Abstract

We propose an electro-optic mode-selective switch based on cascaded three-dimensional lithium-niobate waveguide directional couplers fabricated with a single-step annealed proton-exchange process. To compensate for discrepancies due to uncertainties in the fabrication process, we develop a post-tuning technique to improve the performance of the coupler by means of depositing a layer of titanium oxide (TiO2) onto one of the waveguides of the coupler. By integrating two cascaded dissimilar directional couplers, we experimentally demonstrate switchable (de)multiplexing of the LP01, LP11a, and LP11b modes, where the LP11a mode can be switched at an efficiency over 75% from 1530 nm to 1612 nm with an applied voltage varying between –9 V and +30 V, and the LP11b mode can be switched at an efficiency higher than 90% from 1534 nm to 1577 nm with an applied voltage varying between –21 V to 0 V. The switching times are 230–300 ns. Our proposed waveguide platform could be employed to develop advanced switches for applications in areas where high-speed switching of spatial modes is required, such as reconfigurable mode-division-multiplexing communication.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

A mode (de)multiplexer, which serves to combine (separate) different spatial modes of a few-mode fiber (FMF), is a key device in a mode-division-multiplexing (MDM) system [1,2]. Among different technologies for realizing mode (de)multiplexers, waveguide-based mode (de)multiplexers offer some distinct advantages: material and structure flexibility, fiber compatibility, and integration capability. Conventional coplanar waveguide structures, such as horizontal directional couplers (DC) [3] and Y-junctions [4], can operate for the modes that have the same symmetry in the vertical direction, but not for the modes that have opposite symmetries in the vertical direction. To solve this problem, one may apply a mode converter [5,6] to change the symmetry property of the problematic mode or employ three-dimensional (3D) waveguide structures, such as vertical DCs [79] and 3D waveguide branches [10]. The use of 3D waveguide structures adds much flexibility to the design architecture, but the formation of such structures normally requires a multi-step fabrication process and precise position alignment of different layers [9,10]. In addition to passive mode (de)multiplexers, switchable mode (de)multiplexers, or mode-selective switches, that allow different modes to be switched to different waveguides are required for the construction of reconfigurable MDM networks.

In general, a mode-selective switch can be implemented by connecting a passive mode demultiplexer to a single-mode switching matrix [11], or by connecting a switchable mode converter to a passive mode demultiplexer [12]. Integrated mode-selective switches based on the thermo-optic (TO) effect have been demonstrated for the two lowest-order modes (the LP01 and the LP11a mode) with various coplanar waveguide structures, such as asymmetric Y-junctions [12], cascaded multimode interference (MMI) couplers [13,14], asymmetric DCs [15,16]. 3D polymer waveguide mode switches based on vertical couplers [17] and 3D Mach-Zehnder interferometers [18,19] for more spatial modes are also available. Limited by the TO effect, however, the switching speeds of these devices are slow (∼1 ms). The availability of electro-optic (EO) material, in particular, lithium niobite (LN), makes possible the realization of waveguide devices for high-speed control of spatial modes. Several integrated LN mode-controlling devices have been demonstrated, which include EO mode converters based on the structures of long-period gratings [2022] and a Mach-Zehnder interferometer [23], and a two-mode spatial switch based on an asymmetric DC [24]. There are no integrated EO spatial switches that can operate for more than two modes. In this paper, we demonstrate a high-speed mode-selective switch with cascaded LN waveguide DCs fabricated with the anneal proton exchange (APE) process. The asymmetric DCs formed with such a process are intrinsically 3D waveguide structures and, therefore, can serve as an effective platform for the implementation of mode-controlling devices. As an example, we design and fabricate an EO spatial switch formed with two cascaded dissimilar asymmetric DCs, where the LP11a mode and the LP11b mode in a few-mode waveguide (FMW) are selectively switched to two separate single-mode waveguides (SMWs) by applying voltages to the respective DCs.

The main challenge in the realization of the device lies in the production of matching waveguides by the APE process. The FMW and the two SMWs that form the two DCs must be precisely made, so that the coupled modes are phase-matched. As the APE process is sensitive to environmental disturbances, such as fluctuations in temperature and humidity, perfect matching between the coupled modes of both DCs is difficult to achieve. To overcome this problem, we propose a post-tuning technique, where a layer of high-index oxide, such as titanium oxide (TiO2), is deposited onto one of the waveguides to improve phase matching. Our fabricated device can provide a switching efficiency for the LP11a mode higher than 75% from 1530 nm to 1612 nm with an applied voltage varying between –9 V and +30 V, and a switching efficiency for the LP11b mode higher than 90% from 1534 nm to 1577 nm with an applied voltage varying between –21 V and 0 V. The switching times of the two DCs are 230–300 ns, which are several orders of magnitude shorter than those of TO devices.

2. Design methodology

Figure 1(a) is a schematic diagram showing the top view of the structure of the mode-selective switch, which consists of two cascaded asymmetric DCs formed by the APE process on an x-cut, y-propagation LN crystal. As shown in Fig. 1(a), the middle waveguide is an FMW, whose input end is tapered to a narrower width with Taper 1 for single-mode input, and the two side waveguides are SMWs. The first DC is designed for switching between the lower SMW and the LP11a mode of the FMW (the LP11a mode switch), and the second DC is designed for switching between the upper SMW and the LP11b mode of the FMW (the LP11b mode switch). The FMW is tapered to a larger width with Taper 2 to match the requirement for the design of the second DC. The LP01 mode launched into the FMW stays in the FMW. Separate sets of electrodes are deposited on the two DCs to achieve independent switching. Here we name the modes of the FMW as the LP modes, as they can evolve into the corresponding LP modes of a few-mode fiber with a suitable buried adiabatic waveguide taper. Figure 1(b) illustrates how a waveguide DC is formed with the standard APE process [2024]. A chromium (Cr) film is first deposited on the surface of the LN substrate by radio-frequency (RF) sputtering. The desired pattern is next formed on the Cr film with a mask by the photolithography process. The sample is then submerged in stearic acid for proton exchange and annealed. Such an APE process, which requires only a single mask to define the widths of the waveguides, naturally leads to an asymmetric DC where the wider waveguide has a larger height, which can be considered as a 3D waveguide structure. As the APE process increases only the extraordinary refractive index of an x-cut LN crystal, the modes supported by the waveguides are transverse-electric (TE) polarized, i.e., they have dominant electric-field components along the x direction.

 

Fig. 1. Scheme diagrams showing (a) the top view of a mode-selective switch formed with two cascaded LN asymmetric DCs, together with the dimensions of the waveguide and electrode parameters used in the final design, and (b) the cross-sectional views of an asymmetric DC formed at different stages of the APE process.

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To design the LN waveguides needed for the construction of the DCs, we fabricated many sets of trial LN waveguides with different widths by the APE process using different fabrication parameters. The effective indices of the modes of the resultant waveguides were measured with a prism-coupler system (Metricon, Model 2010) [25] at the wavelength 1538 nm. The uncertainties in the measurements were ±0.0004. We then chose a set of waveguides fabricated with the same APE parameters suitable for the implementation of the DCs.

The effective indices measured for a set of waveguides are shown in Table 1. The waveguides were fabricated with a proton exchange time of 40 min at 240°C and an annealing time of 6 hours at 350°C. There are four waveguides, which correspond to four different nominal waveguide widths defined by the waveguide masks. The 4- and 6-µm wide waveguides are SMWs, the 8-µm wide waveguide supports the LP01 and LP11a modes, and the 10-µm wide waveguide supports the LP01, LP11a, and LP11b modes. As shown by the results in Table 1, we can identify the waveguides for providing phase matching between the spatial modes (phase matching refers to the condition at which the two coupled modes have equal effective indices). For the LP11a switch, we choose the 8-µm wide waveguide as the FMW and the 6-µm wide waveguide as the SMW, while, for the LP11b switch, we choose the 10-µm wide waveguide as the FMW and the 4-µm wide waveguide as the SMW. To find the refractive-index profile n(x, z) of the waveguides, we employ the following model developed for an APE LN waveguide [26]:

$$\begin{array}{l} n({x,z} )= {n_{LN}} + \Delta n \times \\ \frac{{\left\{ {\textrm{erf} \left[ {\frac{{d - z}}{{2{d_z}}}} \right] + \textrm{erf} \left[ {\frac{{d + z}}{{2{d_z}}}} \right]} \right\}}}{{2{\textrm{erf}}\left( {\frac{d}{{2{d_z}}}} \right)}} \times \frac{{\left\{ {\textrm{erf} \left[ {\frac{{w - 2x}}{{2{w_x}}}} \right] + \textrm{erf} \left[ {\frac{{w + 2x}}{{2{w_x}}}} \right]} \right\}}}{{2\textrm{erf}\left( {\frac{w}{{2{w_x}}}} \right)}} \end{array}$$
where nLN = 2.1381 is the extraordinary refractive index of the LN substrate, Δn (>0) is the index change by the APE process, and w, d, wx, and dz are the parameters related to the APE process [26]. The coordinates for the profile are shown in Fig. 1(b). We calculated the effective indices of the waveguides at the wavelength 1538 nm with the commercial mode solver COMSOL and tuned the profile parameters to ensure that the calculated effective indices equaled the measured values. The profile parameters obtained for the three-mode FMW are Δn = 0.0245, w = 9.7 µm, d = 1.6 µm, wx = 3.5 µm, and dz = 1.9 µm. Figure 2 shows the intensity patterns calculated for the LP01, LP11a, and LP11b modes of the FMW.

 

Fig. 2. Intensity patterns calculated for the three modes supported by the 10-µm wide FMW.

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Tables Icon

Table 1. Effective indices of LN waveguides of different widths fabricated with a set of APE parameters

To determine the waveguide separations and the lengths of the DCs, we conducted extensive numerical simulation on the performances of the DCs at 1550 nm with the beam-propagation method (BPM) (RSoft BPM). From the BPM results, the center-to-center waveguide separations for the LP11a coupler and the LP11b coupler are chosen to be G1 = 13 µm and G2 = 16 µm, respectively, and the corresponding lengths of the two couplers are L1 = 8 mm and L2 = 10 mm, respectively. The lengths of Taper 1 and Taper 2 are both 500 µm, which are sufficient for achieving adiabatic mode transition. The lengths of the S-bends that separate the SMWs and FMW of the DCs are 5 mm. Figures 3(a) and (b) show the propagation of the modes for the LP11a mode coupler and the LP11b mode coupler, respectively, where the LP01 mode is launched into the respective SMW and shown to couple to the corresponding LP11 mode of the FMW along the DC. The coupling efficiencies of both DCs exceed 99%. As the performance of the asymmetric DC is highly sensitive to the phase-matching condition, the modal crosstalks, i.e., the couplings to modes other than the desired one, are low. According to our BPM simulation, the modal crosstalks are lower than –35 dB. To complete the design, the widths of the electrodes are taken as T1 = 10 µm, T2 = 3 µm, and T3 = 5 µm, respectively. The dimensions of the waveguide and electrode parameters of the device used for the fabrication work are also shown in Fig. 1(a).

 

Fig. 3. BPM simulation of optical power transfer along (a) the LP11a mode coupler and (b) the LP11b mode coupler at the wavelength 1550 nm, when the LP01 mode is launched into the respective SMW.

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3. Device fabrication and characterization

We applied the APE parameters given in Table 1 to fabricate the device. After fabricating the waveguides, we formed aluminum (Al) electrodes to a thickness of ∼300 nm on the sample with the lift-off method. The total length of the fabricated device was ∼35 mm. Figure 4(a) shows a photograph of the device and Fig. 4(b) shows microscope images of the end faces of the two SMWs and the FMW. As shown in Fig. 4(b), the two SMWs and FMWs have different widths and heights. We characterized the performances of the two cascaded switches independently.

 

Fig. 4. (a) Photograph of the fabricated device and (b) microscope images showing the end faces of the SMWs (left and right) and the FMW (middle).

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3.1 LP11a mode switch

To characterize the performance of the LP11a mode switch, light from a broadband source (NKT PS10), whose spectral range covered 500–1800nm, was launched into the SMW of the switch with a single-mode fiber through a polarization controller and the normalized output spectrum from the SMW was measured with an optical spectrum analyzer (Anristu MS97740A). Figure 5(a) shows the transmission spectra of the SMW of the switch measured at different applied voltages, where a positive (negative) voltage means that the voltage between the middle electrode and the side electrodes is positive (negative). By varying the voltage from +10 V to the –8 V, the maximum change of the transmission is ∼3 dB in the C band (1530–1570 nm), which indicates that the maximum switching efficiency is ∼50%. To demonstrate the change in the spectrum is the result of coupling from the SMW to the FMW, we took the output near-field images at 1550 nm at different applied voltages and the results are shown in Fig. 5(b). At +10 V, almost all the input power stays in the SMW, while at –8 V, a maximum of ∼50% power appears as the LP11a mode in the FMW, which agrees with the result obtained from the transmission spectra. The limited switching efficiency is due to the presence of significant phase mismatch between the two waveguides. Nevertheless, the near-field images confirm that the switch operates for the LP11a mode as expected.

 

Fig. 5. Experimental results for the LP11a mode switch: (a) normalized transmission spectra of the SMW measured at different applied voltages; (b) output near-field images taken at 1550 nm.

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We applied our post-process technique to the LP11a mode switch to increase its switching efficiency. The oxide we used is TiO2, which has a refractive index of ∼2.05 and can be deposited onto the waveguide with a well-controlled thickness by RF sputtering. To determine which waveguide should be deposited with TiO2, we covered the SMW or the FMW with polymer, which had a refractive index of ∼1.62 and then measured the switching efficiency. We found that, when the SMW was covered with polymer, the switching efficiency was slightly improved by ∼5%. This result suggested that we should deposit a layer of TiO2 onto the SMW to improve the performance of the switch. With the polymer coating removed, we coated a layer of photoresist onto the switch and exposed the SMW with the photolithography process. After curing the photoresist, a layer of TiO2 was deposited on the SMW by RF sputtering. Figure 6(a) shows a schematic diagram of the TiO2-coated structure and Fig. 6(b) shows microscope images where the electrodes, the FMW, and the TiO2-coated SMW are highlighted.

 

Fig. 6. (a) Schematic diagram showing the SMW coated with a layer of TiO2 and (b) microscope images of the fabricated switch showing the electrodes, the FMW, and the TiO2-coated SMW.

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We started the post-tuning process with a thin TiO2 layer. We measured the switching efficiency of the sample and then deposited more TiO2 onto the sample. We found that the switching efficiency increased with the thickness of the TiO2 layer. The transmission spectra of the switch with a 1100-nm thick TiO2 layer deposited on the SMW are shown in Fig. 7(a). There exist clear rejection bands in the spectra. The rejection band shifts from 1530 nm to 1610 nm, as the applied voltage varies from –9 V to +30 V. The switching efficiency is higher than 75% in the C band. The output near-field images taken at 1550 nm at different applied voltages are shown in Fig. 7(b), which gives a switching efficiency of ∼86%, as the voltage varies from +12 V (the “off” state) to –3 V (the “on” state). As confirmed by these results, with the post-tuning technique, the switching efficiency of the LP11a mode switch is significantly increased. However, after post-processing, the insertion loss of the switch is increased from ∼5.2 dB to ∼9.0 dB. The increase in the insertion loss could be due to the roughness of the thick TiO2 layer used. The use of a high-index polymer instead of TiO2 could yield better results.

 

Fig. 7. Experimental results for the post-tuned LP11a mode switch: (a) transmission spectra of the SMW measured at different applied voltages; (b) output near-field images taken at 1550 nm.

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3.2 LP11b mode switch

We characterized the LP11b mode switch of the device in the same way as the LP11a mode switch. Figure 8(a) shows the transmission spectra of the SMW of the switch measured at different applied voltages. At 0 V, there is little coupling from the SMW to the FMW, so the transmission spectrum is quite flat. At 21 V, the coupling from the SMW to the FMW is strongest, as shown by the strong rejection band centered at 1552 nm, which has a 10-dB bandwidth from 1534 nm to 1577 nm. As shown in Fig. 8(a), the switching efficiency is higher than 90% in the C band by varying the voltage from 0 V (the “off” state) to –21 V (the “on” state). Figure 8(b) shows the output near-field images taken at 1550 nm at different applied voltages, which confirms strong power switching from the SMW to the LP11b mode of the FMW by varying the voltage from 0 V to –21 V. The insertion loss of the switch is ∼4.5 dB. Post-tuning of this switch is unnecessary.

 

Fig. 8. Experimental results for the LP11b mode switch: (a) transmission spectra of the SMW measured at different applied voltages; (b) output near-field images taken at 1550 nm.

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3.3 Modal crosstalks

The structure of cascaded DCs for demultiplexing different modes allows estimation of modal crosstalks with simple power measurements [9]. With reference to Fig. 1(a), to determine the crosstalk from the LP11a mode to the LP11b mode in the second switch, we launched power into the SMW at Port 3 and turned on the first switch to generate the LP11a mode in the FMW. We then measured the output power from the SMW at Port 4, with the second switch turned off or on, and calculated the crosstalk by taking the ratio of the output power from Port 4 to the reference power, which is the total output power from Port 4 and Port 5. To determine the crosstalk from the LP11b mode to the LP11a mode in the first switch, we launched power into the SMW at Port 4 and turned on the second switch to generate the LP11b mode in the FMW. We then measured the output power from the SMW at Port 3, with the first switch turned on or off. However, the taper at Port 2 blocked the reference power from Port 2. Instead, we turned off the second switch and measured the output power from Port 1 and used it as the reference power for the calculation of the crosstalk. To determine the crosstalk from the LP01 mode to the LP11a (LP11b) mode, we launched power into the LP01 mode of the FMW at Port 2 and measured the output power from the SMW of the first (second) switch at Port 6 (Port 4), with the switch turned off or on. The crosstalk results measured at 1550 nm are summarized in Table 2. As shown by the results, the LP01-to-LP11a and LP01-to-LP11b crosstalks are much lower than the LP11a-to-LP11b and LP11a-to-LP11b crosstalks. The crosstalks at the “on” and “off” states of the relevant switch are comparable.

Tables Icon

Table 2. Measured modal crosstalk for the mode-selective switch

3.4 Switching response

To measure the switching speed of the device, we applied a 100 kHz, ±7 V square-wave signal to the electrodes and monitored the output optical power from the FMW with a photodetector (with a bandwidth of 125 MHz) and an oscilloscope. Figures 9(a) and (b) show the waveforms of the electric signal (black curve) and the output optical signals at 1550 nm from the LP11a mode switch and the LP11b mode switch, respectively. The rise and fall times of the LP11a mode switch are ∼260 ns and ∼300 ns, respectively, as shown in Fig. 9(a), while those of the LP11b mode switch are ∼230 ns and ∼270 ns, respectively, as shown in Fig. 9(b). The switching times of our device are several orders of magnitude shorter than those of TO devices.

 

Fig. 9. (a) Temporal switching characteristics of (a) the LP11a mode switch and (b) the LP11b mode switch showing the rise and fall times.

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4. Mode transition for fiber coupling

The APE process generates highly asymmetric refractive-index profiles and, as a result, the patterns of the high-order modes of LN waveguides deviate significantly from those of fibers, as shown in Fig. 2 and the output near-field patterns taken from our device. For LN few-mode waveguides to be used in fiber systems, it is necessary to convert the LN waveguide modes into fiber-compatible modes. Here we propose an LN waveguide taper structure to achieve this goal.

The structure is shown schematically in Fig. 10(a), which consists of an asymmetric surface FMW and a symmetric buried FMW connected by a vertical adiabatic taper. As an example, we perform numerical simulation with a mode solver (COMSOL) to show the evolutions of modes for the three-mode waveguide used in our study at 1550 nm. With reference to Fig. 10(a), the refractive-index profile of the taper is given by

$$\begin{array}{l} n({x,z,y} )= {n_{LN}} + \Delta n(y )\times \\ \frac{{\textrm{erf} \left[ {\frac{{d(y )- z - D(y )}}{{2{d_z}(y )}}} \right] + \textrm{erf} \left[ {\frac{{d(y )+ z + D(y )}}{{2{d_z}(y )}}} \right]}}{{2\textrm{erf} \left[ {\frac{{d(y )}}{{2{d_z}(y )}}} \right]}} \times \frac{{\textrm{erf} \left[ {\frac{{w(y )- 2x}}{{2{w_x}(y )}}} \right] + \textrm{erf} \left[ {\frac{{w(y )+ 2x}}{{2{w_x}(y )}}} \right]}}{{2\textrm{erf} \left[ {\frac{{w(y )}}{{2{w_x}(y )}}} \right]}} \end{array}$$
with
$$\begin{array}{l} D(y )= {d_t} \times \frac{y}{{{L_t}}},\;d(y )= {d_{in}} - ({d_{in}} - {d_{out}}) \times \frac{y}{{{L_t}}},\;\\ {d_\textrm{z}}(y )= {d_{zin}} - ({{d_{zin}} - {d_{zout}}} )\times \frac{y}{{{L_t}}}, \Delta n(y )= \Delta {n_{in}} - ({\Delta {n_{in}} - \Delta {n_{out}}} )\times \frac{y}{{{L_t}}},\;\\ w(y )= {w_{in}} - ({{w_{in}} - {w_{out}}} )\times \frac{y}{{{L_t}}},\;{w_x}(y )= {w_{xin}} - ({{w_{xin}} - {w_{xout}}} )\times \frac{y}{{{L_t}}}, \end{array}$$
where Δnin = 0.0245, win = 9.7 µm, din = 1.6 µm, wxin = 3.5 µm, and dzin = 1.9 µm are the profile values for the input waveguide; Δnout = 0.018, wout = 7 µm, dout= 1.4 µm, wxout = 2.0 µm, and dzout = 1.5 µm are the profile values for the output buried waveguide, and Lt is the taper length. Assuming Lt= 100 µm, which corresponds to a depth of dt = 4 µm for the buried waveguide, all the three waveguide modes evolve into the corresponding fiber-like modes, as shown in Fig. 10(b). The buried LN waveguide together with the vertical taper could be fabricated with the reverse APE process [27] or possibly with a bonding process [28].

 

Fig. 10. (a) Schematic diagrams showing the proposed LN waveguide structure for the conversion of LN waveguide modes into fiber-compatible modes. (b) Evolution of the three modes along the vertical taper.

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We calculated the coupling losses between a commercial FMF (FM SI-2 2010-B, Yangtze Optical Fiber and Cable Company) and the buried LN FMW shown in Fig. 10(a). The fiber has a core radius of 7 µm and refractive indices of 1.4485 and 1.444 for the core and the cladding, respectively. The calculated fiber-waveguide coupling losses for the LP01 mode, LP11a, and LP11b mode (at 1550 nm) are 2.81 dB, 3.42 dB, and 3.27 dB, respectively. We also calculated the coupling losses for a ring core erbium-doped FMF [29], which has an inner core with a radius of 2.1 µm and a refractive index of 1.448, an outer core with a radius of 4.4 µm, and a relative refractive-index difference of 1%. The coupling losses for the LP01 mode, LP11a, and LP11b mode (at 1550 nm) are 5.26 dB, 1.63 dB, and 1.85 dB, respectively. Our present device is not designed for optimal connection with any specific FWF. For a given FMF, it should be possible to obtain a better matching of the fiber modes by tuning the refractive-index profile of the LN waveguide. A more effective way to reduce fiber-waveguide coupling losses is the use of properly lensed FMFs [30].

5. Conclusion

We have demonstrated an EO mode-selective switch for the operation of three spatial modes based on the integration of two cascaded LN 3D waveguide asymmetric DCs. We have also proposed a technique of post-tuning the performance of the switch by depositing a TiO2 layer on a waveguide of the DC. The fabricated device can switch the LP11a mode with an efficiency higher than 75% from 1530nm to 1612nm with an applied voltage varying between –9V and +30V, and switch the LP11b mode with an efficiency higher than 90% from 1534nm to 1577nm with an applied voltage varying between –21V and 0V. The switching times are 230300ns. In principle, our proposed device can be scaled up to more modes by cascading more directional couplers. In practice, the number of modes that can be handled is limited by the size of the LN substrate and the fabrication process. The adiabatic waveguide taper shown in Fig. 10(a) can also be designed to work for more modes. Our device is designed for the operation of the TE polarization only. To achieve polarization-independence operation, we may apply the conventional polarization-diversity approach, where the output light from the fiber is split into two orthogonal linear polarizations by means of a polarization splitter and the two split light beams are processed independently by separate devices. This approach has been employed in single-mode LN lightwave circuits (see, for example, [31,32]) and should be applicable to few-mode circuits. Our proposed LN waveguide devices and the associated technology could be further developed for the implementation of advanced mode-controlling devices for reconfigurable MDM systems, where fast mode switching and routing are required.

Funding

Research Grants Council, University Grants Committee (CityU 11205715); City University of Hong Kong (9610452); Key R & D Program of Sichuan Province (2020YFSY0003); Fundamental Research Funds for the Central Universities (ZYGX2019J050, ZYGX2019Z005); Open Fund of the State Key Laboratory of Integrated Optoelectronics (IOSKL2018KF12).

Disclosures

The authors declare no conflicts of interest.

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14. D. Melati, A. Alippi, and A. Melloni, “Reconfigurable photonic integrated mode (de) multiplexer for SDM fiber transmission,” Opt. Express 24(12), 12625–12634 (2016). [CrossRef]  

15. Z. Zi, L. Wang, K. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018). [CrossRef]  

16. L. Wang, D. Zhang, D. Niu, T. Lian, M. Jiang, F. Wang, and X. Wang, “Polymeric waveguide MZI thermo-optic mode switch based on asymmetric directional coupler,” IEEE Photonics Technol. Lett. 32(4), 200–203 (2020). [CrossRef]  

17. Q. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 6602714 (2018). [CrossRef]  

18. Q. Huang, W. Jin, and K. S. Chiang, “Broadband mode switch based on a three-dimensional waveguide Mach–Zehnder interferometer,” Opt. Lett. 42(23), 4877–4880 (2017). [CrossRef]  

19. Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Broadband mode router based on three-dimensional Mach-Zehnder interferometer and waveguide branches,” Conference on Lasers and Electro-Optics (Optical Society of America2018), paper STh1A.2.

20. W. Jin and K. S. Chiang, “Mode switch based on electro-optic long period waveguide grating in lithium niobate,” Opt. Lett. 40(2), 237–240 (2015). [CrossRef]  

21. Z. Chang, W. Jin, and K. S. Chiang, “Graphene electrodes for lithium-niobate electro-optic devices,” Opt. Lett. 43(8), 1718–1721 (2018). [CrossRef]  

22. W. Jin and K. S. Chiang, “Reconfigurable three-mode converter based on cascaded electro-optic long-period gratings,” IEEE J. Sel. Top. Quantum Electron. 26(5), 4500906 (2020). [CrossRef]  

23. M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Electro-optic mode switch based on lithium-niobate Mach–Zehnder interferometer,” Appl. Opt. 55(16), 4418–4422 (2016). [CrossRef]  

24. M. Zhang, W. Ai, K. Chen, and K. S. Chiang, “A lithium-niobate waveguide directional coupler for switchable mode multiplexing,” IEEE Photonics Technol. Lett. 30(20), 1764–1767 (2018). [CrossRef]  

25. K. S. Chiang and S. Y. Cheng, “Technique of applying the prism-coupler method for accurate measurement of the effective indices of channel waveguides,” Opt. Eng. 47(3), 034601 (2008). [CrossRef]  

26. X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightwave Technol. 10(9), 1302–1313 (1992). [CrossRef]  

27. Yu. N. Korkishko, V. A. Fedorov, T. M. Morozova, F. Caccavale, F. Gonella, and F. Segato, “Reverse proton exchange for buried waveguides in LiNbO3,” J. Opt. Soc. Am. A 15(7), 1838–1842 (1998). [CrossRef]  

28. M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Symmetric lithium-niobate waveguide fabricated by bonding for mode-division-multiplexing applications,” Opt. Fiber Comm. Conference (Optical Society of America 2018), paper W1E.5.

29. H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express 23(21), 27405–27418 (2015). [CrossRef]  

30. H. Wen, H. Liu, Y. Zhang, J. Zhao, P. Sillard, P. A. Correa, and G. Li, “Few-mode lensed fibers,” J. Lightwave Technol. 36(24), 5794–5799 (2018). [CrossRef]  

31. J. Hauden, H. Porte, J.-P. Goedgebuer, J. Abiven, C. Gibassier, and C. Gutierrez-Martinez, “Polarization independent bidirectional fiber link using coherence multi/demultiplexing LiNbO3 integrated electrooptical circuits,” J. Lightwave Technol. 14(7), 1630–1638 (1996). [CrossRef]  

32. C. W. Hsu, C. F. Huang, and W. S. Tsai, “Lithium niobate polarization-independent modulator using integrated polarization splitters and mode converters,” J. Lightwave Technol. 35(9), 1663–1669 (2017). [CrossRef]  

References

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  1. G. F. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
    [Crossref]
  2. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
    [Crossref]
  3. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, K. Tsujikawa, M. Koshiba, and F. Yamamoto, “Two-mode PLC-based mode multi/demultiplexer for mode and wavelength division multiplexed transmission,” Opt. Express 21(22), 25752–25760 (2013).
    [Crossref]
  4. J. D. Love and N. Riesen, “Single-, few-, and multimode Y-junctions,” J. Lightwave Technol. 30(3), 304–309 (2012).
    [Crossref]
  5. K. Saitoh, N. Hanzawa, T. Sakamoto, T. Fujisawa, Y. Yamashita, T. Matsui, K. Tsujikawa, and K. Nakajima, “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol. 35, 80–92 (2017).
    [Crossref]
  6. W. Jin and K. S. Chiang, “Three-dimensional long-period waveguide gratings for mode-division-multiplexing applications,” Opt. Express 26(12), 15289–15299 (2018).
    [Crossref]
  7. N. Riesen, S. Gross, J. D. Love, and M. J. Withford, “Femtosecond direct-written integrated mode couplers,” Opt. Express 22(24), 29855–29861 (2014).
    [Crossref]
  8. S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
    [Crossref]
  9. Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Mode multiplexer with cascaded vertical asymmetric waveguide directional couplers,” J. Lightwave Technol. 36(14), 2903–2911 (2018).
    [Crossref]
  10. Y. Wu and K. S. Chiang, “Ultra-broadband mode multiplexers based on three-dimensional asymmetric waveguide branches,” Opt. Lett. 42(3), 407–410 (2017).
    [Crossref]
  11. N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, R. Maruyama, N. Kuwaki, K. Takenaga, H. Uemura, S. Matsuo, and K. Kitayama, “Mode-selective optical packet switching in mode-division multiplexing networks,” Opt. Express 23(18), 23660–23666 (2015).
    [Crossref]
  12. W. K. Zhao, J. Feng, K. X. Chen, and K. S. Chiang, “Reconfigurable broadband mode (de)multiplexer based on an integrated thermally induced long-period grating and asymmetric Y-junction,” Opt. Lett. 43(9), 2082–2085 (2018).
    [Crossref]
  13. W. Y. Chan and H. P. Chan, “Reconfigurable two-mode mux/demux device,” Opt. Express 22(8), 9282–9290 (2014).
    [Crossref]
  14. D. Melati, A. Alippi, and A. Melloni, “Reconfigurable photonic integrated mode (de) multiplexer for SDM fiber transmission,” Opt. Express 24(12), 12625–12634 (2016).
    [Crossref]
  15. Z. Zi, L. Wang, K. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
    [Crossref]
  16. L. Wang, D. Zhang, D. Niu, T. Lian, M. Jiang, F. Wang, and X. Wang, “Polymeric waveguide MZI thermo-optic mode switch based on asymmetric directional coupler,” IEEE Photonics Technol. Lett. 32(4), 200–203 (2020).
    [Crossref]
  17. Q. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 6602714 (2018).
    [Crossref]
  18. Q. Huang, W. Jin, and K. S. Chiang, “Broadband mode switch based on a three-dimensional waveguide Mach–Zehnder interferometer,” Opt. Lett. 42(23), 4877–4880 (2017).
    [Crossref]
  19. Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Broadband mode router based on three-dimensional Mach-Zehnder interferometer and waveguide branches,” Conference on Lasers and Electro-Optics (Optical Society of America2018), paper STh1A.2.
  20. W. Jin and K. S. Chiang, “Mode switch based on electro-optic long period waveguide grating in lithium niobate,” Opt. Lett. 40(2), 237–240 (2015).
    [Crossref]
  21. Z. Chang, W. Jin, and K. S. Chiang, “Graphene electrodes for lithium-niobate electro-optic devices,” Opt. Lett. 43(8), 1718–1721 (2018).
    [Crossref]
  22. W. Jin and K. S. Chiang, “Reconfigurable three-mode converter based on cascaded electro-optic long-period gratings,” IEEE J. Sel. Top. Quantum Electron. 26(5), 4500906 (2020).
    [Crossref]
  23. M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Electro-optic mode switch based on lithium-niobate Mach–Zehnder interferometer,” Appl. Opt. 55(16), 4418–4422 (2016).
    [Crossref]
  24. M. Zhang, W. Ai, K. Chen, and K. S. Chiang, “A lithium-niobate waveguide directional coupler for switchable mode multiplexing,” IEEE Photonics Technol. Lett. 30(20), 1764–1767 (2018).
    [Crossref]
  25. K. S. Chiang and S. Y. Cheng, “Technique of applying the prism-coupler method for accurate measurement of the effective indices of channel waveguides,” Opt. Eng. 47(3), 034601 (2008).
    [Crossref]
  26. X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightwave Technol. 10(9), 1302–1313 (1992).
    [Crossref]
  27. Yu. N. Korkishko, V. A. Fedorov, T. M. Morozova, F. Caccavale, F. Gonella, and F. Segato, “Reverse proton exchange for buried waveguides in LiNbO3,” J. Opt. Soc. Am. A 15(7), 1838–1842 (1998).
    [Crossref]
  28. M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Symmetric lithium-niobate waveguide fabricated by bonding for mode-division-multiplexing applications,” Opt. Fiber Comm. Conference (Optical Society of America 2018), paper W1E.5.
  29. H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express 23(21), 27405–27418 (2015).
    [Crossref]
  30. H. Wen, H. Liu, Y. Zhang, J. Zhao, P. Sillard, P. A. Correa, and G. Li, “Few-mode lensed fibers,” J. Lightwave Technol. 36(24), 5794–5799 (2018).
    [Crossref]
  31. J. Hauden, H. Porte, J.-P. Goedgebuer, J. Abiven, C. Gibassier, and C. Gutierrez-Martinez, “Polarization independent bidirectional fiber link using coherence multi/demultiplexing LiNbO3 integrated electrooptical circuits,” J. Lightwave Technol. 14(7), 1630–1638 (1996).
    [Crossref]
  32. C. W. Hsu, C. F. Huang, and W. S. Tsai, “Lithium niobate polarization-independent modulator using integrated polarization splitters and mode converters,” J. Lightwave Technol. 35(9), 1663–1669 (2017).
    [Crossref]

2020 (2)

L. Wang, D. Zhang, D. Niu, T. Lian, M. Jiang, F. Wang, and X. Wang, “Polymeric waveguide MZI thermo-optic mode switch based on asymmetric directional coupler,” IEEE Photonics Technol. Lett. 32(4), 200–203 (2020).
[Crossref]

W. Jin and K. S. Chiang, “Reconfigurable three-mode converter based on cascaded electro-optic long-period gratings,” IEEE J. Sel. Top. Quantum Electron. 26(5), 4500906 (2020).
[Crossref]

2018 (8)

Z. Zi, L. Wang, K. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

Z. Chang, W. Jin, and K. S. Chiang, “Graphene electrodes for lithium-niobate electro-optic devices,” Opt. Lett. 43(8), 1718–1721 (2018).
[Crossref]

M. Zhang, W. Ai, K. Chen, and K. S. Chiang, “A lithium-niobate waveguide directional coupler for switchable mode multiplexing,” IEEE Photonics Technol. Lett. 30(20), 1764–1767 (2018).
[Crossref]

H. Wen, H. Liu, Y. Zhang, J. Zhao, P. Sillard, P. A. Correa, and G. Li, “Few-mode lensed fibers,” J. Lightwave Technol. 36(24), 5794–5799 (2018).
[Crossref]

Q. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 6602714 (2018).
[Crossref]

W. K. Zhao, J. Feng, K. X. Chen, and K. S. Chiang, “Reconfigurable broadband mode (de)multiplexer based on an integrated thermally induced long-period grating and asymmetric Y-junction,” Opt. Lett. 43(9), 2082–2085 (2018).
[Crossref]

W. Jin and K. S. Chiang, “Three-dimensional long-period waveguide gratings for mode-division-multiplexing applications,” Opt. Express 26(12), 15289–15299 (2018).
[Crossref]

Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Mode multiplexer with cascaded vertical asymmetric waveguide directional couplers,” J. Lightwave Technol. 36(14), 2903–2911 (2018).
[Crossref]

2017 (4)

2016 (2)

2015 (3)

2014 (4)

N. Riesen, S. Gross, J. D. Love, and M. J. Withford, “Femtosecond direct-written integrated mode couplers,” Opt. Express 22(24), 29855–29861 (2014).
[Crossref]

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
[Crossref]

G. F. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

W. Y. Chan and H. P. Chan, “Reconfigurable two-mode mux/demux device,” Opt. Express 22(8), 9282–9290 (2014).
[Crossref]

2013 (2)

2012 (1)

2008 (1)

K. S. Chiang and S. Y. Cheng, “Technique of applying the prism-coupler method for accurate measurement of the effective indices of channel waveguides,” Opt. Eng. 47(3), 034601 (2008).
[Crossref]

1998 (1)

1996 (1)

J. Hauden, H. Porte, J.-P. Goedgebuer, J. Abiven, C. Gibassier, and C. Gutierrez-Martinez, “Polarization independent bidirectional fiber link using coherence multi/demultiplexing LiNbO3 integrated electrooptical circuits,” J. Lightwave Technol. 14(7), 1630–1638 (1996).
[Crossref]

1992 (1)

X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightwave Technol. 10(9), 1302–1313 (1992).
[Crossref]

Abiven, J.

J. Hauden, H. Porte, J.-P. Goedgebuer, J. Abiven, C. Gibassier, and C. Gutierrez-Martinez, “Polarization independent bidirectional fiber link using coherence multi/demultiplexing LiNbO3 integrated electrooptical circuits,” J. Lightwave Technol. 14(7), 1630–1638 (1996).
[Crossref]

Ai, W.

M. Zhang, W. Ai, K. Chen, and K. S. Chiang, “A lithium-niobate waveguide directional coupler for switchable mode multiplexing,” IEEE Photonics Technol. Lett. 30(20), 1764–1767 (2018).
[Crossref]

Alippi, A.

Bai, N.

G. F. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Caccavale, F.

Cao, X. F.

X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightwave Technol. 10(9), 1302–1313 (1992).
[Crossref]

Chan, H. P.

Chan, W. Y.

Chang, Z.

Chen, K.

M. Zhang, W. Ai, K. Chen, and K. S. Chiang, “A lithium-niobate waveguide directional coupler for switchable mode multiplexing,” IEEE Photonics Technol. Lett. 30(20), 1764–1767 (2018).
[Crossref]

Z. Zi, L. Wang, K. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Electro-optic mode switch based on lithium-niobate Mach–Zehnder interferometer,” Appl. Opt. 55(16), 4418–4422 (2016).
[Crossref]

M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Symmetric lithium-niobate waveguide fabricated by bonding for mode-division-multiplexing applications,” Opt. Fiber Comm. Conference (Optical Society of America 2018), paper W1E.5.

Chen, K. X.

Cheng, S. Y.

K. S. Chiang and S. Y. Cheng, “Technique of applying the prism-coupler method for accurate measurement of the effective indices of channel waveguides,” Opt. Eng. 47(3), 034601 (2008).
[Crossref]

Chiang, K. S.

W. Jin and K. S. Chiang, “Reconfigurable three-mode converter based on cascaded electro-optic long-period gratings,” IEEE J. Sel. Top. Quantum Electron. 26(5), 4500906 (2020).
[Crossref]

Z. Chang, W. Jin, and K. S. Chiang, “Graphene electrodes for lithium-niobate electro-optic devices,” Opt. Lett. 43(8), 1718–1721 (2018).
[Crossref]

Q. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 6602714 (2018).
[Crossref]

M. Zhang, W. Ai, K. Chen, and K. S. Chiang, “A lithium-niobate waveguide directional coupler for switchable mode multiplexing,” IEEE Photonics Technol. Lett. 30(20), 1764–1767 (2018).
[Crossref]

W. K. Zhao, J. Feng, K. X. Chen, and K. S. Chiang, “Reconfigurable broadband mode (de)multiplexer based on an integrated thermally induced long-period grating and asymmetric Y-junction,” Opt. Lett. 43(9), 2082–2085 (2018).
[Crossref]

Z. Zi, L. Wang, K. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Mode multiplexer with cascaded vertical asymmetric waveguide directional couplers,” J. Lightwave Technol. 36(14), 2903–2911 (2018).
[Crossref]

W. Jin and K. S. Chiang, “Three-dimensional long-period waveguide gratings for mode-division-multiplexing applications,” Opt. Express 26(12), 15289–15299 (2018).
[Crossref]

Y. Wu and K. S. Chiang, “Ultra-broadband mode multiplexers based on three-dimensional asymmetric waveguide branches,” Opt. Lett. 42(3), 407–410 (2017).
[Crossref]

Q. Huang, W. Jin, and K. S. Chiang, “Broadband mode switch based on a three-dimensional waveguide Mach–Zehnder interferometer,” Opt. Lett. 42(23), 4877–4880 (2017).
[Crossref]

M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Electro-optic mode switch based on lithium-niobate Mach–Zehnder interferometer,” Appl. Opt. 55(16), 4418–4422 (2016).
[Crossref]

W. Jin and K. S. Chiang, “Mode switch based on electro-optic long period waveguide grating in lithium niobate,” Opt. Lett. 40(2), 237–240 (2015).
[Crossref]

K. S. Chiang and S. Y. Cheng, “Technique of applying the prism-coupler method for accurate measurement of the effective indices of channel waveguides,” Opt. Eng. 47(3), 034601 (2008).
[Crossref]

Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Broadband mode router based on three-dimensional Mach-Zehnder interferometer and waveguide branches,” Conference on Lasers and Electro-Optics (Optical Society of America2018), paper STh1A.2.

M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Symmetric lithium-niobate waveguide fabricated by bonding for mode-division-multiplexing applications,” Opt. Fiber Comm. Conference (Optical Society of America 2018), paper W1E.5.

Correa, P. A.

Diamantopoulos, N. P.

Fedorov, V. A.

Feng, J.

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fujisawa, T.

K. Saitoh, N. Hanzawa, T. Sakamoto, T. Fujisawa, Y. Yamashita, T. Matsui, K. Tsujikawa, and K. Nakajima, “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol. 35, 80–92 (2017).
[Crossref]

Gibassier, C.

J. Hauden, H. Porte, J.-P. Goedgebuer, J. Abiven, C. Gibassier, and C. Gutierrez-Martinez, “Polarization independent bidirectional fiber link using coherence multi/demultiplexing LiNbO3 integrated electrooptical circuits,” J. Lightwave Technol. 14(7), 1630–1638 (1996).
[Crossref]

Goedgebuer, J.-P.

J. Hauden, H. Porte, J.-P. Goedgebuer, J. Abiven, C. Gibassier, and C. Gutierrez-Martinez, “Polarization independent bidirectional fiber link using coherence multi/demultiplexing LiNbO3 integrated electrooptical circuits,” J. Lightwave Technol. 14(7), 1630–1638 (1996).
[Crossref]

Gonella, F.

Gross, S.

N. Riesen, S. Gross, J. D. Love, and M. J. Withford, “Femtosecond direct-written integrated mode couplers,” Opt. Express 22(24), 29855–29861 (2014).
[Crossref]

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
[Crossref]

Gutierrez-Martinez, C.

J. Hauden, H. Porte, J.-P. Goedgebuer, J. Abiven, C. Gibassier, and C. Gutierrez-Martinez, “Polarization independent bidirectional fiber link using coherence multi/demultiplexing LiNbO3 integrated electrooptical circuits,” J. Lightwave Technol. 14(7), 1630–1638 (1996).
[Crossref]

Hanzawa, N.

K. Saitoh, N. Hanzawa, T. Sakamoto, T. Fujisawa, Y. Yamashita, T. Matsui, K. Tsujikawa, and K. Nakajima, “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol. 35, 80–92 (2017).
[Crossref]

N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, K. Tsujikawa, M. Koshiba, and F. Yamamoto, “Two-mode PLC-based mode multi/demultiplexer for mode and wavelength division multiplexed transmission,” Opt. Express 21(22), 25752–25760 (2013).
[Crossref]

Hauden, J.

J. Hauden, H. Porte, J.-P. Goedgebuer, J. Abiven, C. Gibassier, and C. Gutierrez-Martinez, “Polarization independent bidirectional fiber link using coherence multi/demultiplexing LiNbO3 integrated electrooptical circuits,” J. Lightwave Technol. 14(7), 1630–1638 (1996).
[Crossref]

Hayashi, M.

Hosokawa, T.

Hsu, C. W.

Huang, C. F.

Huang, Q.

Q. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 6602714 (2018).
[Crossref]

Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Mode multiplexer with cascaded vertical asymmetric waveguide directional couplers,” J. Lightwave Technol. 36(14), 2903–2911 (2018).
[Crossref]

Q. Huang, W. Jin, and K. S. Chiang, “Broadband mode switch based on a three-dimensional waveguide Mach–Zehnder interferometer,” Opt. Lett. 42(23), 4877–4880 (2017).
[Crossref]

Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Broadband mode router based on three-dimensional Mach-Zehnder interferometer and waveguide branches,” Conference on Lasers and Electro-Optics (Optical Society of America2018), paper STh1A.2.

Ichii, K.

Jiang, M.

L. Wang, D. Zhang, D. Niu, T. Lian, M. Jiang, F. Wang, and X. Wang, “Polymeric waveguide MZI thermo-optic mode switch based on asymmetric directional coupler,” IEEE Photonics Technol. Lett. 32(4), 200–203 (2020).
[Crossref]

Jin, W.

W. Jin and K. S. Chiang, “Reconfigurable three-mode converter based on cascaded electro-optic long-period gratings,” IEEE J. Sel. Top. Quantum Electron. 26(5), 4500906 (2020).
[Crossref]

Z. Chang, W. Jin, and K. S. Chiang, “Graphene electrodes for lithium-niobate electro-optic devices,” Opt. Lett. 43(8), 1718–1721 (2018).
[Crossref]

Q. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 6602714 (2018).
[Crossref]

W. Jin and K. S. Chiang, “Three-dimensional long-period waveguide gratings for mode-division-multiplexing applications,” Opt. Express 26(12), 15289–15299 (2018).
[Crossref]

Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Mode multiplexer with cascaded vertical asymmetric waveguide directional couplers,” J. Lightwave Technol. 36(14), 2903–2911 (2018).
[Crossref]

Q. Huang, W. Jin, and K. S. Chiang, “Broadband mode switch based on a three-dimensional waveguide Mach–Zehnder interferometer,” Opt. Lett. 42(23), 4877–4880 (2017).
[Crossref]

M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Electro-optic mode switch based on lithium-niobate Mach–Zehnder interferometer,” Appl. Opt. 55(16), 4418–4422 (2016).
[Crossref]

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K. Saitoh, N. Hanzawa, T. Sakamoto, T. Fujisawa, Y. Yamashita, T. Matsui, K. Tsujikawa, and K. Nakajima, “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol. 35, 80–92 (2017).
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K. Saitoh, N. Hanzawa, T. Sakamoto, T. Fujisawa, Y. Yamashita, T. Matsui, K. Tsujikawa, and K. Nakajima, “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol. 35, 80–92 (2017).
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L. Wang, D. Zhang, D. Niu, T. Lian, M. Jiang, F. Wang, and X. Wang, “Polymeric waveguide MZI thermo-optic mode switch based on asymmetric directional coupler,” IEEE Photonics Technol. Lett. 32(4), 200–203 (2020).
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Yamamoto, F.

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K. Saitoh, N. Hanzawa, T. Sakamoto, T. Fujisawa, Y. Yamashita, T. Matsui, K. Tsujikawa, and K. Nakajima, “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol. 35, 80–92 (2017).
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L. Wang, D. Zhang, D. Niu, T. Lian, M. Jiang, F. Wang, and X. Wang, “Polymeric waveguide MZI thermo-optic mode switch based on asymmetric directional coupler,” IEEE Photonics Technol. Lett. 32(4), 200–203 (2020).
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M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Electro-optic mode switch based on lithium-niobate Mach–Zehnder interferometer,” Appl. Opt. 55(16), 4418–4422 (2016).
[Crossref]

M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Symmetric lithium-niobate waveguide fabricated by bonding for mode-division-multiplexing applications,” Opt. Fiber Comm. Conference (Optical Society of America 2018), paper W1E.5.

Zhang, Y.

Zhao, J.

Zhao, N.

G. F. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Zhao, W. K.

Zi, Z.

Z. Zi, L. Wang, K. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

Adv. Opt. Photonics (1)

G. F. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

W. Jin and K. S. Chiang, “Reconfigurable three-mode converter based on cascaded electro-optic long-period gratings,” IEEE J. Sel. Top. Quantum Electron. 26(5), 4500906 (2020).
[Crossref]

IEEE Photonics J. (1)

Q. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 6602714 (2018).
[Crossref]

IEEE Photonics Technol. Lett. (3)

Z. Zi, L. Wang, K. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

L. Wang, D. Zhang, D. Niu, T. Lian, M. Jiang, F. Wang, and X. Wang, “Polymeric waveguide MZI thermo-optic mode switch based on asymmetric directional coupler,” IEEE Photonics Technol. Lett. 32(4), 200–203 (2020).
[Crossref]

M. Zhang, W. Ai, K. Chen, and K. S. Chiang, “A lithium-niobate waveguide directional coupler for switchable mode multiplexing,” IEEE Photonics Technol. Lett. 30(20), 1764–1767 (2018).
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[Crossref]

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[Crossref]

C. W. Hsu, C. F. Huang, and W. S. Tsai, “Lithium niobate polarization-independent modulator using integrated polarization splitters and mode converters,” J. Lightwave Technol. 35(9), 1663–1669 (2017).
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J. D. Love and N. Riesen, “Single-, few-, and multimode Y-junctions,” J. Lightwave Technol. 30(3), 304–309 (2012).
[Crossref]

Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Mode multiplexer with cascaded vertical asymmetric waveguide directional couplers,” J. Lightwave Technol. 36(14), 2903–2911 (2018).
[Crossref]

J. Opt. Soc. Am. A (1)

Laser Photonics Rev. (1)

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
[Crossref]

Nat. Photonics (1)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Opt. Eng. (1)

K. S. Chiang and S. Y. Cheng, “Technique of applying the prism-coupler method for accurate measurement of the effective indices of channel waveguides,” Opt. Eng. 47(3), 034601 (2008).
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Opt. Express (7)

Opt. Fiber Technol. (1)

K. Saitoh, N. Hanzawa, T. Sakamoto, T. Fujisawa, Y. Yamashita, T. Matsui, K. Tsujikawa, and K. Nakajima, “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol. 35, 80–92 (2017).
[Crossref]

Opt. Lett. (5)

Other (2)

M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Symmetric lithium-niobate waveguide fabricated by bonding for mode-division-multiplexing applications,” Opt. Fiber Comm. Conference (Optical Society of America 2018), paper W1E.5.

Q. Huang, Y. Wu, W. Jin, and K. S. Chiang, “Broadband mode router based on three-dimensional Mach-Zehnder interferometer and waveguide branches,” Conference on Lasers and Electro-Optics (Optical Society of America2018), paper STh1A.2.

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Figures (10)

Fig. 1.
Fig. 1. Scheme diagrams showing (a) the top view of a mode-selective switch formed with two cascaded LN asymmetric DCs, together with the dimensions of the waveguide and electrode parameters used in the final design, and (b) the cross-sectional views of an asymmetric DC formed at different stages of the APE process.
Fig. 2.
Fig. 2. Intensity patterns calculated for the three modes supported by the 10-µm wide FMW.
Fig. 3.
Fig. 3. BPM simulation of optical power transfer along (a) the LP11a mode coupler and (b) the LP11b mode coupler at the wavelength 1550 nm, when the LP01 mode is launched into the respective SMW.
Fig. 4.
Fig. 4. (a) Photograph of the fabricated device and (b) microscope images showing the end faces of the SMWs (left and right) and the FMW (middle).
Fig. 5.
Fig. 5. Experimental results for the LP11a mode switch: (a) normalized transmission spectra of the SMW measured at different applied voltages; (b) output near-field images taken at 1550 nm.
Fig. 6.
Fig. 6. (a) Schematic diagram showing the SMW coated with a layer of TiO2 and (b) microscope images of the fabricated switch showing the electrodes, the FMW, and the TiO2-coated SMW.
Fig. 7.
Fig. 7. Experimental results for the post-tuned LP11a mode switch: (a) transmission spectra of the SMW measured at different applied voltages; (b) output near-field images taken at 1550 nm.
Fig. 8.
Fig. 8. Experimental results for the LP11b mode switch: (a) transmission spectra of the SMW measured at different applied voltages; (b) output near-field images taken at 1550 nm.
Fig. 9.
Fig. 9. (a) Temporal switching characteristics of (a) the LP11a mode switch and (b) the LP11b mode switch showing the rise and fall times.
Fig. 10.
Fig. 10. (a) Schematic diagrams showing the proposed LN waveguide structure for the conversion of LN waveguide modes into fiber-compatible modes. (b) Evolution of the three modes along the vertical taper.

Tables (2)

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Table 1. Effective indices of LN waveguides of different widths fabricated with a set of APE parameters

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Table 2. Measured modal crosstalk for the mode-selective switch

Equations (3)

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n ( x , z ) = n L N + Δ n × { erf [ d z 2 d z ] + erf [ d + z 2 d z ] } 2 erf ( d 2 d z ) × { erf [ w 2 x 2 w x ] + erf [ w + 2 x 2 w x ] } 2 erf ( w 2 w x )
n ( x , z , y ) = n L N + Δ n ( y ) × erf [ d ( y ) z D ( y ) 2 d z ( y ) ] + erf [ d ( y ) + z + D ( y ) 2 d z ( y ) ] 2 erf [ d ( y ) 2 d z ( y ) ] × erf [ w ( y ) 2 x 2 w x ( y ) ] + erf [ w ( y ) + 2 x 2 w x ( y ) ] 2 erf [ w ( y ) 2 w x ( y ) ]
D ( y ) = d t × y L t , d ( y ) = d i n ( d i n d o u t ) × y L t , d z ( y ) = d z i n ( d z i n d z o u t ) × y L t , Δ n ( y ) = Δ n i n ( Δ n i n Δ n o u t ) × y L t , w ( y ) = w i n ( w i n w o u t ) × y L t , w x ( y ) = w x i n ( w x i n w x o u t ) × y L t ,