In recent years, research on photonic crystal (PhC) waveguides has been focused almost entirely on structures formed in slabs of high refractive index surrounded by low-index claddings such as suspended membranes [1–3] and silicon-on-insulator [4]. These so-called membrane-type waveguides outperform their substrate-type counterparts (weak vertical refractive index contrast) in terms of propagation losses by more than two orders of magnitude ($2\mathrm{dB}/\mathrm{cm}$ in membranes [5] versus $600–800\mathrm{dB}/\mathrm{cm}$ on substrates [6]). It is generally recognized that the high losses in substrate-type waveguides are due to a combination of inaccurate fabrication of the PhC holes [7] and the fact that the excited propagation modes are not guided in a strict sense. Substrate-type PhC waveguides are interesting for electrical carrier injection, but they are typically operated above the light line [8] or, more precisely, the background line, as introduced in [9]. This means that the propagating Bloch mode contains a Fourier component that does not decay to zero at infinite distances from the waveguide core. The nonguided nature of such Bloch modes intrinsically leads to propagation losses. The magnitude of these losses is not easy to estimate. It is not a priori clear that they are intolerably high for practical applications. To make predictions about the potential of substrate-type PhC waveguides for photonic integrated circuits, it is essential to understand the limiting loss mechanisms.

Does the dominant contribution come from technological imperfections or from the fact that the excited modes are not strictly guided? To answer this question, the manufactured structures must be benchmarked against reliable simulation results. Until recently, efforts to optimize the fabrication process of PhCs were done without knowledge of the theoretical limitations. In this Letter, we compare the loss figures measured from our manufactured structures to finite-difference time-domain (FDTD) simulation results obtained with perfectly cylindrical holes. We show that technological imperfections are not the limiting factor in terms of loss performance.

The interpretation of the following results strongly relies on trustworthy loss simulations. We perform brute-force simulations with a three-dimensional (3D) FDTD code based on the freely available MEEP [10]. The simulation does not require experimental calibration of any kind of phenomenological or semi-empirical parameters. It was validated against experimental data in [11] for cylindroconical hole shapes. The drawback in our approach is the huge computational effort. However, we believe the single most important criterion is the quantitative reliability of the computed propagation loss figures. So far, we can get that only with the computationally expensive method.

The waveguide we investigated is a single line-defect (W1) waveguide in a triangular-lattice PhC with lattice constant $a=380\mathrm{nm}$ and circular holes of nominal radius $r=100\mathrm{nm}$. It supports TE modes (i.e., there is no E-field component along the PhC hole axis). The waveguide was formed in a heterostructure grown on InP with an InGaAsP core of 640 nm thickness and an InP top cladding of 300 nm. The PhC holes were etched into the semiconductor structure by ${\mathrm{Cl}}_2$-based dry etching using an 800 nm thick ${\mathrm{SiN}}_x$ hardmask. The optical characterization was performed by port-to-port transmission measurements on waveguides of five different lengths (cutback method), given by $30\times 2^n$ lattice periods, $n\in \{1,5\}$. Monochromatic cw light from a tunable laser source (1470–1630 nm) was used (TE-polarized). The resulting loss figure is plotted versus wavelength in Fig. 1 (thick black line).

To appraise the fabrication quality of the PhC waveguides, we compare them with numerical simulations using perfectly cylindrical hole shapes. Since the dry-etched holes are slightly conical, there is some uncertainty in choosing the appropriate hole radius in the simulations for comparison of the loss data. From scanning electron microscopy (SEM) images, the radii of the manufactured holes are determined to be $r=100\mathrm{nm}$ at the chip surface. The corresponding FDTD data are plotted as a purple line in Fig. 1. To account for the conicity, the simulations were repeated for two slightly smaller hole radii, $r=95\mathrm{nm}$ (red) and $r=90\mathrm{nm}$ (blue). An excellent quantitative agreement is obtained with the curves for $r=95\mathrm{nm}$ and $r=100\mathrm{nm}$, although there is a wavelength shift (about 20 nm in the case of $r=95\mathrm{nm}$). The minimum loss figure is around $335\pm 5\mathrm{dB}/\mathrm{cm}$ in the simulations as well as in the experiment. We conclude that a further improvement of the fabrication quality will not significantly reduce the propagation losses. Hence, the design of the waveguide itself has to be addressed to achieve further improvements.

 

Fig. 1. Propagation loss of a W1 substrate-type PhC waveguide with lattice constant $a=380\mathrm{nm}$. Experimental data (thick black line) are compared to FDTD results (thin colored lines). For the simulations, a cylindrical hole shape is assumed. Since manufactured holes are slightly conical, the simulations were performed for three different hole radii, $r=90\mathrm{nm}$ (red), $r=95\mathrm{nm}$ (blue), $r=100\mathrm{nm}$ (purple). The best agreement is found for $r=95\mathrm{nm}$.

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Compared to state-of-the-art loss values of $600–800\mathrm{dB}/\mathrm{cm}$ in substrate-type PhC waveguides [6], our results constitute an improvement by a factor of about 2. Our approach to obtain high-quality etching results mainly rests on the use of a thick hardmask of 800 nm of ${\mathrm{SiN}}_x$. Its fabrication required several steps: First, layers of 42 nm of Ti and 200 nm PMMA were added on top of the ${\mathrm{SiN}}_x$ film. After electron beam lithography, the intermediate Ti mask was opened in an ${\mathrm{SF}}_6/{\mathrm{N}}_2$-based reactive ion etching (RIE) process. Subsequently, the ${\mathrm{SiN}}_x$ layer was etched to a depth of about 450 nm in a ${\mathrm{CHF}}_3$-based RIE step. At this point, the intermediate Ti mask had to be renewed by evaporating an additional 45 nm layer of Ti on top while the sample was mounted at an angle of 25° with respect to the deposition direction (to avoid covering the bottom surfaces of the holes with masking material). During this self-aligned mask renewal [12], the sample was rotating about an axis perpendicular to its surface, such that uniform sidewall depositions were obtained. After this procedure, an additional ${\mathrm{CHF}}_3$-based RIE step was performed to etch through the remaining ${\mathrm{SiN}}_x$. This process yields an excellent hardmask, but it is limited to circular features of a fixed size. This means that the access waveguide structures required for a cutback measurement have to be added separately and aligned to the PhC waveguides. We used alignment markers composed of circles that were written together with the PhC waveguides. Figure 2 shows an SEM top view of a manufactured waveguide, including the transitions to the access waveguides.

 

Fig. 2. SEM micrograph of a PhC waveguide of 30 periods with well-aligned access waveguides. The taper sections are 100 μm long and make a transition from 5 μm wide access waveguides to the W1 PhC waveguide. The contribution of the tapers on the overall power loss cancels out when using the cutback method. The propagation loss figure of the access waveguides, however, has to be taken into account: It is $6\pm 1.5\mathrm{dB}/\mathrm{cm}$, measured by the Fabry–Pérot method on a reference waveguide.

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Our PhC waveguide fabrication process, while providing good results, is rather complicated and might not be attractive for large-scale applications. However, to obtain high-quality PhC holes, there are alternative approaches to using thick hardmasks. For instance, the cylindricity of dry-etched holes can be improved by applying a thermal postprocessing that induces a reflow of the semiconductor crystal. This treatment has improved the filtering capabilities of a ministop band in a W3 waveguide (a line defect composed of three rows of holes) [13], and we also expect it to be competitive in terms of propagation losses.

Now that we know that technological imperfections are not responsible for the propagation losses in our waveguides, the question remains: Can the loss figure be further reduced by means other than improving the fabrication quality? The simulated loss curves of Fig. 1 show that the minimum loss depends on the hole size. More generally speaking, the loss critically depends on the design of the PhC pattern, and to our knowledge, there are no reliable rules of thumb that can be used to optimize the design. For instance, consider the intuitive notion that the losses increase with hole radius. Figure. 1 visualizes that, although this statement seems to be correct for fixed wavelengths above 1500 nm, it fails if we look at the loss minimum, which is lower for $r=95\mathrm{nm}$ and 100 nm than for $r=90\mathrm{nm}$. Since simulations are time consuming, finding an optimum design is a tedious task, even if we restrict ourselves to W1 waveguides in triangular-lattice PhCs (not only the $r/a$ ratio needs to be optimized but also the thicknesses of the guiding and cladding layers in the heterostructure). If, in addition, a “flat band” of slow-light propagation [14] is of interest, then the optimization procedure must include modifications of the PhC pattern, and a trade-off between low losses and desirable slow-light properties will have to be made.

Although finding an optimum PhC waveguide design is difficult and depends on the specifications required for a given application, we will briefly discuss one for which a significantly lower loss figure is expected compared to the results shown in Fig. 1. According to Kuang et al., a promising design modification is to shift the PhC on one side of the waveguide by half a period along the waveguide axis [15]. The new symmetry is predicted to reduce the propagation losses. In the FDTD simulation of such a waveguide with $r/a=0.34$, we find a loss figure slightly below $80\mathrm{dB}/\mathrm{cm}$ at a reduced frequency of 0.255 (Fig. 3). This number is comparable to loss values observed in conventional rib waveguides with doped claddings for electrical carrier injection. Further investigations will show if even lower values are possible and if these numerical results can be verified experimentally.

 

Fig. 3. Simulated propagation loss of a W1 waveguide with $r/a=0.34$ and a shift between the PhC on either side of the waveguide, as indicated by the dashed lines in the inset. An interesting window of low propagation loss opens around a reduced frequency of 0.25. The loss minimum is below $80\mathrm{dB}/\mathrm{cm}$ at a reduced frequency of 0.255.

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To summarize, we have demonstrated propagation losses around $335\mathrm{dB}/\mathrm{cm}$ in substrate-type PhC waveguides. Not only is this number an improvement by a factor of 2 with respect to the state of the art, but also it agrees well with the losses simulated by FDTD. This agreement suggests that technological imperfections are not the main limiting factor and that a further reduction of the propagation losses can only be achieved by choosing a different design of the PhC waveguide. One option would be to introduce a shift between the PhC patterns on each side of the waveguide by half a period along the propagation direction. According to numerical predictions, this design could provide a loss figure around $80\mathrm{dB}/\mathrm{cm}$, a value at which the substrate-type PhC waveguides can become interesting for integrated optics.