The ordinary negative changing refractive index for estimation of optical confinement factor

Ahmad S. Abdullah; Sadeq Adnan Hbeeb

Dziennik i szczegóły wydania

International Journal on Smart Sensing and Intelligent Systems

Informacje o czasopiśmie

Format: Czasopismo
eISSN: 1178-5608
Pierwsze wydanie: 01 Jan 2008
Częstotliwość wydawania: 1 raz w roku
Języki: Angielski

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).

Applied electric field along z-direction changes the refractive index of crystal.

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 Q-factor is diminished, and the size of the resonators is enlarged (Qi and Li, 2020). These performance degradations are attributed to the weak optical confinement factor (i.e., the overlap is small) resulting from the low relative refractive index variance (Yi-Yan, 1983; Korkishko et al., 1996; Cai et al., 2016). Some materials possess optical and structural properties that make them usable in many fields such as hydrogen production and wastewater treatment (Scharnberg et al., 2020). There is research concerned with studying the optical, structural, and electronic properties of some materials (Akhtar, 2022). Lithium niobate (LN) indicates the possibility to improve the overall performance of electro-optic modulators at the expense of its environmental properties. Examples of these improvements are powerful linear effect (i.e., Pockels effect), enormous transparency window, massive electro-optic coefficient (30 pm/V), and the stability of the temperature are at its best (Wooten et al., 2000). Thus, the low refractive index with large switching voltage–length product (Vπ·L, usually >10 V cm (Janner et al., 2009)) can create a problem for diffused or proton-exchange waveguide of commercial bulk LN modulators because it reflects a weak optical confinement factor. A standard length of a lithium niobate insulator (LNOI) photonic waveguide is much less than 1 μm², which helps reach a small mode dimension and a strong optical confinement factor (Janner et al., 2009; Poberaj et al., 2012; Chang et al., 2016; Fathpour, 2017; Boes et al., 2018). This can coincide with the overlap between optical and electrical fields as a great performance of overlap and reduction switching voltage–length product (Xu et al., 2019). Furthermore, this strategy opens new levels of overall performance improvements for LN modulators due to a strong optical confinement factor and a large relative refractive index difference (Guarino et al., 2007; Janner et al., 2009; Poberaj et al., 2012; Chen et al., 2014; Jin et al., 2015; Rao et al., 2016; Chang et al., 2017; Rao and Fathpour, 2017; Boes et al., 2018; Mercante et al., 2018; Wang et al., 2018; Weigel et al., 2018; He et al., 2019; Xu et al., 2020). In hybrid LN-Si (silicone) electro-optic modulator (EOM), the performance of the LN overlap is 81%, and Si is 5% (Weigel et al., 2018; Wang et al., 2019), while the oxide SiO₂ includes the remaining of the light. The performance of the overlap (i.e., strong optical confinement factor) can be increased by etching the thin-film LN (He et al., 2019) as demonstrated in Figure 2. Assuming the process is flawless. Some developers use a variety of methods to detect defects resulting from manufacturing errors, such as automatic visual inspection (Priscilla et al., 2020).

(a) A Mach–Zehnder interferometer modulator MZIM. (b) The cross-sectional diagram of the MZIM and the channel of the waveguides.

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., 2017 Alexander 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.

Analytical model

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).

Integrated LN Mach-Zehnder modulator MZM: (a) top view and (b) cross-section area.

Table 1

Electro-optic coefficients (r₃₃), refractive index (n_o) and wavelengths (λ), for LN.4.

r₃₃ (pm/V)	Wavelength (nm)	n_o	Reference
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 E in V/m as follows (Figura, 2000): (1) $E = E_{o} e^{i (Kx - wt)}$ E = {E_o}{e^{i\left( {Kx - wt} \right)}} where E_o is the static electric field in V/m, i is the imaginary part, K is the wavenumber which equals 2π/λ, λ is the optical wavelength in nm, w is the angular frequency in Hz, and t is the time domain in sec.

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. (2) $I = I_{o} \cos^{2} (\frac{Δ ϕ}{2})$ I = {I_o}{\cos ^2}\left( {{{\Delta \phi } \over 2}} \right) (3) $E = E_{o} \cos (\frac{Δ ϕ}{2}) e^{i (Kx - wt)}$ E = {E_o}\cos \left( {{{\Delta \phi } \over 2}} \right){e^{i\left( {Kx - wt} \right)}}

MZI electro-optic modulator based on LiNbO₃.

where, I is the output intensity in lum and Δϕ is the phase difference. Therefore, the ordinary refractive index changes Δn₀ that results from the applied electrical field in the direction of the extraordinary axis of the medium as follows (Figura, 2000): (4)

Δ n_{o} = - \frac{1}{2} n_{o}^{3} r_{33} E

\Delta {n_o} = - {1 \over 2}n_o^3{r_{33}}E

where n₀ is the ordinary refractive index, r₃₃ is the electro-optic coefficient pm/V · r_ij represented by second rank tensor and r_ij is the matrix in which i = 1, …,6 and j = 1, 2, 3, thus for r33, i = 3 and j = 3. When applying an external voltage on the arms, a phase difference ΔØ induces and the half-wave voltage (i.e., switching voltage) Vπ for MZM can then be calculated using (Figura, 2000): (5)

Δ \emptyset = \frac{π {Lr}_{33} n_{o}^{3} E}{λ}

\Delta \emptyset = {{\pi L{r_{33}}n_o^3E} \over \lambda }

where λ is the optical wavelength in nm, and L is the length of arms in µm. (6)

V π = \frac{d λ}{{Lr}_{33} n_{o}^{3}}

V\pi = {{d\lambda } \over {L{r_{33}}n_o^3}}

where d is the separation distance in between arms in μm. Moreover, the equation of MZM shows that the incident laser light splits into two components, I_o1 and I_o2, that separate optical path and combined again at the last part of the device as optical power (i.e. I₂ = I_o1 + I_o2) a, and I₁ = electro-optical input power (Luff et al., 1998; Hagn, 2001). Thus, (7)

\frac{2 I_{1}}{I_{2}} = - \frac{4 Δ n_{o}}{r_{33} Γ n_{o}^{3}} [(- \frac{2 Δ n_{o}}{r_{33} Γ n_{o}^{3}} - 1) + (1 + \frac{2 Δ n_{o}}{r_{33} Γ n_{o}^{3}}) \cos Δ \emptyset] + 1

{{2{I_1}} \over {{I_2}}} = - {{4\Delta {n_o}} \over {{r_{33}}\Gamma n_o^3}}\left[ {\left( { - {{2\Delta {n_o}} \over {{r_{33}}\Gamma n_o^3}} - 1} \right) + \left( {1 + {{2\Delta {n_o}} \over {{r_{33}}\Gamma n_o^3}}} \right)\cos \Delta \emptyset } \right] + 1

where I₁ is the input optical power in Watt, I₂ is the electro-optical output power in Watt, and Γ is the optical confinement factor (unitless). (8)

\begin{array}{l} \frac{2 I_{1}}{I_{2}} = - \frac{4 Δ n_{o}}{r_{33} Γ n_{o}^{3}} [- \frac{2 Δ n_{o} - r_{33} Γ n_{o}^{3}}{r_{33} Γ n_{o}^{3}} + \frac{(r_{33} Γ n_{o}^{3} + 2 Δ n_{o})}{r_{33} Γ n_{o}^{3}} \cos Δ \emptyset] + 1 \\ \cos Δ \emptyset = \frac{2 I_{1} r_{33}^{2} Γ^{2} n_{o}^{6} - I_{2} r_{33}^{2} Γ^{2} n_{o}^{6} - 8 Δ n_{o}^{2} I_{2} - 4 Δ n_{o} I_{2} r_{33} Γ n_{o}^{3}}{I_{2} (4 Δ n_{o} r_{33} Γ n_{o}^{3} + 8 Δ n_{o}^{2})} \end{array}

\matrix{ {{{2{I_1}} \over {{I_2}}} = - {{4\Delta {n_o}} \over {{r_{33}}\Gamma n_o^3}}\left[ { - {{2\Delta {n_o} - {r_{33}}\Gamma n_o^3} \over {{r_{33}}\Gamma n_o^3}} + {{\left( {{r_{33}}\Gamma n_o^3 + 2\Delta {n_o}} \right)} \over {{r_{33}}\Gamma n_o^3}}\cos \Delta \emptyset } \right] + 1} \hfill \cr {\cos \Delta \emptyset = {{2{I_1}r_{33}^2{\Gamma ^2}n_o^6 - {I_2}r_{33}^2{\Gamma ^2}n_o^6 - 8\Delta n_o^2{I_2} - 4\Delta {n_o}{I_2}{r_{33}}\Gamma n_o^3} \over {{I_2}\left( {4\Delta {n_o}{r_{33}}\Gamma n_o^3 + 8\Delta n_o^2} \right)}}} \hfill \cr }

(9)

\cos Δ \emptyset = \frac{(2 I_{1} - I_{2}) r_{33}^{2} Γ^{2} n_{o}^{6}}{I_{2} (4 Δ n_{o} r_{33} Γ n_{o}^{3} + 8 Δ n_{o}^{2})} - 1

\cos \Delta \emptyset = {{\left( {2{I_1} - {I_2}} \right)r_{33}^2{\Gamma ^2}n_o^6} \over {{I_2}\left( {4\Delta {n_o}{r_{33}}\Gamma n_o^3 + 8\Delta n_o^2} \right)}} - 1

(10)

\cos Δ \emptyset + 1 = \frac{(2 I_{1} - I_{2}) r_{33}^{2} Γ^{2} n_{o}^{6}}{I_{2} (4 Δ n_{o} r_{33} Γ n_{o}^{3} + 8 Δ n_{o}^{2})}

\cos \Delta \emptyset + 1 = {{\left( {2{I_1} - {I_2}} \right)r_{33}^2{\Gamma ^2}n_o^6} \over {{I_2}\left( {4\Delta {n_o}{r_{33}}\Gamma n_o^3 + 8\Delta n_o^2} \right)}}

(11)

∵ Δ ϕ = \frac{π {Ln}_{o}^{3} r_{33} V}{λ d}

\because \Delta \phi = {{\pi Ln_o^3{r_{33}}V} \over {\lambda d}}

where V is the applied voltage in volt. Plugging Eq. (10) into Eq. (11) yields: (12)

\begin{matrix} Δ n_{o} = A \pm B \\ A = \frac{- (4 I_{2} r_{33} Γ n_{o}^{3} \cos Δ \emptyset + 4 I_{2} r_{33} Γ n_{o}^{3})}{16 (1 + \cos Δ \emptyset)} \\ B = \frac{\sqrt[2]{\begin{matrix} {(4 I_{2} r_{33} Γ n_{o}^{3} \cos Δ \emptyset + 4 I_{2} r_{33} Γ n_{o}^{3})}^{2} \\ - 4 (I_{2} - 2 I_{1}) r_{33}^{2} Γ^{2} n_{o}^{6} (8 + 8 \cos Δ \emptyset) \end{matrix}}}{16 (1 + \cos Δ \emptyset)} \end{matrix}

\matrix{ {\Delta {n_o} = A \pm B} \cr {A = {{ - \left( {4{I_2}{r_{33}}\Gamma n_o^3\cos \Delta \emptyset + 4{I_2}{r_{33}}\Gamma n_o^3} \right)} \over {16\left( {1 + \cos \Delta \emptyset } \right)}}} \cr {B = {{\root 2 \of {\matrix{ {{{\left( {4{I_2}{r_{33}}\Gamma n_o^3\cos \Delta \emptyset + 4{I_2}{r_{33}}\Gamma n_o^3} \right)}^2}} \cr { - 4\left( {{I_2} - 2{I_1}} \right)r_{33}^2{\Gamma ^2}n_o^6\left( {8 + 8\cos \,\Delta \emptyset } \right)} \cr } } } \over {16\left( {1 + \cos \Delta \emptyset } \right)}}} \cr }

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 V/L, and the phase change is π (i.e., the polarities are not opposite). The study utilizes the relation between the changing of negative ordinary refractive index and the optical confinement factor as expressed in Eqs. (17) and (7). Hence, the designed system mathematical model is presented as in Eq. (12). The study was carried out when the large change in the ordinary negative refractive index due to large confinement factor (i.e, large overlap). The data were analyzed through a proposed mathematical model to explain the relationship between the changing of the ordinary negative refractive index −Δno and the confinement factor Γ, as Eq. (12).

Results and discussion

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 n_o) is affected by applying an electric field (E) at a value of 4V/µm. This can be even better when the larger ordinary negative change in the refractive index is associated with as small length as 3–8 µm of the waveguide branch which consequently leads to a large optical confinement factor (large overlap). This emphasizes how vital it is to select a suitable length of arms with respect to the applied electric field with a large negative ordinary change in the refractive index Δ n_o, as shown in Figures 5 and 6. Furthermore, the refractive index and electro-optic coefficient change with an ordinary negative change in refractive index Δ n_o for LN where the length of the branch is an effective factor to shape the required large ball lightning, as shown in Figures 7 and 8. In addition, a better change in the ordinary negative of refractive index Δ no can be obtained when using a window (near-infrared–visible) optical wavelength which has improved the modulation performance of MZM as presented in Figure 9.

The ordinary negative changing of refractive index by applying electric field versus different lengths of arms.

The ordinary negative changing of refractive index as a function of the confinement factor under different intensity of the applied electrical field.

The ordinary negative changing of refractive index as a function of refractive index versus different lengths of arms for LiTaO₃.

The ordinary negative changing of refractive index as a function of electro-optic coefficient versus different lengths of arms for LiTaO₃.

The ordinary negative changing of refractive index with wavelength under different applied electric fields for LiTaO₃.

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): (13) $E = \frac{V}{d}$ E = {V \over d} where d is the waveguide electrode spacing which is directly proportional to the confinement factor. The confinement factor can be slightly degraded by decreasing the waveguide electrode spacing d as expressed in the following equations (Hagn, 2001; Maldonado, 1995): (14) $Δ n_{o} = - \frac{n^{3} r_{13} Γ V}{2 d}$ \Delta {n_o} = - {{{n^3}{r_{13}}\Gamma V} \over {2d}} where r₁₃ is the electro-optic coefficient. (15) $Pm / V, Γ = \frac{2 π Δ nL}{λ}$ Pm/V,\Gamma = {{2\pi \Delta nL} \over \lambda }

In this paper, used a small waveguide electrode spacing d and focused in this paper on the waveguide electrode spacing d, thus, a large ordinary changing of refractive index Δn, then a large confinement factor.

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): (16) $E = \frac{V}{L}$ E = {V \over L} where L is the length of the modulator arm in μm where the used values of L in the proposed design are 3 μm, 5 μm, 7 μm, and 8 μm. Since the proposed structure adopts small lengths of arm (in μm), the change in the refractive index Δn is large and hence the confinement factor is large as well based on the following formula (Hagn, 2001): (17) $Δ n_{o} = - \frac{n^{3} r_{13} Γ V}{2 L}$ \Delta {n_o} = - {{{n^3}{r_{13}}\Gamma V} \over {2L}}

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.

Table 2

The comparison between the reference paper (Chang et al., 2017; Qi and Li, 2020) and this work.

Reference	Δn	L	d	ΔØ	E	Γ	Modulator type
(Qi and Li, 2020) and (He et al., 2019)	Large	Large In mm	Small	π/2	E = V/d	Large	Transvers
This work	Large	Small In μm	–	π	E = V/L	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 L and d are equal (Maldonado, 1995), thus the electric field E is restricted. Finally, the future work is to experimentally assemble this design.

The challenges and difficulties of this design are in the selection of the values of variables such as the length of the modulator arm (L) and the separation distance between arms (d) in micrometers because of a small applied electric field E through the small area of these arms (i.e., E < 10 V/μm). Meantime, a large applied electric field (E) is not feasible here because the design is limited by small size whereas for commercial modulators, E can be hundreds of voltages per millimeter with a big size of the available systems in mm or even in cm. Therefore, in the longitudinal configuration, the electric field E is restricted because (L = d), and the electric field (E = V/L). As a result, the aspect ratio (L/d) is unity and d is not controlled by the electric field E. On the other hand, in the transverse configuration, the electric field is not restricted as (d ≪ L), and d operates as a capacitor in the device. Therefore, a reduction in d due to the electric field E has increased the aspect ratio (L/d) and hence d is controlled by E, where L is also large.

Conclusions

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.

Ilustracje i tabele

MZI electro-optic modulator based on LiNbO3.

The ordinary negative changing of refractive index as a function of refractive index versus different lengths of arms for LiTaO3.

The ordinary negative changing of refractive index as a function of electro-optic coefficient versus different lengths of arms for LiTaO3.

The ordinary negative changing of refractive index with wavelength under different applied electric fields for LiTaO3.

Electro-optic coefficients (r33), refractive index (no) and wavelengths (λ), for LN.4.

r₃₃ (pm/V)	Wavelength (nm)	n_o	Reference
31	633	2.2864	(Casson et al., 2004)
25	1560	2.2108	(Casson et al., 2004)

The comparison between the reference paper (Chang et al., 2017; Qi and Li, 2020) and this work.

Reference	Δn	L	d	ΔØ	E	Γ	Modulator type
(Qi and Li, 2020) and (He et al., 2019)	Large	Large In mm	Small	π/2	E = V/d	Large	Transvers
This work	Large	Small In μm	–	π	E = V/L	Large	Longitudinal

Referencje

Akhtar, M. B. 2022. The use of a convolutional neural network in detecting soldering faults from a printed circuit board assembly. HighTech and Innovation Journal 3(1): 1–14. AkhtarM. B. 2022 The use of a convolutional neural network in detecting soldering faults from a printed circuit board assembly HighTech and Innovation Journal 3 1 1 14 10.28991/HIJ-2022-03-01-01 Search in Google Scholar

Alexander, K., George, J. P., Verbist, J., Neyts, K., Kuyken, B., Van Thourhout, D. and Beeckman, J. 2018. Nanophotonic Pockels modulators on a silicon nitride platform. Nature communications 9(1): 3444. AlexanderK. GeorgeJ. P. VerbistJ. NeytsK. KuykenB. Van ThourhoutD. BeeckmanJ. 2018 Nanophotonic Pockels modulators on a silicon nitride platform Nature communications 9 1 3444 10.1038/s41467-018-05846-6611076830150757 Search in Google Scholar

Bea, S. and Teich, M. 1991. Fundamentals of photonics, Wiley, New York, p. 313. BeaS. TeichM. 1991 Fundamentals of photonics Wiley New York 313 Search in Google Scholar

Boes, A., Corcoran, B., Chang, L., Bowers, J. and Mitchell, A. 2018. Status and potential of lithium niobate on insulator (LNOI) for photonic integrated circuits. Laser & Photonics Reviews 12(4): 1700256. BoesA. CorcoranB. ChangL. BowersJ. MitchellA. 2018 Status and potential of lithium niobate on insulator (LNOI) for photonic integrated circuits Laser & Photonics Reviews 12 4 1700256 10.1002/lpor.201700256 Search in Google Scholar

Cai, L., Kang, Y. and Hu, H. 2016. Electric-optical property of the proton exchanged phase modulator in single-crystal lithium niobate thin film. Optics Express 24(5): 4640–4647. CaiL. KangY. HuH. 2016 Electric-optical property of the proton exchanged phase modulator in single-crystal lithium niobate thin film Optics Express 24 5 4640 4647 10.1364/OE.24.00464029092292 Search in Google Scholar

Casson, J. L., Gahagan, K. T., Scrymgeour, D. and Jain, R. K. 2004. Electro-optic coefficients of lithium tantalate at near-infrared wavelengths. JOSA B 21(11): 1948–1952. CassonJ. L. GahaganK. T. ScrymgeourD. JainR. K. 2004 Electro-optic coefficients of lithium tantalate at near-infrared wavelengths JOSA B 21 11 1948 1952 10.1364/JOSAB.21.001948 Search in Google Scholar

Chang, L., Pfeiffer, M. H. P., Volet, N., Zervas, M., Peters, J. D., Manganelli, C. L., Stanton, E. J., Li, Y., Kippenberg, T. J. and Bowers, J. E. 2017. Heterogeneous integration of lithium niobate and silicon nitride waveguides for wafer-scale photonic integrated circuits on silicon. Optics Letters 42(4): 803–806. ChangL. PfeifferM. H. P. VoletN. ZervasM. PetersJ. D. ManganelliC. L. StantonE. J. LiY. KippenbergT. J. BowersJ. E. 2017 Heterogeneous integration of lithium niobate and silicon nitride waveguides for wafer-scale photonic integrated circuits on silicon Optics Letters 42 4 803 806 10.1364/OL.42.00080328198869 Search in Google Scholar

Chang, L., Li, Y., Volet, N., Wang, L., Peters, J. and Bowers, J. E. 2016. Thin film wavelength converters for photonic integrated circuits. Optica 3(5): 531–535. ChangL. LiY. VoletN. WangL. PetersJ. BowersJ. E. 2016 Thin film wavelength converters for photonic integrated circuits Optica 3 5 531 535 10.1364/OPTICA.3.000531 Search in Google Scholar

Chen, L., Xu, Q., Wood, M. G. and Reano, R. M. 2014. Hybrid silicon and lithium niobate electro-optical ring modulator. Optica 1(2): 112–118. ChenL. XuQ. WoodM. G. ReanoR. M. 2014 Hybrid silicon and lithium niobate electro-optical ring modulator Optica 1 2 112 118 10.1364/OPTICA.1.000112 Search in Google Scholar

Deshpande, R., Zenin, V. A., Ding, F., Mortensen, N. A. and Bozhevolnyi, S. I. 2018. Direct characterization of near-field coupling in gap plasmon-based metasurfaces. Nano Letters 18(10): 6265–6270. DeshpandeR. ZeninV. A. DingF. MortensenN. A. BozhevolnyiS. I. 2018 Direct characterization of near-field coupling in gap plasmon-based metasurfaces Nano Letters 18 10 6265 6270 10.1021/acs.nanolett.8b0239330216727 Search in Google Scholar

DeVault, C. T., Zenin, V. A., Pors, A., Chaudhuri, K., Kim, J., Boltasseva, A., Shalaev, V. M. and Bozhevolnyi, S. I. 2018. Suppression of near-field coupling in plasmonic antennas on epsilon-near-zero substrates. Optica 5(12): 1557–1563. DeVaultC. T. ZeninV. A. PorsA. ChaudhuriK. KimJ. BoltassevaA. ShalaevV. M. BozhevolnyiS. I. 2018 Suppression of near-field coupling in plasmonic antennas on epsilon-near-zero substrates Optica 5 12 1557 1563 10.1364/OPTICA.5.001557 Search in Google Scholar

Figura, C. C. 2000. Second order nonlinear optics in ionically self-assembled thin films. PhD Dissertation, Virginia Tech. FiguraC. C. 2000 Second order nonlinear optics in ionically self-assembled thin films PhD Dissertation, Virginia Tech. Search in Google Scholar

Girouard, P., Chen, P., Jeong, Y. K., Liu, Z., Ho, S. and Wessels, B. W. 2017. X-2 modulator with 40-GHz modulation utilizing BaTiO₃ photonic crystal waveguides. IEEE Journal of Quantum Electronics 53(4): 1–10. GirouardP. ChenP. JeongY. K. LiuZ. HoS. WesselsB. W. 2017 X-2 modulator with 40-GHz modulation utilizing BaTiO₃ photonic crystal waveguides IEEE Journal of Quantum Electronics 53 4 1 10 10.1109/JQE.2017.2718222 Search in Google Scholar

Guarino, A., Poberaj, G., Rezzonico, D., Degl’Innocenti, R. and Günter, P. 2007. Electro–optically tunable microring resonators in lithium niobate. Nature Photonics 1(7): 407–410. GuarinoA. PoberajG. RezzonicoD. Degl’InnocentiR. GünterP. 2007 Electro–optically tunable microring resonators in lithium niobate Nature Photonics 1 7 407 410 10.1038/nphoton.2007.93 Search in Google Scholar

Hagn, G. 2001. Electro-optic effects and their application in indium phosphide waveguide devices for fibre optic access networks. PhD dissertation, ETH Zurich. HagnG. 2001 Electro-optic effects and their application in indium phosphide waveguide devices for fibre optic access networks PhD dissertation, ETH Zurich Search in Google Scholar

He, M., Xu, M., Ren, Y., Jian, J., Ruan, Z., Xu, Y., Gao, S., Sun, S., Wen, X., Zhou, L., Liu, L., Guo, C., Chen, H., Yu, S., Liu, L. and Cai, X. 2019. High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s⁻¹ and beyond. Nature Photonics 13(5): 359–364. HeM. XuM. RenY. JianJ. RuanZ. XuY. GaoS. SunS. WenX. ZhouL. LiuL. GuoC. ChenH. YuS. LiuL. CaiX. 2019 High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s⁻¹ and beyond Nature Photonics 13 5 359 364 10.1038/s41566-019-0378-6 Search in Google Scholar

Janner, D., Tulli, D., García-Granda, M., Belmonte, M. and Pruneri, V. 2009. Micro-structured integrated electro-optic LiNbO₃ modulators. Laser & Photonics Reviews 3(3): 301–313. JannerD. TulliD. García-GrandaM. BelmonteM. PruneriV. 2009 Micro-structured integrated electro-optic LiNbO₃ modulators Laser & Photonics Reviews 3 3 301 313 10.1002/lpor.200810073 Search in Google Scholar

Jin, S., Xu, L., Zhang, H. and Li, Y. 2015. LiNbO₃ thin-film modulators using silicon nitride surface ridge waveguides. IEEE Photonics Technology Letters 28(7): 736–739. JinS. XuL. ZhangH. LiY. 2015 LiNbO₃ thin-film modulators using silicon nitride surface ridge waveguides IEEE Photonics Technology Letters 28 7 736 739 10.1109/LPT.2015.2507136 Search in Google Scholar

Korkishko, Y. N., Fedorov, V., De Micheli, M., Baldi, P., El Hadi, K. and Leycuras, A. 1996. Relationships between structural and optical properties of proton-exchanged waveguides on Z-cut lithium niobate. Applied Optics, 35(36): 7056–7060. KorkishkoY. N. FedorovV. De MicheliM. BaldiP. El HadiK. LeycurasA. 1996 Relationships between structural and optical properties of proton-exchanged waveguides on Z-cut lithium niobate Applied Optics 35 36 7056 7060 10.1364/AO.35.00705621151307 Search in Google Scholar

Lu, H., Sadani, B., Ulliac, G., Courjal, N., Guyot, C., Merolla, J.-M., Collet, M., Baida, F. I. and Bernal, M.-P. 2012a. 6-micron interaction length electro-optic modulation based on lithium niobate photonic crystal cavity. Optics Express 20(19): 20884–20893. LuH. SadaniB. UlliacG. CourjalN. GuyotC. MerollaJ.-M. ColletM. BaidaF. I. BernalM.-P. 2012a 6-micron interaction length electro-optic modulation based on lithium niobate photonic crystal cavity Optics Express 20 19 20884 20893 10.1364/OE.20.02088423037212 Search in Google Scholar

Lu, H., Sadani, B., Courjal, N., Ulliac, G., Smith, N., Stenger, V., Collet, M., Baida, F. I. and Bernal, M.-P. 2012b. Enhanced electro-optical lithium niobate photonic crystal wire waveguide on a smart-cut thin film. Optics Express 20(3): 2974–2981. LuH. SadaniB. CourjalN. UlliacG. SmithN. StengerV. ColletM. BaidaF. I. BernalM.-P. 2012b Enhanced electro-optical lithium niobate photonic crystal wire waveguide on a smart-cut thin film Optics Express 20 3 2974 2981 10.1364/OE.20.00297422330535 Search in Google Scholar

Luff, B. J., Wilkinson, J. S., Piehler, J., Hollenbach, U., Ingenhoff, J. and Fabricius, N. 1998. Integrated optical Mach–Zehnder biosensor, in. Journal of Lightwave Technology 16(4): 583–592. LuffB. J. WilkinsonJ. S. PiehlerJ. HollenbachU. IngenhoffJ. FabriciusN. 1998 Integrated optical Mach–Zehnder biosensor in Journal of Lightwave Technology 16 4 583 592 10.1109/50.664067 Search in Google Scholar

Maldonado, T. A. 1995. Electro-optic modulators. Handbook of optics 2: 13–11. MaldonadoT. A. 1995 Electro-optic modulators Handbook of optics 2 13 11 Search in Google Scholar

Mercante, A. J., Shi, S., Yao, P., Xie, L., Weikle, R. M. and Prather, D. W. 2018. Thin film lithium niobate electro-optic modulator with terahertz operating bandwidth. Optics Express 26(11): 14810–14816. MercanteA. J. ShiS. YaoP. XieL. WeikleR. M. PratherD. W. 2018 Thin film lithium niobate electro-optic modulator with terahertz operating bandwidth Optics Express 26 11 14810 14816 10.1364/OE.26.01481029877417 Search in Google Scholar

Poberaj, G., Hu, H., Sohler, W. and Guenter, P. 2012. Lithium niobate on insulator (LNOI) for micro-photonic devices. Laser & photonics reviews 6(4): 488–503. PoberajG. HuH. SohlerW. GuenterP. 2012 Lithium niobate on insulator (LNOI) for micro-photonic devices Laser & photonics reviews 6 4 488 503 10.1002/lpor.201100035 Search in Google Scholar

Priscilla, S. J., Judi, V. A., Daniel, R. and Sivaji, K. 2020. Effects of chromium doping on the electrical properties of ZnO nanoparticles. Emerging Science Journal 4(2): 82–88. PriscillaS. J. JudiV. A. DanielR. SivajiK. 2020 Effects of chromium doping on the electrical properties of ZnO nanoparticles Emerging Science Journal 4 2 82 88 10.28991/esj-2020-01212 Search in Google Scholar

Qi, Y. and Li, Y. 2020. Integrated lithium niobate photonics, Nanophotonics, 9(6): 1287–1320. QiY. LiY. 2020 Integrated lithium niobate photonics Nanophotonics 9 6 1287 1320 10.1515/nanoph-2020-0013 Search in Google Scholar

Rao, A., Patil, A., Rabiei, P., Honardoost, A., DeSalvo, R., Paolella, A. and Fathpour, S. 2016. High-performance and linear thin-film lithium niobate Mach–Zehnder modulators on silicon up to 50 GHz. Optics Letters 41(24): 5700–5703. RaoA. PatilA. RabieiP. HonardoostA. DeSalvoR. PaolellaA. FathpourS. 2016 High-performance and linear thin-film lithium niobate Mach–Zehnder modulators on silicon up to 50 GHz Optics Letters 41 24 5700 5703 10.1364/OL.41.00570027973493 Search in Google Scholar

Rao, A. and Fathpour, S. 2017. Compact lithium niobate electrooptic modulators. IEEE Journal of Selected Topics in Quantum Electronics 24(4): 1–14. RaoA. FathpourS. 2017 Compact lithium niobate electrooptic modulators IEEE Journal of Selected Topics in Quantum Electronics 24 4 1 14 10.1109/JSTQE.2017.2779869 Search in Google Scholar

Roussey, M., Baida, F. I. and Bernal, M.-P. 2007. Experimental and theoretical observations of the slow-light effect on a tunable photonic crystal. JOSA B 24(6): 1416–1422. RousseyM. BaidaF. I. BernalM.-P. 2007 Experimental and theoretical observations of the slow-light effect on a tunable photonic crystal JOSA B 24 6 1416 1422 10.1364/JOSAB.24.001416 Search in Google Scholar

Roussey, M., Bernal, M.-P., Courjal, N., Van Labeke, D., Baida, F. and Salut, R. 2006. Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons. Applied physics letters 89(24): 241110. RousseyM. BernalM.-P. CourjalN. Van LabekeD. BaidaF. SalutR. 2006 Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons Applied physics letters 89 24 241110 10.1063/1.2402946 Search in Google Scholar

Scharnberg, A. A., de Loreto, A. C. and Alves, A. K. 2020. Optical and structural characterization of Bi2FexNbO7 nanoparticles for environmental applications. Emerging Science Journal 4(1): 11–17. ScharnbergA. A. de LoretoA. C. AlvesA. K. 2020 Optical and structural characterization of Bi2FexNbO7 nanoparticles for environmental applications Emerging Science Journal 4 1 11 17 10.28991/esj-2020-01205 Search in Google Scholar

Sulser, F., Poberaj, G., Koechlin, M. and Günter, P. 2009. Photonic crystal structures in ion-sliced lithium niobate thin films. Optics Express 17(22): 20291–20300. SulserF. PoberajG. KoechlinM. GünterP. 2009 Photonic crystal structures in ion-sliced lithium niobate thin films Optics Express 17 22 20291 20300 10.1364/OE.17.02029119997255 Search in Google Scholar

Tavlykaev, R. F. and Ramaswamy, R. V. 1999. Highly linear Y-fed directional coupler modulator with low intermodulation distortion. Journal of Lightwave Technology 17(2): 282. TavlykaevR. F. RamaswamyR. V. 1999 Highly linear Y-fed directional coupler modulator with low intermodulation distortion Journal of Lightwave Technology 17 2 282 10.1109/50.744238 Search in Google Scholar

Thomaschewski, M., Zenin, V. A., Wolff, C. and Bozhevolnyi, S. I. 2020. Plasmonic monolithic lithium niobate directional coupler switches. Nature Communications 11(1): 1–6. ThomaschewskiM. ZeninV. A. WolffC. BozhevolnyiS. I. 2020 Plasmonic monolithic lithium niobate directional coupler switches Nature Communications 11 1 1 6 10.1038/s41467-020-14539-y700515632029717 Search in Google Scholar

Wang, C., Zhang, M., Chen, X., Bertrand, M., Shams-Ansari, A., Chandrasekhar, S., Winzer, P. and Lončar, M. 2018. Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature 562(7725): 101–104. WangC. ZhangM. ChenX. BertrandM. Shams-AnsariA. ChandrasekharS. WinzerP. LončarM. 2018 Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages Nature 562 7725 101 104 10.1038/s41586-018-0551-y30250251 Search in Google Scholar

Wang, X., Weigel, P. O., Zhao, J., Ruesing, M. and Mookherjea, S. 2019. Achieving beyond-100-GHz large-signal modulation bandwidth in hybrid silicon photonics Mach Zehnder modulators using thin film lithium niobate. APL Photonics 4(9): 096101. WangX. WeigelP. O. ZhaoJ. RuesingM. MookherjeaS. 2019 Achieving beyond-100-GHz large-signal modulation bandwidth in hybrid silicon photonics Mach Zehnder modulators using thin film lithium niobate APL Photonics 4 9 096101 10.1063/1.5115243 Search in Google Scholar

Weigel, P. O., Zhao, J., Fang, K., Al-Rubaye, H., Trotter, D., Hood, D., Mudrick, J., Dallo, C., Pomerene, A. T., Starbuck, A. L., DeRose, C. T., Lentine, A. L., Rebeiz, G. and Mookherjea, S. 2018. Bonded thin film lithium niobate modulator on a silicon photonics platform exceeding 100 GHz 3-dB electrical modulation bandwidth. Optics Express 26(18): 23728–23739. WeigelP. O. ZhaoJ. FangK. Al-RubayeH. TrotterD. HoodD. MudrickJ. DalloC. PomereneA. T. StarbuckA. L. DeRoseC. T. LentineA. L. RebeizG. MookherjeaS. 2018 Bonded thin film lithium niobate modulator on a silicon photonics platform exceeding 100 GHz 3-dB electrical modulation bandwidth Optics Express 26 18 23728 23739 10.1364/OE.26.02372830184869 Search in Google Scholar

Wooten, E. L., Kissa, K. M., Yi-Yan, A., Murphy, E. J., Lafaw, D. A., Hallemeier, P. F., Maack, D., Attanasio, D. V., Fritz, D. J., McBrien, G. J. and Bossi, D. E. 2000. A review of lithium niobate modulators for fiber-optic communications systems. IEEE Journal of Selected Topics in Quantum Electronics 6(1): 69–82. WootenE. L. KissaK. M. Yi-YanA. MurphyE. J. LafawD. A. HallemeierP. F. MaackD. AttanasioD. V. FritzD. J. McBrienG. J. BossiD. E. 2000 A review of lithium niobate modulators for fiber-optic communications systems IEEE Journal of Selected Topics in Quantum Electronics 6 1 69 82 10.1109/2944.826874 Search in Google Scholar

Xu, M., Chen, W., He, M., Wen, X., Ruan, Z., Xu, J., Chen, L., Liu, L., Yu, S. and Cai, X. 2019. Michelson interferometer modulator based on hybrid silicon and lithium niobate platform. APL Photonics 4(10): 100802. XuM. ChenW. HeM. WenX. RuanZ. XuJ. ChenL. LiuL. YuS. CaiX. 2019 Michelson interferometer modulator based on hybrid silicon and lithium niobate platform APL Photonics 4 10 100802 10.1063/1.5115136 Search in Google Scholar

Xu, M., He, M., Zhang, H., Jian, J., Pan, Y., Liu, X., Chen, L., Meng, X., Chen, X., Li, Z., Xiao, X., Yu, S. and Cai, X. 2020. High-performance coherent optical modulators based on thin-film lithium niobate platform. Nature Communications 11(1): 1–7. XuM. HeM. ZhangH. JianJ. PanY. LiuX. ChenL. MengX. ChenX. LiZ. XiaoX. YuS. CaiX. 2020 High-performance coherent optical modulators based on thin-film lithium niobate platform Nature Communications 11 1 1 7 10.1038/s41467-020-17806-0741101532764622 Search in Google Scholar

Yi-Yan, A. 1983. Index instabilities in proton-exchanged LiNbO₃ waveguides. Applied Physics Letters, 42,(8): 633–635. Yi-YanA. 1983 Index instabilities in proton-exchanged LiNbO₃ waveguides Applied Physics Letters 42 8 633 635 10.1063/1.94055 Search in Google Scholar

Zenin, V. A., Choudhury, S., Saha, S., Shalaev, V. M., Boltasseva, A. and Bozhevolnyi, S. I. 2017. Hybrid plasmonic waveguides formed by metal coating of dielectric ridges. Optics Express 25(11): 12295–12302. ZeninV. A. ChoudhuryS. SahaS. ShalaevV. M. BoltassevaA. BozhevolnyiS. I. 2017 Hybrid plasmonic waveguides formed by metal coating of dielectric ridges Optics Express 25 11 12295 12302 10.1364/OE.25.01229528786587 Search in Google Scholar

Zenin, V. A., Volkov, V. S., Han, Z., Bozhevolnyi, S. I., Devaux, E. and Ebbesen, T. W. 2012. Directional coupling in channel plasmon-polariton waveguides. Optics Express 20(6): 6124–6134. ZeninV. A. VolkovV. S. HanZ. BozhevolnyiS. I. DevauxE. EbbesenT. W. 2012 Directional coupling in channel plasmon-polariton waveguides Optics Express 20 6 6124 6134 10.1364/OE.20.00612422418492 Search in Google Scholar

International Journal on Smart Sensing and Intelligent Systems

The ordinary negative changing refractive index for estimation of optical confinement factor

Ahmad S. Abdullah oraz
Ahmad S. Abdullah oraz
Sadeq Adnan Hbeeb
Sadeq Adnan Hbeeb

Data publikacji: 29 Jun 2022

Tom & Zeszyt: Tom 15 (2022) - Zeszyt 1 (January 2022)

Zakres stron: -

Otrzymano: 23 Dec 2021

Dziennik i szczegóły wydania

International Journal on Smart Sensing and Intelligent Systems

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Figure 1

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Ilustracje i tabele

Figure 1

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Figure 9

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.

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International Journal on Smart Sensing and Intelligent Systems

The ordinary negative changing refractive index for estimation of optical confinement factor

Ahmad S. Abdullah orazAhmad S. Abdullah orazSadeq Adnan HbeebSadeq Adnan Hbeeb

Data publikacji: 29 Jun 2022

Tom & Zeszyt: Tom 15 (2022) - Zeszyt 1 (January 2022)

Zakres stron: -

Otrzymano: 23 Dec 2021

Dziennik i szczegóły wydania

International Journal on Smart Sensing and Intelligent Systems

Podgląd PDF

Artykuł

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Ilustracje i tabele

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

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.

Referencje

Najnowsze artykuły

Zaplanuj zdalną konferencję ze Sciendo

Ahmad S. Abdullah oraz
Ahmad S. Abdullah oraz
Sadeq Adnan Hbeeb
Sadeq Adnan Hbeeb