1. Introduction

Multiple optical elements utilize crossing of channel optical waveguides [1,2]. Thus, different approaches of waveguide crossing became the subject of multiple investigations and related publications [1–12]. A lot of papers were focused on waveguide crossing realized in the single layer, which is the most difficult to realize in high index contrast waveguides used in silicon photonics [3,4]. Different approaches were proposed in order to improve the crossing quality (i.e., to reduce crossing loss and crosstalk). For the case of intersecting of silicon nano-wires, crosstalk can be optimized by changing crossing angle [5], using sub-wavelength gratings [6] or optimizing offset crossing structures [7]. High quality waveguide crossing can be done by widening intersection areas [8–12]. Unfortunately, all these technologies have the principal limitation in the presence of moderate reflection as well as undesired scattered fields in crossing arms, which can lead to degradation of device performances in multiple waveguide crossings. Multilayer waveguide crossing can be a good solution for this case. For example, adiabatic interlayer coupling [1] provides 0.2 dB pass-through loss for multiple (30) cross number. Efficient vertical coupling between channel waveguides with different index (Δ) contrast (2.5% and 0.3%) was obtained by inverted taper. Unfortunately, this technology hardly can be directly applied to silicon-on-insulator (SOI) waveguide structures, due to very complicated task to stack laterally three silicon optical waveguides.

Current paper further evaluates the general idea of adiabatic interlayer coupling [1] and implements it to design silicon wire waveguide crossing on SOI structures with polymer over guide, in order to provide negligible loss and crosstalk.

2. Waveguide crossing by vertical coupling with polymer upper channel waveguide

General idea of excellent waveguide crossing is to make possible optical beam to pass over the crossed channel waveguide [1] by means of inverse tapers. Adiabatic inverted tapers are widely used as beam transformers for coupling Si wire waveguide with optical fiber [3,4,13–18]. Recently, vertical waveguide coupler with −0.2 dB loss is designed for TE single mode transmission from a bottom SOI channel waveguide to a top a-Si channel waveguide [19]. Impedance matching is provided by contra directed inverse tapers in the respective waveguides. This design is good for waveguide crossing but it needs an advanced technology for a-Si manufacturing of over layered waveguide, as well as carefully adjusting in space of two nano tapers. Current paper proposes and studies the design solution with polymer over layered waveguide, simpler from a technological point of view.

The proposed structure of cross coupler of Si wire waveguides is shown in Fig. 1a . It contains two Si single mode wire waveguides with height h = 220 nm and width w = 450 nm on 2 μm buried oxide (BOX) silicon substrate with two contra directed inverse tapers [15], which are separated by a small distance L_g = 3 µm from taper ends. We use refractive indices 3.478 and 1.447 for silicon and BOX, respectively. The taper has a parabolic shape. It is characterized by a taper length L and a tip width d. The spacing between waveguide tips contains similar Si wire intersecting waveguides in cross direction (X). The waveguides are covered through spin-on 〉owable oxide (FOX) [20] buffer with refractive index 1.4 and height W_g and by an upper strip waveguide of width W and height H built by polymer SU-8 (with refractive index N_w = 1.56 [21,22] at optical wavelength 1.55 μm), which is situated just over the through pass Si wire (along Z). This refractive index 1.56 becomes suboptimum for the widely used Si wires with 220 × 450 nm² cross section (see Fig. 1b). The final structure is additionally covered by FOX for protection of polymer waveguide from environment.

 

Fig. 1 Design of cross coupler. a) General view (from the bottom) of the structure based by Si wire tapers vertically coupled with wide polymer waveguide. Buried oxide and Si substrate are not shown; b) Through pass transmitting efficiency T for Si wires of different cross section as a function of refractive index of upper waveguide in optimum structure.

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The proposed structure has been numerically investigated by three-dimensional finite difference time domain (FDTD) method by FullWave software [23]. We have used the same mesh size 50 nm for all simulations. It represents a trade-off between the computer power requirement and simulation accuracy which was 1% and 0.1% for absolute and relative power measurements, respectively. We launch and analyze propagation of fundamental mode of Si wire thought the structure and measure the relevant intensities, normalized to the input power for transmitted wave (T), back reflected wave (Back) and wave in the cross waveguide (Side), describing the crosstalk. Counter map of power transmittance is presented in Fig. 2 .

 

Fig. 2 Counter map of power transmittance through cross coupler of fundamental guided mode of Si wire waveguide. a) X-cut, b) Y-cut (due to symmetry we use half structure, X ≥ 0). 3D FDTD simulation. L_g = 3 μm, W = 1.5 μm, H = 1.7 μm, W_g = 200 nm, L = 30 μm, d = 160 nm.

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Figure 3 presents the power distribution at different cross-sections. One can observe from Fig. 2 and Fig. 3 that the optical power is coupled up and down into the upper polymer waveguides by means of Si wire tapers, and thus it passes over the crossed Si wire waveguide.

 

Fig. 3 Power distribution in different cross-section. a) begin of structure (z = 4.5 μm) - the main of power is in the Si wire; b) middle of structure (z = 36.5 μm) - the main of power is in the upper polymer waveguide; c) end of structure (z = 72 μm) - the main of power is returned to the Si wire; 3D FDTD simulation. L_g = 3 μm, W = 1.5 μm, H = 1.7 μm, W_g = 200 nm, L = 30 μm, d = 160 nm.

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In order to make a device optimization, we have completed a set of numerical simulations and found the general dependences of Si wire waveguide crossing features as a function of main structure parameters and optical wavelength (see Figs. 4 –6 ). At first from data in Fig. 4, we have got sub-optimum parameters of inverse taper L = 30 μm and d = 160 nm and use them for the next round of simulations. Figure 5 presents the influence of the parameters of upper polymer waveguide with refractive index 1.56 on crossing characteristics. One can see that the quality of waveguide crossing is slightly dependent on W and H. This fact can simplify the manufacturing of polymer waveguide with optimum structure parameters by conventional spin off technology and optical lithography.

 

Fig. 4 Power transmittance of fundamental guided mode of Si wire waveguide through cross coupler as a function of parameters of Si wire taper. a) versus taper length; b) versus width of taper tip. 3D FDTD simulation. L_g = 3 μm, W = 1.5 μm, H = 1.7 μm, L = 32 μm, W_g = 200 nm, d = 160 nm.

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Fig. 6 Characterization of optimum cross coupler. a) Transmitting characteristics as a function of height of oxide buffer between Si wire and upper polymer waveguide; b) Wavelength dependences of transmitting characteristics. 3D FDTD simulation. L_g = 3 μm, W = 1.5 μm, H = 1.7 μm, W_g = 180 nm, L = 30 μm, d = 160 nm.

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Fig. 5 Power transmittance of fundamental guided mode of Si wire waveguide through cross coupler as a function of parameters of upper polymer waveguide. a) as a function of polymer waveguide height; b) as a function of polymer waveguide width. 3D FDTD simulation. L_g = 3 μm, W = 1.5 μm, H = 1.5 μm, W_g = 200 nm, L = 30 μm, d = 160 nm.

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Results of final optimization of the proposed structure are illustrated in Fig. 6. They prove that, at optimal conditions, the through pass efficiency can exceed 98% with back reflection and side scattering about −50 dB and −70 dB, respectively. It is important that these high performances are valid within practically needed spectral range (as shown in Fig. 6b), which is used for telecommunication or sensing purposes. One can see that our device provides the high transmission efficiency 98% and 97%, respectively, within 20 nm and 60 nm bandwidth around the optical wavelength 1.55 μm. To get this figure, we used the conventional Fast Fourier Transform (FFT) procedure [23] with pulse excitation. In order to increase the accuracy, we have deleted the parasitic signal from the time response and then fulfilled FFT to measure both reflected and transmitted waves at different optical wavelengths. For the current device, the material dispersion has a negligible role relative to the structure waveguide dispersion, thus we have used the refractive indices taken at single optical wavelength 1.55 μm. In order to prove this assumption, additional simulations have been performed with changes by 0.000187 and 0.004338 of refractive indices of polymer [22] and silicon [24], respectively, corresponding to an optical wavelength shift from 1.55 μm to 1.50 μm. Figure 5b shows that this data (see curve T(1.50)) has a small deviation from previous results (see curve T(1.55)) in comparison with moderate signal variation over 100 nm optical range. Transmitting efficiency depends on the technology tolerance. The key parameter is the tip width d, which is better to control with ± 6 nm or ± 20 nm accuracy in order to provide transmitting loss below −0.2 dB or 0.4 dB, respectively (see Fig. 4b).

For structure with optimal through pass parameters, the features of perpendicular cross pass architecture will be even better as X-directed waveguide has negligible coupling with other Si and polymer waveguides due to large distance separation, providing optical isolation. Note that propagation of optical wave along X produces too small cross scattering which is below the FDTD method sensitivity. In order to study the crossing for this case of extremely small loss, we have positioned 16 identical cross wires on the pass of X-directed waveguide. The total power transmittance is presented in Fig. 6b as additional curves (Cross(16)). From these data, it is possible to estimate total transmitting (−0.01 dB) and reflecting (−53 dB) coefficients for 16 wire crossing for Cross pass geometry. One has to mention that an error in measuring power amplitude for current 3D FDTD simulation is about 1%, thus corresponding value −0.04 dB could be regarded as the maximum of actual possible loss for the case of Si wire waveguide crossed by 16 Si wires. For the single wire crossing, the loss is smaller than this value by 16 times and thus transmitting efficiency could be better than 99.9%.

One has to point out this structure contains two coupled waveguides with drastically different refractive indices and sizes, thus it is not evident that it can provide the high efficiency of waveguide crossing for any set of device parameters. For the specific case of upper polymer waveguide, we find the set of structure parameters providing 98% power transmission. It is interesting that the power distribution in polymer waveguide at crossing point has an asymmetric structure (see Fig. 3b). It means that about 62% of total power is transmitted by the fundamental mode of polymer waveguide and, thus, the significant amount of power (38%) corresponds to other waveguide modes (first mode, radiated and evanescent). Thus we have different mechanisms of power coupling between single mode silicon wires to two-mode polymer waveguide. They could add constructively or destructively, thus making the coupling efficiency to be a complicated function of the structure parameters. It makes difficult to find an universal relation of the crossing performance on the waveguide geometry and the effective indexes of Si and polymer waveguides. Thus for different optical waveguide structures, one needs to complete the optimization procedure from the very beginning. For example, for the case of typical Si wire with h = 340 nm and w = 340 nm we have got suboptimum refractive N_w = 1.6 of the upper waveguide (see Fig. 1b). All other structure parameters are chosen the same as for optimized structure with h = 220 nm and w = 450 nm.

These simulations prove that the proposed structure can provide excellent crossing characteristics. We regard an ideal structure without propagation loss. Taking into account the small structure sizes (length 70 μm and width 3 μm), it does not make a significant error as the crossing loss (−0.1 dB) corresponds to “the effective per length” loss of about −14 dB/cm, which is much smaller propagation loss. The most important advantage of this optical element will be realized for the case of optical devices which implements multiple (up to hundreds) crossings in X directions and several crossings in Z directions. These structures could be manufactured by modern technology which is available in different nanophotonics centers [4,6,13,14,22].

4. Conclusion

Numerical experiments by 3D FDTD prove that vertical coupling through silica buffer of tapered Si wires and upper polymer waveguide could be used as low loss wire crossing with negligible crosstalk. It provides small power reflection (−50 dB) and scattering into crossing waveguide (−70 dB), as well as small loss for through pass (<0.1 dB) of fundamental guided mode. It has to be mentioned that loss for cross path is even smaller (<0.002 dB) due to a small coupling of crossed Si and polymer waveguides, which are separated from Si wire by silica buffer. New waveguide crossing could be manufactured by CMOS compatible technology and can find wide applications in silicon photonics and censoring for the cases if multiple and nondestructive waveguide crossing needed for high device performance.