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Abstract
We propose a low-insertion-loss electro-optic modulator formed with LNOI bonded on a D-shaped SMF. The proposed modulator employs high-performance Mach-Zehnder interferometer (MZI) formed with ridge LNOI waveguides and driven by travelling-wave electrodes. The light from the fiber core is coupled into a thin strip LNOI waveguide and then launched into the MZI via a ridge LNOI waveguide with tapered slab height and vice versa. Such all-fiber configuration exempts the need of the butt-coupling with an SMF. The calculated results show that our proposed modulator is capable of achieving a low insertion loss of less than 1.5 dB, an EO modulation efficiency (Vπ·L) of 2.05 V·cm, and a 3-dB modulation bandwidth of larger than 80 GHz. Our all-fiber LNOI modulator is feasible in practice and opens a new door to realize high-speed fiber devices by the integration of an optical fiber and thin film LN.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past few decades, there has been a strong push towards the development of high-performance external electro-optic (EO) modulators to meet the ever-increasing demand for broadband and high-capacity optical communication infrastructure in backbone networks [1,2]. In this scenario, lithium niobate (LN) EO modulator became eminent by virtue of its excellent performances, including large and continuously increasing bandwidth, zero-chirp or adjustable-chirp operation, and reasonable driving voltage and insertion loss [3–5]. However, suffering from the weak optical confinement of the involved waveguides formed by the annealed proton-exchange process or the Ti-diffusion process [6], conventional LN EO modulators are bulky and can only be used as discrete devices [3,7], which are contrary to the tendency of miniaturization and integration of the current photonic devices [7–9].
Thanks to the emerging of lithium niobate on insulator (LNOI), it is possible now to fabricate LN waveguides with strong optical confinement because of the high index contrast between LN and silica [10]. Consequently, a significant reduction in optical mode area and bent waveguide radius can be achieved, and a large enhancement in EO efficiency and a drastic shrink in device size could be expected with the LNOI waveguides [7,10,11], in comparison with the traditional LN waveguides. Based on LNOI platform, lots of efforts have been made towards the development of compact and high-performance modulators now [12–17]. A modulator operating at a CMOS-compatible voltage has been demonstrated, while the device length is much shorter than these conventional modulators [16].
Although modulators based on LNOI platform are capable of achieving outstanding performance, its applications are limited by the large coupling loss between the submicron-scale LNOI waveguide and the standard single mode fiber (SMF) due to the high difference in the mode field sizes between them. The insertion losses of the existing LNOI modulators are usually larger than 10 dB [12,14]. Such high losses will cause a great deterioration of the modulating performance. Generally, there are two solutions to address the issue. One is reducing the mode size of fibers by using a lensed fiber or a tapered fiber. Another solution is expanding the mode size of the LNOI waveguide to match that of an SMF. In [18], a low-loss mode size converter for LNOI devices was fabricated and the coupling loss of 1.7 dB per facet was obtained using lensed fiber. However, the above methods are sensitive to the fiber-to-waveguide misalignment and not compatible with the standard fiber, which makes packaging and assembly difficult.
All-fiber configurations, where the input and output interfaces are both fibers and hence exempts the need of the butt-coupling, are quite effective to address the issues of the insertion loss and device packaging. Moreover, all-fiber configurations are better compatible with the deployed optical fiber communication system. Up to now, several all-fiber optical modulators have been proposed based on functional materials, including graphene [19–21], electro-optical polymer [22], and bulk LN [23]. With all-fiber configurations, a low insertion loss of less than 1 dB has been demonstrated experimentally in [19,23].
In this study, a low-insertion-loss thin-film LN EO modulator based on all-fiber configuration is proposed for the first time to the best of our knowledge. Our proposed modulator is formed with LNOI bonded on D-shaped SMF. The device employs Mach-Zehnder interferometer (MZI) configuration structured with the optimized ridge LNOI waveguides to enhance the EO efficiency and driven by travelling-wave electrodes to realize high speed modulation. The light from the fiber core is coupled into a thin strip LNOI waveguide, and then launched into the input end of the MZI via a ridge LNOI waveguide with tapered slab height and vice versa. The evanescent coupling between the D-shaped fiber and the strip LNOI waveguide was analyzed carefully. And the involved waveguides and electrodes were designed meticulously to achieve high performance. The calculated results show that our proposed modulator is capable of achieving a low total insertion loss of less than 1.5 dB, an EO modulation efficiency (Vπ·L) of 2.05 V·cm, and a 3-dB modulation bandwidth of larger than 80 GHz. In addition, the possible fabrication processes are introduced, which indicate that our all-fiber LNOI modulator is feasible in practice.
2. Structure and principles
The proposed all-fiber EO modulator, shown schematically in Fig. 1(a), is formed with X-cut LNOI bonded on D-shaped SMF, which can be functionally divided into input and output coupling regions R1 and R5, input and output transition regions R2 and R4, and modulation region R3. Two sections of identical thin strip LNOI waveguides with width w and height t1, as shown in Fig. 1(b), are located symmetrically in R1 and R5 regions and coupled evanescently to the fiber core, respectively, with the same gap g. An MZI structured with identical ridge LNOI waveguide with width w, height t, and ridge height t2, as shown in Fig. 1(c), is located in R3 region. Two sections of identical ridge waveguides with tapered slab height, located symmetrically in R2 and R4 regions, are used to connect adiabatically the MZI at its two ends to the two strip waveguides, respectively, as shown in Fig. 1(a). All waveguides located in R2, R3, and R4 are designed to decouple from the fiber core. In addition, the two waveguide arms of the MZI are designed to deliver light signals along y direction and hence the employed electrodes can exploit the largest EO coefficient (γ33) of LN crystal.
Fig. 1. (a) Schematic of the proposed all-fiber modulator, (b) cross-sectional view of the coupling region together with the involved parameters, (c) cross-sectional view of the modulation region together with the involved parameters.
In R1 region, light propagating along the fiber is coupled evanescently into the thin strip LNOI waveguide. Compared with the inefficient facet to facet coupling, once the phase-match condition is satisfied, the evanescent coupling could achieve much higher coupling efficiency. After the light in the fiber being fully transferred into the strip LNOI waveguide, the coupling needs to be stopped. Otherwise, the light will return to the fiber. In R2 region, a ridge LNOI waveguide with tapered slab height is designed to stop the coupling and deliver the light into the MZI. With the increase in the slab height, the effective index difference between the D-shaped fiber and the ridge waveguide becomes larger, resulting in the decoupling from the fiber. At the same time, the profile of the waveguide changes from the strip to the ridge type, as shown in Fig. 1(a). For the LNOI modulators, employing ridge waveguides can realize higher EO efficiency than employing strip waveguides, which will be proven in subsection 3.2.
Travelling-wave electrodes of the coplanar waveguide (CPW) structure are used to provide push-pull operation and high-speed modulation. The cross-sectional view of the modulation region R3 together with the structural parameters of the used CPW is shown in Fig. 1(c). To exploit the highest electro-optic tensor component γ33 of LN, the optical mode needs to be TE polarization, thus, at 1550 nm wavelength, the effective index of optical mode No must be less than the extraordinary refractive index of LN (ne = 2.1381). However, compared with the optical field, the microwave field generated by the electrodes is distributed over a much larger area. Thus, the effective index Nm of the microwave depends on the distribution of dielectrics in the overall modulation region, which can be defined as Nm = (εe)1/2, where εe is the effective permittivity. For conventional LN modulators, the devices are fabricated on bulk LN (εLN = 28). Therefore, Nm is significantly larger than No. Suffering from the large velocity mismatch, the bandwidth of conventional modulators is quite limited. For the proposed structure, since the thin film LN is only distributed over a tiny area, Nm is dominated by the fiber and quartz substrate (εsilica = 4). Thus, Nm is close to No and the velocity mismatch can be easily eliminated, which will be expounded in subsection 3.3.
Our proposed device could be fabricated as follows. A conventional SMF-28 fiber is firstly embedded into the pre-prepared quartz block and then side-polished carefully to form the required D-shaped fiber with adiabatic transitions. With fine mechanical or chemical mechanical polishing process, here the D-shaped fiber is capable of achieving the surface roughness below 1 nm rms [12], which helps to reduce the scattering losses and enable subsequent bonding process. Moreover, the thickness g of the remaining cladding in D-shaped fiber is designed carefully and maintained across a long enough polishing region to lay out the designed modulator, as shown in Figs. 1(b) and 1(c). As a result, the transmission loss of the polished fiber is negligible. After the polishing process, an X-cut LN thin film with desired thickness t is then formed on the polishing surface with the mature direct bonding process used in [10] or [17], resulting in the desired LNOI structure. At last, the designed waveguides and electrodes that constitute the proposed modulator shown in Fig. 1(a) are formed by the standard photolithography, dry etching, and chemical etching processes used in [14] or [24]. So far, various fabricated methods of vertical tapers or the more complicated 3D tapers have been developed on SOI [25] and polymer [26], which can also be used to fabricate the involved ridge LNOI waveguide with tapered slab height. All of these aforementioned processes are available now, thus our proposed all-fiber LNOI modulator is feasible in practice.
3. Designing and optimization
3.1 Strip LN waveguide
As mentioned above, evanescent coupling is employed to transfer the light signals from the D-shaped fiber to the strip LNOI waveguide and vice versa, which is critical for the modulator operation. However, because of the large refractive index difference between LN and silica, the phase-match condition is hard to be satisfied. To achieve high coupling efficiency, the width and thickness of the strip waveguide must be meticulously designed. For this purpose, we calculate the effective refractive indices of the strip LNOI waveguides and the D-shaped fiber with a FEM mode solver (COMSOL). The parameters of the involved fiber are chosen to be the same as the standard SMF-28 fiber. The cladding of the waveguide is air. The height t1 of the strip LNOI waveguide is set to be 150, 200, and 250 nm, respectively, while the width w changes from 0.50 to 1.80 μm. The calculated results are shown in Fig. 2. It can be observed in Fig. 2(a), the effective index of the D-shaped fiber has little change with the increasing of g. For simplicity, we set the approximate effective index of the D-shaped fiber to be 1.4680. The calculated results of LN strip waveguide are shown in Fig. 2(b). In the simulation range of the strip LN waveguide, TM mode does not exist because of the large aspect ratio and small thickness, which means here the strip LN waveguide only supports fundamental TE mode.
Fig. 2. (a) Calculated neff of the D-shaped fiber for different g from 1.0 to 5.0 μm. (b) Calculated neff of the fundamental TE mode of the strip LN waveguide for different w from 0.50 to 1.80 μm at different t1 of 150, 200, and 250 nm. Fiber indicates approximate neff of the D-shape fiber (∼1.4680), which is irrelevant to w. (c) Calculated dispersion curves of the ridge LN waveguides in R3. (d) Calculated coupling length for different g from 1.0 to 3.0 μm.
To simplify the structure of the proposed all-fiber modulator, in our design, waveguides in different regions have the same width w. Generally, the ridge waveguides in R3 should provide single-mode operation. To decide the appropriate single mode width w, the dispersion curves of the ridge LN waveguide are calculated. Here the thickness t is set to be 500 nm, and two cases of etch depth t2 = 200 nm and t2 = 300 nm are investigated, which are the commonly used etch depth for the thin film LN ridge waveguide with t = 500 nm. The calculated dispersion curves for the TE mode are shown in Fig. 2(c). It can be observed that the suitable single mode widths for both cases are ∼1.0 μm, which is the width we used in our previously work [24]. Further, from Fig. 2(b), for t1=250 nm, the corresponding width is too narrow, which results in weak horizontal light confinement. For t1=150 nm, the corresponding width is obviously larger than the single mode width for both cases shown in Fig. 2(c). Thus, the thickness of the strip waveguide is designed to be 200 nm. The corresponding width w is 0.88 μm. With these parameters, we calculate the coupling length for different g from 1.0 to 3.0 μm, and the results are shown in Fig. 2(d).
Since this strip waveguide is thin (t1 = 200 nm), the transmission loss will be higher than a typical LNOI single mode waveguide (0.03-3 dB/cm) [7]. Thus, the strip waveguide should avoid being too long. As shown in Fig. 2(d), with the decreasing of g, the coupling length can be reduced to ∼300 μm. The transmission loss of such a short strip waveguide has no significant impact on the total insertion losses.
3.2 Ridge LN waveguide
For LN EO modulators, the etch depth t2 of the involved ridge LN waveguides has an impact on the EO efficiency. A larger t2 will result in better optical confinement, allowing a smaller gap ge between electrodes and hence a higher EO efficiency. However, it should be noted that there is an abrupt change of permittivity (ε0 = 1 → εLN = 28) at the sidewall of the ridge LN waveguide. According to the boundary conditions of electromagnetic field, a drastic drop of the electric field intensity inside the LN waveguide will happen when the external electric fields aligned along the z-axis extend into the inside of the LN waveguide from air cladding, as shown in Fig. 3(a), which means that a larger t2 will result in a lower EO efficiency. Therefore, there must be an optimum etch depth to achieve a trade-off between a maximum optical confinement and a maximum EO efficiency.
Fig. 3. (a) Simulated external electric field. (b) Metal-induced optical propagation loss for different ge from 2.0 to 8.5 μm at different etch depth t2. (c) Electrodes gap ge extracted from (b) and the corresponding Vπ·L.
To this purpose, we first derive the expression for the EO efficiency (Vπ·L). Due to the EO effect of LN, the change of refractive index caused by the external electric field is:
where Em is the external electric field along the Z-axis. Δn can be treated as a perturbation to the waveguide. Based on couple-mode theory, the optical field Eo is the solution of the coupling equation below: where χ is the self-coupling coefficient. The optical field Eo can also be written as: where Eo(0) is the optical field at the input of the modulation region, β is the propagation constant of the fundamental TE mode in ridge LNOI waveguide, Δβ is the change of the β caused by the external electric field. Comparing Eq. (2) and Eq. (3), we can deduce that Δβ is equal to χ. Thus, Δβ can be expressed as:3.3 Travelling-wave electrodes
The modulation performance of the LN EO modulator is mainly affected by three parameters: velocity mismatch between the microwave and optical mode (Δn = Nm - No), characteristic impedance Z0, and RF loss of the CPW electrodes [3]. Adopting the theoretical model given in [28], these three parameters of the designed CPW electrodes with dimensions: wc = 10 μm, wl = 20 μm, te = 1.5 μm and ge = 3.6 μm can be calculated using COMSOL.
It can be observed in Fig. . 4(a) that the percentage of index difference defined as Δn/No is less than 5% at f > 20 GHz (No = 1.7888), which means that the proposed modulator has potential to realize ultra-high-speed modulation as predicted in Section 2. As shown in Fig. 4(b), the impedance is close to 50 Ω at f > 25 GHz, while the RF loss is kept less than 12 dB·cm-1 up to 200 GHz. Finally, the frequency responses can be derived from these three parameters. The results are shown in Fig. 4(c). It is evident that the length of electrodes L has significant impact on the modulation bandwidth. For L = 15 mm, the 3 dB bandwidth is ∼40 GHz. For L = 10 mm, the 3 dB bandwidth is larger than 80 GHz. Theoretically, at the cost of increasing drive voltage, further reducing the lengths of the electrodes could realize ultra-high-speed modulation.
Fig. 4. (a) Calculated microwave index and the percentage of index difference Δn/No. (b) Calculated characteristic impedance Z0 and RF loss. (c) Calculated frequency response for different lengths L of CPW electrodes.
4. Insertion loss analysis
In considering that the optical mode in the modulation region is stable and an LNOI MZI modulator with on-chip optical loss of less than 0.5 dB is possible based on the technology in [16], thus the insertion loss of our proposed all-fiber modulator is dominated mainly by the light coupling and propagation in other four regions, including R1, R2, R4, and R5. In view of this, we employ a simplified model with removal of the modulation region, as shown in Fig. 5, to simulate the light coupling and propagation through these four regions with a three-dimensional finite-difference beam propagation method (3DFD-BPM) (BeamPROP, RSoft). Here, the aforementioned waveguides parameters of w = 0.88 μm, t1 = 200 nm, t2 = 300 nm, and t = 500 nm are used and two cases of g = 1.0 μm and 2.0 μm are investigated. According to the calculated results shown in Fig. 2(d), L1 is designed to be 300 μm for g = 1.0 μm and 450 μm for g = 2.0 μm, while L2 is designed to be 200 μm for both cases. For these two cases, when the TE polarized LP01 mode is launched into the D-shaped fiber core, the simulated light propagations through these four regions are presented in Figs. 6(a) and 6(b), respectively.
Fig. 5. Simplified model for simulation of the light coupling and propagating in R1, R2, R4, and R5 regions.
According to the simulated normalized optical power in the D-shaped fiber core, shown in Figs. 6(a) and 6(b), one can deduce that the light is coupled into the thin strip LN waveguide in input coupling region R1 and coupled back into the fiber core in output coupling R5 with a high coupling efficiency and a low mode transition loss as expected. For the case g = 1.0 μm shown in Fig. 6(a), the normalized output power of the fiber is 0.746, indicating an insertion loss of 1.27 dB, while for the case g = 2.0 μm shown in Fig. 6(b), the normalized output power of the fiber is 0.803, indicating an insertion losses of 0.95 dB.
Fig. 6. Simulated light propagation through the simplified model for (a) g = 1.0 μm and (b) g = 2.0 μm when the TE polarized LP01 mode is launched into the D-shaped fiber core. Mode 0 indicates the normalized power in the fiber.
It can be observed in both Fig. 6(a) and Fig. 6(b) that there is some fluctuation of the mode field, which can be attributed to the residual weak coupling between the ridge LN waveguide and the fiber. According to couple-mode theory, the coupling coefficient is decided by the overlap of the mode fields. When the gap between the fiber core and the LN waveguide increase from 1.0 μm to 2.0 μm, the mode fields overlap will decrease. Thus, compared with Fig. 6(a), the fluctuation become significantly lower in Fig. 6(b). Moreover, the reduction in the loss can also be attributed to the fact that with the expanding of the gap, the light propagation becomes steadier. Further, in considering the loss in modulation region, it is possible for our proposed all-fiber LNOI modulator to achieve a low insertion loss of less than 1.5 dB.
5. Conclusions
We propose a low-insertion-loss thin film LN EO modulator using all-fiber configuration. The proposed device is formed with the LNOI bonded on the D-shaped fiber, which consists of different waveguide types being used to realize various critical functionalities, including light coupling, mode transition, and light modulation in combination with CPW electrodes. These waveguides could be designed meticulously to achieve their respective optimal performance. The frequency response of the proposed modulator is evaluated by investigating the characteristic parameters of the designed CPW electrodes with COMSOL, while the insertion loss is evaluated by investigating the light propagating in the design coupling and transition regions with 3DFD-BPM. The results show that the proposed all-fiber modulator is capable of achieving a lower insertion loss of less than 1.5 dB, an EO modulation efficiency of 2.05 V·cm, and a modulation bandwidth of larger than 80 GHz. Our all-fiber LNOI modulator is feasible in practice. And the proposed integration of fiber and thin film LN enables low-insertion loss LNOI photonic devices and opens a new door to realize high-speed fiber devices.
Funding
Wuhan National Laboratory for Optoelectronics (2019WNLOKF001); Fundamental Research Funds for the Central Universities (ZYGX2017J050); National Natural Science Foundation of China (61177054); Key R & D Program of Sichuan Province (2020YFSY0003); Open Fund of the State Key Laboratory of Integrated Optoelectronics, China (IOSKL2018KF12).
Disclosures
The authors declare no conflicts of interest.
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