1. Introduction

Fabricating waveguide devices in optical monocrystal chips is intriguing compared to its epitaxy competitors, due to better preservation of crystalline lattices, easy fabrication and low costs [1]. Up to now, ion implantation and femtosecond laser micro-machining emerged to be two of most important strategies in the fabrication of monocrystal waveguide devices [2–5]. Various of passive and active waveguide devices have been reported using these methods as while as the combination of the two, including waveguide splitters, ring resonators, waveguide lasers and frequency converters [6–13].

Waveguide splitters are one of the basic components in optical circuits. Its wide applications include but not limited to waveguide interferometers, optical switches, sensors and multiplexing devices [14–16]. In the last decade, efforts also have been made among researchers to fabricate compact, reliable beam splitters in monocrystals [17–22].

In 2012, H. Hui et al. reported the fabrication of Y-branch splitter in LiNbO₃ by photolithography assisted ion implantation [19]. In such a scheme, the splitting angle is small due to tiny refractive index contrast between waveguide core and substrate, which usually causes difficulties in further compactness of the device. In 2016, J. Lv et al. reported LiNbO₃ beam splitters by utilizing femtosecond laser inscription [18]. However, the structure is extreme complicated. Hundreds of laser traces were employed as different patterns were defined at each independent cross-section. The whole length of the splitter is several millimeters, making it hard to be integrated on chips. Recently, C. Chen et al. have reported the fabrication of Y-branch beam splitter in KTiOASO₄ crystal by oxygen ion implantation combined with femtosecond laser ablation [7]. However, the device still suffers from high insertion loss which is mainly caused by waveguide bending and mode mismatch.

In contrast to Y-branch geometries, the multi-mode interference (MMI) beam splitter show some intriguing advantages such as compactness, better fabrication tolerance, low loss and also feasibility to achieve 1 × N splitting [23–25]. Besides signal processing, MMI devices have also been widely applied in areas such as wavelength multiplexing/demultiplexing, polarization splitters and mode filters [26–29]. In recent years, it has also been proven that MMI structure could find its application in active devices, such as to improve the waveguide laser performances [30,31].

In this work, the feasibility of fabricating MMI-based beam splitter in monocrystal was discussed by numerical analyzes. We choose LiNbO₃ crystal as substrate material due to its promising optical properties and also its wide applications. The propagation properties were studied for modes with different orders centered at 1550 nm wavelength. The Effect of tilt angles of ablated grooves, as well as fabrication tolerances were also discussed. We demonstrated that by utilizing a combination of ion implantation and femtosecond laser micro-machining, functional MMI devices could be achieved in monocrystal chips with good compactness and simple fabricating processes.

2. Theory and device configuration

The operation principle of MMI splitters is based on the self-imaging effect, which means that N-fold self-imaging of input field reproduced along specific distances [32]. For a central input 1 × N MMI splitter, the working distance of multi-mode area could be calculated by:

In which the integer p donates the periodic nature of imaging, chosen to be 1 here in order to minimize the device size; N represented the number of outputs, set to be 2 in the following as to construct a simple 1 × 2 splitter. The beating length L_π is defined as:

Where λ is the operating wavelength, set to be 1550 nm in this work; n_eff represents the effective refractive index of fundamental mode in the interference region; And We the effective width of interference region, which may slightly differ from the structural width according to evanescent field penetrating.

We employed the refractive index data of reference [19] as defining the MMI splitter. In such a scheme, z-cut LiNbO₃ crystal wafer was implanted with multi-energy oxygen ions with energy ranging from 3.0 to 4.0 MeV, accumulating to a total fluence of 8.5 × 10¹⁴ ions/cm². After proper thermal annealing, waveguides with extremely low propagation loss could be achieved. The extraordinary refractive index n_e (corresponding to TM polarization) at 1550 nm after ion implantation is presented in Fig. 1(a), showing optical “Barrier” and enhanced “Well”, which was typical for ion implanted LiNbO₃ waveguides.

 

Fig. 1 (a) Refractive index n_e of implanted LiNbO₃ versus depth, at 1550 nm; (b) 2D refractive index profile of input cross section of the MMI splitter.

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After ion implantation, the waveguides of the MMI splitter is defined by employing femtosecond laser abated grooves into the wafer. In this case, the waveguides were of ridge type, constructed by two adjacent grooves, as shown in Fig. 1(b) the geometry and refractive index distribution. The grooves may also be achieved by similar etching techniques, such as Focused Ion Beam (FIB) technique or a combination of proton exchange and reactive ion etching. By considering the practical fabrication parameters, a tilt side wall of grooves was employed, with tilting angle of θ. The ridge waveguide width w1 and groove width w2 were then defined as the upper width of individual parts. As refractive index change mainly restricted in regions with depth less than 7 μm, the grooves depth is set slightly larger than that, however no rigorous control of the depth needed in practical fabrications. The schematic diagram of probable fabrication process is illustrated in Fig. 2.

 

Fig. 2 Schematic plot of probable fabrication process. (a) Ion implantation to form planar waveguide layer; (b) Femtosecond laser ablation to define the splitter configuration.

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Another suggested fabrication strategy is to first ablate the grooves with femtosecond laser, then anneal the sample at 1120 °C for several tens of hours, at last to form the waveguides by ion implantation. In such scheme, the side walls will be smoothed, and lower scattering loss can be expected [33].

The overall schematic view of the designed MMI splitter is shown in Fig. 3, in which, darker strips represents the laser ablated grooves. As can be seen, the input, output waveguides and MMI section are all defined by the same straight grooves, which are easy to fabricate, while no transversal grooves needed to separate adjacent sections. Thus, only 2N + 4 grooves are needed to fabricate a 1 × N beam splitter, showing remarkable simplicity. The width of MMI section Wmmi is defined as distance between inner edges of two side grooves. One should notice that the length of MMI section Lmmi is defined as longitudinal distances between endpoints of input and output waveguides. The length of grooves defining the MMI section only need to be no less than the distance, with no rigorous restrictions needed. The Out_x parameter here refers to distance between output waveguide centers and central axis of the whole device.

 

Fig. 3 Top view of the MMI splitter.

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3. Simulations and analyses

The mode calculation and simulation of field propagation were carried out by employing the Beam Propagation Method (BPM), by the help of Rsoft Photonics Suite software.

3.1 Mode calculation

For mode calculation, we first set the w1 and w2 value to be 2 μm and 3 μm respectively, and the tilt angle θ to be 8° for generality. A TM polarized 1550 nm beam was set as input. In such case, the modes supported by the input waveguide is calculated by BPM based correlation method [34]. The modal profiles were shown in Fig. 4. As shown, 5 different ordered modes were obtained by properly setting the launching source position. In general, as the proportion of ${\text{E}}_{21}^y$ and ${\text{E}}_{22}^y$ mode could be suppressed to very low level by central align the input signal, the field could be equivalent to a superposition of ${\text{E}}_{11}^y$, ${\text{E}}_{12}^y,$ and ${\text{E}}_{13}^y$ modes. Although the ${\text{E}}_{13}^y$ mode is actually leaky, by considering a propagation length of 500 μm (longer than splitters designed below), the total loss of ${\text{E}}_{13}^y$ mode is only ~0.1 dB. In addition, the ${\text{E}}_{12}^y$ and ${\text{E}}_{13}^y$ modes cannot be completely suppressed according to the asymmetry of index distribution in vertical direction, therefore MMI effects were studied here for each of these modes separately.

 

Fig. 4 Figure 4(a)-4(e) show modes with different orders of the designed LiNbO₃ ridge waveguide, with a tilt angle of 8°.

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3.2 Splitter performance

We firstly study on the propagation of fundamental mode. In such cases, the geometrical parameters of the splitter were optimized using BPM simulation, with the input and output waveguide length set to be 50 μm. The Wmmi value was set to be 21 μm for tradeoff of splitting distance and device compactness. The optimized Lmmi and Out_x was 332 μm and 5.35 μm respectively. The fundamental mode propagation was simulated as illustrated in Fig. 5(a). Two symmetrical power monitors aligned with output waveguides were set to monitor the power flux, one of these is shown in Fig. 5(a) with white dash line. Because of symmetry, the power flux in each monitor coincides with each other, shown here in Fig. 5(b). As can be seen, incident power was divided into two output waveguides with 1:1 splitting ratio. The total insertion loss was found to be 0.244 dB.

 

Fig. 5 (a) the fundamental mode (${\text{E}}_{11}^y$) propagation in optimized MMI splitter, the white dashed defines the boundary of power monitor; (b) Normalized power flux in the monitor.

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The performance of the optimized splitter for higher ordered modes was also studied, with the insertion loss to be 0.706 dB and 1.244 dB for ${\text{E}}_{12}^y$ and ${\text{E}}_{13}^y$ modes respectively. It is noticeable that the insertion loss is higher for modes with a higher mode order as input, while the loss for fundamental mode is also slightly higher than the average level of similar MMI splitters. To unveil the reason behind, we took sight on the field evolution during propagation in the interference region.

The simulated field distribution of different ordered modes when propagation in the splitter was presented in Fig. 6. One could notice that the electrical fields at MMI/Output interface diverged from the eigenmodes, the higher mode order n the more severe its deviation is. It could also be confirmed by contrast with the field profile at final output end-face as shown in Figs. 6(d)-6(f). The additional losses could then be attributed to mismatches between the field profiles. This means that strict self-imaging could not be realized in such tilted ridge waveguides. To further explore the effect of sidewall tilting on the splitter performance, comparative studies were taken place as shown in Table 1.

 

Fig. 6 Figure 6(a)-6(c) the field intensities at MMI/Output interface for ${\text{E}}_{11}^y$, ${\text{E}}_{12}^y$ and ${\text{E}}_{13}^y$ modes respectively; 6(d)-6(f) the field intensities at final cross section of output waveguides for${\text{E}}_{11}^y$, ${\text{E}}_{12}^y$ and ${\text{E}}_{13}^y$ modes respectively.

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Table 1. Insertion loss of different modes as well as optimized Lmmi corresponding to different sidewall angles

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The result in Table 1 was obtained by firstly calculating each mode corresponding to different tilt angle θ, then optimize the structure in fundamental mode launching condition. Every higher ordered modes propagation was calculated based on the corresponding optimized structures. We found that the insertion loss for fundamental modes decreases as larger tilt angle, while remained in low level of θ no more than 12°. Considering formula 1 and 2, this phenomenon may find explanation as the modal profile encounters different effective width We as depth increasing when θ≠0, thus rigorous self-imaging prohibited due to varied beating length L_π with depth change. Another noticeable phenomenon is that even for the situation of θ = 0, insertion losses rises significantly for higher ordered modes. The loss increase could be attributed to different effective refractive index, causing L_π to be different for ${\text{E}}_{11}^y$, ${\text{E}}_{12}^y$ and ${\text{E}}_{13}^y$ modes. In other words, the optimized length of interference region differs for modes with different orders. However, it is interesting to notice that the difference could be partially offset by properly choosing the tilt angle. As shown in the table, in this case, θ with a value around 4° could diminish the insertion loss of ${\text{E}}_{12}^y$ and ${\text{E}}_{13}^y$ modes to maximum extent. Thus it is demonstrated here low loss MMI splitter could be applied in multi-mode input situations by carefully choosing the sidewall angles.

3.3 Fabrication tolerance

We further took a sight on the fabrication tolerance of the splitter. For practical launching condition where the input signal was Gaussian with diameter larger than several microns, ${\text{E}}_{12}^y$ and ${\text{E}}_{13}^y$ modes took much smaller proportion than the fundamental mode, therefore we only discuss the ${\text{E}}_{11}^y$ mode propagation in the following. Again, the tilt angle was chosen to be 8°. The tolerances for length (Lmmi) and width (Wmmi) of the interference region were shown in Fig. 7, with vertical axis the proportion of energy flux of one output waveguide endface, normalized to input power.

 

Fig. 7 7(a) and 7(b) indicates the power flow at one of the output waveguide endface in relationship of Lmmi and Wmmi, respectively.

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As shown in Fig. 7, good fabrication tolerance demonstrated for Lmmi, as insertion loss remained below 10% for Lmmi deviation of −3.6 to + 3.3 μm. On the other side, the insertion loss is more sensitive to Wmmi. Total insertion loss remained below 20% only when Wmmi deviation no more than ± 0.2μm.

Another common fabrication deviation in femtosecond laser ablated structures is the width of grooves, defined w2 as mentioned before. Figure 8 depicts the power output at arbitrary output waveguide normalized to the input power, in which the centers of input/output waveguides are fixed. During the calculation, the launching filed was set to the fundamental modes of input waveguides corresponding to each w2. It is interesting that during the range of 2.2~3.6 μm, total insertion loss drops as w2 decreasing. This phenomenon may attribute to alleviated field mismatch with a larger waveguide width w1, as w1 and w2 trades off each other in this case. No matter how, a total insertion loss below 0.65dB could be ensured as w2 error no more than ± 0.6 μm, showing good fabrication tolerances.

 

Fig. 8 the power flux of arbitrary output waveguide, normalized to the input power, versus groove width w2.

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4. Conclusion

In this work, MMI waveguide power splitter in LiNbO₃ monocrystal was designed, based on a combination of ion implantation and femtosecond laser ablation as the fabrication strategy. Due to the fabrication process, the MMI structure here differs from traditional MMI devices such as gradual refractive index change and tilt sidewalls. We demonstrated that by carefully choosing the geometrical parameters of the MMI device, low-loss beam splitting could be achieved for ${\text{E}}_{mn}^y$ modes with n>1, which extend the application of self-imaging principle to multi-mode input signals. The MMI splitter presented here is easy to fabricate, also with low insertion loss and good fabrication tolerances. The MMI length could be further reduced to sub-100 μm if shorter splitting distance is acceptable, showing superb compactness to traditional Y-branch splitters using ion implantation or femtosecond laser inscription as fabrication strategy. This work provides an alternative choice to fabricate beam splitter in various optical monocrystal chips. Exploration of achieving other MMI-based devices using this strategy, such as multiplexers, polarization filters and waveguide lasers are expected in the future.