**2. Theory, Fabrication, and Performance of a Ti: LiNbO3 YBB-MZI Modulator**

#### *2.1. Device Theory*

The YBB-MZI modulator consists of a 3 dB directional coupler at the output and has two complementary output waveguides, as shown in Figure 1. A dipole patch antenna was placed around the arm of the MZI structure to detect the electric field.

**Figure 1.** Schematic diagrams and dimensions of (**a**) a Ti: LiNbO3 1 × 2 Y-fed balanced-bridge Mach–Zehnder interferometer (YBB-MZI) modulator and (**b**) a dipole patch antenna.

The operating characteristics of a 2 × 2 directional coupler are represented by the coupling length *Lc*, the coupling coefficient κ, and the wavenumber β of the waveguide. If the transmission loss is ignored, the transfer matrix of a directional coupler is expressed by [20]:

$$
\left(\frac{\overline{E\_{01}}}{\overline{E\_{02}}}\right) = e^{-j\beta L\_{\text{c}}} \begin{pmatrix} \cos \kappa L\_{\text{c}} & -j \sin \kappa L\_{\text{c}} \\ -j \sin \kappa L\_{\text{c}} & \cos \kappa L\_{\text{c}} \end{pmatrix} \begin{pmatrix} \overline{E\_{i1}} \\ \overline{E\_{i2}} \end{pmatrix}.\tag{1}
$$

where *Ei*1, *Ei*2, and *E*01, *E*<sup>02</sup> are the input and output optical modes, respectively. The incident single-mode optical-wave is equally divided in two by a 3 dB power splitter located at the input stage and can be expressed as follows:

$$
\overline{E\_{i1}}\,\,\,\overline{E\_{i2}} = \,\,\frac{1}{\sqrt{2}}e^{-j\,0} \tag{2}
$$

where θ is the initial phase.

The dipole patch antenna with an electrode, as shown in Figure 1b, creates an electric field on one of the two arms of the MZI, which eventually induces a change of the refractive index and an unbalanced modulation. Before going into the output directional coupler, the optical wave in the two arms has an extrinsic phase mismatch Φ(*Ee*) due to the detected electric field. This phase mismatch Φ(*Ee*) can be expressed as

$$
\Phi(E\_{\mathfrak{c}}) = \pm \frac{\pi}{\lambda} n\_{\mathfrak{c}}^3 \gamma\_{33} \Gamma l\_{\mathfrak{c}} E\_{\mathfrak{c}} \tag{3}
$$

where *le* is the length of the electrode connected to the dipole patch antenna, *r*<sup>33</sup> is the electro-optic coefficient of lithium niobate (~30 pm/V), λ is the optical wavelength, *ne* is the extraordinary refractive index of lithium niobate, *Ee* is the electric-field strength through the waveguide, and Γ (0 < Γ < 1) is the overlap integral between the applied electrical field and the optical wave. Therefore, the optical-wave going into the output coupler can be represented as

$$\overline{E}\_{i1} = \frac{1}{\sqrt{2}} e^{-j(\theta + \Phi(E\_\varepsilon))} \tag{4a}$$

$$
\overline{E}\_{i2} = \frac{1}{\sqrt{2}} e^{-j\theta}.\tag{4b}
$$

Combining (1) with (4), the output power of the YBB-MZI modulator is expressed as

$$P\_{01} = \frac{1}{2} [1 + \sin(\pi y) \cdot \sin(\pi x)] = \frac{1}{2} [1 + \sin(2kL\_c) \cdot \sin(\Phi(E\_t))] \tag{5a}$$

$$P\_{02} = \frac{1}{2} [1 - \sin(\pi y) \cdot \sin(\pi \mathbf{x})] = \frac{1}{2} [1 - \sin(2kL\_c) \cdot \sin(\Phi(E\_c))] \tag{5b}$$

where *x* = Φ(*Ee*)/π is the normalized phase-mismatch, *y* = *Lc*/*lc* is the normalized coupling length, and *lc* = π/2*k* is the coupling conversion length.

The output intensity *P*o1 is simulated and plotted for the YBB-MZI electric-field sensor, as shown in Figure 2. The YBB-MZI sensor shows a sinusoidal transfer function for different y-values. The value of y only affects the extinction ratio, which can be represented as sin(π*y*). For most cases (where sin(π*y*) - 0), the transfer function is acceptable as the extinction ratio only impacts the E-field measurement sensitivity. To support the maximum sensitivity, the coupling length should satisfy the condition

$$
\sin(2k \cdot L\_c) = 1,\tag{6}
$$

where *<sup>k</sup>*·*Lc* <sup>=</sup> (2*n*+1)<sup>π</sup> <sup>4</sup> ,( *n* = 0, 1, 2, ...) .

#### *2.2. Designs and Fabrication*

Using single-mode Ti:LiNbO3 channel waveguides, a symmetric 1 × 2 YBB-MZI modulator with a dipole patch antenna was designed for operation at a wavelength of ~1.3 μm in an x-cut, y-propagating LiNbO3 substrate, as shown in Figure 1. The device consists of a Y-branch splitter, a phase modulator, and a directional coupler. The entire device's structure is similar to that of a Mach–Zehnder interferometer with two output ports. The waveguide width is 7.5 μm for single-mode operation, and the splitting angle of the Y-branch is 0.6◦ for decreasing the propagation loss as low as possible and for fabrication tolerance. The gap interval between the two adjacent waveguides of the directional coupler and the parallel coupling length are 5 μm and 2.8 mm, respectively, to split

the optical power equally into two output channels with a nominal coupling constant-length product, κ·Lc of π/4. The interval between the inner edges of the two output waveguides is 50 μm, thereby preventing optical power coupling between the two output channels. As shown in Figure 1b, the gap and length of the modulation electrode connected to the dipole patch antenna are 12 μm and 10 mm, respectively. The results of the BPM-CAD 3D simulation of the optical wave propagating through the YBB-MZI modulator are shown in Figure 3 [21]. When no voltage was applied, the two intensity profiles were approximately identical, with ~1% or lower accuracy because of the nearly equal intensity splitting, as shown in Figure 3a. Therefore, the YBB-MZI modulator was intrinsically set at the 3 dB half-power point. While the driving voltage increased to 5 V and 10 V, the light in the lower branch of the device was coupled with the upper branch, where the light intensity of the lower branch decreased and the intensity of the upper branch increased, as shown in Figure 3b,c. When 10 V was applied, the light of the lower branch almost disappeared, and the light intensity of the upper branch reached the highest level. Therefore, it could be theoretically confirmed that the switching voltage required to modulate the light intensity of either branch from a bar state (maximum intensity) to a cross state (minimum intensity) was ~10 V.

**Figure 2.** Simulation results for the light output intensity versus driving voltage with y = 0.2, 0.5, 1, and 1.3.

An investigation of the formation of optical waveguides in LiNbO3 by metal ion diffusion indicated an increase or decrease in the refractive index depending on the valence of the in-diffused ion. Higher-valence ions such as Ti3<sup>+</sup>, Fe3<sup>+</sup>, and Cr3<sup>+</sup> increase both the ordinary and extraordinary indices. It appears that lower-valence ions replace Li<sup>+</sup> sites, while higher-valence ions replace Nb5<sup>+</sup> sites. Experimental results indicated that the in-diffused Ti metal in LiNbO3 was all tetravalent (i.e., Ti atoms are fully ionized). There are no electrons in particularly filled d-orbitals to absorb the electromagnetic energy at visible wavelengths. This explains the measurement of low losses of waveguides fabricated by Ti diffusion into LiNbO3 [22–24]. The dominant sources of waveguide loss are scattering from LiNbO3 surface imperfections due to diffusion and possibly absorption by the metal ions.

The 1 × 2 YBB-MZI waveguide structure, as shown in Figure 1a, was fabricated on an x-cut, 3-inch, 1-mm-thick LiNbO3 wafer as the substrate using UV photolithography and thermal diffusion. First, a 1050-Å-thick Ti-film on the LiNbO3 substrate was deposited by an e-beam evaporator, and then the desired Ti-film patterns with 7.5 μm widths were formed by photolithography and the wet-etching process, followed by thermal diffusion for 8 hours at 1050 ◦C in wet-ambient. The resulting Ti-diffused channel waveguides grew to a thickness two or three times that of the Ti-film stripe. Such surface growth makes it easy to observe Ti-diffused waveguides with a microscope, as shown in Figure 4. Furthermore, the diffused waveguide has Gaussian index profiles in its depths. The effective index increases in linear proportion to the Ti film's thickness. This feature indicates that the propagation constant of the fundamental mode can easily be controlled by changing the film thickness alone.

**Figure 3.** Three-dimensional BPM-CAD simulation results with the following applied voltages: (**a**) 0 V, (**b**) 5 V, and (**c**) 10 V.

**Figure 4.** Photograph of the implemented device with pig-tailed optical fibers. W/G is the abbreviation for waveguide.

The waveguide edges were optically polished to allow butt-coupling and pig-tailing. A silicon dioxide buffer layer with a thickness of ~3000 Å was deposited on the substrate using an electron beam and 99.99% pure SiO2 pellets to reduce the propagation loss due to the absorption of the light wave of the antenna's metal. An aluminum dipole patch antenna and electrode ~5000 Å thick (as shown in Figure 1b) were formed along one of the two arms of the YBB-MZI to allow sensing of the electric field. A polarization-maintaining single-mode optical fiber and multi-mode fiber were attached to the input and output waveguides, respectively. Figure 4 shows a photograph of the implemented device with the attached optical fibers and a dipole patch antenna. The insertion loss of the device, including the input/output fiber, was measured to be about 11.7 dB, which includes the fiber-connector loss, pig-tailing loss, mode-mismatch loss, and propagation loss of the waveguides.
