Symmetric longitudinal Mach-Zehnder modulator using lithium niobate

ABSTRACT


INTRODUCTION
Lithium niobate (LN) contains preferred specifications among other materials. The broad transparent band of LN fabric provides about 4.6-340 µm that can be applicable for a variety of applications in visible to mid infrared wavelength windows [1]- [3]. Soft dispersion with lower absorption losses of smaller than 0.15%/cm can be achieved through the wavelength of 1.06 µm. Consequently, LN is becoming essential for challenging implementations such as modulation of wideband devices of high-bit long haul optical telecommunications [4], body of LN [5], [6] that extends for greater broadband frequencies, in the Mach-Zehnder interferometer (MZI) configuration, and modulators of imprinted LN [7]- [9]. Lately, LN insulator membranes (LNOI) have appeared as a promising platform for forming well-contained waveguide devices (i.e., better confinement factor) [10]- [12]. Meantime, LNOI modulators with ultra-high EO bandwidth and low drive voltage have recently been established [13], [14]. Non-centrosymmetric fabrics are well recognized for exhibiting second-order electrical sensitivity. Electro-optic effects together with nonlinear effects and Pockel effects were used for a wide spectrum of applications such as quantum photonics, devices of optical communications, safety, aviation, and biology [15]- [18]. LN is utilized in many applications because of the big second-order electrical sensitivity, among other things, which can afford effective and high-speed modulation for electro-optic systems [19]. In comparison to LN [17], silicon nitride SiN is centrosymmetric, affecting pockel-based modulation in the waveguide center itself [20], [21]. Moreover, compared to semiconductors that electrically modulate light absorption across the impact of Franz-Keldysh, the modulator of LN modifies the intensity of light without phase disturbance, i.e. without chirping. Thus, despite the excellent achievements of semiconductors in systems of short-haul telecommunications, the modulation with no chirping supplied using LN-based parts remains protected through its transmission of high-bit rate optical signal via long-haul telecommunication [22], [23]. It has been shown, for almost two decades, that after surface stimulation [24], [25], the silicon surrounded the fabric of the thin substratum of the LN, and several accounts of the modulators by thin substratum LN were released by electro-optic effect [7], [13], [26]. Complicated wave guiding systems can be constructed with one surrounding coating and various perpendicular changes. That can be done by utilizing one silicon coating lithography to regulate the light route below the surrounding LN area in addition to the two ends of sides of the surrounding region [27]. Controllable resonator rings [28], switches [26], modulators in separate phases [29]- [31], and MZI [32], [33] are noteworthy instruments using the elevated variation of the index which used a thin substratum of the LN. Different hybrid systems, which depend on Si3N4 or Si [18], [34] to load and guide an optical mode, are developed by conjunction. A prevalent theme among these systems owns a decreased mode volume. Therefore, it results in significantly increased electro-optical efficiency in comparison to its predecessors in large volumes. Then, a half-wave voltage is mainly reduced. Thus, the significantly reduced application of perfect footprint is an advanced optic technique. This is due to the reduced products of half wave voltage duration combined across the ability to control the variance of high indexes of guides. In addition, the thin substratum of the LN up to this point is the material system's considerably reduced permittivity and this is the main advantage of this technique [31], [35], [36]. Rao and Fathpour [14] intended a theoretical work by LN for the MZI modulator. This modulator worked with deferential arm lengths of approximately 2 and 10 cm, with a low half wave voltage of about 1 volt. This reference used a large length of arms (i.e., length of arm in cm) reflecting a large size device and a low applied half-wave voltage.
In this paper, the LN symmetrical push-pull MZI modulator is introduced with different lengths of the arm of approximately 2, 3, and 10 mm. Therefore, the presented design offers a low small size device with a low half-wave voltage of about 1.2 V. The size of the length arm of MZM is an effective factor because decreasing the length of the arm due to increasing relative refractive index difference leads to achieving better modulation. The previously mentioned reference used a length of arm in cm, while this paper uses the length of arm in mm. At the same time, the proposed design in this paper uses a wide window of optical wavelength from visible-to-infrared (i.e, 633-1560 nm), while in the compared reference a wide window of optical wavelength is not applied. Moreover, in [14], the arms are equal in length or not imbalance and hence the delay time is never inducing between arms, and the optical path difference between arms is the same and the optical delay is not found.

RESEARCH METHOD 2.1. Symmetrical push-pull MZIM
A MZI push-pull modulator is symmetric because the length of the arms for the waveguide are equal in length. Therefore, the optical path difference for arms is the same. An applied voltage is driven on both sides of the waveguide (i.e., dual drive voltage), accordingly, the MZIM is called a push-pull, as shown in Figure 1. In this work, the longitudinal modulator is introduced so that the mechanism of this modulator is represented by applying a voltage in parallel to the direction of the transmitting light in the modulator. The fundamental concept of an electro-optic device changes the optical properties of a material with an applied voltage [37]. These changes result in a change in the refractive index ∆n of material by applying an electric field on the material of crystal [38].
is the ordinary refractive index, r is electro-optic coefficient, and E is the electric field for longitudinal modulator = V , where V is applied voltage and L is the length of arm for MZM modulator. A technique of phase modulator (longitudinal phase modulator) is presented in this study, as shown in Figure 2. Where an electrical field is applied across the axes of the crystal. The polarized light along the axis suffers from the change of refractive index, which is related to the applied electrical field. Therefore, phase modulation induces, and the phase shift can be calculated using [38].
Where ∆Ø is a phase difference, λ is the optical wavelength, ∆n is relative refractive index difference, and L is the length of the arm modulator. Thus, the ∆∅ for longitudinal phase modulator is [29].
Where, no 3 is the ordinary refractive index, r is the electro-optic coefficient and V is the applied voltage. The half-wave voltage is the voltage required for a 180° phase change (i.e. ∆∅ = ). Therefore, the half-wave voltage for the ordinary longitudinal phase modulator is [38].  Table 1. In this modulator design, three regions of wavelength are accomplished: (632.8-634) nm and (646-647.5) nm, using a short-haul application. In addition, the long-haul applications achieved by the window are 1550-1560 nm. The refractive index difference depends on a low applied voltage and large wavelength.

Mathematical model
In the MZI modulator, the incident light is split into two components (I1 and I2) with symmetric arm lengths (i.e., L1 and L2 are the same length). The components are combined on the end of the device (i.e. In (6), for the longitudinally uniform push-pull modulator is [38]: Where, Iout is the output laser power in watts, Io is initial laser power in watts, neff is the effective refractive index, 4 is the extraordinary refractive index, and Γ is the confinement factor. Hence, The term "△ ∅" is the complex phase difference in which a power absorption loss α dB/mm can be considered [42]. Also, Δ is the phase shift of the modulator with the effect of an electric field, and fm is a modulation bandwidth.
Where, neff =ne, reff is effective electro-optic coefficient, E is electric field, and Lm is length of arm modulator.
The substitution of in (5) These (16) and (17), reflect the model of modulation output power and output optical power, respectively, for the MZI modulator. In this paper, we used MATLAB 2018b simulation. Where the initial power laser Io is 100 W, and the length of the arm modulator is about 2-3 mm, and 10 mm. The confinement factor Γ is 10^-4 to 1 unit less [43]. The relative refractive index difference ∆n 0.009 to 0.01, effective refractive index neff is 1.0688 to 1.1011. The power absorption loss α is 0.085 to 0.12 dB/mm for L is 2, 3 mm, and α is 0.02 dB/mm for L is10 mm, also see Table 1.

RESULTS AND DISCUSSION
This paper suggests a mathematical model for a symmetric longitudinal push-pull MZIM. This modulator can work with a wide window of wavelength which considers the best application for high-speed optical communication systems. This device can be used for different regions of light including a visibleinto-infrared region as a window (632.  nm. The presented structure shows improved modulation specifications that can convey optical signals through short or long-haul optical communication. A wavelength window (1550-1560) nm is very helpful as the optical modulated signal transmission can operate with high-quality modulation. The window is characterized by low dispersion and attenuation. Also, two windows of wavelength (632.8-634) nm and (646-647.5) nm are used with a length of modulator 2-3 mm and 10mm respectively. These windows are used for modulation of the optical signal via transmission of short haul. Therefore, the effect of attenuation and dispersion can be reduced. The small length of the modulator arm leads to a large relative refractive index difference and lower applied voltage V leading to a higher quality of modulation. The best modulation is achieved when the length of the arm is 2-3mm, if compared with 10 mm, as in (18) [44], [45] (see Figures 3(a) and (b), Figure 4, and Figures 5(a) and (b)).  The refractive index difference depends on a low applied voltage and large wavelength, as in (19) and (20) [38]. The refractive index can be changed due to the control of phase modulation where the phase difference induces between arms. After this change, the induced phase shift converts from phase modulation into intensity modulation. Consequently, the phase shift depends on the applied voltage V and length of modulator arms L. In another case, the applied voltage V induces phase modulation without intensity modulation by an input polarizer. Hence the applied voltage V works as on or off. If V is on, the voltage applied and phase modulation induces, and otherwise, if the V is off, the phase modulation is not induced. The half-wave voltage Vπ is considered the small part of applied voltage V. When the Vπ decreases to a smaller value, this results in high quality of modulation because the half-wave voltage Vπ is an effective factor to improve the electro-optical device. Thus, the operation half-wave voltage used in the value of 1.2 V.
The driving voltage for the modulator represents a suitable value (i.e., 250 V) as it gives a better performance for the modulator using a half-wave voltage about 1 V or ≤2 V. This is considered a low power for a modulator with plan an MZIM. It can use an applied electric field of at least 233 V/mm, and a driving voltage about 100 V. In Figures 6 and 7, a window of wavelength (633-647) nm is used, with a length of arms L of (2-3) mm. In Figures 8 and 9, a window of wavelength (633-1560) nm is used with a length of arms L of (2-10) mm. In these two cases, the effective factor is the wavelength. Decreasing the wavelength leads to decreasing the applied voltage and half-wave voltage. Therefore, the refractive index also increases to result in a high-quality phase-modulation or intensity modulation, as (20). Furthermore, increasing the refractive index results in a low driving voltage and better performance of the optical modulator. Thus, Figures 6 and 7 are considered a better case of the optical modulators because the case is the real and imaginary parts. In addition, the operation half-wave voltage started from an approximate value of 0.8 V which is a smaller value of half-wave voltage Vπ, (i.e., approximately 1.2 V). Also, the optical confinement factor can be used to measure the size of the overlap between the optical field and the electrical field by changing the index of refraction of the LN material through a certain length of the modulator. Utilizing a good confinement factor (large overlap) of about ≤1 unitless, good performance of the modulator can be achieved with a length of the modulator of about 2 mm with applying an electric field of 175 V/mm. Moreover, it achieves an electric field of 233 V/mm by it is poling about 100 V as shown in Figure 10. Eventually, the contribution of this work is to design asymmetric longitudinal MZM by improving the modulation technique. Further, it used a wide window of wavelength from visible-into IR and used a length of arms in mm, see Table 2.

CONCLUSION
This paper presented a mathematical model to solve the problems of a narrow window of wavelength for MZM, a large half-wave voltage, and a small optical confinement factor. This designed model was applied using a symmetric push-pull MZIM based on LN material. The proposed structure achieved a wide window of wavelength of 632.8-1560 nm or visible-to-infrared. Furthermore, in this modulator design, three regions of wavelength are accomplished: (632.8-634) nm and (646-647.5) nm, using a short-haul application. In addition, the long-haul applications achieved by the window are 1550-1560 nm. The three windows give a better modulation performance as they give lower attenuation and dispersion. The modulator's accomplishments of better performance and high efficiency also reflected smaller operation halfwave voltage which is about 1.2 V. Where the applied voltage is an appropriate value (i.e. 250 V), by poling on the arms of the modulator. Also, it creates an applied electric field of 233 V/mm by a poling voltage of 100 V. Thus, a good confinement factor of ≤1 (i.e, large overlap) can be obtained when utilizing a small length of the modulator of about 2 mm, and an electric field of 175 V/mm because the large overlap occurs with good tuning between the intensity of light and electric field.