Switching behavior engineerable, electro-optic directional couplers in aperiodic optical superlattice waveguides

Optics Communications 458 (2020) 124800

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Switching behavior engineerable, electro-optic directional couplers in aperiodic optical superlattice waveguides Shih-Yuan Yang a , Hung-Pin Chung a,b , Sung-Lin Yang a , Tsai-Yi Chien a , Kuang-Hsu Huang a , Yen-Hung Chen a,b ,∗ a b

Department of Optics and Photonics, National Central University, No. 300, Zhongda Rd., Zhongli District, Taoyuan City, 32001, Taiwan Center for Astronautical Physics and Engineering, National Central University, No. 300, Zhongda Rd., Zhongli District, Taoyuan City, 32001, Taiwan

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Keywords: Optical waveguides Optical directional couplers Electro-optic devices Simulated annealing Domain engineering

ABSTRACT We report on the first study and a proof-of-principle demonstration of aperiodically alternating-𝛥𝛽 couplers in LiNbO3 waveguides whose switching behavior can be engineered with a high degree of freedom. A high fabrication-tolerance and broad working-bandwidth electro-optic (EO) coupler is developed based on a unique 𝛥𝛽 scheme derived using a simulated annealing algorithm and realized in Ti-diffused aperiodically poled lithium niobate (APPLN) waveguides. The waveguide fabrication tolerance and the working bandwidth (149.2 nm) of the APPLN EO coupler are found to be increased by 2.7 and 2.4 times, respectively, over that of a conventional periodically alternating-𝛥𝛽 (PPLN) coupler for ≥99% power transfer efficiency under a fixed switching voltage at the 1550 nm band. The results even hold for a domain poling-width error of ≤9%. An interesting APPLN EO coupler capable of working on a certain coupling state over a broad voltage operating range is also studied. The technology developed in this work should enable the production of coupler devices whose switching characteristics can be tailored and realized with much more relaxed fabrication and bandwidth control, which would be beneficial for the application in efficient and compact integrated-optic circuits/systems.

1. Introduction Optical directional couplers are one of the most common elements for building integrated-optic and fiber-optic systems and play a significant roles in emerging quantum photonic circuit technology [1–5]. In optical circuits, directional couplers usually work on two parallel and closely spaced waveguides, enabling the exchange of energy between modes of the two waveguides via the evanescent coupling [6]. Electro-optic (EO) mechanisms have been used to achieve a fast and active (power) switching in directional couplers as first demonstrated in lithium niobate (LiNbO3 ) waveguides by Papuchon et al. in 1975 [7]. However, the issue of small device fabrication tolerance remains the major limitation for the application of such devices. Fabrication error control is particularly challenging and involved with many photonic materials including one of the most popular platforms, LiNbO3 , which depends upon ion exchange or ion indiffusion technology as the waveguide formation method [8]. To release the influence of the fabrication factor on the behavior of directional couplers, an alternating-𝛥𝛽 coupler configuration has been

proposed and demonstrated [9], where the sign of the propagationconstant difference (𝛥𝛽) between the two coupling modes in respective waveguides is periodically changed under the EO effect. In this scheme, the EO control makes complete power switching possible without depending on the initial coupling state (before any external control) which is a sensitive function of the device fabrication condition. Nevertheless, this seemingly successful solution is still unsatisfactory in terms of allowing a high fabrication tolerance for the production of directional couplers designed to have a specific EO switching behavior (see below). The switching behavior of an EO directional coupler can be verified by examining the switching diagram plotting the relationship between the L/l𝑐 and the 𝛥𝛽𝐿∕𝜋, where L is the length of the coupler and l𝑐 is the shortest coupler length for a complete power transfer (termed the coupling length) [9]. Fig. 1 shows the switching diagrams calculated for alternating-𝛥𝛽 couplers built in periodically poled lithium niobate (PPLN) waveguides with domain numbers 𝑁 = 2 and 10, respectively. In PPLN EO couplers, simple uniform electrodes are used instead of sectioned electrodes, as schematically shown in the inset to Fig. 1. The gray and red lines in Fig. 1 represent the complete (100%) ‘‘straight-through’’ and ‘‘crossover’’ conditions where all the

∗ Corresponding author at: Department of Optics and Photonics, National Central University, No. 300, Zhongda Rd., Zhongli District, Taoyuan City, 32001, Taiwan. E-mail addresses: [email protected] (S.-Y. Yang), [email protected] (H.-P. Chung), [email protected] (S.-L. Yang), [email protected] (T.-Y. Chien), [email protected] (K.-H. Huang), [email protected] (Y.-H. Chen).

https://doi.org/10.1016/j.optcom.2019.124800 Received 8 July 2019; Received in revised form 16 October 2019; Accepted 18 October 2019 Available online 23 October 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.

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Optics Communications 458 (2020) 124800

Fig. 1. Calculated switching diagrams for alternating-𝛥𝛽 couplers built in PPLN waveguides with domain numbers (a) 𝑁 = 2 and (b) 𝑁 = 10. The inset shows a schematic of a PPLN waveguide directional coupler using uniform electrodes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

coupling behavior in such a waveguide system can be modeled by the coupled-mode theory [9], described by [ ] [ ] 𝐸𝑇 (0) 𝐸𝑇 (𝐿) , (1) = 𝑀1 𝑀2 𝑀3 ...𝑀𝑁 𝐸𝑋 (0) 𝐸𝑋 (𝐿)

power will exit from the ‘‘straight-through’’ arm (denoted as ‘‘T ’’) and the ‘‘crossover’’ arm (denoted as ‘‘X ’’) of the two-waveguide coupler system (see the inset), respectively, when the light is input into the ‘‘straight-through’’ (T ) arm. As illustrated in Fig. 1(a) (for 𝑁 = 2) we can now find complete power switching conditions between the X and T waveguides (e.g., the a, b and c, d states indicated in the plot) for a large range of L/l𝑐 (see those unshadowed regions). Since 𝛥𝛽 is a function of the applied voltage, the difference between the two working voltages for switching such EO devices between two coupling states is called the switching voltage. The complete power switching conditions can be attained for almost the full range of L/l𝑐 except those with L/l𝑐 <1 when N >2 (see Fig. 1(b)). The best switching condition always occurs at L/l𝑐 =N, with the lowest switching voltage. However, since the value of l𝑐 is determined by the coupling strength of the couplers and therefore by the waveguide characteristics which are highly dependent on the fabrication conditions, the switching behavior, such as the switching voltage (and the working voltages) of a directional coupler could deviated significantly from the design values, making the manufacture of (a plurality of) directional couplers, having a specific and uniform EO switching behavior beneficial for building efficient and compact integrated-optic circuits/systems, a difficult task. In this work, we propose and demonstrate, the first, to the best of our knowledge, EO directional couplers based on aperiodically poled lithium niobate (APPLN) waveguides whose switching behavior can be designed with great freedom and be realized with a high fabrication tolerance and/or broad voltage operating range.

where E 𝑇 and E 𝑋 are the complex field envelopes of the modes in the T and X waveguides, respectively; and [ ] [ ∗ ] 𝐴 −𝑖𝐵 𝐴 −𝑖𝐵 − = 𝑀𝑖 = 𝑀 + = 𝑜𝑟 𝑀 = 𝑀 (2) 𝑖 −𝑖𝐵 ∗ 𝐴∗ −𝑖𝐵 ∗ 𝐴 is the unit transfer matrix for deriving the field evolution of the modes passing through the ith positive- or negative-polarity domain (corresponding to a +𝛥𝛽 or ( −𝛥𝛽 ) of the(APPLN ) √respectively. √ segment) √ coupler, In Eq. (2), 𝐴 = cos 𝛥𝑥 𝜅 2 + 𝛿 2 + 𝑖𝛿 sin 𝛥𝑥 𝜅 2 + 𝛿 2 ∕ 𝜅 2 + 𝛿 2 and ) √ ( √ 𝐵 = 𝜅 sin 𝛥𝑥 𝜅 2 + 𝛿 2 ∕ 𝜅 2 + 𝛿 2 , where 𝜅 = 𝜋∕2𝑙𝑐 , 𝛿 = 𝛥𝛽∕2. Eq. (1) can be graphically solved by plotting the relationship between the 𝐿∕𝑙𝑐 and the 𝛥𝛽𝐿∕𝜋, which yields the switching diagram. We develop a simulated annealing (SA) [12] algorithm based on Eq. (1), a methodology similar to that used in the aperiodic optical superlattice (AOS) technique [13], to derive an optimal domain (polarity) sequence (which is exactly the sign sequence of 𝛥𝛽 and determines the combination configuration of 𝑀 + and 𝑀 − in the unit transfer matrix sequence appearing in Eq. (1)) needed for building the APPLN coupler that best agrees with the target device specifications. The capability of the SA algorithm has been discussed and compared with other algorithms elsewhere [14–16]. Although the SA algorithm usually requires a fine enough unit domain size (𝛥𝑥) (which is restricted to a few microns by the present poling technique) to facilitate optimizing the construction of an APPLN nonlinear wavelength converter, this issue is not critical for building the APPLN coupler in this study, because the employed unit domain size (100 μm) is far larger than that limited by poling and is sufficient to reach an optimized result (see below). Moreover, the design freedom of the SA method allows us to pursue multiple design targets (see Eq. (3) below) with a satisfactory working efficiency [16]. In this work, we first design an EO directional coupler that can work at a fixed switching voltage over a broad 𝐿∕𝑙𝑐 range under a power transfer efficiency of ≥ 99% (−20 dB power extinction ratio). This design target is pursued by the application of an objective function (OF ) in the SA algorithm, given by ( ) ( ) 𝑂𝐹 = 𝑤𝑋,1 𝛥𝑝𝑋,0 − 𝛥𝑝𝑋 |𝑞𝑋 ,𝜂𝑋 + 𝑤𝑋,2 𝑞𝑋,0 − 𝑞𝑋 ( ) ( ) , (3) + 𝑤𝑇 ,1 𝛥𝑝𝑇 ,0 − 𝛥𝑝𝑇 |𝑞𝑇 ,𝜂𝑇 + 𝑤𝑇 ,2 𝑞𝑇 ,0 − 𝑞𝑇

2. Device design and fabrication The idea behind using an aperiodically alternating-𝛥𝛽 scheme in EO directional couplers is to free the device configuration which is constrained by the periodically alternating-𝛥𝛽 scheme so as to achieve a specific device performance that it is not possible to attain with stereotypical couplers. 2.1. Design methodology and optimization algorithm To model these novel EO couplers, assume two identical, parallel waveguides of interaction length L and waveguide separation S. They are formed by the titanium thermal diffusion (TTD) method [10] and are constructed in an APPLN crystal composed of a sequence of N crystal domain segments, each with a thickness 𝛥x and a domain polarity of either +1 or −1 denoting the +z or −z crystallographic orientation of the segment, respectively. The configuration of the waveguides determines the coupling length (l𝑐 ), coupling coefficient (k), and propagation constant difference between the two waveguides (𝛥𝛽 (E 𝑑𝑐 ), induced by the applied electric field E𝑑𝑐 ) of the coupler system [11]. The power

where the subscripts 𝑋 and 𝑇 denote the quantities associated with the crossover and straight-through waveguides, respectively, 𝛥𝑝𝑋 and 𝛥𝑝𝑇 are the continuous ranges of 𝐿∕𝑙𝑐 with respect to a default value (𝑝0 ) within which the calculated ratios of the output powers from the 𝑋 and 𝑇 waveguide arms of the coupler to the total output power (𝑃𝑋 ∕𝑃0 and 𝑃𝑇 ∕𝑃0 ) are equal to or more than the set values 𝜂𝑋 and 2

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Optics Communications 458 (2020) 124800

Fig. 2. Calculated switching diagrams of the (a) APPLN and (b) 𝑁 = 10 PPLN EO directional couplers for 99%-X and 99%-T coupling states. The L/l𝑐 ranges satisfying the design switching condition are highlighted. The dashed lines labeled by xa to xn in (a) indicate the 𝛥𝛽𝐿∕𝜋-dependent power coupling characteristics of the fabricated couplers. (c) Schematic of the calculated domain polarity distribution of the APPLN (black: positive domain, white: negative domain). (d) The application of the aperiodic domain structure in a coupler scheme (electrodes are not shown). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

𝜂𝑇 when working at 𝛥𝛽𝐿∕𝜋 = 𝑞𝑋 and 𝑞𝑇 , respectively; 𝛥𝑝𝑋,0 and 𝛥𝑝𝑇 ,0 are the target values for 𝛥𝑝𝑋 and 𝛥𝑝𝑇 , while 𝑞𝑋,0 and 𝑞𝑇 ,0 are the target values for 𝑞𝑋 and 𝑞𝑇 , respectively, for pursuing continuous ranges of 𝐿∕𝑙𝑐 which are as wide as possible under working voltages as low as possible. Those ’’𝑤’’ parameters appearing in each term of Eq. (3) are the corresponding weighting factors. Fig. 2(a) shows the switching diagram of an EO directional coupler calculated using the algorithm developed in this work. The design was based on a 1550 nm fundamental TM mode. Fig. 2(c) shows the calculated domain polarity distribution (black and white regions denote the crystal domains with positive and negative polarities, respectively), which exhibits an aperiodic barcode-like structure (i.e., forming an APPLN). Its application in a coupler scheme is illustrated in Fig. 2(d). The mechanism can be understood to operate as follows: the barcodelike domain structure aperiodically modulates the phase velocities of the interacting waves spatially along the waveguides, creating a 𝛥𝛽 configuration capable of providing multiple modulation periodicities that can satisfy specific (multiple) phase-matching conditions required to broaden the workable L/l𝑐 range for a desired switching behavior (i.e., to increase the fabrication tolerance) and the operating bandwidth of an EO coupler device. In this calculation, 𝐿 = 20 mm, 𝑁 = 200, 𝛥𝑥 = 𝐿∕𝑁 = 100 μm, 𝜂𝑋 = 𝜂𝑇 = 0.99, 𝛥𝑝𝑋,0 = 𝛥𝑝𝑇 ,0 = 4 with respect to 𝑝0 = 10 (i.e. 𝐿∕𝑙𝑐 = 10 ± 2), 𝑞𝑋,0 = 𝑞𝑇 ,0 = 1, 𝑤𝑋,1 = 𝑤𝑇 ,1 = 1, and 𝑤𝑋,2 = 𝑤𝑇 ,2 = 0.02 have been set. We do not obtain reasonably good results with 𝑁 ≤ ∼100, on the other hand, we find the calculation has yielded an optimized result with 𝑁∼200. Specifically, we find no

obvious difference in the switching diagrams obtained for 𝑁 > 200 from that obtained with 𝑁 = 200 (Fig. 2(a)) in the range of interest of 𝛥𝛽𝐿∕𝜋 < 12 (corresponding to a moderate driving voltage of < 70𝑉 ). This indicates that 𝛥𝑥 = 100 μm has been a sufficiently fine unit thickness to constitute an optimized 𝛥𝛽 configuration for the coupler to best reach the target device specifications. A switching diagram calculated for a periodically alternating-𝛥𝛽 (PPLN) coupler with 𝐿 = 20 mm, 𝜂𝑋 = 𝜂𝑇 = 0.99 and 𝐿∕𝑙𝑐 = 10 is also plotted (Fig. 2(b)) for the comparison. The red and gray areas represent the solutions satisfying coupling conditions where the power conversion efficiencies are 𝜂𝑋 ≥ 99% and 𝜂𝑇 ≥ 99% (the 99%-X and 99%-T states), respectively. The areas highlighted in the respective diagrams mark the 𝐿∕𝑙𝑐 range within which switching between the 99%-X and 99%-T states can be attained by switching between two fixed voltage (or 𝛥𝛽) values (denoted as V 𝑋 and V 𝑇 ). It can be clearly seen that the APPLN EO coupler can work on a −20 dB power extinction switching for an 𝐿∕𝑙𝑐 ranging from 8.6 to 10.7, about 2.7 times wider than that for a PPLN EO coupler, under a fixed switching voltage of 17.5 V (when a simulated overlap efficiency of the mode field and the external electric field of 𝜗 ∼ 0.25, is used). Since 𝑙𝑐 is a function of the waveguide fabrication condition, the result suggests large improvement in the fabrication tolerance with this design. It deserves to note that the SA algorithm will turn out a periodic domain structure (i.e., a PPLN) when 100% coupling efficiency (i.e., when 𝜂𝑋 = 𝜂𝑇 = 1) is set in the calculation, giving a switching behavior exactly as that shown in Fig. 1(b) with, however, a zero tolerance for 𝑙𝑐 when the switching has to be made between 3

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Fig. 3. Microscopic image of a portion of the test APPLN couplers fabricated in the same sample chip after local HF-etching, revealing the structures of the Ti:LiNbO3 coupler waveguides and the aperiodically poled domains.

3. Device characterization and discussion of the results

two fixed voltage values. The lowering of the coupling efficiency is an unavoidable cost for relaxing the fabrication tolerance and broadening the operating bandwidth of the coupler devices. An interesting analogy can be made in the application of a similar technique (AOS technique) to broaden the acceptance bandwidth in a quasi-phase-matched (QPM) second harmonic generation (SHG) process (at the cost of the SHG efficiency) [17].

The switching behavior of the developed APPLN EO directional coupler device was then characterized in an optical test bed using an external cavity laser (ECL; linearly polarized, tunable between 1495 and 1640 nm) as the light source. The polarization of the fiber coupled laser output was controlled to maintain and excite the TM mode of the T waveguide arm of a coupler through the but coupling scheme. The input power before coupling into the waveguides was 1 mW. The crystal was mounted (vacuum fastened) on a multi-axis precision translation stage. The output powers from the T and X waveguide arms of a coupler were respectively collected through a translatable objective lens and iris system and measured using a photodetector. The characterized propagation loss of the waveguides was around 0.3 dB/cm for the TM mode at the 1550 nm band, and showed no obvious change under the application of external voltages in the experiment. First we measured the output powers from the X and T arms (P 𝑋 and P 𝑇 ) of all the waveguide couplers on the chip as a function of the applied voltage. From the measured data, we can easily identify and fit the correspondence of the power coupling characteristics of the 14 couplers shown in the switching diagram in Fig. 2(a) (denoted as xa to xn, located in a L/l𝑐 range of from 7.4 to 11.2. The range has been shifted by ∼ 0.6 with respect to the design. A shift from predicted range is not surprising as l𝑐 is fabrication dependent). We failed to do the fitting for the three other couplers due to damage to their electrodes during the fabrication process, but this did not have much influence on the results presented in this study. Fig. 4 shows a plot of the measured and simulated X power coupling ratios (≡ 𝑃𝑋 ∕(𝑃𝑋 + 𝑃𝑇 )) versus 𝛥𝛽𝐿∕𝜋 for some representative couplers (xb, xc, xf , xg , xk, and xn) at 1550 nm. Here, the 𝛥𝛽𝐿∕𝜋 values are derived from the applied voltages with a fitted 𝜗 ∼ 0.23 which is fairly close to the simulated value 0.25. 𝜗 can be further increased by a more sophisticated electrode design and fabrication. The measured coupling characteristics are in good agreement with the simulation. However, a certain but non-systematic discrepancy exists between the measured and simulated results for different couplers which can be mainly attributed to nonuniform domain poling errors over the poling area and the non-ideal polarization control of the input light during measurement. The gray and dotted gray lines in Fig. 4(f) represent the simulated results considering an average of 5% and 13% domain over-poled errors [21], respectively. The results show that domain engineering error (not addressed in this study) does play a non-negligible role in limiting the device performance, although they also suggest that the switching behavior of the device is to some extent tolerant of the error (5% (9%) domain width error for −24.5 (−20) dB powerextinction switching; the simulation results for the 9% domain width

2.2. Device fabrication methods and process For a proof-of-principle experiment, we fabricated a set of directional couplers (including several test couplers for examination of the fabrication conditions) on a single z-cut LiNbO3 chip of 40 mm in length, 15 mm in width, and 0.5 mm in thickness. The coupling length 𝑙𝑐 is first assumed to be 2 mm for the 1550 nm TM mode according to our latest fabrication result [18]. Since the variation of the 𝑙𝑐 values of these couplers built on such a chip scale can be small, to experimentally verify the high tolerance (with a broad 𝐿∕𝑙𝑐 range) of the proposed APPLN EO directional coupler, we resort to change L instead of 𝑙𝑐 for this chip design. This emulates (real) situation where L is fixed but a relatively large variation of 𝑙𝑐 can occur in a full-wafer production or more commonly, in different production runs. An array of 17 waveguide couplers with different coupler lengths L ranging from 16 to 24 mm (with an incremental step of 0.5 mm; see Fig. 2(c) for the device dimensions), expected to cover a range of an 𝐿∕𝑙𝑐 from 8– 12 (i.e., 10±2), were fabricated on the -z surface of an LiNbO3 chip using the TTD method (see [18] for more detailed information about the fabrication details). The waveguides support the guiding of the single TM (as well as TE) mode in the spectral range 1400–1700 nm. Couplers were then produced using the aperiodic domain structure derived above (the thickness of the constituent unit domain block varied according to the different 𝐿 as 𝛥𝑥 = 𝐿∕𝑁, where 𝑁 = 200 was set) using the standard electric-field poling technique [19] after the removal of the domain-inverted layer on the +z surface of the LiNbO3 chip formed during the TTD process [20] by optical polishing. Fig. 3 shows a microscopic image of a portion of the test APPLN couplers fabricated on the same chip after the local HF-etching, where the structures of the Ti:LiNbO3 coupler waveguides and the aperiodically poled domains are revealed. The fabrication result suggests an over-poled domain condition. The effect on the device performance is discussed below. The end faces of the chip were then 10◦ angle polished. No optical coating was applied. Device fabrication was completed after coating of the stripe electrodes (Ti/Au) over the waveguides which were buffered by an oxide (SiO2 ) layer in the coupler sections for the voltage application. 4

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Fig. 4. Measured and simulated X power coupling ratios versus 𝛥𝛽𝐿∕𝜋 for the fabricated couplers (a) xb, (b) xc, (c) xf , (d) xg , (e) xk, and (f) xn at 1550 nm. The solid and dotted gray lines in (f) represent the simulated results for 5% and 13% domain over-poled errors, respectively.

attained for a bandwidth of 149.2 nm (from 1493.9 to 1643.1 nm) for the (xkth) coupler with L/l𝑐 ∼ 10 at 1550 nm. The bandwidth is 2.4 times broader than that obtained with PPLN scheme. Fig. 6 shows the measured and calculated X power coupling ratios versus the applied voltage and the corresponding 𝛥𝛽𝐿∕𝜋 for several input wavelengths in the tuning range of the ECL for the xkth coupler. Again, the measured coupling characteristics are in good agreement with the design results, demonstrating the potential of the proposed technology for realizing an EO coupler device with high fabrication tolerance and broad working bandwidth. The technology can thus benefit on-chip integration of such a key functional element (a directional coupler) with many LiNbO3 photonic devices such as QPM wavelength converters and quantum light sources, as well as other EO elements [24–26] usually having a narrowband (less than a few nanometers) acceptance bandwidth to facilitate building integrated and quantum photonic circuits. Moreover, EO couplers capable of working at a certain coupling condition over a wide range of applied voltages could also be attractive for many applications. Fig. 7 shows a simulated switching diagram for such a unique couplers designed using the developed SA algorithm. The red and gray areas represent the solutions satisfying the coupling conditions where the power conversion efficiency 𝜂𝑋 is ≥ 0.5 and 𝜂𝑇 is ≥ 0.5 respectively. In a tolerant range of L/l𝑐 =10±>1 (as defined by two dashed lines), the original coupling condition (at 0 V or 𝛥𝛽=0) can be preserved for a voltage range of >70 V (corresponding to 𝛥𝛽𝐿∕𝜋 ∼ 13.8). A similarly broad-range working voltage can also be obtained with the device when switched to the other coupling condition (red to gray or gray to red areas). An electro-optically fast voltage breaker can be realized using this intriguing APPLN EO coupler, which would not to be possible to implement using the existing periodically alternating-𝛥𝛽 (PPLN) technique.

Fig. 5. Experimentally derived coupling length l𝑐 as a function of the laser wavelength for the xkth coupler.

error are not shown). Further consideration of how to minimize the effect of domain poling errors in the presented calculation model is underway. In fact, the issue of the domain over- (under-) poling found in this APPLN device (and generally, in all domain poled devices, including PPLN ones) is similar to the concern raised in conventional alternating-𝛥𝛽 couplers using interdigitated electrodes where certain gaps exist between electrode segments. Phase errors are introduced in the gap (passive-coupling) regions that generally lead to degradation of the coupler performance [22]. While several more sophisticated domain engineering techniques have been demonstrated to achieve high-fidelity domain patterning [23], the existence of electrode gaps in non-poled couplers is unavoidable. In addition, since l𝑐 is also a function of the working wavelength, broadband operation of the developed coupler device can be expected. Fig. 5 shows the experimentally derived coupling length l𝑐 as a function of the laser wavelength for the xkth coupler. From the linear fit of the data and the device dispersion, we find that the switching condition (≥99% power extinction switching between two fixed voltages) can be

4. Conclusions We have developed the first aperiodically alternating-𝛥𝛽 schemes for EO directional couplers to enable a highly tailorable switching behavior and achieve a more advantageous device performance that 5

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Fig. 6. Measured and simulated X power coupling ratios versus the applied voltage and the corresponding 𝛥𝛽𝐿∕𝜋 for the xkth coupler at (a) 1500, (b) 1550, and (c) 1600 nm.

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Fig. 7. Simulated switching diagram of an APPLN EO directional coupler whose coupling states (initial and switched states) can be held for a wide voltage range. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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is unattainable with stereotypical couplers. An APPLN EO directional coupler whose switching voltage is invariant without depending on the fabrication factor over a wide L/l𝑐 range (8.6 to 10.7) is built for a 20 dB power extinction ratio. There is an increase in the resultant fabrication tolerance and working bandwidth (149.2 nm) of the unique device by a factor of 2.6 and 2.4, respectively, in contrast to the conventional PPLN device. The simulation results show the switching behavior of the device which can tolerate 9% domain-width error for a −20 dB powerextinction switching. We also present an APPLN EO directional coupler, designed using the same technology, whose original and switched coupling states can be held for a wide voltage range. These unique devices are attractive for building photonic switching networks.

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Acknowledgments

[18] H.P. Chung, K. Huang, S.L. Yang, W.K. Chang, et al., Adiabatic light transfer in titanium diffused lithium niobate waveguides, Opt. Express 23 (24) (2015) 30641–30650.

The authors would like to acknowledge the funding support from the Ministry of Science and Technology (MOST), Taiwan under contracts 106-2221-E-008-068-MY3, 107-2627-E-008-001, 108-2911-I008-506, and 104-2923-E-007-001-MY4.

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