1. Introduction

Three-dimensional (3D) photonic crystals are expected to provide a variety of artificial manipulation of photons in three dimensions [1–12]. 3D light guiding and the control of spontaneous emission inside 3D photonic crystals have been successfully demonstrated by embedding artificial defects and emitters inside them [1–6,8–10,12]. Furthermore, in recent studies, the surface of such 3D photonic crystals provides a new route for manipulating photons [7]. The existence of surface modes has been experimentally demonstrated [7,11], and the possibility of forming a surface-mode gap, which inhibits the existence of photons at the surface, has been shown by modifying the surface structures [7]. Based on this, the creation of surface nanocavities has been successfully demonstrated [7]. We expect such photon manipulations at the surface of 3D photonic crystals to produce new applications of 3D photonic crystals because a variety of unique 3D designs is possible for structures around the surface of 3D photonic crystals. Surfaces would open up an attractive way for the manipulation of photons, through which various types of access from outside become straightforward compared with the case inside the 3D photonic crystals. Moreover, surface modes are expected to be applicable as a field for new sensing applications, utilizing electromagnetic-field distributions penetrating into air [13]. However, previous investigations on the surface nanocavities have only focused on their primitive design and their demonstrations. The demonstrated cavities only possess TE-like polarization, where the electric field is polarized in the in-plane direction, despite the availability of a polarization-independent surface-mode gap which enables the manipulation of photons with either TE-like and TM-like polarizations. Their experimental quality-factors (Q-factors), which indicate the strength of the light confinement in cavities, remain around 9,000 [7].

In this work, we study the creation of surface nanocavities by addressing the advantages of a high degree of design freedom and the polarization-independent surface-mode gap. We discuss the possibility of increasing the Q-factor of surface nanocavities with TE-like polarization by introducing two design concepts. We also discuss the creation of cavities with desired polarization, focusing on the formation of TM-like nanocavities where the electric field is polarized in the surface-normal direction. We then experimentally fabricate the designed nanocavities and demonstrate their resonant characteristics. We believe that these results will become important foundations for the manipulation of photons at the surface of 3D photonic crystals.

2. Nanocavity designs

Figure 1 shows a schematic image of a nanocavity at the surface of a 3D photonic crystal. We used a 3D photonic crystal with a stacked-stripe (or woodpile) structure [1], which has successfully demonstrated a variety of photon manipulations. At the surface of such a 3D photonic crystal, the formation of a surface-mode gap has been experimentally proven [7], within which the existence of photons with any polarizations (including TE/TM polarizations) is inhibited. Figure 2(a) shows the calculated photonic band diagram of the surface modes by a 3D finite-difference time-domain (FDTD) method, showing the formation of the surface-mode gap. We set the width and the height of the rods as 0.4a and 0.4a. Here, a is the center-to-center separation of parallel rods. Figures 2(b) and 2(c) illustrate representative electric-field distributions of the upper- and lower-edge modes of the surface-mode gap at the X point in the reciprocal space [(k_x,k_y) = (π/a,0)]. It can be seen in Figs. 2(b) and 2(c) that the dominant component of the higher- and lower-edge modes are E_y and E_z, respectively, thus the polarization of those modes are classified as TE-like and TM-like. Those results suggest that the cavity modes with TE-like or TM-like polarizations can be obtained by introducing adequate defect structures around the surface, utilizing the polarization characteristics of those band-edge modes of the surface-mode gap.

 

Fig. 1 Schematic illustration of a nanocavity at the surface of 3D photonic crystal with stacked-stripe structures, whose surface possess the cross-geometric pattern.

Download Full Size | PDF

 

Fig. 2 Characteristics of surface-mode gap. (a) Calculated band diagram. The insets show the representative directions in real and reciprocal spaces. (b), (c) Calculated electric-field distributions of higher- and lower-edge modes of surface-mode gap, respectively.

Download Full Size | PDF

Now, we discuss the TE-like nanocavities. We consider point defects formed by increasing the volume of dielectrics around the surface. Such a type of defect is called as the donor-type defect due to the similarity with the behavior of donor ions in semiconductor crystals [14]. Since the effective refractive index of the mode becomes high around a donor-type defect, cavity modes originated from the upper-edge mode of the surface-mode gap are formed within the gap range. Here, the upper-edge mode possesses TE-like polarization [Fig. 2(b)], therefore TE-like nanocavity is expected to be obtained by introducing those defects. Previous work introduced primitive donor-type defects constructed by simply increasing the width of the rods within a particular range at the very surface layer, and demonstrated TE-like nanocavity [7]. In this work, we investigate two kinds of advanced designs about such TE-like nanocavities to increase the Q-factors of them by reducing the loss of photons from the cavity. First, we modified the envelope function of the cavity mode to suppress the leakage of photons into air; such a consideration was even advanced in nanocavities at two-dimensional photonic-crystal slabs [15–17]. Figure 3(a) illustrates one example structure, where the rod widths are gradually modulated in the surface layer. Figure 3(b) shows the result of the actual design based on a method discussed in ref [17]. We made an envelope function of a cavity mode as a Gaussian function with a full-width at half-maximum of 6.8 a by modulating the widths of the rods. Figure 3(c) shows the calculated electric-field distribution (dominant component of E_y) of the cavity mode and successful modulation of the envelope function. Figure 3(c) also illustrates that the electric-field distribution is evidently originated from the upper-edge mode of the surface-mode gap shown in Fig. 2(b). After the calculation of the Q-factor of such a nanocavity, we found that the Q-factor can exceed 2.3 million at the surface of a 3D photonic crystal with sixteen stacked layers and be further improved by increasing the number of stacked layers.

 

Fig. 3 Design of TE-like nanocavities composed of the rods with modulated widths in the surface layer. (a) Schematic images of the structure (upper panel) and the band diagram (lower panel). (b) Designed rod widths at each position. (c) Calculated electric field distribution (E_y component), showing the formation of a cavity mode with Gaussian-function envelope.

Download Full Size | PDF

In our second design consideration, we expanded the design area by moving artificial defects from the very surface to slightly inside the photonic crystals, such as the second or third layer. In this case, the center of the electric-field distribution is also expected to move to slightly inside the photonic crystal, and the amount of the electric field just at the interface between the photonic-crystal surface and air is reduced. As a result, the loss into air from the cavity might be reduced. This consideration is unique at the surface of 3D photonic crystals, differing from the low-dimensional structures. Figure 4(a) shows the considered structure, where we increased the rod width in the second layer within a particular range instead of increasing the rod width in just the surface layer. As shown in Fig. 4(b), the dominant component of the electric field was also E_y, as is the case of introducing the cavity in the surface layer [Fig. 3 (c)]. Figure 4(c) shows the calculated Q-factors by varying the defect length L_d, where the width of the defect rod was 0.60a. The Q-factors of the cavities just at the surface layer are also shown for comparison, where the width of the defect rod was 0.52a. In both cases the number of stacked layers was sixteen. Figure 4(c) shows that the Q-factors increase about twofold when cavities are introduced in the second layer. These results suggest that the reduction of the optical loss into air is possible by changing the positions of the artificial defects, which is unique consideration in the use of 3D structures. Here, it is noteworthy that these two advanced design considerations for increasing the Q-factor of surface nanocavities are expected to be similarly applicable when using the surfaces of the other types of 3D photonic crystals.

 

Fig. 4 Design of TE-like nanocavities composed of the defects formed in the second layer. (a) Schematic images of the structure. (b) Calculated electric-field distribution (E_y component). (c) Calculated Q-factors for the cases with the defects in the second layer and the surface layer.

Download Full Size | PDF

We also investigated whether the creation of TM-like nanocavities is possible. We focused on the fact that the lower-edge mode of the surface-mode gap possesses TM-like polarization [Fig. 2(c)]. Based on this, it is expected that TM-like cavities can be obtained by introducing defects where the volume of the rods around the surface is partially decreased; such defects can be called as acceptor-type defects due to the similarity with the acceptor ions in semiconductors [14]. Figure 5(a) shows a schematic of the designed structure for TM-like nanocavity. As an example, we narrowed the rod in the second layer within a particular range. Of course, we can also introduce such acceptor-type defects into the other layers, such as the surface layer. We set the width 0.21a and calculated the electric field distributions. As shown in Fig. 5(b), we confirmed that the dominant component at the surface is E_z as the lower-edge mode of the surface-mode gap [Fig. 2(c)], and TM-like nanocavity is obtained. Figure 5(c) shows the calculated Q-factors, and we expect that the Q-factors of such TM-like nanocavities could increase by incorporating the method about the gradual modification of the rod widths as discussed in Fig. 3.

 

Fig. 5 Design of TM-like nanocavities. (a) Schematic images of the structure. (b) Calculated electric field distribution (E_z component). (c) Calculated Q-factors.

Download Full Size | PDF

3. Fabrication and experiments

Next, we fabricated the designed nanocavities at the surface of the 3D photonic crystals with sixteen stacked layers and examined their resonant characteristics. For the fabrication, we employed highly-precise alignment and wafer-bonding techniques [1,12,18]. We used GaAs or Si for the constituent materials. The period of stripe pattern was a = 500 nm, and the width and the height of the rods were set at 200 nm ( = 0.4a). Figure 6 shows the experimental results of the TE-like nanocavities with two designs. Figure 6(a) shows the SEM image of the fabricated nanocavity composed by gradually increasing the rod width in the surface layer as designed in Fig. 3. For this nanocavity, we measured a resonant spectrum with a measurement technique in which we irradiated light in an oblique direction (45° with respect to the surface normal) and collected the radiated light from the cavity in the same direction [7]. We used a wavelength-tunable continuous laser as the light source. Figure 6(b) shows the obtained result. We successfully obtained a Q-factor of ~40,000. In addition to such a nanocavity in the surface layer, we also fabricated the nanocavities formed in the second layer. Figure 6(c) shows representative SEM image, showing that we successfully realized the designed structure in the second layer. Figure 6(d) shows the observed resonant spectrum for the case with L_d = 3a. From Fig. 6(d), we estimated the maximum experimental Q-factor as ~40,000.

 

Fig. 6 Experimental demonstrations of TE-like nanocavities. (a), (b) Top-view SEM image of a cavity constructed by gradually modifying the rod widths and its resonant spectrum, respectively. The constituent material of the photonic crystal was Si. (c), (d) Top-view SEM image of a cavity constructed by introducing defect in the second layer and its resonant spectrum, respectively. The constituent material of the photonic crystal was GaAs.

Download Full Size | PDF

By employing the advanced designs discussed in Figs. 3 and 4, we successfully demonstrated the increase of the Q-factor to ~40,000 at the surface of the 3D photonic crystal with sixteen stacked layers. The obtained Q-factor is more than four-times higher than that in previous work (Q~9,000 at eight-layered structure) and as high as the Q-factors of the cavities completely embedded in the center of 3D photonic crystals; the highest reported Q-factor was 38,500 within a structure with twenty-five stacked layers [10]. At this time, although the experimental Q-factors of the surface nanocavities are in the same order with those of the cavities completely embedded inside the photonic crystals, surface nanocavities possess advantages toward applications compared with those inside the photonic crystals; a variety of accesses from outside is straightforward, and relatively small numbers of stacked layers are sufficient for obtaining high Q-factors. Here, note that the experimental Q-factor reached a ceiling around ~40,000 in both types of experimental surface nanocavities, although the calculations revealed that Q-factors can exceed two millions even at the surface of 3D photonic crystals with sixteen layers. This suggests that there is a room for further improvements in surface nanocavities. One possible cause of such Q-factor limitations includes the fabrication errors, which include the fluctuations in the fabricated structures during the fabrication process. Our investigation of such fabrication error will be described elsewhere.

In addition to TE-like nanocavities, we fabricated TM-like nanocavities and examined their characteristics. Figures 7(a) and 7(b) show a SEM image of the fabricated nanocavity and the measured resonant spectrum, respectively. An acceptor-type defect was well fabricated by decreasing the rod width in the second layer [Fig. 7(a)]. In Fig. 7(b), which shows the resonant spectrum where L_d = 6a, we obtained a Q-factor up to 22,000 in the TM-like nanocavity. Although the obtained Q-factor is slightly high compared with the calculation result [Fig. 5(c)], this is thought to be due to the difference between the calculated and fabricated structures. To the best of our knowledge, this experimental Q-factor is the highest among the TM-like nanocavities in photonic crystals, including 1D or 2D systems, suggesting that the surfaces of 3D photonic crystals are essentially useful fields for manipulating photons with any polarizations. Furthermore, note that our TM-like cavity possesses a high Q-factor from the viewpoint of acceptor-type nanocavities; for example, Q-factors of ~1,000 were reported in an acceptor-type nanocavity in 2D photonic crystals [19]. Since the electromagnetic fields of surface modes tend to penetrate into air, surface modes are expected to be applicable as a field for efficient sensing applications [13]. Advancements in acceptor-type nanocavities, where we can obtain electromagnetic fields penetrating into air only at a certain location, would be advantageous for new sensing applications.

 

Fig. 7 Experimental demonstration of TM-like nanocavities. (a), (b) Top-view SEM image of a cavity constructed by decreasing the rod width in the second layer and its resonant spectrum, respectively. The constituent material of the photonic crystal was GaAs.

Download Full Size | PDF

4. Conclusions

We have investigated the nanocavities at the surface of 3D photonic crystals. We have first investigated the new designs of TE-like nanocavities to increase their Q-factors and introduced two designs for this purpose; one adequately modifies the envelope function of the electromagnetic field of cavity modes, and the other is based on a consideration of moving nanocavities from the surface to slightly into the 3D photonic crystal, such as the second layer, that is unique to the surface of 3D photonic crystals. Both designs have successfully demonstrated the increase of designed Q-factors from different viewpoints. We have then argued that TM-like nanocavities are possible at the surface by introducing new acceptor-type defects. We have finally fabricated designed nanocavities at the surface of 3D photonic crystals with sixteen stacked layers, and examined their characteristics. In TE-like nanocavities, we obtained Q-factors of ~40,000, which is four times higher than previous work. This result is as high as the Q-factor of the cavities completely embedded in the center of 3D photonic crystals. Furthermore, TM-like nanocavities were experimentally demonstrated for the first time, and a Q-factor of ~22,000 was obtained. We believe that our results are an important foundation for the application of the surfaces of 3D photonic crystals.