Inexorable demand for increasing bandwidth is driving future wireless communications systems into the 100 GHz–1 THz region, thereby fueling demand for new sources and modulators but also complementary devices such as resonators, phase shifters, and filters. Few such devices exist at present, and the electromagnetic properties of those available at millimeter-wavelengths are generally fixed and characterized by broad (i.e., low Q) resonances. We introduce a class of 3D plasma/metal/dielectric photonic crystals (PPCs), operating in the 120–170 GHz spectral range, that are dynamic (tunable and reconfigurable at electronic speeds) and possess attenuation and transmission resonances with bandwidths below 50 MHz. Interference between sublattices of the crystal, which controls the resonance line shapes, is manipulated through the crystal structure. Incorporating Bragg arrays of low-temperature plasma microcolumns into a dielectric/metal scaffold that is itself a static crystal forms two interwoven and electromagnetically coupled crystals. Plasma-scaffold lattices produce multiple, narrowband attenuation resonances that shift monotonically to higher frequencies by as much as 1.6 GHz with increasing plasma electron density. Controlling the longitudinal geometry of the PPC through electronic activation of successive Bragg planes of plasma columns reveals an unexpected double-crystal symmetry interaction at 138.4 GHz and resonance Q values above 5100. The introduction of point or line defects into plasma column/polymer/metal crystals increases transparency at resonances of the scaffold (Borrmann effect) and yields Fano line shapes characteristic of coupled resonators. The experimental results suggest the suitability of PPC-based metamaterials for applications including multichannel communications, millimeter-wave spectroscopy, and fundamental studies of multiple, coupled resonators.
At least as early as 1919, plasma was recognized for its potential value to electromagnetic and communications devices.1 Over several of the decades to follow, low-temperature plasma was incorporated into oscillators, voltage regulators, modulators, detectors, and alphanumeric displays, assuming a key role in radio frequency (RF) and microwave communications.2,3 In the 1990s, plasma was also pursued as the basis for microwave mirrors.4,5 Reflectivities equivalent to those for a metal mirror were achieved for incident 10 GHz (X-band) radiation, but the power necessary to generate and sustain the plasma sheet remains prohibitive for photonics and microwave applications.
Because of the unique dielectric permittivity (ɛp) and controllable conductivity of nonequilibrium low-temperature plasma, Faith et al.6 and Hojo and Mase7 followed the proposal of Yablonovich in 19878 for three-dimensional (3D) photonic crystals by suggesting the substitution of plasma for at least one of the two dielectrics responsible for the spatially periodic variation of the crystal's refractive index. Sakai and Tachibana9–12 pioneered the early development of plasma photonic crystals (PPCs), reporting resonances in the transmission spectra of two-dimensional (2D) microplasma arrays at frequencies as high as 105 GHz. However, these and more recent efforts13–15 to develop 2D and 3D PPCs have generally pursued lattices consisting solely of plasma elements (such as Ar/Hg-filled tubes) that have low electron densities. Consequently, previous PPCs have been almost exclusively confined to frequencies below 20 GHz and typically comprised bulky structures that provide modest attenuations and broad resonances with correspondingly reduced Q factors.
The signature of all photonic crystals is the periodic modulation of the refractive index (n) along at least one spatial coordinate, and the multilayer dielectric mirror is a long-standing example of a one-dimensional photonic crystal derived from the contrast between the refractive indices of alternating dielectric layers in the multilayer stack. Bragg gratings having a subwavelength periodicity in the refractive index, and fabricated in optical materials such as Si, the III-V compound semiconductors and polymers, are the foundation of the preponderance of photonic crystals and metamaterials developed in recent years.16 Such crystals have been designed for controlling optical mode profiles in integrated photonic devices, including waveguides and lenses,16 and have also proven effective as chemical and biomedical photonic sensors.17,18 For the 3D crystals described here, contrast in n is accentuated by the difference between the frequency-dependent permittivity of a low temperature plasma (ɛp) and those for a metal and one or more dielectrics. Specifically, plasma is a unique dielectric in that ɛp, as given by the Drude model,19,20 is expressed as
where is the plasma frequency , ω is the radian frequency of an incoming electromagnetic wave, νm is the electron-neutral collision frequency for momentum transfer, and ne is the electron number density of the plasma. Consequently, is a function of the gas pressure and plasma electron density, enabling the behavior of the plasma to be manipulated so as to appear at any instant as a time-varying metallic or dielectric medium.
We report here the demonstration of dynamic, 3D photonic crystals comprising planar arrays of low-temperature plasma microcolumns embedded within a polymer/metal/dielectric scaffold that acts as a static, reference crystal. Because the columnar microplasmas are generated within a 3D network of microchannels fabricated in a polymer, the result is a transient, artificial material or metamaterial in which the microplasma lattice and polymer scaffold interact in a manner similar to two coupled photonic resonators or LC networks. These devices constitute one crystal within another, and the introduction of transient (pulsed), atmospheric-pressure microplasmas into an otherwise static 3D photonic crystal matrix has the effect of blue-shifting the crystal resonances and increasing significantly both the peak attenuation (or transmission) and Q factor associated with a given spectral feature.
If microplasmas are generated within every microchannel of the crystal, the observed resonances of such “all-plasma” structures are broad (2.5–3.5 GHz), but the addition of metal and dielectric Bragg layers, interspersed with several one-dimensional arrays of plasmas, results in a more than one order of magnitude reduction in the resonance linewidths. Specifically, the measured 3 dB bandwidths of plasma/metal/dielectric PPC resonances are unexpectedly small (≤100 MHz), particularly in view of the large values of νm that are associated with atmospheric-pressure plasmas (typically ≥ 200 GHz). When metal and dielectric gratings are introduced to the PPC structure, we attribute the resultant collapse of the resonant bandwidths of the crystal to the establishment of, and interference between, two or more sublattices, as exhibited by the observed resonance line profiles. PPCs having a subwavelength lattice constant (a) of 1.0 mm exhibit multiple resonances between 120 and 170 GHz, and specific attenuation peaks upshift in frequency by as much as 1.6 GHz when plasma that has a peak electron density of (1–3) × 1016 cm−3 occupies a portion of the crystal network, which consists of microcapillaries fabricated in a polymer host. Since the plasma frequency associated with the maximum electron densities generated in these experiments is ∼1 THz, all of the data presented here were acquired for probe frequencies well below ωp/2π. The option of filling individual capillaries, or specific planes of capillaries within the microfabricated crystal network, with metal or a dielectric results in attenuation resonances that are blue-shifted relative to those for plasma-only PPCs because the contrast in the dielectric permittivity (and refractive index) between adjacent layers can readily be increased. Perhaps most importantly, the symmetry and spectral characteristics of coupled plasma-scaffold crystals and resonators can be altered at will by electronically activating or “dropping” single plasma columns, or entire layers of columns, because each plasma microcolumn can be addressed individually. In this regard, a pronounced longitudinal symmetry effect, attributed to a plasma array-scaffold interaction, has been observed when successive Bragg planes of microplasma columns are activated. Maximum Q values above 5100 are measured for an attenuation peak at 138.4 GHz (corresponding to a 3 dB bandwidth of 27 MHz) when three plasma layers are energized, whereas Q falls by 50% and 70% for two or four plasma layers, respectively. Similarly, the introduction of point or line defects into plasma/metal/dielectric crystals and asymmetric lattice geometries results in the observation of several phenomena associated with coupled oscillators, such as the Borrmann effect,21,22 which manifests itself as an increase in crystal transparency and the cancelation of most of the on-resonance scaffold attenuation. In addition, line profiles of spectral features at 121.4 and 151.6 GHz, for example, are transformed into Fano line shapes with measured q (Fano parameter) and δ (phase shift) values of −2.4 and −0.39 rad and −7.2 and −0.14 rad, respectively, suggesting that the introduction of plasmas is effective in decoupling the two crystals. Consequently, we introduce here a class of artificial, electromagnetically active crystals in which the nature and degree of the interference controlling the resonance line shapes can be manipulated.
One concludes that the insertion of Bragg arrays of plasma microcolumns into a dielectric/metal microchannel network yields photonic crystals and electromagnetically active synthetic materials that are tunable and dynamic (reconfigurable and/or altered at electronic speeds), offering crystal geometries and artificial materials properties not available previously. Therefore, the plasma/metal/dielectric lattice structures described below provide the opportunity to explore fundamental processes such as probing weak electromagnetic interactions between high-Q resonators. Although the spectral operating range of the PPCs described here (120–170 GHz) was chosen partially for its implications for wireless communications,23–25 more than three years of constructing and testing these devices reveals no barriers to realizing plasma crystals and plasma-based metamaterials acting as resonators, filters, reflectors, or interferometers at frequencies up to and beyond 1 THz. Testing of multiple crystals also demonstrates unprecedented capability in the millimeter-wave region with respect to resonance Q (up to 5100) and continuous tunability (≤ 1.6 GHz).
Plasma crystal design and theoretical performance
Figure 1(a) is an illustration of one PPC structure adopted for the experiments described here. A woodpile crystal geometry consists of a series of layers, each of which comprises a planar array of parallel, equally spaced, cylindrical microplasmas with a diameter of 355 ± 10 μm. The microcapillary network in which the plasmas are generated is fabricated in polydimethylsiloxane (PDMS) by a replica-molding process that consistently yields channels of precisely controlled diameter and position. The pitch (center-to-center spacing) between the microcolumn plasmas within a given layer, and the spacing between adjacent planes, are both set to a = 1.000 ± 0.010 mm, which corresponds to a frequency of ∼300 GHz. Precision in the diameters and positioning of the microchannels translates directly into the performance of these crystals as microwave resonators, which is reflected by the quality factor Q for any specific resonance. Each layer of 6 or 7 microcolumn plasmas constitutes a one-dimensional grating with a nominal Bragg frequency of 150 GHz. Furthermore, the orientation of the microplasmas alternates from horizontal [parallel to the x-coordinate of Fig. 1(a)] to vertical (y-coordinate) with each successive layer of the crystal, and the locations of the plasmas in every layer are staggered by a/2 with respect to those for the planes immediately preceding and following. Finally, the z axis of Fig. 1(a) will hereafter be referred to as the longitudinal axis. For further details concerning crystal design and fabrication, see the Methods section.
Figure 1(b) shows a photograph of an entire 8-layer PPC, viewed slightly off the longitudinal (z) axis. For illustrative purposes, the x-oriented microplasmas are produced in ∼1 atm. of Ar, whereas helium has been introduced into the vertical (y) columns of the microcapillary network. The PDMS scaffold is optically transparent, and columnar microplasmas are generated with a sinusoidal voltage waveform delivered to electrode pairs inserted into opposing ends of every microchannel (not shown). Each layer of the crystal consists of 6 or 7 plasma microcolumns, and the active cross-sectional area of the crystal is ∼36 mm2. Figure 1(c) shows a photograph of another crystal with the same structure as Fig. 1(b) but operating with Ne and Ar in the horizontal and vertical arrays of microchannels, respectively. A magnified view of a portion of a PPC employing He alone, presented in Fig. 1(d), verifies the spatial uniformity of the microplasmas (as evidenced by the vertically oriented microplasma columns). The crescent-shaped pattern of the optical intensity distribution superimposed onto the x-oriented microplasmas is an optical artifact associated with reflections within the PPC. Figure 1(e) is an optical micrograph that shows a small section of the top two layers of a PPC. It indicates the diameter of the capillaries in the PDMS host (in which He plasma is generated). In order to convey a sense of the size of the photonic crystal devices fabricated to date, Fig. 1(f) provides a comparison between a representative PPC scaffold and a U.S. quarter dollar. The active crystal occupies only the central portion of the polymer block in the figure, the device has a thickness of 10.5 mm, and the electrical connections have not been installed. No metal-filled microchannels within the crystal are shown in this image, and the upper and lower sets of horizontal channels serve to accommodate electrodes. We should hasten to add that the process by which a single PPC is fabricated also enables the production of large sheets of such devices.
Figure 2(a) displays calculations of , the real part of the dielectric permittivity of low temperature plasma [Eq. (1)], for the 120–170 GHz frequency interval and for three values of νm, the collision frequency for momentum transfer (1, 100, and 250 GHz). The dashed and solid curves of Fig. 2(a) represent solutions for electron number densities of 3.1 × 1016 cm−3 and 1.4 × 1016 cm−3 (the peak values produced in the microcolumns, cf. Fig. 7 in the Materials and Methods section), respectively, and the region between these values of ne, for a given value of νm, are shaded in Fig. 2(a). Since and are given by
where is the dielectric permittivity of free space, e is the electronic charge, and me and ne are the rest mass of an electron and the electron density, respectively, raising ne results in becoming increasingly negative. Not surprisingly, therefore, microplasmas will appear to be more metallic and behave less as a dielectric as the electron density rises. As illustrated in Fig. 2(a), larger values of ω (the radian frequency of the probe wave) and νm suppress this trend, but the point to be made is that plasma, and microplasma arrays, in particular, can be viewed as an artificial metal/dielectric material whose electromagnetic properties can be manipulated and controlled precisely in real time through the electron and neutral gas number densities.
Reflectance (and transmission) spectra for the PPC structure of Fig. 1(a) have been calculated (assuming the Drude model expression for ɛ), and representative results are presented in Fig. 2(b) for a plasma array immersed in air and assumed to have time-averaged, microplasma electron densities () in the range of 1014 cm−3 to 1016 cm−3, and νm =1 GHz. Multiple resonances are predicted to lie in the 40–170 GHz spectral region, and, in particular, strong attenuation features are observed in the vicinity of λ = 2 mm, the Bragg wavelength for the one-dimensional microplasma arrays, when = 1015–1016 cm−3. As expected on the basis of Eqs. (2) and (3), rising values of ne progressively shift resonances of the PPC to higher frequencies because the magnitude of increases and is linear in ne. As noted above, the calculations of Fig. 2(b) assumed that the plasma microcolumn lattice is immersed in air and νm is fixed at 1 GHz. For rare gas plasmas at atmospheric pressure, however, νm would normally be expected to be >200–300 GHz. It must be emphasized, therefore, that the simulations of Fig. 2(b) are intended only to illustrate the behavior of plasma-only PPC attenuation resonances as ne is increased. Furthermore, although the value of νm adopted for the calculations is two orders of magnitude below that expected for microplasmas operated near atmospheric pressure, the results to be described later confirm the experiments of Ref. 26 in showing the measured resonance line shapes to be considerably narrower than those expected theoretically. A more extensive description of the results of the calculations will appear elsewhere.
Measurements of the transmission spectra for all of the photonic crystals reported here were acquired with the experimental arrangement illustrated in Fig. 2(c). For clarity, the PDMS scaffold is cut away to show several plasma microcolumns and their associated ignition electrodes. The probe microwave signal was launched into the crystal along the z axis with a minihorn, and radiation emerging from the downstream face of the structure was received by an identical horn. A computer recorded much of the data in increments of 100 MHz, but spectral resolutions as small as 15 kHz were available. The reproducibility of all the data presented below is such that measurements repeated after several months consistently yielded virtually identical results.
Plasma/dielectric/metal crystals: Resonance tunability and lines shapes
Three prominent attenuation features, peaking at 137.8, 146.0, and 152.9 GHz, are observed in the transmittance spectrum of a woodpile structure PPC [Fig. 1(a)] when microplasmas occupy only the x-oriented (horizontal) microchannels in an 8-layer crystal. All of the data presented here were obtained with Ar plasma. Figure 2(d) shows an expanded view of the spectrum for this plasma/dielectric (PDMS) crystal in the 149–156 GHz interval, measured with room air in the even-numbered layers (where layer No. 1 faces the incoming microwave probe field). Because each of the layers in the PPC is a one-dimensional grating with a Bragg frequency of 150 GHz, we anticipated that the largest differences between the polymer scaffold and PPC transmission spectra would be associated with the resonances in this wavelength region. The blue data points and curve of Fig. 2(d) (denoted PC) represent the transmission of the PDMS scaffold alone, which is itself a static crystal and, therefore, exhibits resonances in the absence of plasma. However, when microplasmas are generated in the capillary network by a 20 kHz train of 6 kV [V1, Fig. 2(d)] pulses with a width of 8 μs, the frequency at which attenuation is maximum shifts from 152.9 GHz (blue curve) to 153.5 GHz (red), an increase of ∼0.6 GHz. Raising the pulse voltage to 7 kV [V2, green curve of Fig. 2(d)] increases the frequency at which peak attenuation occurs to 154.5 GHz, or an increase of 1.6 GHz to the “blue” side of the resonance peak for the polymer scaffold alone. Of greater interest, however, is the observation that increasing the electron density results in the Q of the resonance rising from 47 (red curve) to 62 (green). Although the Q values for the plasma-dielectric crystals of Fig. 2(d) are modest and reflect 3 dB bandwidths for this resonance of 3.2 and 2.5 GHz, respectively, these and all other experiments conducted to date demonstrate that raising the microplasma electron density has the effect of blue-shifting and narrowing the resonances of the plasma/polymer crystal. Before leaving Fig. 2, a few comments concerning the insertion (background) loss of the crystal are warranted. The scaffold material for these experiments, PDMS, was chosen primarily because of the precision with which microchannel networks can be formed within the polymer block by replica molding. Another asset of this material is its optical transparency, thus allowing for the plasma uniformity and emission spectra to be monitored readily. We wish to note, therefore, that the insertion loss of Fig. 2(d) (∼26 dB) is not an inherent limitation of the crystal design. Instead, it is expected that the insertion loss of PPCs will be reduced to ≤10 dB by minimizing the thickness of the scaffold material and resorting to a different dielectric or polymer in which to fabricate the network.
Experiments conducted with multiple crystals confirm that blue frequency shifts as large as ∼1% of f0 are observed in plasma-only microchannel networks, and it must be reiterated that the measured attenuations and frequency shifts are time-averaged (as opposed to instantaneous) values. The ability to electronically tune the crystal (by way of the average power delivered to the plasma) as well as to switch rapidly between the plasma on/off states suggests the application of these crystals to transitioning between two or more communications channels.
PPC resonators exhibiting superior performance with respect to tunability, linewidth (Q factor), and dynamic range are those in which microplasma Bragg gratings are interwoven with a metal sublattice. Interspersing plasma columns with metal and dielectric gratings yields two superimposed crystals exhibiting strengthened resonances owing to coupling between the microplasma and dielectric/metal lattices. The spectral characteristics of such double-crystal resonators are sensitive to the placement of microplasma because of the contrast afforded by the permittivity of the plasma columns relative to that for a dielectric, for example. The insertion of plasma microcolumns at selected sites in the crystal also allows for the PPC characteristics to be controlled by the microplasmas, thereby increasing the influence of the transient plasma elements on the resonator behavior while reducing power consumption. Several series of crystals of different designs have been fabricated and characterized, and Fig. 3(a) presents transmission spectra recorded over the 120–170 GHz region for an 8-layer PPC in which metal is introduced only into the last layer (far right) of the crystal, as indicated by the illustrations in Figs. 3(a) and 3(b) in which the red cylinders represent microplasma columns. An array of metal microcolumns was inserted at one end of the lattice for several reasons, one of which is the known electromagnetic behavior of periodic metal structures in the THz and millimeter-wave regions. In the 1970s, for example, metal Bragg gratings and grids were employed widely as partial reflectors for far-infrared (THz) and millimeter-wave lasers (wavelengths of ∼100 μm–2 mm; Refs. 27 and 28).
Microwave probe radiation is incident on the crystal in Figs. 3(a) and 3(b) from the left, and plasma is generated in the odd-numbered, x-oriented microchannels by a 20 kHz train of 8 μs, 7 kV pulses. For these experiments, the even-numbered channels (except No. 8) contain only room air, which serves as a dielectric. Filling these channels with Ar was observed to have a negligible effect on the spectra. The strongest attenuation peaks in the PDMS scaffold spectrum [Fig. 3(a), shown in blue] lie at 131.4, 138.0, 145.0, 153.4, and 160.0 GHz, and the appearance of plasma in the layers with horizontally oriented channels (Nos. 1, 3, 5, and 7) has the effect, as discussed previously for all-plasma PCs, of blue-shifting each of these by as much as 1.0 GHz (145.0 GHz → 146.0 GHz, for example). Of particular interest is the primary resonance at 138.0 GHz, whose peak is moved to 138.5 GHz by the introduction of plasma into the crystal. As illustrated by the expanded view of the 130–140 GHz frequency interval in Fig. 3(b), the microplasma layers not only blue-shift this resonance by 500 MHz but the spectral profile also narrows significantly. Specifically, the Q of the resonance for the scaffold itself (636 ± 5, given by the 3 dB spectral width) is increased by a factor of 2.3 (to 1467 ± 5) when the plasmas are introduced. As mentioned previously, the bandwidth of this resonance is considerably narrower than would be expected for values of the plasma collision frequency νm of several hundred GHz, and the value of Q for the red profile of Fig. 3(b) is more than a factor of 20 larger than that for the ∼154 GHz resonance of Fig. 2(d). We attribute this result to coupling between the plasma and scaffold (metal/dielectric) crystals, an effect that arises from electromagnetic interference between sublattices of the crystal. The result is that, as demonstrated below, the collision frequency associated with atmospheric pressure plasmas is no longer detrimental to realizing resonance bandwidths below 30 MHz. It should also be mentioned that the attenuation of this tunable filter/reflector at 138.5 GHz increases by more than 19 dB due to the presence of plasma. Similar comments could be made for the scaffold resonance at 131.4 GHz. In view of the peak electron densities of ∼1016 cm−3 generated in the microchannels (a value negligible in comparison with that of the metal columns, cf. Fig. 7), this impact of the microplasmas on the electromagnetic response of the crystal is remarkable.
For several experiments, a vector network analyzer (VNA) was available, which enabled the transmission and phase shift spectra associated with both of the resonances of Fig. 3(b) to be measured concurrently. The upper half Figs. 3(c) and 3(d) summarize measurements that essentially repeat those of Fig. 3(b) by showing the dependence of the S21 parameter amplitude on frequency over the 128.2–134.0 GHz and 135.7–139.0 GHz intervals. Measurements for the polymer/metal scaffold alone are illustrated in blue, and those for the same crystal scaffold with plasma generated in layer Nos. 1, 3, 5, and 7 [Fig. 3(b)] are represented by the red curves. The lower portions of Figs. 3(c) and 3(d) compare the results of phase measurements for the metal/polymer scaffold alone (blue curves) with those observed when the four plasma layers were generated in the PPC (red curves). For the 138 GHz attenuation peak [Fig. 3(d)], note that the phase associated with the scaffold falls abruptly by more than 135 degrees on the high-frequency side of the resonance, but, in contrast, the introduction of plasma to the crystal narrows the spectral profile considerably, and line-center coincides with a phase shift of ±90°.
Increasing the influence of the plasma Bragg gratings on PPC behavior is achieved with the 4-layer structure of Fig. 4. Metal now occupies both layers 2 and 4, which consist of seven and six equally spaced columns, respectively. The two strongest attenuation modes lie at 138.7 and 145.2 GHz in the absence of plasma. Figure 4(b) is a magnified view of the 138.7 GHz resonance, illustrating the transformation of the spectral profile as the pulse repetition frequency (PRF) of the voltage pulse train (8 μs, 6 kV) is raised from 17 kHz to 35 kHz. Extensive measurements have been made of the dependence of the 138.7 GHz mode line shape on the time-averaged electron density ( in the microplasma columns, which is controlled primarily through the driving voltage waveform. Increasing the PRF (for a fixed pulse width) is tantamount to raising , and, as shown in Fig. 4(c), measurements found that the peak attenuation varies linearly with the PRF over the entire range studied (15–35 kHz). Corresponding experiments exploring the influence of the voltage pulse width were conducted for values between 500 ns and 16 μs, and the maximum attenuation at 138.8 GHz was found to scale linearly with pulse width up to 12 μs but rapidly saturate thereafter. Furthermore, the peak wavelength for the mode is observed to shift monotonically to the blue with increasing PRF [Fig. 4(b)] and, as illustrated by Fig. 4(d), the Q of the resonance rises rapidly with driving frequency, from 496 ± 21 at 15 kHz to 1978 ± 56 at 35 kHz. Of particular interest is the observed nonlinear increase in Q for PRF values above 30 kHz. At this point, the duty cycle for excitation of the plasma is 6% [assuming a 2 μs full-width at half maximum (FWHM) plasma current pulse], which corresponds to microplasma-generation conditions approaching a quasisteady state in which a background electron density on the order of 1012 cm−3 is present between pulses.
Isolating the contribution of the plasma crystal to the composite (overall) line shapes of Figs. 3 and 4 requires normalization of the experimental profiles to those associated with the scaffold alone (i.e., in the absence of plasma). We define T0 = Tp(λ)/Ts(λ), where Tp(λ) and Ts(λ) are the experimentally determined line shapes for the PPC and its scaffold, respectively. Figure 5(a) is an example of T0(λ) for the 8-layer crystal of Fig. 3 in the 125–145 GHz interval. Note that the ordinate is logarithmic and the dashed horizontal line denotes the relative response of the crystal scaffold alone (i.e., microplasmas extinguished). Of particular interest is the observed increase in the transmission of the hybrid crystal (plasma/dielectric/metal) immediately to the low frequency side of both resonances. Indications of this effect have been reported previously26 but we measured a factor of ∼3.6 improvement in transmission at 137.9 GHz here. Elsewhere, studies have recorded larger enhancements in transmission, such as an order of magnitude increase for this resonator at 145.2 GHz, when plasma is introduced. Such improvements in transmission do not overcome the insertion loss of the PPCs (cf. Figs. 3 and 4), but the crystal is brought closer to transparency at specific wavelengths. We attribute the increase in transmission of these plasma/metal/dielectric crystals near a resonance to the Borrmann effect, which is due to Bragg diffraction in an absorbing crystal and has been observed in photonic crystals at optical frequencies.21,22
Azimuthal and longitudinal symmetries
Examining the symmetry properties of these PPCs provides one fundamental test of their authenticity. As one example, the crystalline structures of Figs. 1–4 require that their electromagnetic properties be periodic with respect to rotation about the z axis. To confirm this expectation, crystals were installed in a three-axis, precision positioning stage, and Fig. 5(b) verifies the azimuthal symmetry of the 4-layer, plasma/dielectric/metal resonator of Fig. 4. The inset to Fig. 5(b) illustrates the rotational geometry for which the θ = 0 coordinate is aligned with the x axis of Fig. 1(a). Normalized transmittance spectra [T0(λ)] in the 149–158 GHz interval are given for four values of θ, and it is evident that the θ = 0° and 180° spectra are identical to within experimental uncertainty. Similarly, the 90° data were found to be matched by the 270° measurements (not shown for clarity).
Perhaps the most appealing aspect of PPCs is the potential for electronically reconfiguring the crystal structure, and doing so in such a way as to realize new symmetries and spectral signatures. As an initial study of the control of PPC characteristics afforded by microplasma arrays, we examined the spectral response of the 8-layer polymer/metal/dielectric device of Fig. 3 as differing numbers of microcolumn plasma layers were activated. Fig. 5(c) shows a summary of an experimental survey of the 121–139 GHz region, obtained with a system resolution of 100 MHz, for the crystal oriented such that the incoming microwave probe signal impinged on the first plasma layer (layer No. 1) at normal incidence. The blue trace represents the response of the polymer/metal/dielectric scaffold alone, whereas the activation of two, three, or four layers of microcolumn plasmas in the odd-numbered planes of the crystal (channels parallel to the x axis) yields the green, red, and black curves, respectively. The experimental geometry is indicated by the 8-layer inset illustrations of Fig. 5(c) for which the plasma layers (Nos. 1, 3, 5, and 7) are viewed end-on and the microwave probe arrives from the left. All of the spectra presented in this figure were acquired with air in layer Nos. 2, 4, and 6 (oriented vertically) whereas layer No. 8 is a metal Bragg array. In the absence of plasma, the prominent attenuation features lie at 122.0, 131.4, and 138 GHz. With the addition of microplasma layers, however, the maximum attenuation for the 131.4 GHz peak, as well as the shift of the resonance line shape to higher frequencies, is observed to increase monotonically with the number of plasma layers (N). With the addition of the fourth plasma layer (black curve), the maximum attenuation, relative to the scaffold, rises to ∼10 dB as the peak of the resonance has shifted by more than 400 MHz to 131.7 GHz.
Quite different behavior is observed for the ∼138 GHz attenuation feature of Fig. 5(c). Figure 5(d) presents expanded views of the transmittance profiles, recorded in the 136.5–140 GHz region as successive layers of plasma columns are activated. Multiple scans are shown for N = 0–4 layers of plasma microcolumns introduced to the scaffold (represented by the blue, violet, green, red, and black points, respectively), and data were recorded in 10 MHz increments with a source resolution of 15 kHz. One immediately notices that attenuation, resonance linewidth, and frequency shift no longer vary monotonically as additional plasma layers are produced within the scaffold. Instead, the resonance line shape narrows dramatically with increasing N until the corresponding Q value reaches a maximum of 5152 ± 332 for N = 3 (f0 = 138.43 GHz). Expressed in other terms, the 3 dB bandwidth for this attenuation resonance is 27 MHz. As illustrated by the inverted and normalized line shapes of Fig. 5(e), the spectral bandwidth descends most rapidly between N = 2 and 3, but, remarkably, the addition of the fourth plasma layer [black data, Figs. 5(d) and 5(e)] actually results in broadening of the profile and Q falling to 1454 ± 123 [cf. Fig. 5(f)]. Overlaying the N = 4 and N = 1 spectral profiles shows them to be virtually identical, demonstrating that the N = 4 line shape reverts back to that for only a single plasma layer in the crystal. Similarly, the maximum attenuation of each line shape in Fig. 3(d), relative to the background (polymer/metal scaffold), reaches ∼34.6 dB for N = 3 (red data) but declines to 18.2 dB when the last (4th) plasma layer is added. It should also be noted that the blue-shift (Δf) of the 138 GHz peak is linear in N up to N = 3 [Fig. 5(f)]. The addition of the fourth plasma array layer increases Δf only marginally.
The behavior of Figs. 5(c) through 5(f), verified repeatedly by experiments, points to crystal symmetry as being responsible. When three plasma layers are activated, the crystal of Fig. 5(d) contains three pairs of plasma/dielectric (air-filled, y-oriented) column arrays, thereby establishing a periodic refractive-index structure along the z-coordinate. We, therefore, attribute the ultranarrow resonance at 138.43 GHz (red curve) to a longitudinal symmetry in which two, 5-layer crystals share layers 7 and 8, and are coupled. The first comprises layer Nos. 2, 4, 6, 7, and 8 whereas the second consists of Layer Nos. 1, 3, 5, 7, and 8. An equivalent circuit model for the 3- and 4-plasma layer devices of Figs. 5(c) through 5(f) is that of two LC filters, connected in parallel and having resonant frequencies f1 and f2. If f1 ≈ f2, discrete component representations reproduce the observed line shapes and provide an explanation for the rapid transformation of the spectral profile as the four layers are activated sequentially. Such a model also reinforces the presumption that the two superimposed lattices of Figs. 5(c) through 5(f) interact so as to form a double crystal resonator.
Defect introduction, the Borrmann effect, and Fano resonances
The introduction of point and line defects into a plasma/metal/dielectric PPC has been observed to increase the transmission of the crystal at specific wavelengths and to produce the Fano spectral profiles characteristic of coupled resonators. As an example, Fig. 6(a) shows normalized line shapes recorded in the 120–123 GHz interval for an 8-layer crystal having two metal layers and one point defect. As indicated by the illustrations in Fig. 6(a), most of the microchannels in layers 6 and 8 are metal-filled, but the center channel in layer 6 contains only room air or Ar. The blue (lower) curve in Fig. 6(a) is the transmission spectrum for the polymer/metal scaffold itself, normalized to that for the same scaffold but with the metal removed. For this structure, a dominant attenuation peak exists at 121.4 GHz. However, when four plasma array layers are activated [red points in Fig. 6(a)], the transmission at 121.4 GHz is a factor of 7.3 higher than that for the same crystal in the absence of plasma. As noted earlier, this plasma-induced increase in PPC transmission, known as the Borrmann effect,21,22,29,30 is insufficient to overcome the insertion loss of the crystal, but it does bring the PPC closer to full transparency. The Borrmann effect bears a resemblance to electromagnetically induced transparency (EIT, Ref. 31), and arises from Bragg diffraction in lossy crystals. Recently, the observation of the Borrmann effect in the visible (300–750 THz) was reported for photonic crystals with a fixed, one-dimensional structure and consisting of porous silica.30 The data of Figs. 5(a) and 6 demonstrate that the Bragg structure of the present crystals yields a strong Borrmann response at millimeter-wave frequencies.
A similar result is obtained if metallic layer No. 6 in Fig. 6(a) is relocated to layer No. 4 and the point defect is removed. For this structure, strong attenuation is observed at 151.6 GHz in the absence of plasma [Fig. 6(b)]. However, the generation of microplasma in the odd-numbered layers raises the transmission at 151.6 GHz by a factor of ∼53 (17.2 dB). Although the microplasma layers are unable to cancel all of the on-resonance loss of the static crystal at 151 GHz, the increase in transmission brings the PPC to within roughly 7.2 dB of transparency. Of greater significance is the plasma-modified line shape, which is antisymmetric with respect to λ = 151.95 GHz.
The normalized line profiles of Figs. 5(a) and 6 are those of Fano resonances,32 which arise from the interference of a continuum of energy states with an embedded, discrete state and are well-known to atomic spectroscopy and photonics.33–36 Limonov et al.22 have summarized succinctly the interrelationship between Fano resonances, EIT, and the Borrmann effect, each of which is associated with interactions between two coupled resonators. The spectral line shape for Fano resonances is given by the function22
where δ is the phase shift of the continuum relative to that of the discrete state, q is the Fano parameter that reflects the degree of coupling between two resonators, D = 2sin(δ), Ω = 2(E − E0)/Γ, E is the photon energy, Γ is the width (FWHM) of the Fano line shape, and E0 is the energy of line center. Analysis of the spectral profiles of Figs. 5(a) and 6 confirm the Fano nature of the crystal resonances. The profile of the 121.4 GHz resonance of Fig. 6(a), for example, matches Eq. (4) closely and the best fit of experiment to theory yields q = −2.4, δ = −0.39 rad, Γ = 0.39 GHz, and D2 = 0.58. The values of q and δ indicate that the two lattices are weakly coupled.
This study has described the design, fabrication, and demonstration of 3D plasma/metal/dielectric photonic crystals in the 120–170 GHz spectral region. These structures are, in essence, double-crystal, tunable mm-wave resonators. The introduction of low-temperature plasma into an otherwise static photonic crystal results in blue-shifting the scaffold crystal resonances. Shifts of the peak attenuation frequency as large as 1.6 GHz, but Q values below 100, are recorded when the microchannel network within a polymer block (scaffold) is occupied solely by low temperature plasma produced in ∼1 atmosphere of Ar. We reported experimental data for Ar alone because the lower ionization potential of Ar (relative to He) yields increased electron number densities for a given driving voltage and, therefore, a larger electromagnetic response from the crystal. The impact of microplasma on the spectral characteristics of the double-crystal resonator is enhanced by interspersing microplasma Bragg gratings within a polymer/metal/dielectric lattice. Despite the enormous disparity between the peak electron density of the microplasmas and that available in a metal, the insertion of plasma into a static metal/polymer/dielectric lattice is capable of increasing attenuation at a resonance by more than 30 dB. Owing to a longitudinal symmetry, the presence of plasma within three layers of the coupled resonators also narrows the 138 GHz resonance sharply, resulting in the observation of Q factors above 5100, which correspond to 3 dB bandwidths as small as 27 MHz. Pulsed excitation of the microplasma layers in the crystals results in chirping the PPC resonances to higher frequencies, and the ability to activate specific plasma arrays, or individual plasma columns, provides the opportunity to exploit new symmetries. We observed Fano resonance profiles, thereby confirming that the narrow spectral resonances reported here are the result of interference between sublattices of the overall plasma/metal/dielectric crystal. Also, the Borrmann effect increases the transmission of these double crystal structures by as much as 17 dB on the low-frequency (“red”) side of several resonances. The point to be made is that the demonstration of a technology for fabricating dense, 3D arrays of microplasmas interwoven with metal and dielectric columns with precision has enabled the realization of a class of dynamic, functional metamaterials. These hybrid plasma/metal/dielectric materials comprise Bragg (spatially periodic) arrays, thereby providing electromagnetic properties not available previously, such as reconfigurability at electronic speeds and resonance bandwidths below 50 MHz, and are well-suited for millimeter-wave or THz device applications. Specifically, the 3 dB bandwidths of the resonances reported here, as well the ability to electronically tune the transmission spectrum (by way of the average power delivered to the crystal) and switch rapidly between the plasma on/off states, suggests the application of coupled plasma/solid crystals as high-Q resonators, narrowband filters, reflectors, phase-shifters, and interferometers for application to millimeter and THz spectroscopy, multichannel communications, and sensing.
Materials and Methods
Crystal fabrication process
Microchannel networks, in which low-temperature plasma is to be produced, are fabricated with the desired architecture by a replica-molding process that consistently yields microchannels of precise diameter and reproducible position. Following computer design of the scaffold geometry, the network is produced by stereolithography (3D printing, PROTOLABS), along with a polymer frame to support the entire crystal at its perimeter. The resolution of this process allows for the microchannel diameters and locations to be controlled to within ±10 μm. Completed scaffolds have entrance and exit face areas of 20 × 20 mm2, and a depth dependent upon the number of layers required. Each layer of the crystal is planar and consists of a minimum of six parallel microcolumns for which the pitch is 1.0 mm. A negative mold of the scaffold is subsequently produced with a silicone polymer (PDMS – GE RTV615), thereby defining a network of capillaries 355 μm in diameter. When desired, the microchannels in certain planes of the crystal are filled with metal by the introduction of metal wire or powder. The microcolumn plasmas are driven electrically by unipolar pulses having a rise time of less than 50 ns and widths of 500 ns−16 μs. Pulse voltages as large as 7 kV are available with power supplies custom-designed and built by Dr. Z. Liang. The average power dissipated by 4 plasma Bragg arrays in an 8-layer crystal with 8 μs voltage pulses at a PRF of 20 kHz was measured to be 7.7 ± 0.2 W. Consequently, air cooling alone of the crystals was sufficient.
Acquisition of spectra, determination of peak electron densities, and attenuation and phase measurements
Transmission spectra in the 120–170 GHz region of the millimeter-wave region are acquired with essentially the same system as that described in Ref. 26. Microwave minihorns with circular apertures of 1 cm serve to launch the probe signal and detect the transmitted radiation downstream of the crystal. Spatial apertures at both the entrance and exit faces of the crystals ensure that only radiation leaving (and not circumventing) the crystal is detected. In order to increase the data acquisition rate, the entire process for scanning the probe wavelength and recording data is computerized with the assistance of LabVIEW. Data have been obtained over a ≥ two-year period with more than 6 crystals, and the reproducibility of the spectra reported here was demonstrated by rerecording spectra after periods of several months. This procedure was repeated multiple times with several crystals to ensure reliability. For a limited number of experiments, a VNA was available, thereby providing access to the simultaneous measurement of both the attenuation and phase imposed by the plasma-scaffold crystal on the impinging 120–170 GHz wave.
Peak values for the electron number density (ne) were estimated by Stark broadening measurements of the Hα and Hβ transition line shapes at 656.3 nm and 486.1 nm, respectively. Hydrogen line profiles were resolved with a 0.75 m Czerny-Turner monochromator coupled to an intensified, charge-coupled device camera situated at the exit (focal) plane, yielding a spectral resolution of 0.007 nm in first order. Following the analysis of Ref. 36 (accounting for the contributions of instrument resolution, pressure broadening, and van der Waals effects to the linewidth) yielded maximum electron number densities of ne = (1–3) × 1016 cm−3. Representative experimental line profiles for both the Hα and Hβ transitions, measured in an Ar plasma background, are shown in Fig. 7 below.
Simulations of crystal reflectance and transmittance spectra are performed with Lumerical finite-difference, time domain software. The mesh size is set at 40 × 40 × 40 μm3 and the incident microwave field is represented as a plane wave having a wavelength in the 0.8–8.5 mm range. The incoming radiation is assumed to impinge at normal incidence to the front face [an xy or (100) plane] of the crystal.
The technical assistance of S. Zhong, Z. Tong, and Dr. Z. Liang, and the support of the U.S. Air Force Office of Scientific Research (AFOSR) under Grant Nos. FA9550-14-1-0002, FA9550-14-1-0371, and FA9550-08-1-0407 are gratefully acknowledged.
The authors declare that they have no financial, or nonfinancial, conflicts of interest.
All data regarding this study are available from the corresponding author upon request.