We have studied the zero-order transmission of periodic germanium (Ge) subwavelength arrays in an infrared range by using finite-difference time-domain simulations. A special wavelength-selective peak in a triangular hole array of Ge film is observed with an enhanced transmission accompanied by a drastic suppression nearby, which cannot be found in a one-dimensional Ge subwavelength array and is different from the extraordinary transmission related to surface plasmons in a metal film. The electromagnetic field is found to be concentrated on both surfaces of the Ge film at this peak. The unique transmission is verified through measurements on fabricated samples and is interpreted using the photonic band structure.
© 2013 Optical Society of America
Conventional solutions to make a surface anti-reflective or reflective often involve the deposition of multiple thin films with specific refractive indexes and thicknesses. These structures are bulky, costly, and not suitable for an advanced MEMS device. The discovery of extraordinary transmission by T. W. Ebbesen and colleagues  opened the way to achieving wavelength-selective components through surface plasmon (SP) subwavelength optics in single metallic membranes. This method greatly simplified the integration of optical components into MEMS and enabled more compact and faster devices. Related applications such as antenna structures for collecting incoming photons, tunable optical filters, and quantum well/dot infrared photodetectors [2–7] were reported.
SPs are essentially electromagnetic (EM) waves localized at a metallic surface through interaction with the free electrons of the metal . This nature indicates that there is always intrinsic absorption (SP loss), such that the structure would hardly be expected to be highly transparent although transmissions that are 1000 times greater than predicted by the standard aperture theory have been observed . At lower frequencies such as in the infrared range, dissipation caused by the imaginary part of the permittivity becomes more important. Such dissipation always leads to a lower enhancement of the transmission and to broader resonances , which is considered to be a feature that has somewhat limited applications, especially in wavelength-selective sources and detectors. Some researchers tried to use other materials in the infrared range. For example, an SU-8 film  was exploited to make a symmetrical structure to achieve high transmission, but it contains many layers and its fabrication requires several different processes.
In the transmission spectra of metallic subwavelength arrays, the enhanced transmissions are always accompanied by drastic suppressions in a nearby wavelength range [11, 12]. Lezec and Thio discovered similar transmission features in nonmetallic systems that do not support SPs, and they interpreted the mechanism as a composite diffracted evanescent wave (CDEW) . Their findings and other theories of subwavelength arrays such as Bloch-wave modes of dynamic diffraction , show some possibilities of achieving wavelength selectivity along with high transmission by using non-metallic material to overcome the SP loss.
In this paper, we demonstrate wavelength-selective high transmission through germanium (Ge) subwavelength arrays, which are free from SP loss. We perform a three-dimensional finite-difference time-domain (3D-FDTD) simulation of the structures and study the zero-order transmission. Many resonant peaks are observed in a two-dimensional (2D) Ge film with a triangular hole array (hereafter referred to as Ge-THA). Among the resonant peaks there is a transmission peak close to 100% with a drastic suppression in a nearby wavelength range. The properties of the peak are compared with those of both a transmission peak from a metallic array with the same parameters, which is related to SPs, and those of a peak from a film with one-dimensional (1D) periodic Ge stripes. Samples are fabricated and the spectra are measured by Fourier transform infrared (FTIR) spectroscopy. To the best of our knowledge, previous researchers have reported the “anomalous” transmission in the near-infrared or visible region in marginally metallic or non-metallic films such as chromium and tungsten [9, 14]. Both of the materials have large absorption, which causes the attenuation of the transmission. Similar phenomenon is also observed in amorphous silicon (a-Si), which in the as-deposited form is a dielectric having smaller absorption in the visible region . However, there have been few studies of applying Ge, which has no absorption in the infrared region beyond 2 μm, for realizing the wavelength-selective high transmission in this way. The relation between the transmission and the near-field effect is investigated, and the field distributions are also studied. Distinct EM field patterns that concentrate on both surfaces of the Ge film are obtained. We provide a preliminary explanation for the enhanced and suppressed transmission by studying the photonic band structure.
2. FDTD simulation
We use the FullWAVE simulation tool (an Rsoft product) to perform the 3D-FDTD analysis. In research on the transmissions of metallic films, 1D gratings and 2D hole arrays are two popular structures, which can have different transmission properties from each other owing to the waveguide resonance in the 1D grating [15, 16]. Therefore, both 1D periodic Ge stripes and 2D Ge-THAs are studied at a polarized normal incidence in an infrared range from 2 to 6 μm. A quartz substrate with a much larger thickness than that of the Ge film is used. Details of the simulated structures are shown in Fig. 1.Periodic subwavelength structures are designed in the XY plane. In the 1D structure, the stripes are arranged along the x-axis and have an infinite length along the y-axis. The normal incidence is x-polarized so that the electric field is perpendicular to the stripe direction. The transmitted light is recorded by a plane monitor (not shown in the figure) on the substrate side, and then the transmission spectrum is calculated through Fast Fourier Transform (FFT) analysis.
Frequency-dependent dielectric constants obtained from the literature  are applied in our modeling. It should be noted that in the investigated infrared region, Ge has a higher refractive index (n ~4.1) than other nonmetallic materials, which is beneficial for light confinement, and almost zero imaginary part, and thus the transmission of the non-perforated film is originally larger than that of the metal film. The typical parameters of an analyzed model consist of a lattice constant a = 1.8 μm, a width d = 1.0 μm and a thickness t = 0.36 μm as shown in Figs. 1(a) and 1(b). Comparisons of the simulation results for the 1D and 2D structures are shown in Figs. 1(c) and 1(d), respectively. Both the transmissions of the periodic structures (red lines) and of single-lattice structures (black lines) are recorded. In Fig. 1(d), which shows the case of a Ge-THA, there is a resonant peak at 3150 cm−1, which represents an enhanced transmission accompanied by a suppression; these features share similar characteristics to those described in . The transmission maximum becomes as high as 100%, which is enhanced by a factor of 2 compared with the single-lattice case, while the nearby minimum can be as low as 0 (since it is the first peak observed when we initially examine the spectrum from low to high frequency, we call it the “First Peak”). However, in the case of periodic Ge stripes as shown in Fig. 1(c), only one broad-band resonance (~3150 cm−1) is obtained, and it seems like an absorption peak rather than a transmission peak. Although we present here a specific example for the structure based on periodic Ge stripes, we have studied different parameters and the results show similar phenomena.
3. Fabrication and measurement
Samples of 2D Ge-THA are fabricated to verify the findings in our simulation. First, a smooth Ge film is deposited by evaporation (deposition rate: 0.3 nm/s; amorphous) on a plane quartz plate. Air hole arrays are then fabricated in the film by sputtering using a focused-ion-beam (FIB) system (40-keV Ga ions; resolution: 5 nm). Three groups with close parameters are arranged: a = 2.0 μm, d = 1.0 μm (Group 1), a = 1.8 μm, d = 1.0 μm (Group 2), and a = 1.6 μm, d = 1.0 μm (Group 3). The quality of the fabricated structures is tested by using a scanning electron microscope (SEM). A SEM image of Group 2 sample is shown in Fig. 2(a).The uniformity and the surface condition are excellent except for some inevitable slight slopes in the milled holes.
The normalized transmission spectra from the simulation are shown in Fig. 2(b). Compared with the transmission spectrum in the single-lattice case of each group, First Peaks of ~2800 cm−1 and ~3200 cm−1 are found in Group 1 and Group 2, respectively, while in the case of a = 1.6 μm, the peak at 3750 cm−1 seems to have failed to become the First Peak. In the measurement of the fabricated samples, the zero-order transmission spectra, in which the incident and detected light are collinear, are recorded by a NICOLET 8700 FTIR spectrometer. It should be noted that the light path of the spectrometer has a focus angle of 5°, which differs from the normal incidence condition in our simulation. However, the obtained spectra still show the main characteristics of the structure. Figure 2(c) shows a comparison of the FTIR spectrum of Group 1 with the spectra of air (source) and the smooth part of a Ge film (non-perforated). There are intrinsic absorption bands (~3600 cm−1: water absorption; 2350 cm−1: CO2 absorption) in FTIR spectra. Figure 2(d) shows the zero-order transmission spectra of the three groups. The First-Peak-like band of each group (3300 cm−1 for Group 1, 3780 cm−1 for Group 2, and 4350 cm−1 for Group 3) is observed and labeled by an arrow to indicate the related spectral positions from the simulation results in Fig. 2(b). However, the feature of the First Peak is obvious only in Group 1 with a transmission of 83% (2 times that of the smooth Ge film) and a suppression of 22%, while the one in Group 2 is not reliable owing to partial overlap with the water absorption band at ~3600 cm−1. The marked peak in Group 3 has nearly the same transmission as that of the smooth Ge film (the blue line) at 4350 cm−1, which is quite different from the preceding feature that shows 2-time enhancement of transmission. Similar situation can also be observed in the related peak in Fig. 2(b). The feature of the First Peak in Group 3 seems to be weakened owing to the small lattice constant. One may think that in Fig. 2(b), the peak next to the marked one in Group 3 has a feature of the First Peak. However, it is not the peak at the lowest frequency and it does not have the special surface-preferred field distribution, which will be discussed later in this paper. In addition, the real position of this peak is beyond the lower limit of our FTIR spectrometer (~2 μm), so we omit discussions about this peak.
Since the optical properties of the quartz substrate used in real samples are more complicated than the simple SiO2 model in the simulation, all the peaks in the fabricated samples suffer blue-shift deviations from the simulation results. However, there are the same patterns of red shifts in the peak positions in the measurement and the simulation as the lattice constant a increases from 1.6 to 2.0 μm. The results indicate the reliability of our simulations in revealing the nature of this subwavelength structure. The differences between the simulations and the measurements can also be caused by other factors such as processing errors, edge roughness, slopes in the holes, additional optical property of the real material and the 5° focus angle in the collinear configuration. In particular, the measured transmission maxima of 83%, which is less than the predicted value of nearly 100% in the simulation, is strongly affected by the 5° angle since the optical properties of this kind of structure are very sensitive to any dispersion [1, 18]. The zero-order transmission of the 1D periodic Ge stripes is also measured. Instead of enhanced transmission, only absorption bands are observed, which also coincides with our simulation.
4. Distinctive features of the First Peak
4.1. EM field
To study the underlying physics of the phenomena, we pay attention to the near field of the subwavelength structure in the simulation. By placing point monitors just beneath the outgoing surface of the subwavelength structures, the EM field response is recorded. Figure 3(a) shows the obtained vertical electric field (Ez) of the 1D periodic Ge stripes, 2D Ge-THA, and Au-THA where the parameters are a lattice constant a of 1.8 μm, a width d of 1.0 μm and a thickness t of 0.36 μm; in these plots, the amplitudes are normalized to that of the source. In the low-frequency range of each of the three structures, there is one outstanding peak whose intensity (|Ez|2) can be as large as tens of times that of the source: 3400 cm−1 for periodic Ge stripes, 3600 cm−1 for Ge-THA, and 4250 cm−1 for Au-THA. It should be noted that in Ge-THA, there is another peak at a lower frequency (3150 cm−1, labeled by an arrow) that is not observed in the other two cases. As a comparison, Fig. 3(b) shows the related transmission spectra of the three structures. It is easy to find the popular “extraordinary transmission” peak at 4200 cm−1 caused by SPs in the Au-THA, which corresponds to the Ez peak in Fig. 3(a). In the case of Ge, there are also similar related bands: 3450 cm−1 for Ge stripes and 3700 cm−1 for a Ge-THA, both of which are rather valley-like; the shapes of these bands are close to those of weak Fano resonances . The most significant phenomenon is that the First Peak in Ge-THA spectrum, 3200 cm−1, which is labeled by an arrow as in Fig. 3(a), is not located among these bands. Instead, it occurs at a lower frequency where the Ez field is not the strongest compared with the intensity at 3600 cm−1. This is a feature totally different from that in the Au case.
4.2. Spectral positions of resonant peaks
Some calculations are introduced to help better describe this distinction. The peak in the Au case generated by surface plasmons can be estimated in a first approximation by applying the momentum-matching conditions :Fig. 3(a), at a position similar to λsp in Au-THA), but it is omitted in this discussion owing to the weak Ez field and the weak transmission. All the calculated positions (namely λsp ~2.33 μm [4300 cm−1 in frequency] for Au-THA and λstripe ~λGe-THA ~2.7 μm [3700 cm−1 in frequency] for periodic Ge stripes and Ge-THA) coincide with the previous peaks in Section 4.1, while the First Peak seems unusual since its wavelength is much longer than λGe-THA. The features of all the peaks are shown in Table 1. Although the structures are made of different materials, Au and Ge, which play roles in different mechanisms, they share a common feature at these bands: Peaks are always accompanied by suppressions nearby in the transmission spectra. It seems that all of them can be classified as Fano-type resonances [11, 18, 20], which suggests that the phenomena can be attributed to conversions between continuous states and a discrete state.
4.3. Field distributions of the cross-section
The cross-section field distributions of the above three structures are investigated in order to determine what kind of discrete states they have. Note that in our simulation, the model is built upside down from Fig. 1(b) so that the source is located at the bottom. The TM mode is mainly considered, and both the Ez and Hy fields are studied. The Ez field patterns have evanescent features mainly concentrated at the corners of the openings, and thus show no big differences in all three cases. However, the Hy field patterns change drastically from case to case. The patterns in the region of one period can be seen in Fig. 4.In the case of Au-THA, since the gold film is opaque in this frequency range, the Hy field decays quickly in the material and can only exist on the surface, as shown in Fig. 4(a). It has been explained that there are SPs tunneling through the holes  so that the Hy field on the back surface (the top side in the figure) is much stronger than that on the irradiated surface (the bottom side) indicating the transmission enhancement. As noted previously, Ge has a high refractive index and no absorption in the infrared range, so that in periodic Ge stripes, the Hy field concentrates almost inside the Ge material forming a localized pattern, as shown in Fig. 4(b). A similar Hy pattern is also found at λGe-THA in the case of Ge-THA, as indicated in Fig. 4(c). However, in Fig. 4(d), the First Peak, generated simultaneously in Ge-THA, surprises us with a Hy pattern that shares the general features with the Au case: although the Hy field spreads partly inside the Ge, it mainly concentrates on both surfaces of the film. In addition, the Hy field on the outgoing surface is also enhanced so that there is an enhanced transmission with a sharp suppression nearby in the spectrum.
5. Basic analysis of the phenomena
The phenomena of enhanced and suppressed transmissions in Ge-THA can be interpreted using the CDEW theory. As described in , when light emerges from a subwavelength aperture, it is diffracted partly into a continuum of radiative modes of which the in-plane component of the wave vector is Kx < k0ns (blue circle in Fig. 5), and partly into a continuum of evanescent modes propagating along the surface with real Kx > k0ns. In the structure of Ge-THA on a quartz substrate, Ge has a much larger refractive index than that of the substrate, which makes it a good channel as a waveguide for confining light in-plane. As indicated with the yellow curve in Fig. 5, part of the diffracted light can be coupled into the guided modes inside the Ge film, which has been verified in our latest published paper . According to the waveguide theory, the in-plane component of the wave vector of the guided modes satisfies the condition of Kx > k0ns, and their electric fields on the surface of the Ge film are evanescent. Therefore, these modes act as a continuum of evanescent modes forming the “composite diffracted evanescent wave”, which will have constructive or destructive interference with the light directly incident on the hole. In consequence, the transmission peaks as well as the suppressions occur.
The CDEW theory works well in explaining the origin of the enhanced and suppressed transmissions. However, the unique feature of the First Peak is the sharpness and the large amplitude of the peaks or the valleys, whose determinants is not explicitly indicated in the CDEW theory. In fact, the band at 3600 cm−1 for Ge-THA in Fig. 3(b) also shows a peak along with a valley owing to the guided mode inside the Ge film, whose field can be seen in Fig. 4(c), but the amplitude of the peak is much smaller than that of the First Peak. The lineshape and the sharpness of a resonant band can be better estimated by introducing the Fano model as mentioned in Section 4.2. Details of the model can be found in . The model emphasizes the importance of a discrete state in forming a sharp resonance. The field of the discrete state is always bound to the surface, like the one caused by SPs or the one that we find at the First Peak in Ge-THA, as shown in Fig. 4(d). The field pattern in Fig. 4(d) existing in the dielectric periodic structure is reminiscent of an odd discrete mode in photonic crystals , which can be treated as a Bloch wave.
When a normal incidence reaches the surface of a periodic structure, many eigenstates are obtained by solving Hermitian eigenfunctions converted from Maxwell equations. All of the eigenstates can be cast in Bloch form: a periodic function modulated by a plane wave. The field can propagate through the crystal in a coherent manner, as a Bloch wave [13, 16, 22].
There are always Bloch-wave modes on periodic structures that can behave similarly to surface waves. Some modes can be reemitted from the second surface after they interfere with each other and form standing waves in the plane (a conversion between a discrete state and continuous states), thus causing the Fano-type resonance with a large transmission. To prove this surmise, we use a plane wave expansion (PWE) method  to calculate the band structure of the electromagnetic state. It should be noted that the simulation of subwavelength arrays with a substrate is complicated owing to the vertical asymmetry, and the increased leaky modes caused by the substrate will make the band structure too complex to read. To just demonstrate the relation between the peak and the band structure, a free-standing Ge-THA with parameters consisting of a lattice constant a of 1.8 μm, a width d of 1.0 μm and a thickness t of 0.36 μm is used. The transmission spectrum and the related band structure are presented in Fig. 6.In Fig. 6(a), the First Peak at 3250 cm−1 is recognized because it has almost 100% transmission and a suppression of nearly 0%. Its Hy field distribution retains the feature of concentrating on both surfaces. Besides, as λGe-THA moves beyond 5000 cm−1 [calculated with Eq. (2)] owing to the lack of substrate, a peak following the First Peak appears, which has the similar surface-concentrating Hy pattern, so that the transmission is also very high, indicated by a “*” symbol. We can find proof of these phenomena in the band structure as shown in Fig. 6(b). We consider the bands in the light cone where the EM states radiate into free space. The resonant frequencies corresponding to the Bloch wave-vector k = 0 (Γ point) are 3400 cm−1 (tagged as the “A” band) and 3800 cm−1 (tagged as the “B” band), which coincide with the two labeled peaks in Fig. 6(a).
In summary, we have studied the transmission property of Ge subwavelength arrays. A band with nearly 100% transmission and a drastic suppression nearby is observed in Ge-THAs, and we name it the “First Peak”. The near-field EM responses (only Ez was presented) and the calculations of the spectral position show the distinctions from the 1D structure and the normal metallic subwavelength structure, while similar features of Hy field patterns are found in both triangular-hole-array structures made of germanium and gold. The position of the First Peak is well verified by the band edge at the Γ point, but a thorough theoretical analysis would be useful for gaining better insight into the mechanism of creating nearly 100% transmission. The First Peak in Ge-THAs provides a wavelength-selective property together with a high transmission, which can have many applications in optical MEMS such as a single-layer optical filter due to the unique large transmission region surrounded by regions of suppressed transmission, a window for the infrared light sources to improve the emission, and chemical or biological sensors on the subwavelength scale.
We thank Shohei Hayashi for FIB fabrication of our samples, and Yoshitaka Kurosaka and Kazuyoshi Hirose for discussions. We are also grateful for some helpful advice given by T. W. Ebbesen regarding FTIR measurement.
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