2. Design and Simulations
The proposed modulator consists of an optical waveguide in a traveling-wave electrode (TWE) MZI configuration and ground–signal–ground (GSG) Au coplanar microwave electrodes. The optical path includes the input and output mode spot conversion structures, MMI (Multimode Interference Coupler) structures for beam splitting and combining and modulated single-mode optical waveguides. All these structures were prepared on a lithium niobate platform.
Figure 1a shows a schematic diagram of our nanophotonic LN modulator.
Figure 1b,c shows the cross-sectional and top views of the electrodes. The refractive index contrast between the lithium niobate core and the SiO
2 cladding is Δn = 0.67, which is an order of magnitude higher than that of the ion-diffused lithium niobate waveguide. The highly constrained optical mode allowed us to place gold RF electrodes close to the lithium niobate core. This results in a lower operating voltage. LNOI uses an X-cut 525 μm thick high-resistance quartz substrate, 2 μm SiO
2 insulation layer and 360 nm thin-film LN. The maximum electro-optical tensor component (
) of LN mediates the interaction between the transverse electric (TE) optical mode and the in-plane electric field (E
z). The top width w, ridge height h and plate thickness s of the ridge optical waveguide are 1.5 μm, 180 nm and 180 nm, respectively. The electric field strength increases as the electrode spacing decreases, but too close a distance between the electrodes and the waveguide will result in larger metal-induced absorption losses. To increase the electro-optical interaction in the modulation region, we performed design work on waveguide geometry and RF electrode location. The purpose was to achieve the best overlap between the light field and the electric field. The spacing between the RF signal electrode and the ground electrode was set to 3 μm. We used a TO phase shifter made of NiCr heating resistor material to control the phase difference between the phase arms of the modulator, thereby achieving control of the DC bias point of the modulator. This reduced the amount of drift. We also used silica material as the cladding. The thickness of the covering layer of SiO
2 was set to 800 nm.
We observe that, in practice, bandwidth and voltage performance are limited by the following four key factors: first, microwave losses in the transmission line cause the driving voltage to decay over the electrode’s length; second, design trade-offs cause a reduction in electro-optical modulation efficiency; third, design trade-offs reduce modulation efficiency per unit length, requiring larger device sizes to achieve low drive voltages, further limiting bandwidth; and finally, impedance mismatch between the device and external circuitry can also cause problems, such as reflections, and the driving voltage deteriorates. In other words, in order to achieve a high bandwidth and low voltage for the LN modulator, the microwave loss (i.e., the attenuation of the current flowing along the traveling wave direction) should be as low as possible; the effective index of the RF signal should match the group index of the optical signal [
20]; the electric field strength between the signal electrode and the ground electrode needs to be strengthened to facilitate effective matching and accumulation of the modulation phase along the traveling-wave direction; and the LN modulator should match the impedance of the external drive circuit to effectively transmit power to the transmission line.
There are two main sources of microwave electrode loss, namely the absorption loss of the substrate and the ohmic conductor loss. Ohmic losses are caused by the finite resistivity of metals and are the dominant loss mechanism in existing thin-film LN modulators. T-shaped traveling wave electrodes with microstructure can allow electrodes to be more evenly distributed over the electrode area. At the same time, it can effectively limit the current within the electrode area and will not enter the electrode gap. This increases the effective conductor area and reduces ohmic losses. Microwave transmission losses are reduced, resulting in greater bandwidth.
We also need the effective refractive index of microwaves and the group refractive index of light waves to be as close as possible. This means that microwaves can travel along transmission lines at the same speed as light waves. Compared with traditional rectangular electrode designs, the microwave speed of segmented electrodes is significantly reduced, known as the slow-wave effect. This is due to the increase in capacitance per unit length of the segmented electrode during each cycle. Therefore, by fine-tuning the size of the T-shaped segmented electrode, the capacitance value per unit length of the electrode can be changed. In addition, the slow-wave effect is used to accurately match the microwave phase velocity and optical group velocity. However, for thin-film LN on a SOI substrate, additional capacitance is introduced due to the T-shaped electrode structure and the slow-wave effect caused by the silicon substrate. These two points together cause the microwave phase velocity to be smaller than the optical group velocity. At this point, the slow-wave effect will cause the velocity mismatch to reappear. Therefore, we use a substrate with a lower dielectric constant, namely a quartz substrate, to reduce the adverse impact of the slow-wave effect.
Therefore, segmented structures can be designed to achieve precise matching of microwave speed and light-wave speed. The equivalent circuit of the transmission line is shown in
Figure 2. R, C, G and L in the figure are the impedance, capacitance, conductance and inductance of the coplanar waveguide per unit length, respectively. ΔR and ΔL are the impedance and inductance per unit length due to the periodic grooves. According to the theoretical analysis of transmission lines [
21], the characteristic impedance Z
c and microwave index n
m are
where c is the speed of light in vacuum,
is the angular frequency and
,
and
are the attenuation constant, phase constant and propagation constant, respectively.
At frequencies above 10 GHz, inductance and capacitance become dominant in (1) and (2) (
and
); then, we have:
Figure 3 shows the top and partial views of the segmented electrode with the design parameters marked. It can be seen from Equation (4) that the periodic electrode gap will cause an additional inductance ΔL, which will significantly increase the microwave index. That is, the periodic electrode gap can slow down the speed of the microwave signal, thereby achieving wave speed matching. We set the target value of Z
c to 50 Ω and then modified the nm value to match the optical index ng. Therefore, the demand values of L+ΔL and C can be calculated by Equation (4). When the electrode gap width is determined, the value of C is mainly affected by the width of the signal electrode. C can be accurately calculated by conformal transformation and quasi-TEM analysis [
22]. Then, with C and L known, appropriate parameters can be chosen to obtain the desired ΔL. However, the electromagnetic field in the gap region is not quasi-TEM mode. At the same time, the fringe field around the edge of the gap is complex. Therefore, it is difficult to obtain analytical formulas for ΔR and ΔL. In previous studies on capacitively loaded segmented electrode structures [
13,
15], the precise value of capacitive load was obtained by fitting the model with experimental results. Here, in order to obtain accurate values of ΔR and ΔL, a commercial 3D electromagnetic simulator is used to perform numerical finite element simulation.
The height of the electrode was set to 0.9 μm. This was determined through the process. We first used SI9000 software V7.1.0 to calculate the widths of the signal electrode and the ground electrode which were w = 42 μm and Wg = 80 μm, respectively. At this point, the impedance of the electrode is approximately 50 Ω. The two parameters of signal electrode trench length PT and width w have a significant impact on microwave parameters. Therefore, they are the main variable parameters in our design. Other parameters involved in the electrode structure were preliminarily set as follows: PT = 50 μm, WT = 3 μm, GT = 3 μm, t = 2 μm, ST = 3 μm. It is worth noting that if a larger microwave effective refractive index needs to be achieved, a larger gap width GT and a smaller period PT may need to be selected. The reverse is also true.
The segmented structure is designed to achieve precise matching of microwave speed and light-wave speed. The key to obtaining the required nm is to choose appropriate LT and w values. In addition, it is worth noting that as the width of the signal electrode increases, the slot inductance ΔL decreases rapidly. But capacitor C rises much more slowly. Therefore, contrary to conventional CPW, the microwave index nm of the segmented electrode structure does not increase but decreases with increasing signal width.
We simulated the S-parameters and microwave refractive index of multiple sets of structural parameters through finite element analysis and ultimately determined the parameters as follows: P
T = 50 μm, L
T = 47 μm, G
T = 3 μm, t = 2 μm, W
T = 3 μm, S
T = 3 μm. The results are shown in
Figure 4. According to the analysis of the optimization results of TWE, the RF group index value is approximately equal to the group index of the LN waveguide, achieving accurate rate matching. In the 0–80 GHz frequency range, the microwave RF index is 1.97. The design simultaneously achieves extremely low attenuation (α) and a characteristic impedance (Z
0) match of nearly 50 Ω to reduce RF reflections.
On the other hand, since the design of the optical waveguide and microwave electrode will affect the electro-optical modulation after an electric field is applied, in order to achieve matching of the microwave light-wave mode field, the modulation arm cross section needs to be analyzed. After the electrode is designed, the phase shift caused by the external electric field is related to the overlap integration factor of the electric field and the light field, which means that the relative position of the electrode and the waveguide will have a great impact on it. To increase the electric field strength in the waveguide, we placed electrodes on the flat plate of the LN ridge waveguide. The modulation efficiency of the electrodes increases as the electrode spacing decreases, but the electrode spacing cannot be reduced infinitely. When metal is close to the waveguide area, the metal will produce an absorption effect on the light waves. This further increases the transmission loss of the waveguide. We chose the electrode spacing to be 3 μm, at which the metal absorption mode does not appear.
Metal-induced optical loss varies with the cladding thickness in the area where the waveguide and electrode overlap. The loss is not significant when the cladding thickness exceeds 800 nm, so the cladding thickness of this structure was set to 800 nm. Furthermore, replacing the air cladding with silica cladding improves the electric field distribution inside the waveguide, thereby increasing the electro-optical interaction efficiency. We set the modulation length to 8 mm and the entire device length to 10 mm to achieve a lower drive voltage.
Figure 5 shows the electric and optical fields in the waveguide. The corresponding Γ = 29.40%. The calculation method can be found in the references [
23].
Instead of using a DC electro-optical bias controller, we used a TO bias controller built into the LN part shown in
Figure 1a. LN has a thermo-optical effect (dneff/dT = 3.34 × 10
−5 K
−1 at 1523 nm and 300 K wavelength) [
24]. In addition, due to the inherent piezoelectricity and pyroelectric effect of the material, LN will experience DC bias point drift when a static electric field is introduced. This is widely recognized. Feedback compensation control is more complex, but the pyroelectric effect will not be affected by this. The TO solution also eliminates the need for RF bias tees, making packaging and testing more convenient. We can clearly see the advantages of the TO bias controller. Not only is it small in size and high in efficiency, but it can also greatly improve the stability of the bias point and effectively solve the problem of bias drift. This TO bias controller is constructed from two materials. Lithium niobate serves as the waveguide, and the laterally moving heating electrode on the SiO
2 cladding is composed of nickel–chromium. Then, the change in optical phase with temperature at this time can be expressed as
where L is the device length, λ
0 is the free-space wavelength and ΔT is the temperature change. Considering that the resistor is located above the cladding, the gap between the nichrome metal and the waveguide does not cause optical loss but affects heat conduction and temperature distribution. The thickness and width of the NiCr heating resistor in the TO phase shifter were set to 160 nm and 3 μm, respectively, while the length of the overall phase shifter was set to 200 μm. And the resistance was set to 600 Ω. The corresponding power consumption corresponding to the π phase shift is about 160 mW.
4. Results and Discussion
We measured the frequency response of the designed modulator via a 67 GHz network analyzer. The results are shown in
Figure 9. The actual measured 3 dB EE bandwidth is higher than 67 GHz and the 3 dB EO bandwidth is 51.2 GHz. Next, we performed TO and EO characterization using a tunable-wavelength laser source in the communication C-band. The results are as expected. Due to the large TO coefficient of lithium niobate material, TO phase shifters show high efficiency. The V
π of a nickel-chromium heating electrode is approximately 3.5 V. The observed extinction ratio is approximately 15 dB. EO V
π measurements are made by performing a 100 kHz triangular voltage sweep across the device. The response shows a V
π of 10.25 V for the 8 mm long device.
At a wavelength of 1550 nm, the insertion loss of our packaged devices is measured to be −20 dB. This is quite different from theoretical analysis, which we believe is due to the sidewall roughness caused by etching, resulting in significant scattering loss, and the displacement of the optical fiber during the curing process, which is inevitable during packaging. Insertion loss can be reduced by improving the SSC structure and etching process.
The device underwent mechanical impact testing in accordance with GJB 548B-2005. (Test condition A: 500 g, 1.0 ms, direction Y1, five times). After the experiment, there was no significant damage to the surface of the sample, and there were no metal wires falling off or folding. The device was leak tested according to GJB 128A-1997 (Test condition D: fluorine oil, temperature: 85 °C). There were no two or more bubbles generated at the same point of the shell sealing weld, and no bubbles with increased attachment were generated. The experimental results meet the sealing performance requirements of electronic components.
In recent years, most of the reports on thin-film lithium niobate electro-optic modulators have been based on direct testing of bare chips using high-frequency probes on a coupling platform. Compared to these bare chips, the performance of our fabricated devices is not outstanding, but it is noteworthy that our devices are metal-encapsulated and have passed reliability testing, which is very rare in related reports. We believe that this work will provide guidance for researchers interested in the process of manufacturing such devices.