by the photonics community in many differing applications. Therefore fabrication and characterization of these devices are of great interest. This paper outlines our fabrication technique and two optical characterization methods, namely: interferometric (waveguides) and resonant scattering (cavities).

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view ...

Concurrent Quantitative Conductivity and Mechanical Properties Measurements of Organic Photovoltaic Materials using AFM

Organic photovoltaic (OPV) materials are inherently inhomogeneous at the nanometer scale. Nanoscale inhomogeneity of OPV materials affects performance of photovoltaic devices. Thus, understanding of spatial variations in composition as well as electrical properties of OPV materials is of paramount importance for moving PV technology forward.1,2 In this paper, we describe a protocol for quantitative measurements of electrical and mechanical properties of OPV materials with sub-100 nm resolution. Currently, materials properties measurements performed using commercially available AFM-based techniques (PeakForce, conductive AFM) generally provide only qualitative information. The values for resistance as well as Young's modulus measured using our method on the prototypical ITO/PEDOT:PSS/P3HT:PC61BM system correspond well with literature data. The P3HT:PC61BM blend separates onto PC61BM-rich and P3HT-rich domains. Mechanical properties of PC61BM-rich and P3HT-rich domains are different, which allows for domain attribution on the surface of the film. Importantly, combining mechanical and electrical data allows for correlation of the domain structure on the surface of the film with electrical properties variation measured through the thickness of the film.

Organic photovoltaic (OPV) materials are inherently inhomogeneous at the nanometer scale. Nanoscale inhomogeneity of OPV materials affects performance of photovoltaic devices. In this paper, we describe a protocol for quantitative measurements of electrical and mechanical properties of OPV materials with sub-100 nm resolution.

Organic photovoltaic  (OPV) materials are inherently inhomogeneous at the nanometer scale. Nanoscale  inhomogeneity of OPV materials affects performance ...

Fast Imaging Technique to Study Drop Impact Dynamics of Non-Newtonian Fluids

In the field of fluid mechanics, many dynamical processes not only occur over a very short time interval but also require high spatial resolution for detailed observation, scenarios that make it challenging to observe with conventional imaging systems. One of these is the drop impact of liquids, which usually happens within one tenth of millisecond. To tackle this challenge, a fast imaging technique is introduced that combines a high-speed camera (capable of up to one million frames per second) with a macro lens with long working distance to bring the spatial resolution of the image down to 10 &#181;m/pixel. The imaging technique enables precise measurement of relevant fluid dynamic quantities, such as the flow field, the spreading distance and the splashing speed, from analysis of the recorded video. To demonstrate the capabilities of this visualization system, the impact dynamics when droplets of non-Newtonian fluids impinge on a flat hard surface are characterized. Two situations are considered: for oxidized liquid metal droplets we focus on the spreading behavior, and for densely packed suspensions we determine the onset of splashing. More generally, the combination of high temporal and spatial imaging resolution introduced here offers advantages for studying fast dynamics across a wide range of microscale phenomena.

Drop impact of non-Newtonian fluids is a complex process since different physical parameters influence the dynamics over a very short time (less than one tenth of a millisecond). A fast imaging technique is introduced in order to characterize the impact behaviors of different non-Newtonian fluids.

In the field of fluid mechanics, many dynamical processes not only occur over a very short time interval but also require high spatial resolution for ...

Electroactive Polymer Nanoparticles Exhibiting Photothermal Properties

A method for the synthesis of electroactive polymers is demonstrated, starting with the synthesis of extended conjugation monomers using a three-step process that finishes with Negishi coupling. Negishi coupling is a cross-coupling process in which a chemical precursor is first lithiated, followed by transmetallation with ZnCl2. The resultant organozinc compound can be coupled to a dibrominated aromatic precursor to give the conjugated monomer. Polymer films can be prepared via electropolymerization of the monomer and characterized using cyclic voltammetry and ultraviolet-visible-near infrared (UV-Vis-NIR) spectroscopy. Nanoparticles (NPs) are prepared via emulsion polymerization of the monomer using a two-surfactant system to yield an aqueous dispersion of the polymer NPs. The NPs are characterized using dynamic light scattering, electron microscopy, and UV-Vis-NIR-spectroscopy. Cytocompatibility of NPs is investigated using the cell viability assay. Finally, the NP suspensions are irradiated with a NIR laser to determine their effectiveness as potential materials for photothermal therapy (PTT).

A protocol is presented for the synthesis and preparation of nanoparticles consisting of electroactive polymers.

A method for the synthesis of electroactive polymers is demonstrated, starting with the synthesis of extended conjugation monomers using a three-step ...

Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation

We present a protocol for fabricating 1-D Photonic Crystal (PhC) cavities on subwavelength-diameter tapered optical fibers, optical nanofibers, using femtosecond laser-induced ablation. We show that thousands of periodic nano-craters are fabricated on an optical nanofiber by irradiating with just a single femtosecond laser pulse. For a typical sample, periodic nano-craters with a period of 350 nm and with diameter gradually varying from 50 - 250 nm over a length of 1 mm are fabricated on a nanofiber with diameter around 450 - 550 nm. A key aspect of such a nanofabrication is that the nanofiber itself acts as a cylindrical lens and focuses the femtosecond laser beam on its shadow surface. Moreover, the single-shot fabrication makes it immune to mechanical instabilities and other fabrication imperfections. Such periodic nano-craters on nanofiber, act as a 1-D PhC and enable strong and broadband reflection while maintaining the high transmission out of the stopband. We also present a method to control the profile of the nano-crater array to fabricate apodized and defect-induced PhC cavities on the nanofiber. The strong confinement of the field, both transverse and longitudinal, in the nanofiber-based PhC cavities and the efficient integration to the fiber networks, may open new possibilities for nanophotonic applications and quantum information science.

We present a protocol for fabricating 1-D photonic crystal cavities on subwavelength diameter silica fibers (optical nanofibers) using femtosecond laser-induced ablation.

We present a protocol for fabricating 1-D Photonic Crystal (PhC) cavities on subwavelength-diameter tapered optical fibers, optical nanofibers, using ...

In Situ Visualization of the Phase Behavior of Oil Samples Under Refinery Process Conditions

To help address production issues in refineries caused by the fouling of process units and lines, we have developed a setup as well as a method to visualize the behavior of petroleum samples under process conditions. The experimental setup relies on a custom-built micro-reactor fitted with a sapphire window at the bottom, which is placed over the objective of an inverted microscope equipped with a cross-polarizer module. Using reflection microscopy enables the visualization of opaque samples, such as petroleum vacuum residues, or asphaltenes. The combination of the sapphire window from the micro-reactor with the cross-polarizer module of the microscope on the light path allows high-contrast imaging of isotropic and anisotropic media. While observations are carried out, the micro-reactor can be heated to the temperature range of cracking reactions (up to 450 &#176;C), can be subjected to H2 pressure relevant to hydroconversion reactions (up to 16 MPa), and can stir the sample by magnetic coupling. 
Observations are typically carried out by taking snapshots of the sample under cross-polarized light at regular time intervals. Image analyses may not only provide information on the temperature, pressure, and reactive conditions yielding phase separation, but may also give an estimate of the evolution of the chemical (absorption/reflection spectra) and physical (refractive index) properties of the sample before the onset of phase separation.

In Situ Visualization of the Phase Behavior of Oil Samples Under Refinery Process Conditions

This article describes a setup and method for the in situ visualization of oil samples under a variety of temperature and pressure conditions that aim to emulate refining and upgrading processes. It is primarily used for studying isotropic and anisotropic media involved in the fouling behavior of petroleum feeds.

To help address production issues in refineries caused by the fouling of process units and lines, we have developed a setup as well as a method to ...

Characterization of Ultra-fine Grained and Nanocrystalline Materials Using Transmission Kikuchi Diffraction

One of the challenges in microstructure analysis nowadays resides in the reliable and accurate characterization of ultra-fine grained (UFG) and nanocrystalline materials. The traditional techniques associated with scanning electron microscopy (SEM), such as electron backscatter diffraction (EBSD), do not possess the required spatial resolution due to the large interaction volume between the electrons from the beam and the atoms of the material. Transmission electron microscopy (TEM) has the required spatial resolution. However, due to a lack of automation in the analysis system, the rate of data acquisition is slow which limits the area of the specimen that can be characterized. This paper presents a new characterization technique, Transmission Kikuchi Diffraction (TKD), which enables the analysis of the microstructure of UFG and nanocrystalline materials using an SEM equipped with a standard EBSD system. The spatial resolution of this technique can reach 2 nm. This technique can be applied to a large range of materials that would be difficult to analyze using traditional EBSD. After presenting the experimental set up and describing the different steps necessary to realize a TKD analysis, examples of its use on metal alloys and minerals are shown to illustrate the resolution of the technique and its flexibility in term of material to be characterized.

This paper provides a detailed method to characterize the microstructure of ultra-fine grained and nanocrystalline materials using a scanning electron microscope equipped with a standard electron backscatter diffraction system. Metal alloys and minerals presenting refined microstructures are analyzed using this technique, showing the diversity of its possible applications.

One of the challenges in microstructure analysis nowadays resides in the reliable and accurate characterization of ultra-fine grained (UFG) and ...

Experimental Protocol to Determine the Chloride Threshold Value for Corrosion in Samples Taken from Reinforced Concrete Structures

The aging of reinforced concrete infrastructure in developed countries imposes an urgent need for methods to reliably assess the condition of these structures. Corrosion of the embedded reinforcing steel is the most frequent cause for degradation. While it is well known that the ability of a structure to withstand corrosion depends strongly on factors such as the materials used or the age, it is common practice to rely on threshold values stipulated in standards or textbooks. These threshold values for corrosion initiation (Ccrit) are independent of the actual properties of a certain structure, which clearly limits the accuracy of condition assessments and service life predictions. The practice of using tabulated values can be traced to the lack of reliable methods to determine Ccrit on-site and in the laboratory.
Here, an experimental protocol to determine Ccrit for individual engineering structures or structural members is presented. A number of reinforced concrete samples are taken from structures and laboratory corrosion testing is performed. The main advantage of this method is that it ensures real conditions concerning parameters that are well known to greatly influence Ccrit, such as the steel-concrete interface, which cannot be representatively mimicked in laboratory-produced samples. At the same time, the accelerated corrosion test in the laboratory permits the reliable determination of Ccrit prior to corrosion initiation on the tested structure; this is a major advantage over all common condition assessment methods that only permit estimating the conditions for corrosion after initiation, i.e., when the structure is already damaged.
The protocol yields the statistical distribution of Ccrit for the tested structure. This serves as a basis for probabilistic prediction models for the remaining time to corrosion, which is needed for maintenance planning. This method can potentially be used in material testing of civil infrastructures, similar to established methods used for mechanical testing.

We propose a method to measure a parameter that is highly relevant for corrosion assessments or predictions of reinforced concrete structures, with the main advantage of permitting testing of samples from engineering structures. This ensures real conditions at the steel-concrete interface, which are crucial to avoid artifacts of laboratory-made samples.

The aging of reinforced concrete infrastructure in developed countries imposes an urgent need for methods to reliably assess the condition of these ...