Patent Publication Number: US-2022221744-A1

Title: Integrated compact z-cut lithium niobate modulator

Description:
RELATED APPLICATIONS 
     This is the first patent application for the present disclosure. 
     TECHNICAL FIELD 
     The present application relates to electro-optic modulators used in optical communication networks, and in particular to Z-cut lithium niobate electro-optic modulators. 
     BACKGROUND 
     In modern telecommunication systems, optical communication networks can be used to send and receive payload information in the form of optical signals transmitted through components (e.g., amplifier, multiplexer/de-multiplexer, waveguides) and optical fibers connecting the components. 
     In an optical communication network, there is often a need to encode a signal onto an optical beam, which is then transmitted through optical fibers to a distant destination. An electro-optic modulator, which can modulate a beam of light, may be used to encode information onto a continuous light wave, which can be generated by a laser source. 
     An example electro-optic modulator, used in an optical system may be a lithium niobate electro-optic modulator, such as, for example, a lithium niobate piezoelectric-optical modulator. Lithium niobate (LiNbO 3 ), when in crystal form, may have a refractive index as a function of the strength of a local electric field or an applied voltage. Lithium niobate is characterized by its Pockels effect, which changes or produces birefringence in an optical medium induced by an electric field. In the Pockels effect, also known as the linear electro-optic effect, the birefringence is proportional to the electric field. 
     A basic yet important element in the LiNbO 3 -based modulator is the optical waveguide, which is often evaluated based on propagation losses and electro-optical conversion efficiency. 
     There are several ways of manufacturing a LiNbO 3  electro-optic modulator, such as, for example, by metal diffusion, ion exchange, or proton exchange. These conventional manufacturing methods, however, often produce a modulator that has a rather small refractive index change in the waveguide crystal (e.g. LiNbO 3 ). 
       FIG. 1A  illustrates a cross-sectional view of a prior art X-cut LiNbO 3  electro-optic modulator  100  with coplanar waveguide (CPW) radio-frequency electrodes, as discussed in Wooten, E. L. et. al, (2000). A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems. Selected Topics in Quantum Electronics, IEEE Journal of. 6. 69-82. 10.1109/2944.826874, the entire content of which is herein incorporated by reference. 
     Conventionally, X-cut manufacturing technology is used to make the LiNbO 3  waveguide in the modulator  100 , which can be formed with: Titanium (Ti) metal diffusion (at approximately 1000° C.), ion exchange, or proton exchange. Gold (Au) is generally used as the material for electrodes. Electrodes can be fabricated either directly on the surface of the LiNbO 3  wafer (or also known as LiNbO 3  substrate), or on an optically transparent buffer layer to reduce optical loss due to metal loading. In general, an adhesion layer, such as Titanium (Ti), is first vacuum deposited on the wafer, followed by the deposition of a base layer of the metal in which the electrodes are to be made. 
       FIG. 1B  illustrates a cross-sectional view of another prior art LiNbO 3  electro-optic modulator  150 , as shown in Shawn Y. Siew, et. al, “Integrated nonlinear optics: lithium niobate-on-insulator waveguides and resonators,” Proc. SPIE 10106, Integrated Optics: Devices, Materials, and Technologies XXI, 101060B (16 Feb. 2017), the entire content of which is herein incorporated by reference. Modulator  150  has a ridge waveguide made with LiNbO 3  deposited on top of a thin layer of silicon dioxide (SiO 2 ). The manufacturing process uses a Pieozoelectric-On-Insulator (POI) wafer bonding technology. 
       FIG. 3A  illustrates a cross-sectional view of yet another prior art LiNbO 3  electro-optic modulator  300 , which is described in Cheng Wang, et. al, Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature. 2018 October; 562(7725):101-104. doi: 10.1038/s41586-018-0551-y. Epub 2018 Sep. 24. PMID: 30250251, the entire content of which is herein incorporated by reference.  FIG. 3A  shows a monolithically integrated lithium niobate electro-optic modulator  300  that features a CMOS-compatible drive voltage. Optical lithium niobate waveguides run through the dielectric gaps of the Ground-Signal-Ground (GSG) coplanar microwave strip line. As a result, the microwave electric field has opposite signs across the two lithium niobate waveguides, thus inducing (via the Pockels effect) an optical phase delay on one arm and an optical phase advance on the other. The modulator  300  can be fabricated from a commercial X-cut lithium-niobate-on-insulator wafer, where a 600-nm device layer sits on top of a SiO2/Si-stack substrate. Electron-beam lithography and Ar+ ion based reactive ion etching can be carried out to define optical waveguides and Mach-Zehnder interferometers in thin-film lithium niobate. 
     Generally speaking, the drawbacks of the conventional X-cut LiNbO 3  electro-optic modulators  100 ,  150 ,  300  may include: a relatively small refractive index contrast between core and cladding, or a relatively large waveguide length, which can be up to several centimeters long, and a weak optical energy confinement. 
     SUMMARY 
     The present disclosure describes various designs of a lithium niobate (LiNbO 3 )-based modulator and various methods for manufacturing the lithium niobate (LiNbO 3 )-based modulators. In accordance with some aspects, an example LiNbO 3 -based modulator may include: a base substrate; a ground electrode deposited on the base substrate; a first cladding layer on top of the base substrate; an optical waveguide core on top of the first cladding layer; a second cladding layer on top of the optical waveguide core; and a signal electrode deposited on top of the second cladding layer; where the optical waveguide core includes a Z-cut LiNbO 3 , and where the first cladding layer, the optical waveguide core, and the second cladding layer are positioned between the ground electrode and the signal electrode on a z-axis of the Z-cut LiNbO 3 . 
     The disclosed modulator designs, in some example embodiments, are configured to provide a relatively large refractive index change (Δn) in the optical waveguide. In doing so, the confinement of light is strong and the optic mode size is small, which may result in a relatively small half-wave voltage in the Mach Zehnder modulator&#39;s VπL. Since the nonlinear wave mixing efficiency is directly proportional to the light intensity in the waveguide, higher confinement and smaller mode size can result in a modulator with better electro-optical efficiency. Furthermore, due to a large refractive index difference, and less optical energy leakage, bending the waveguide (e.g., for optical ring resonator application) with a radius of curvature of less than a few millimeters is possible. 
     In addition, the proposed piezo-electro-optic can be CMOS compatible, which makes it possible to integrate the optical device with other electronic components on the same wafer. 
     In some embodiments, the base substrate may include a silicon (Si) substrate. 
     In some embodiments, the optical waveguide core may include a ridge portion. 
     In some embodiments, the ridge portion may be made of Z-cut LiNbO 3  or tantalum pentoxide (Ta 2 O 5 ). 
     In some embodiments, the distance between a top surface of the ground electrode and a bottom surface of the signal electrode on the z-axis of the Z-cut LiNbO 3  is equal to or less than 1 micrometer (μm). 
     In some embodiments, the first cladding layer may include silicon dioxide (SiO 2 ). 
     In some embodiments, the second cladding layer may include silicon dioxide (SiO 2 ). 
     In some embodiments, the ground electrode may include one of:
         gold, copper, titanium, zinc, silver, aluminum and platinum.       

     In some embodiments, the signal electrode may include one of:
         gold, copper, titanium, zinc, silver, aluminum and platinum.       

     In some embodiments, the modulator may include a third cladding layer between the ground electrode and the base substrate. 
     In some embodiments, the third cladding layer may include SiO 2 . 
     In some embodiments, the ground electrode may be embedded within the base substrate. 
     In some embodiments, the ground electrode may have a width that is equal to a width of the signal electrode. 
     In some embodiments, the ground electrode may have a width that is equal to a width of the ridge portion of the optical waveguide core. 
     In some embodiments, a distance between a bottom surface of the signal electrode and a top surface of the optical waveguide core is between 50 nanometers (nm) to 200 nm. 
     In some embodiments, a thickness of the first cladding layer is between 200 nm to 600 nm. 
     In some embodiments, the modulator may have a second arm, where the second arm may include: the first base substrate; a second ground electrode deposited on the first base substrate; a third cladding layer on top of the first base substrate; a second optical waveguide core on top of the third cladding layer; a fourth cladding layer on top of the second optical waveguide core; and a second signal electrode deposited on top of the fourth cladding layer; where the second optical waveguide core includes a second Z-cut LiNbO 3 , and where the third cladding layer, the second optical waveguide core, and the fourth cladding layer are positioned between the second ground electrode and the second signal electrode on a z-axis of the second Z-cut LiNbO 3 . 
     In some embodiments, the second optical waveguide core may include a ridge portion made of Z-cut LiNbO 3  or tantalum pentoxide (Ta 2 O 5 ). 
     In some embodiments, the distance between a top surface of the second ground electrode and a bottom surface of the second signal electrode on the z-axis of the second Z-cut LiNbO 3  is equal to or less than 1 micrometer (μm). 
     In some embodiments, a distance between a bottom surface of the second signal electrode and a top surface of the second optical waveguide core is between 50 nanometers (nm) to 200 nm. 
     In some embodiments, a thickness of the third cladding layer is between 200 nm to 600 nm. 
     In some embodiments, the second ground electrode is embedded within the first base substrate. 
     In accordance with some aspects, there is disclosed a method of manufacturing a lithium niobate (LiNbO 3 )-based modulator. The method may include: depositing a metal on a base substrate to form a ground electrode; depositing silicon dioxide (SiO 2 ) on one side of a Z-cut LiNbO 3  wafer to form a first cladding layer; implanting an oxide side of the Z-cut LiNbO 3  wafer with ions; wafer bonding the ion-implanted side of the Z-cut LiNbO 3  wafer with the base substrate; removing a donor layer of the Z-cut LiNbO 3  wafer; dry etching, on the Z-cut LiNbO 3  wafer, with a photoresist mask to obtain a ridge portion of the Z-cut LiNbO 3  wafer; depositing silicon dioxide (SiO 2 ) on the Z-cut LiNbO 3  wafer to form a second cladding layer surrounding the ridge portion; and depositing a metal on the second cladding layer to form a signal electrode; where the ground electrode and the signal electrode are spaced apart and positioned on a z-axis of the Z-cut LiNbO 3 . 
     In some embodiments, the base substrate may include a silicon (Si) substrate. 
     In some embodiments, the ground electrode or signal electrode may include but not restrict to one or a combination of: gold, copper, titanium, zinc, silver, aluminum and platinum. 
     In some embodiments, the method may further include: cleaning the base substrate prior to depositing the metal on the base substrate to form the ground electrode. 
     In some embodiments, the oxide side of the Z-cut LiNbO3 wafer may be ion-implanted with helium or hydrogen ions. 
     In some embodiments, the distance between the ground electrode and the signal electrode on the z-axis of the Z-cut LiNbO3 is equal to or less than 1 micrometer (μm). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing will be provided by the Office upon request and payment of the necessary fee. 
       Reference will now be made, by way of example, to the accompanying figures which show example embodiments of the present application, and in which: 
         FIG. 1A  illustrates a cross-sectional view of a prior art LiNbO 3  electro-optic modulator. 
         FIG. 1B  illustrates a cross-sectional view of another prior art LiNbO 3  electro-optic modulator. 
         FIG. 2  illustrates a simplified view of an example LiNbO 3  with crystal axes. 
         FIG. 3A  illustrates a cross-sectional view of yet another prior art LiNbO 3  electro-optic modulator. 
         FIG. 3B  illustrates a radio-frequency (RF) electric field graph of the LiNbO 3  electro-optic modulator in  FIG. 3A . 
         FIG. 4A  illustrates a cross-sectional view of an example arm of a first example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 4B  illustrates a radio-frequency (RF) electric field graph of the first example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 4C  illustrates an optical power flow graph of the first example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 4D  illustrates a stress graph of the first example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 4E  illustrates an effective refractive index of the first example Z-cut LiNbO 3  waveguide as a buffer layer thickness increases, in accordance with some example embodiments. 
         FIG. 4F  illustrates an electric field within the first example Z-cut LiNbO 3  waveguide as a buffer layer thickness increases, in accordance with some example embodiments. 
         FIG. 4G  illustrates an effective refractive index of the first example Z-cut LiNbO 3  waveguide as a bottom layer thickness increases, in accordance with some example embodiments. 
         FIG. 4H  illustrates an electric field within the first example Z-cut LiNbO 3  waveguide as a bottom layer thickness increases, in accordance with some example embodiments. 
         FIG. 5  illustrates a cross-sectional view of an example arm of a second example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 6  illustrates a cross-sectional view of an example arm of a third example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 7A  illustrates a cross-sectional view of an example arm of a fourth example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 7B  illustrates a radio-frequency (RF) electric field graph of the fourth example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 7C  illustrates an optical power flow graph of the fourth example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 8  illustrates a cross-sectional view of an example arm of a fifth Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 9  is a flow chart illustrating an example method to manufacture the first example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
         FIG. 10  is a flow chart illustrating an example method to manufacture the second example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. 
     
    
    
     Like reference numerals are used throughout the Figures to denote similar elements and features. While aspects of the invention will be described in conjunction with the illustrated embodiments, it will be understood that it is not intended to limit the invention to such embodiments. 
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
     Throughout this disclosure, the term “coupled” may mean directly or indirectly connected, electrically coupled, or operably connected; the term “connection” may mean any operable connection, including direct or indirect connection. In addition, the phrase “coupled with” is defined to mean directly connected to or indirectly connected through one or more intermediate components. Such intermediate components may include both or either of hardware and software-based components. 
     Further, a communication interface may include any operable connection. An operable connection may be one in which signals, physical communications, and/or logical communications may be sent and/or received. An operable connection may include a physical interface, an electrical interface, and/or a data interface. 
     Further, a communication interface may include any operable connection. An operable connection may be one in which signals, physical communications, and/or logical communications may be sent and/or received. An operable connection may include a physical interface, an electrical interface, and/or a data interface. 
     In general, electro-optical modulators, such as, for example, Mach Zehnder (MZ) modulators, can be fabricated with either X-cut or Z-cut LiNbO 3 . X-cut LiNbO 3  modulators have a symmetrical design, which may result in a low frequency-chirp in the modulated signal, while Z-cut LiNbO 3  modulators may provide more efficient modulation (i.e., lower Vπ or half-wave voltage) at the expense of a higher frequency chirp. The half-wavelength voltage Vπ is the voltage required for inducing a phase change of π for the light going through the waveguide of the modulator. Generally speaking, the phase of the light leaving the waveguide can be controlled by changing the electric field in the LiNbO 3  waveguide. 
     It is to be appreciated that the x-axis, y-axis, and z-axis discussed throughout this disclosure, including in the drawings, refer to the crystal axes of a z-cut LiNbO 3 . Referring now to  FIG. 2 , which illustrates a simplified view of an example LiNbO 3    200  with crystal axes x, y, z. A Z-cut (or z-cut) LiNbO 3  wafer  230  can be obtained by cutting the crystal  200  across a surface or plane that is perpendicular to its z-axis. For example, the Z-cut LiNbO 3  wafer  230  has a top surface  235 . The z′-axis of the Z-cut LiNbO 3  wafer  230  is normal to the surface  235 , while the x′-axis and y′-axis lie within the surface  235 . As shown, the x′-axis of the Z-cut LiNbO 3  wafer  230  is perpendicular to the z-axis of the crystal LiNbO 3 . 
     In some example electro-optical modulators, a Mach-Zehnder interferometer (MZI) modulator may have two arms for modulation, where both arms are manufactured on the same base substrate. Each arm may include an optical waveguide (or simply referred to as a “waveguide”). A waveguide may include a longitudinally extended high-index optical medium, which may be known as the “core”, made with LiNbO 3  (or a different material). The high-index optical medium core may be transversely surrounded by a low-index media, which may be known as the “cladding”, made with silicon dioxide (SiO 2 ). A guided optical wave propagates in the waveguide core along its longitudinal direction. 
       FIG. 4A  illustrates a cross-sectional view  400  of an example arm of a first Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. It should be appreciated that, for ease of illustration, the cross-sectional view in each of  FIGS. 4A, 5, 6, 7 and 8  may show only one arm of the electro-optic modulator (or simply the “modulator”), while the modulator may have up to two arms, with both arms having the same structure or each having a different structure. 
     The modulator design shown in each of  FIGS. 4A, 5, 6, 7 and 8  may provide a relatively large refractive index change (Δn) in the optical waveguide (or simply the “waveguide”), which may result in a relatively small half-wave voltage and the Mach Zehnder modulator&#39;s VπL. In doing so, the confinement of light is strong and the optic mode size is small. Since the nonlinear wave mixing efficiency is directly proportional to the light intensity in the waveguide, higher confinement and smaller mode size can result in a modulator with better electro-optical efficiency. Furthermore, due to a large refractive index difference, and less optical energy leakage, bending the waveguide (e.g., for optical ring resonator application) with a radius of curvature of less than a few millimeters is possible. 
     In addition, the proposed piezo-electro-optic modulators shown in each of  FIGS. 4A, 5, 6, 7 and 8  can be CMOS compatible, which makes it possible to integrate the optical device with other electronic components on the same wafer. 
     Referring back to  FIG. 4A , which illustrates a cross-sectional view  400  of an example arm of a first Z-cut LiNbO 3  electro-optic modulator. The modulator arm may be built on a base layer of silicon (Si) substrate (also known as the “wafer”)  450 , which may also be referred to as a base substrate  450 . A ground electrode  440  may be deposited on top of the Si substrate  450  and may be made of a suitable metal, which can be a metal with low electric resistance, such as gold, copper, titanium, zinc, silver, aluminum or platinum. A first cladding layer  420  may be on top of the ground electrode  440 , and may be made of silicon dioxide (SiO 2 ). On top of the first cladding layer  420 , an optical waveguide core  430  made of Z-cut LiNbO 3  may be positioned between the first cladding layer  420  and a second cladding layer  425 , which may be also made of SiO 2 . A signal electrode  410  may be deposited on top of the second cladding layer  425 . A signal electrode may also be known as an active electrode, or an electrode with signal applied on it. The optical waveguide core  430  may include a ridge portion  435 , which can also be made of Z-cut LiNbO 3 . In other embodiments, the ridge portion  435  may be made of a different material other than LiNbO 3 . 
     As shown in  FIG. 4A , the bottom surface  415  of the signal electrode  410  and the top surface of the ground electrode  440  are spaced apart a distance t D , and are each parallel to a longitudinal axis  432  of the Z-cut LiNbO 3  waveguide  430 , where the longitudinal axis  432  extends through the Z-cut LiNbO 3  waveguide  430  along the x-axis of the waveguide core  430 . In addition, the optical waveguide  460 , which includes the waveguide core  430  and the adjacent cladding layers  420 ,  425 , may be positioned between the signal electrode  410  and the ground electrode  440  on the z-axis of the Z-cut LiNbO 3 . In comparison, in the conventional X-cut LiNbO 3  modulators, the hot and ground electrodes tend to be on the same plane with the waveguide, and at both sides of the waveguide, as shown in  FIG. 3A . 
     The waveguide core  430  (which may include a ridge portion  435 ), and the immediately adjacent (or surrounding) cladding layers  420 ,  425  may be collectively referred to as the waveguide  460 . 
     By placing electrodes  410 ,  440  on the z-axis of a Z-cut LiNbO 3 , the distance between the signal-carrying electrode  410  and ground electrode  440 , t D  may be reduced to less than 1 micrometer (μm), significantly less than the distance (4-5 μm) between electrodes aligned in the x-direction in the integrated LiNbO 3  modulators. A buffer layer  427  between the optical waveguide core  430  (including the ridge portion  435 ) and the signal electrode  410  may be implemented to lower the conductive loss of optical signal within the microwave electrodes. The buffer layer  427  may have a thickness t B , which may be defined as a distance, along the z-axis of the Z-cut LiNbO 3 , between a bottom surface  415  of the signal electrode  410  and a top surface of the optical waveguide core  430 . When the optical waveguide core  430  includes a ridge portion  435  as a protruding portion of the waveguide core  430  as shown in  FIG. 4A , the thickness t B , may be defined as a distance, along the z-axis of the Z-cut LiNbO 3 , between a bottom surface  415  of the signal electrode  410  and a top surface of the ridge portion  435 . 
     A buffer layer thickness t B  that is too large may negatively affect: 1) the effective refractive index, which leads to a larger VπL; 2) the characteristic impedance Z C ; 3) the conductor loss α 0  (dB/(cm*GHz{circumflex over ( )}0.5)); and 4) the velocity match between RF (microwave, or millimeter wave) and optical wave. For example, as shown in  FIG. 4E  and  FIG. 4F , when the waveguide core  430  is operating in a TE 0  mode with 1V driving voltage, as the buffer layer thickness increases from 50 nm to 130 nm while maintaining the bottom buffer layer thickness t S  at 200 nm, the effective refractive index of the waveguide core  430  increases from around 2.118 to 2.13, and the electric field within the waveguide core  430  decreases in magnitude from −360,000 to −260,000 V/m. Therefore, it is beneficial to keep the buffer layer  427  between the optical waveguide core  430  and the signal electrode  410  as thin as possible, preferably in the range of 50-200 nanometers (nm). Similarly, it is beneficial to keep the bottom buffer layer thickness t S , which is the thickness of the SiO 2  cladding layer  420 , under 600 nm. In some embodiments, the bottom buffer layer thickness may be as low as 200 nm.  FIGS. 4G and 4H  show that when the waveguide core  430  is operating in a TE 0  mode, as the bottom buffer layer thickness increases from 200 nm to 500 nm while keeping the top buffer layer thickness t B  at 100 nm, the effective refractive index of the waveguide core  430  increases from around 2.128 to 2.13, and the electric field within the waveguide core  430  decreases in magnitude from −300,000 to just above −280,000 V/m. 
     For the signal electrodes  410  (or also known as “data electrodes”) carrying a light signal, a positive electrical potential can be applied to one signal electrode on one of the two arms of the MZI modulator, and a negative electrical potential can be applied to the signal electrode on the other arm of the MZI modulator to obtain smallest VπL. 
       FIG. 4D  illustrates a stress graph of the first example Z-cut LiNbO 3  electro-optic modulator shown in  FIG. 4A , in accordance with some example embodiments. The electro-optic and stress-optic effects of the embodiment modulator shown in  FIG. 4A , as well as in each of  FIGS. 5 to 8  may be generally represented by the following equation: 
       Δ(1/ n   2 ) ij ≡Δε −1   ij   =r   S   ijk   E   k   +p   E   ijkl   S   kl   (1)
 
     Where n 2  is the optic refractive index, r S  is the electro-optic tensor (Pockels) at zero strain (clamped), S kl  is the strain within the optical waveguide, and p E  is the elasto-optic (stress-optic) tensor at constant electric field. 
     In the LiNbO 3  electro-optic modulator  300  shown in  FIG. 3A , the strain (S kl ) within the optical waveguide is minimal. In comparison, in the first example Z-cut LiNbO 3  electro-optic modulator shown in  FIG. 4A , the strain S kl  as indicated by the bright spot in  FIG. 4D , is concentrated in and around the waveguide core  430 , therefore according to equation (1) above, the contribution of the second term (p E   ijkl  S kl ) in the first example Z-cut LiNbO 3  electro-optic modulator shown in  FIG. 4A  is larger, as compared to the conventional LiNbO 3  electro-optic modulator  300 . The modulator design shown in  FIG. 4A  also applies electric bias in the z-direction of the LiNbO 3  waveguide, which has the largest piezoelectric constant. This can further enhance the refractive index modulation through the stress-optic effect, as piezoelectricity leads to mechanical stress, which in turn leads to the change in optical refractive index. 
     From equation (1), it can be seen that a stronger electric field (E k ) and stronger elastic stress (S kl ) can result in a stronger modulation on optic refractive index n 2   ij . 
     In some embodiments, when the signal electrode  410  is placed on top of the optical waveguide core  430  in the z-direction of the LiNbO 3  waveguide, and with a buffer or cladding layer  425  between the signal electrode  410  and the optical waveguide core  430  to lower the conductive loss of optical signal within the microwave electrodes, the modulation of the refractive index can be improved (i.e., increased) through stronger Pockels effect (electro-optic effect). That is, according to equation (1) above, the value of E k  by the first example Z-cut LiNbO 3  electro-optic modulator shown in  FIG. 4A  is larger, which leads to a bigger refractive index change as compared to the conventional LiNbO 3  electro-optic modulator  300 . 
       FIG. 4B  illustrates a RF electric field graph of the first example Z-cut electro-optic modulator shown in  FIG. 4A  when applied with a voltage of 1V, in accordance with some example embodiments. As the Z-cut LiNbO 3  waveguide  430  has the highest electro-optic coefficient along the z-axis, a very strong electric field, identified by arrows along the z-direction in the optical waveguide core  430  can be obtained. For example, within the optical waveguide core  430 , there can be an electric field strength more than ten times greater than that of a conventional X-cut LiNbO 3  waveguide device. 
       FIG. 4C  illustrates an optical power flow graph of the first example Z-cut LiNbO 3  electro-optic modulator shown in  FIG. 4A  when applied with a voltage of 1V, in accordance with some example embodiments. Most of the energy is shown to be contained within the optical waveguide core  430 , which demonstrates that the example embodiment of the modulator design illustrated in  FIG. 4A  can enhance the electro-optic interaction and help to confine the optical energy within the waveguide while reducing energy leakage. 
       FIG. 3B  illustrates a RF electric field graph of the LiNbO 3  electro-optic modulator  300  in  FIG. 3A . It can be seen that the electrical field with 1V drive voltage, represented by the arrows, of the modulator in  FIG. 3A  point from one electrode (e.g. signal electrode “S”) to another electrode (e.g. ground electrode “G”), surrounding the waveguide core  310 . The electrical field in  FIG. 4B  is generated with 1V drive voltage, represented by the arrows, flows from the signal electrode  410  to the ground electrode  440 , but mostly concentrating within the waveguide core  430  including the ridge portion  435 . Compared to that shown in  FIG. 3B , it is clear that the modulator shown in  FIG. 4B  (which is also in  FIG. 4A ) is more efficient: with the same driving voltage of 1V the electric field in the optical waveguide core in  FIG. 4B  is much stronger than that in  FIG. 3B , therefore generate much stronger modulation of optical refractive index, according to Eq.(1). In other words, it requires less driving voltage to reach the π phase shift under the same waveguide length L or it requires less waveguide length L, therefore reduce the device size, while keeping the same driving voltage. Further, as the nonlinear wave mixing efficiency is directly proportional to the light intensity in the waveguide, higher confinement and smaller mode size can result in a modulator with better electro-optical efficiency. Furthermore, due to a large refractive index difference, and less optical energy leakage, bending the waveguide (e.g., for optical ring resonator application) with a radius of curvature of less than a few millimeters is possible, by the modulator shown in  FIG. 4A  (as well as the modulators shown in  FIGS. 5 to 8 ). 
       FIG. 9  illustrates a flow chart illustrating an example method  900  to manufacture the first example Z-cut LiNbO 3  electro-optic modulator shown in  FIG. 4A , in accordance with some example embodiments. At step  910 , a silicon (Si) base substrate or wafer  450  may be prepared and cleaned. At step  915 , a metal may be deposited on the cleaned Si wafer  450  to form a ground electrode  440 . The metal may be, for example, one or combination of gold, copper, titanium, zinc, silver, aluminum and platinum. At step  920 , a Z-cut LiNbO 3  wafer or substrate may be prepared and cleaned. At step  930 , SiO 2  may be deposited on the Z-cut LiNbO 3  wafer to form a first SiO 2  cladding layer  420 . At step  940 , the cleaned Z-cut LiNbO 3  wafer may be put through ion implantation with helium (He) and/or hydrogen ions on the oxide side (i.e., the side that is deposited with SiO 2  in step  930 ). At step  950 , the side with ion implantation of the Z-cut LiNbO 3  wafer may be bonded to Si wafer on the side with ground electrode  440  of the Si wafer. At step  960  the ion-implanted LiNbO 3  may be split at the thickness damaged by the ion-implantation with a temperature treatment, leaving the part with the SiO 2  on the Si substrate, which means that the LiNbO 3  donated part of it to the bonded LiNbO 3 /Si substrate, which is commonly referred to as a donor LiNbO 3  wafer layer. At step  970 , the thin slice of LiNbO 3  wafer may be dry etched with photoresist mask to obtain a ridge portion  435 . At step  980 , SiO 2  may be deposited on top of the LiNbO 3  wafer to form a second SiO 2  cladding layer  425 , surrounding the ridge portion  435 . At step  990 , the metal electrode  410  may be deposited on top of the SiO 2  cladding layer  425 , where the metal may be, for example but not restricted to, one or combination of gold, copper, titanium, zinc, silver, aluminum and platinum. 
       FIG. 5  illustrates a cross-sectional view  500  of an example arm of a second example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. The modulator arm may be built on a layer of Si substrate (also known as the “wafer”)  450 . A ground electrode  440  may be deposited on top of the Si substrate  450  and may be made of a suitable metal, such as gold, copper, titanium, zinc, silver, aluminum or platinum. A first cladding layer  420  may be on top of the ground electrode  440 , and may be made of silicon dioxide (SiO 2 ). On top of the first cladding layer  420 , an optical waveguide core  430  made of Z-cut LiNbO 3  may be positioned between the first cladding layer  420  and a second cladding layer  425 , which may be also made of SiO 2 . A signal electrode  410  may be deposited on top of the second cladding layer  425 . The optical waveguide core  430  may include a ridge portion  435 , which in this example embodiment may be made of tantalum pentoxide (Ta 2 O 5 ). Ta 2 O 5  is an inert material with a high refractive index, for example, it may have a refractive index of 2.1 to 2.2 in the 1550 nm range, which is close to that of LiNbO 3 , which may have a refractive index of 2.21 in the same range. Ta 2 O 5  may also have high dielectric constant, and low absorption. Using Ta 2 O 5  to form the ridge portion  435  of the optical waveguide core  430  can overcome the difficulty of etching the LiNbO3 described above in connection with method  900 . Typically the Ta 2 O 5  ridge portion  435  is fabricated prior to the deposition of the second cladding of SiO 2    425 . 
     By placing electrodes  410 ,  440  on the z-axis of a Z-cut LiNbO 3 , the distance between the signal-carrying signal electrode  410  and ground electrode  440 , t D  may be reduced to less than 1 micrometer (μm), significantly less than the distance (4-5 μm) between electrodes aligned in the x-direction in the integrated LiNbO3 modulators. A buffer layer between the optical waveguide core  430  (including the ridge portion  435 ) and the signal electrode  410  may be implemented to lower the conductive loss of optical signal within the microwave electrodes. The buffer layer may have a thickness t B , which may be defined as a distance, along the z-axis of the Z-cut LiNbO 3 , between a bottom surface of the signal electrode  410  and a top surface of the optical waveguide core  430 . When the optical waveguide core  430  includes a ridge portion  435  as a protruding portion of the waveguide core  430  as shown in  FIG. 5 , the thickness t B , may be defined as a distance, along the z-axis of the Z-cut LiNbO 3 , between a bottom surface of the signal electrode  410  and a top surface of the ridge portion  435 . 
     A buffer layer thickness t B  that is too large may negatively affect: 1) the effective refractive index, which leads to a larger VπL; 2) the characteristic impedance Z C ; 3) the conductor loss α 0  (dB/(cm*GHz{circumflex over ( )}0.5)); and 4) the velocity match between RF (microwave, or millimeter wave) and optical wave. Similarly, it is beneficial to keep the bottom buffer layer thickness t S , which is the thickness of the SiO 2  cladding layer  420 , under 600 nm. In some embodiments, the bottom buffer layer thickness may be as low as 200 nm. 
       FIG. 10  is a flow chart illustrating an example method  1000  to manufacture the second example Z-cut LiNbO 3  electro-optic modulator shown in  FIG. 5 , in accordance with some example embodiments. At step  1100 , a silicon (Si) base substrate or wafer  450  may be prepared and cleaned. At step  1150 , a metal may be deposited on the cleaned Si wafer  450  to form a ground electrode  440 . The metal may be, for example but not restricted to, one or combination of gold, copper, titanium, zinc, silver, aluminum and platinum. At step  1200 , a Z-cut LiNbO 3  wafer or substrate may be prepared and cleaned. At step  1300 , SiO 2  may be deposited on the Z-cut LiNbO 3  wafer to form a first SiO 2  cladding layer  420 . At step  1400 , the cleaned Z-cut LiNbO 3  wafer may be put through ion implantation with helium (He) and/or hydrogen ions on the oxide side (i.e., the side that is deposited with SiO 2  in step  1300 ). At step  1500 , the side with ion implantation of the Z-cut LiNbO 3  wafer may be bonded to Si wafer on the side with ground electrode  440  of the Si wafer. At step  1600 , temperature treatment may be carried out on the Z-cut LiNbO 3  wafer to remove the donor LiNbO 3  wafer layer, leaving behind a thin slice of LiNbO 3  wafer. At step  1700 , tantalum deposition and oxidation, using a SiO 2  mask, may be carried out on the thin slice of LiNbO 3  wafer to obtain a ridge portion  435  made of Ta 2 O 5 . At step  1750 , the SiO 2  mask may be removed, and the Ta 2 O 5  ridge portion  435  remains on the LiNbO 3  wafer. At step  1800 , SiO 2  may be deposited on top of the LiNbO 3  wafer to form a second SiO 2  cladding layer  425 , surrounding the Ta 2 O 5  ridge portion  435 . At step  1900 , the metal electrode  410  may be deposited on top of the SiO 2  cladding layer  425 , where the metal may be, for example, one of gold, copper, titanium, zinc, silver, aluminum and platinum. 
       FIG. 6  illustrates a cross-sectional view  600  of an example arm of a third example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. When compared to the modulator designs in  FIG. 4A  and  FIG. 5 , this cross-sectional view  600  shows a modulator with an extra SiO 2  layer  445  between the ground electrode  440  and the Si substrate  450 . The extra SiO 2  cladding layer  445  may be deposited directly on the Si substrate  450  to compensate the temperature coefficient of the LiNbO 3  optical waveguide core  430 , and stable performance of the modulator in this embodiment may be obtained over a specified operating temperature range. The ridge portion  435  of the optical waveguide core  430  can either be dry etched LiNbO 3  (as in  FIG. 4A ) or oxidized Ta 2 O 5  (as in  FIG. 5 ). It is worth noting that the extra SiO 2  cladding layer  445  is not part of waveguide cladding (e.g.  420 ,  425 ), but a layer for temperature compensation to keep the device stable temperature-wise. 
     By placing electrodes  410 ,  440  on the z-axis of a Z-cut LiNbO 3 , the distance between the signal-carrying signal electrode  410  and ground electrode  440 , t D  may be reduced to less than 1 micrometer (μm), significantly less than the distance (4-5 μm) between electrodes aligned in the x-direction in the integrated LiNbO3 modulators. A buffer layer between the optical waveguide core  430  (including the ridge portion  435 ) and the signal electrode  410  may be implemented to lower the conductive loss of optical signal within the microwave electrodes. The buffer layer may have a thickness t B , which may be defined as a distance, along the z-axis of the Z-cut LiNbO 3 , between a bottom surface of the signal electrode  410  and a top surface of the optical waveguide core  430 . When the optical waveguide core  430  includes a ridge portion  435  as a protruding portion of the waveguide core  430  as shown in  FIG. 5 , the thickness t B , may be defined as a distance, along the z-axis of the Z-cut LiNbO 3 , between a bottom surface of the signal electrode  410  and a top surface of the ridge portion  435 . 
     A buffer layer thickness t B  that is too large may negatively affect: 1) the effective refractive index, which leads to a larger VπL; 2) the characteristic impedance Z C ; 3) the conductor loss α 0  (dB/(cm*GHz{circumflex over ( )}0.5)); and 4) the velocity match between RF (microwave, or millimeter wave) and optical wave. Similarly, it is beneficial to keep the bottom buffer layer thickness t S , which is the thickness of the SiO 2  cladding layer  420 , under 600 nm. In some embodiments, the bottom buffer layer thickness of the SiO 2  cladding layer  420  may be as low as 200 nm. 
       FIG. 7A  illustrates a cross-sectional view  700  of an example arm of a fourth example Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. When compared to the modulator designs in  FIG. 4A ,  FIG. 5 , and  FIG. 6 , this cross-sectional view  700  shows a modulator with a ground electrode  440  embedded within the Si substrate  450  having a much narrower width W G . The ground electrode  440  in this embodiment may have a width W G  equal to, or around the same as, the width of the signal electrode  410 . In some embodiments, the ground electrode  440  may have a width that is equal to a width of the ridge portion  435  of the optical waveguide core  430 . 
     By placing electrodes  410 ,  440  on the z-axis of a Z-cut LiNbO 3 , the distance between the signal-carrying signal electrode  410  and ground electrode  440 , t D  may be reduced to less than 1 micrometer (μm), significantly less than the distance (4-5 μm) between electrodes aligned in the x-direction in the integrated LiNbO3 modulators. A buffer layer between the optical waveguide core  430  (including the ridge portion  435 ) and the signal electrode  410  may be implemented to lower the conductive loss of optical signal within the microwave electrodes. The buffer layer may have a thickness t B , which may be defined as a distance, along the z-axis of the Z-cut LiNbO 3 , between a bottom surface of the signal electrode  410  and a top surface of the optical waveguide core  430 . When the optical waveguide core  430  includes a ridge portion  435  as a protruding portion of the waveguide core  430  as shown in  FIG. 5 , the thickness t B , may be defined as a distance, along the z-axis of the Z-cut LiNbO 3 , between a bottom surface of the signal electrode  410  and a top surface of the ridge portion  435 . 
     A buffer layer thickness t B  that is too large may negatively affect: 1) the effective refractive index, which leads to a larger VπL; 2) the characteristic impedance Z C ; 3) the conductor loss α 0  (dB/(cm*GHz{circumflex over ( )}0.5)); and 4) the velocity match between RF (microwave, or millimeter wave) and optical wave. Similarly, it is beneficial to keep the bottom buffer layer thickness t S , which is the thickness of the SiO 2  cladding layer  420 , under 600 nm. In some embodiments, the bottom buffer layer thickness of the SiO 2  cladding layer  420  may be as low as 200 nm. 
       FIG. 7B  illustrates a radio-frequency (RF) electric field graph of the fourth example Z-cut LiNbO 3  electro-optic modulator, while  FIG. 7C  illustrates an optical power flow graph of the fourth example Z-cut LiNbO 3  electro-optic modulator. Compared to the modulator shown in  FIG. 4A , the electric field generated by the fourth example Z-cut LiNbO 3  electro-optic modulator is better contained within the optical waveguide core  430 . The optical waveguide core  430  may be made of LiNbO 3 . The ridge portion  435  of the optical waveguide core  430  can either be dry etched LiNbO 3  (as in  FIG. 4A ) or oxidized Ta 2 O 5  (as in  FIG. 5 ). 
       FIG. 8  illustrates a cross-sectional view  800  of an example arm of a fifth Z-cut LiNbO 3  electro-optic modulator, in accordance with some example embodiments. When compared to the modulator designs in  FIG. 4A ,  FIG. 5 , and  FIG. 6 , this cross-sectional view  800  shows a modulator with a ground electrode  440  embedded within the Si substrate  450  having a much narrower width W G . The ground electrode  440  in this embodiment may have a width W G  equal to, or around the same as, the width of the signal electrode  410 . In some embodiments, the ground electrode  440  may have a width that is equal to a width of the ridge portion  435  of the optical waveguide core  430 . 
     In addition, the LiNbO 3  optical waveguide may include three individual portions, with a SiO 2  layer  420  between the first and the second portions of the LiNbO 3  optical waveguide core  430  along the x-axis of the Z-cut LiNbO 3 , and another SiO 2  layer  420  between the second and the third portions of the LiNbO 3  optical waveguide core  430  along the x-axis of the Z-cut LiNbO 3 . 
     Although the present disclosure describes methods and processes with steps in a certain order, one or more steps of the methods and processes may be omitted or altered as appropriate. One or more steps may take place in an order other than that in which they are described, as appropriate. 
     Certain adaptations and modifications of the described embodiments can be made. Therefore, the above discussed embodiments are considered to be illustrative and not restrictive. Although this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments, as well as other embodiments of the invention, will be apparent to persons skilled in the art upon reference to the description. It is therefore intended that the appended claims encompass any such modifications or embodiments.