The optical properties of materials vary under the influence of an electro-optic caused by an electrical field which is progressively changing with the optical light. The applied electric field changes the refractive index of the exposed material using an electro-optic effect as illustrated in Figure 1 (Bea and Teich, 1991).
The performance of many devices can be degraded under such exposure. For instance, the size of the Mach–Zehnder modulator (MZM) becomes larger (i.e., the length of branches MZM is increased), the bending losses of waveguides are greater, the
In the integrated metal-diffused, the optical waveguides own a weak optical confinement factor that restricts an electro-optic exchange as a result of the lower efficiency of an electro-optic modulation and large footprints of devices (Priscilla et al., 2020). Lately, a larger optical confinement factor (big overlap) has been achieved using a uniform thin-film LN modulator integration that leads to enhancements in terms of compactness, information measure, and energy potency. This interesting technique has attracted multiple studies presented in (Tavlykaev and Ramaswamy, 1999; Zenin et al., 2012; Zenin et al., 2017Alexander et al., 2018; DeVault et al., 2018; Deshpande et al., 2018; Thomaschewski et al., 2020). However, for commercial demand, the length of the branches is still relatively long within the limit of mm-scale, because the extraction is limited within an overlap of an electro-optic field (Priscilla et al., 2020). Moreover, a photonic crystal PC (crystal is a type of a barium titanate BaTiO3) can be used as a confined device for optical light and utilized with LN-Si devices. Nonetheless, this technique has reflected a weak optical confinement factor (i.e., small overlap) because of the small amount of confined optical light (Roussey et al., 2006, 2007; Lu et al., 2012a). Indeed, this problem is solved using a film of smart-cut LN (Sulser et al., 2009; Lu et al., 2012b), where it utilized a BaTiO3 PC structure in which the confined optical light has been magnified. This approach is named as high-speed PC modulator (Girouard et al., 2017). To design a small size system in micrometer is always challenging because of the required large enough confinement factor to consequently achieve high-quality modulation. In this design, the variation value of the ordinary negative refractive index (−Δn), in which the power is −7, is good because it is close to previous results. In addition, the development of the system using as small as 3 to 8 μm length of the modulator arm, low-energy consumption of about 4 V/µm, a large negative ordinary relative refractive index difference of about—0.2 × 10−7. Therefore, from the results of combining the optical light with the electric field, the system indicates a better overlap with a sufficiently large change in the negative ordinary refractive index.
This paper employs an electro-optic effect technique based on LN Mach–Zehnder modulator (MZM), as shown in Figure 3 and Table 1. This technique has reduced the electric field and minimized the length of arms to micrometer with suitable level of refractive index and strong optical confinement factor (i.e., a large overlap).
Electro-optic coefficients (r33), refractive index (no) and wavelengths (λ), for LN.4.
|31||633||2.2864||(Casson et al., 2004)|
|25||1560||2.2108||(Casson et al., 2004)|
For the Mach–Zehnder interferometer (MZI), where the initial intensity of light Io in lum is modulated with the applied electric field
The optical wave is divided into two branches of the modulator with equal lengths and refractive indices. Since the optical path length through each branch is the same, it will have a constructive interference at the end of the arms where the waves are recombined (Figura, 2000). Figure 4 visualizes MZI electro-optic modulator based on LiNbO3.
Eq. (12) expresses the fundamental model of Mach–Zehnder modulator (MZM) in the optical communication systems. The study was designed by selecting a longitudinal optical modulator in which the electric field is
In this paper, an analytical model is proposed to enhance the optical confinement factor of the MZM based on the material of LN. The performance of the proposed modulator can be estimated by employing Eq. (12) where the techniques of electro-optic effect and electro-refractive are considered. The large energy of the optical light (i.e., high energy of light intensity) is merged with the electrical field to shape large ball lightning into the inner waveguide. The high modulation of light intensity of the modulator depends on how strong the ball lightning is and that indicates the high performance of modulating that light intensity in the modulator. Thus, the phenomena of a ball lightning are named as the overlap due to the overlapping between the electric field and the optical light where the large ball light is called big overlap (i.e., large optical confinement factor). Therefore, the large relative refractive index variation indicates a large overlap (i.e., large optical confinement factor). In this paper, it is shown that the ordinary negative change in the refractive index (Δ
In 2020, Qi and Li (2020) and in 2019 He et al. (2019), designed the integrated electro-optical devices such as the modulator using a high refractive index to increase the optical confinement factor where the lengths of the modulator’s arms are 3 mm, and 13 mm while the waveguide lengths are 0.62 cm, 1.86 cm, and 4.43 cm. Because the length of the arm is large (in mm), the changing of the refractive index is small. adding the electric field induced using a phase change is π/2 (i.e, opposite polarities). Moreover, transverse type modulator is used where the applied electric field is (Maldonado, 1995):
In this paper, used a small waveguide electrode spacing
Thus, in this paper, the electro-optic modulator is designed using a high refractive index that induces a large confinement factor. The proposed design has deployed a longitudinal modulator type in which the applied electric field can be evaluated by (Maldonado, 1995):
Furthermore, the electric field induces using a phase change is π (i.e, polarities not opposite), where it selects a suitable electric field, that induces a large changing of refractive index. Eventually, the main benefit of this work is the enhancement of the confinement factor as well as the improvement in the modulation efficiency of the modulator, see Table 2.
|(Qi and Li, 2020) and (He et al., 2019)||Large||Large In mm||Small||π/2||Large||Transvers|
|This work||Large||Small In μm||–||π||Large||Longitudinal|
In the presented results, the longitudinal configuration of the separation distance between arms (d) does not have any effect on the electric field because
The challenges and difficulties of this design are in the selection of the values of variables such as the length of the modulator arm (
The proposed structure has accomplished good performance with large optical confinement factor resulting from as small as 8 µm length of arms which consequently led to a compact MZM. The large ordinary negative changing of the refractive index when applying lower driving power of the electric field of 1–4 V/µm to the MZM has reflected better performance. With LN, the best length of arms was about 8 µm with a large negative change in the refractive index when using near-infrared and visible wavelengths with the electric field of 4V/µm.
Electro-optic coefficients (r33), refractive index (no) and wavelengths (λ), for LN.4.
The comparison between the reference paper (Chang et al., 2017; Qi and Li, 2020) and this work.
||Large||Large In mm||Small||π/2||Large||Transvers|
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