Abstract:
The invention discloses phase-shifters, modulators, and method that produces a smaller π by means of a field excitation using multiple electrodes. A negative signal is introduced that travels with the positive signal, which enhances the electric field significantly. The field enhancement is provided by the superposition of the fields accumulated from each electrode. A base or substrate material can be made from any compound having linear electro-optic properties, such as lithium niobate, lithium tantalite, potassium lithium niobate, potassium titanyl phosphate or gallium-arsenide. For lithium niobate, there are two possible orientations of electric field, z-cut orientation or x-cut orientation.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application relates to concurrently filed, co-pending application U.S. patent application Ser. No. 09/791,956, entitled “Tri-Electrode Traveling Wave Optical Phase Shifters and Methods” by Marc Hill et al., owned by the assignee of this application and incorporated herein by reference. 
     This application relates to concurrently filed, co-pending application U.S. patent application Ser. No. 09/792,220, entitled “Tri-Electrode Traveling Wave Optical Modulators and Methods” by Marc Hill et al., owned by the assignee of this application and incorporated herein by reference. 
     This application relates to concurrently filed, co-pending application U.S. patent application Ser. No. 09/792,219, entitled “Dual-Electrode Traveling Wave Optical Phase Shifters and Methods” by Marc Hill et al., owned by the assignee of this application and incorporated herein by reference. 
    
    
     BACKGROUND INFORMATION 
     1. Field of the Invention 
     The present invention relates to the field of optical devices, and particularly to light modulators such as traveling-wave modulators, phase shifters, and switches. 
     2. Description of Related Art 
     Telecommunication companies seek to increase the amount of information throughput with fatter pipes and at higher speed to meet the demand from the industrial, business, and consumer markets. This in turn requires a light transmitting system to enlarge transmission and receiving capacity drastically. At present, the light transmission speed of 10 Gb/second has already been reduced to practice for commercial use, with the next hurdle set at 40 Gb/second. 
     Several testings are underway to find a suitable material for use as an optical waveguide in a traveling-wave light modulator that is capable of operating in broad band at high frequency, such material includes lithium niobate (LiNbO), lithium tantalite, potassium lithium niobate, potassium titanyl phosphate or gallium-arsenide. Lithium niobate and lithium tantalite are excellent ferroelectric materials, with large electro-optical coefficients, which can control a light phase proportional to an electrical field strength within an optical waveguide generated by an electrical signal applied to electrical electrodes. 
     Factors which effect the modulation of a traveling-wave light modulator include velocity mismatch, impedance mismatch, dispersion, electrode power loss, and the electrical field generation. Among them, velocity mismatch, impedance mismatch and dispersion are principally determined by the structure of the traveling-wave light modulator, which can be achieved with careful electrode design. However, the electrical field strength is determined by the applied electrical signal amplitude, the electrode power loss and the electrode structure, and the excitation mode in the electrode structure. For 40 Gb/sec. modulation, one of the major challenges is to reduce the required driving voltage of the modulator, which is generally dictated by high electrode loss and the difficulties of generating high-voltage swing with semiconductors at this speed. 
     In electrical field generation and the phase modulation, at the input of one electrical waveguide or electrode, a high-speed electrical signal is applied and triggers an electromagnetic wave propagating along the waveguide. The field strength at a certain point along the waveguide is determined by the particular way in which the EM wave was excited for a given input voltage, and the propagation attenuation along the waveguide. The optical index of the optical waveguide is changed linearly by the applied electrical field, and the overall phase change of the optical signal is an integration of all the incremental phase changes along the waveguide and is proportional to the product of the driving voltage and the modulation length. Due to bandwidth considerations, the effective modulation length cannot be increased beyond a limit and hence a driving voltage above a threshold is required to achieve a required optical modulation. For high-speed communications systems transmitting at 10 Gb/sec or higher, the electrode loss is significant and typically leads to a very high required driving voltage. 
     Given the high loss and the limited voltage swing, it adds more complexity and cost to realize a practical communication system using such a modulator, if not impossible. The under-driven modulator would lead to significant degradation of the modulated light signal and significantly limits its use to many communication systems. Therefore, a light modulator having a lower driving voltage is in demand. 
     Attempts have been made to reduce a driving voltage. One method has been a two stage electrode design which uses the first stage of the electrode to primarily achieve the maximum overlap of the electrical field and the optical field, and uses the second stage to achieve the phase velocity match the between the electrical and the optical signals. However, it is difficult to realize due to phase matching required of the two stages of the electrode. Further, it just introduces one more freedom to alleviate the constraints for simultaneous phase and field matching. It does not provide an effective means to reduce the driving voltage. 
     A ridge structure is a modification of a conventional CPW (co-planar waveguide) design, by raising the center electrode conductor above the two grounding planes. It does provide the advantage of lowering the driving voltage. For example, see K. Noguchi et al, “Highly efficient 40-GHz bandwidth Ti: LiNbO optical modulator employing ridge structure”, IEEE Photonics Technology Letters, Vol. 5, No.1, January 1993. However, it is difficult to realize due to the additional processes and the additional optical signal losses incurred by fabricating the ridge. Moreover, the reduction of the driving voltage is very limited, which is about 20% typically. 
     A conventional broadband optical communication uses a Mach-Zehnder interferometer to modulate laser signals in a transmitter. An electric field applied to an optical waveguide changes its index of refraction. A signal strip and ground plane (a zero voltage), form an electrical waveguide (EWG), where the induced electric field creates a change in the refractive index of the inlayed optical waveguide (OWG). The index of the material, for example, LiNbO3 or GaAs, depends on the amplitude and direction of the applied electric field. 
     Lithium-Niobate Mach-Zehnder modulators require a large voltage and length to provide a π phase shift through an active length L. The voltage level required is too large relative to amount provided by ultra-fast electronic transistors. The length of the modulator is limited by the synchronism of the electric and optical propagating waves. For this reason, the length cannot be increased without a regenerative amplification of the signal or a multistage system that requires precise synchronization. 
     Accordingly, it is desirable to have phase shifters, modulators, and methods that decrease a V π  value or shortening of an active length. 
     SUMMARY OF THE INVENTION 
     The invention discloses phase-shifters, modulators, and methods that produce a smaller Vπ by means of a field excitation using multiple electrodes. A negative signal is introduced that travels with the positive signal, which enhances the electric field significantly. The field enhancement is provided by the superposition of the fields accumulated from each electrode. A base or substrate material can be made from any compound having linear electro-optic properties, such as lithium niobate, lithium tantalite, potassium lithium niobate, potassium titanyl phosphate or gallium-arsenide. For lithium niobate, there are two possible orientations of the crystal, z-cut or x-cut orientation. Horizontal electrical field is typically used to drive the x-cut crystal, and vertical electrical field is typically used to drive the z-cut crystal. 
     In a first aspect of the invention, tri-electrode traveling wave optical phase shifters and methods are disclosed. The optical shifters employing a tri-electrode configuration that are driven differentially and allows for a lower voltage to accumulate a phase shift. This type of shifter can be used in a Mach-Zehnder interferometer or a fast optical switch. Phase shifting an optical signal is desired in optical communications, i.e. in modulators or switches. 
     In a second aspect of the invention, tri-electrode traveling wave optical modulators and methods are disclosed. The optical modulators employing a tri-electrode configuration that are driven differentially and allow for a lower voltage to modulating an optical signal. 
     In a third aspect of the invention, dual-electrode traveling wave optical phase shifters and methods are disclosed. The optical shifters employing a differentially-driven dual-electrode that allows for a lower voltage to accumulate a phase shift. 
     In a fourth aspect of the invention, dual-electrode traveling wave optical modulators and methods are disclosed. The optical modulators employing differential strip fields with a dual-electrode that allow for a lower voltage to modulating an optical signal. One of ordinary skill in the art should know that the term differentially driven could mean the application of driving signals that have opposite polarity from one electrode to another electrode, or other similar definitions. 
     Optionally, a buffer layer is inserted between electrodes and a substrate to improve phase matching between an electrical signal and an optical signal. Advantageously, the present invention employing tri-electrodes or dual-electrodes allows for a better match of phase velocity and for a reduced buffer layer thickness that may be used between the optical and electrical waveguide. 
     Other structures and methods are disclosed in the detailed description below. This summary does not purport to define the invention. The invention is defined by the claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is structural diagram illustrating a cross-sectional view of a tri-electrode phase-shifter with a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 2 is a circuit diagram illustrating a tri-electrode phase-shifter with a vertical field in the optical waveguide in accordance with the present invention. 
     FIG. 3 is a circuit diagram illustrating a single arm modulator with a tri-electrode phase-shifter with a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 4 is a circuit diagram illustrating one embodiment of two optical phase-shifters to form an optical switch, a Mach-Zehnder type interferometer or modulator in accordance with the present invention. 
     FIG. 5 is a structural diagram illustrating a cross-sectional view of a tri-electrode phase-shifter utilizing a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 6 is a circuit diagram illustrating a tri-electrode phase-shifter utilizing a horizontal field in the optical waveguide in accordance with the present invention. 
     FIG. 7 is a circuit diagram illustrating a single arm modulator with a tri-electrode phase-shifter utilizing a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 8 is a circuit diagram illustrating a first embodiment of two optical phase-shifters in constructing an optical switch, a modular, or a Mach-Zehnder type interferometer in accordance with the present invention. 
     FIG. 9 is a circuit diagram illustrating a second embodiment of a two phase-shifters in constructing an optical switch, a modular, or a Mach-Zehnder type interferometer in accordance with the present invention. 
     FIG. 10 is a circuit diagram illustrating a third embodiment of two optical phase-shifters in constructing an optical switch, a modular, or a Mach-Zehnder type interferometer in accordance with the present invention. 
     FIG. 11 is a circuit diagram illustrating a fourth embodiment of two optical phase-shifters in constructing an optical switch, a modular, or a Mach-Zehnder type interferometer in accordance with the present invention. 
     FIG. 12 is a structural diagram illustrating a first embodiment of a cross-sectional view of an optical phase-shifter employing a tri-electrode with a buffer layer utilizing a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 13 is a structural diagram illustrating a second embodiment of a cross-sectional view of a tri-electrode optical shifter with a buffer layer utilizing a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 14 is a structural diagram illustrating a third embodiment of a cross-sectional view of an optical phase-shifter employing a tri-electrode with a buffer layer utilizing a horizontal field in the optical waveguide in accordance with the present invention. 
     FIG. 15 is a structural diagram illustrating a fourth embodiment of a cross-sectional view of a tri-electrode optical phase shifter with a buffer layer utilizing a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 16 is a process diagram illustrating a first embodiment of a cross-sectional view of an optical modulator with a tri-electrode utilizing a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 17 is a circuit diagram illustrating the first embodiment of an optical modulator with a tri-electrode utilizing a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 18 is a process diagram illustrating a first embodiment of a cross-sectional view of an optical modulator with a tri-electrode utilizing a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 19 is a circuit diagram illustrating the second embodiment of an optical modulator with a tri-electrode utilizing a vertical electric field in the optical waveguide in the optical waveguide in accordance with the present invention. 
     FIG. 20 is a process diagram illustrating a phase shifter employing dual-electrode with a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 21 is a process diagram illustrating a phase shifter employing dual-electrode with a horizontal electric field in the optical waveguide with a buffer layer in accordance with the present invention. 
     FIG. 22 is a circuit diagram illustrating a phase-shifter employing dual-electrode with a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 23 is a circuit diagram illustrating a single arm modulator employing dual-electrodes with a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 24 is a circuit diagram illustrating two phase shifters connected in parallel to form a MZ modulator utilizing a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 25 is a process diagram illustrating a phase shifter employing dual-electrode with a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 26 is a circuit diagram illustrating a phase shifter employing dual-electrode with a vertical electric field in the optical waveguide with a buffer layer in accordance with the present invention. 
     FIG. 27 is a process diagram illustrating a phase shifter employing dual-electrode with a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 28 is a circuit diagram illustrating a single arm modulator employing dual-electrode with a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 29 is a circuit diagram illustrating two phase-shifters connected in parallel to form a MZ modulator utilizing a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 30 is a structural diagram illustrating a dual-electrode modulator where two optical waveguides are placed in regions of utilizing a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 31 is a circuit diagram illustrating a dual-electrode modulator driven from an electrical amplifier with two optical waveguides utilizing a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 32 is a process diagram illustrating a ridge structure employing tri-electrodes utilizing a vertical electric field in the optical waveguide in accordance with the present invention. 
     FIG. 33 is a process diagram illustrating a ridge structure employing dual-electrode with a horizontal electric field in the optical waveguide in accordance with the present invention. 
     FIG. 34 is a process diagram illustrating a modulator employing a ridge structure with tri-electrode with a horizontal field in the optical waveguides in accordance with the present invention. 
     FIG. 35A is a graphical diagram illustrating one example of a pair of time-varying signals having opposite polarity. 
     FIG. 35B is a graphical diagram illustrating electric field lines at time t 1 . 
     FIG. 35C is a graphical diagram illustrating electric field lines at time t 2 . 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 1 is structural diagram illustrating a cross-sectional view of a tri-electrode phase-shifter  10  with a vertical electric field in a z-cut orientation. A basic structure of the tri-electrode phase-shifter  10  has three electrodes, a negative electrode S−  13 , a positive electrode S+  14 , and a negative electrode S−  15 , in which signals are applied on and trigger a traveling wave whose phase velocity matches that of an optical waveguide (WG)  17 . The traveling electrical signal induces a change in the refractive index in the optical waveguide  17  and hence induces a phase change. The optical waveguide (WG)  17 , which has a slightly higher refractive index than the surrounding material, is positioned underneath the base of the positive electrode S+  14 , thereby creating a vertical electric field in the optical waveguide  17 . The optical waveguide  17 , for example, is achieved by doping Ti in LiNbO3. An electrical field E  18  exists between the positive electrode S+  14  and the negative electrode S−  13 , and an electric field E  19  exists between the positive electrode S+  14  and the negative electrode S−  15 . The ground electrodes  12  and  16  are used to suppress the couplings to parasitic modes at high frequencies. A substrate  11  can be selected from a material such as like GaAs, KDP, or LiNbO3, which demonstrates a linear electro-optic effect. 
     Preferably, the optical waveguide (WG)  17  is placed in a center position underneath the positive electrode S+  14 . However, one of ordinary skill in the art should recognize that the optical waveguide (WG)  17  can be shifted to the left or the right of the positive electrode S+  14 , or align to the left edge or the right edge of the positive electrode S+  14 . The optical waveguide  17  can be doped or diffused with a material that has a slightly higher refractive index than the surrounding material. For example, Ti can be diffused into the material LiNbO3 to cause a higher index of refraction that guides a wave. 
     A negative signal is introduced from the electrode S−  13  that travels with the positive signal S+  14  to enhance an electrical field significantly. The field enhancement is provided by the superposition of the fields created by each electrode giving better performance. The material  11  can be made of any compound having linear electro-optic properties. Lithium Niobate has a preferred direction, depending on the direction of a crystal. For the case of Lithium Niobate, there are two possible orientations of the electric field, z-cut or x-cut. Lithium Niobate is an anisotropic material, in which the z-axis possesses the highest electro-optical coefficient. FIG. 1 is intended as one illustration of the tri-electrode phase shifter  10  with the optical waveguide, for example, in z-cut orientation crystal. It is apparent to one of skill in the art that various types of optically active material, such as gallium-arsenide or lithium niobate x-cut, can be practiced without departing from the spirits of the present invention. 
     FIG. 2 is a circuit diagram illustrating a tri-electrode phase-shifter  20  with a vertical electric field. An amplifier  23  receives an input  22  and generates three electrical outputs through a transmission line S 1   24   a , a transmission line S 2   24   b , and a transmission line S 3   24   c . The transmission line S 1   24   a  extends through the electrode  13  to a load L 1  or termination resistor  25   a  and a ground  26   a . The transmission line S 2  extends through the electrode  14  to a load L 2  or termination resistor  25   b  and a ground  26   b . The transmission line S 3   24   c  extends through the electrode  15  to a load L 3  or termination resistor  25   c  and a ground  26   c . Between the negative electrode  13  and the positive electrode  14 , a traveling electrical wave ω 1   27  is created due to the proximity of the S 1   24   a  transmission line and the S 2   24   b  transmission line  24   b . Between the positive electrode  14  and the negative electrode  15 , a traveling electrical wave ω 2   28  is created from the proximity of the S 2   24   b  transmission line and the S 3   24   c  transmission line. In this embodiment, an optical wave λin  21  received from, far example, an optical fiber (not shown), travels underneath the electrode S+  14 , generating an output rout  29 . The optical signal λin  21  travels co-spatially with the electrical signal ω 1   27  and ω 2   28 . Preferably, the traveling wave ω 1   27  is identical or substantially similar to the traveling electrical wave ω 2   28 . Furthermore, the optical signal λin  21  travels with the same or substantially the same velocity as the traveling wave ω 1   27  and ω 2   28 . 
     The amplifier  23  matches the impedance of the transmission lines S 1   24   a , S 2   24   b , and S 3   24   c , and matches with the impedance of the loads L 1   25   a , L 2   25   b , and L 3   25   c . In the preferred mode, the amplitudes of the negative electrodes S−  13  and S−  15  have the same amount of negative amplitude as the amplitude of the positive electrode S+  14 . The amount of signal amplitude applied affects the amount of phase shift. The amount of phase shift is linearly proportional to the signal amplitude generated from the amplifier  23 . For example, if applying 1-volt, a 45° phase shift may result, and if applying 2-volts, a 90° phase shift may result. 
     A reduction of Vπ×L is caused by the superposition of the field induced by the electrodes, resulting in the enhancement in the electrical field. In one embodiment, the traveling electrical wave ω 1   27  modulation is doubled due to the field excitation between the electrodes  13  and  14 . However, the modulation can be more than 2 times, or less than 2×, depending on the distance between the electrodes  13  and  14 , the height of each electrode  13  or  14 , and the thickness of a buffer layer. Preferably, the ω 1   27  modulation is symmetrical to the traveling electrical wave ω 1   28  modulation. One of ordinary skill in the art, however, should recognize that the traveling electrical wave ω 1   27  modulation and the traveling electrical wave ω 1   28  modulation can be designed to be asymmetrical. 
     Optionally, a direct current (DC) bias field can be applied to each of the at electrodes S−  13 , S+  14 , and S−  15 , by direct or indirect coupling. 
     FIG. is a circuit diagram illustrating a single arm modulator  30  with a tri-electrode phase-shifter with a vertical electric field. The single arm or single arm modulator  30  receives a light signal input λin  31  and split the light signal λin  31  into two optical paths, a λ 1   32  and a λ 2    33 . The λ 1   32  travels in an optical waveguide (not shown) that is routed away from the electrode S−  13 , S+  14 , and S−  15 . The λ 2    33  travels underneath the electrode S+  14 . The λ 1   32  and λ 2    33  are combined to generate a single optical output λout  34 . The amplifier  23  receives the input  22  and generates three electrical outputs through the transmission line S 1   24   a , the transmission line S 2   24   b , and the transmission line S 3   24   c . The transmission line S 1   24   a  extends through the electrode  13  to the load L 1  or termination resistor  25   a  and the ground  26   a . The transmission line S 2  extends through the electrode  14  to the load L 2  or termination resistor  25   b  and the ground  26   b . The transmission line S 3   24   c  extends through the electrode  15  to the load L 3  or termination resistor  25   c  and the ground  26   c . Between the negative electrode  13  and the positive electrode  14 , a traveling electrical wave ω 1   27  is created due to the close proximity of a gap between them. Between the positive electrode  14  and the negative electrode  15 , the traveling electrical wave ω 2   28  is created due to the close proximity of the gap between them. In this embodiment, an optical wave λin  31  received from, for example, an optical fiber travels through the electrode S+  14 , in generating an output λout  34 . The optical signal λin  31  travels beneath traveling the electrical signal ω 1   27 . Preferably, the traveling wave ω 1   27  is identical or substantially similar to the traveling electrical wave ω 2   28 . 
     FIG. 4 is a circuit diagram illustrating one embodiment of two optical phase-shifters to form an optical switch, a Mach-Zehnder type interferometer or modulator  40 , having an upper phase-shifter  41  and a lower optical phase-shifter  30 . The light signal input λin  31  is split into two paths, the λ 1    32  and the λ 2    33 , which are re-combined to generate a the λ out    49 . An amplifier  42  receives the input  22  and generates a first output to an amplifier  43 , and a second output to the amplifier  23 . The amplifier  43  receives then generates three electrical outputs through a transmission line S 1   44   a , a transmission line S 2   44   b , and a transmission line S 3   44   c . The transmission line tS 1   44   a  extends through a first electrode  45   a  to the load L 1  or termination resistor  46   a  and the ground  47   a . The transmission line S 2   44   b  extends through the electrode  45   b  to the load L 2  or termination resistor  46   b  and the ground  47   b . The transmission line S 3   44   c  extends through the electrode  45   c  to the load L 3  or termination resistor  46   a  and the ground  47   c . Between the positive electrode  45   b  and the negative electrode  45   a , a traveling electrical wave ω 1   48   a  is created due to the close proximity of a gap between them. Between the negative electrode  45   c  and the positive electrode  45   b , the traveling electrical wave ω 2   48   b  is created due to the close proximity of the gap between them. 
     Preferably for wide band applications, the electrical wave ω 1   27  matches or substantially matches the electrical wave ω 2   28 . Similarly, electrical wave ω 3   48   a  matches or substantially matches the electrical wave ω 4   48   b . In addition, the light wave λ 1    32  matches or substantially matches the light wave λ 2    33 . Optionally, the electrodes  13 ,  14 ,  15 ,  45   a ,  45   b , and  45   c  can be connected to a voltage supply (not shown), to generate a DC bias field in the optical waveguide. 
     Advantageously, this embodiment with three electrodes in the present invention allow for a better match of phase velocity and allow for a reduced buffer layer thickness that may be used between the optical and electrical waveguide. 
     FIG. 5 is a structural diagram illustrating a cross-sectional view of a tri-electrode phase-shifter  50  utilizing a horizontal electric field and with an x-cut orientation. The basic structure of the tri-electrode phase-shifter  50  has three electrodes, a negative electrode S−  53 , a positive electrode S+  54 , and a negative electrode S−  55 . An optical waveguide (WG)  57  is positioned in a gap underneath and in between the positive electrode S+  54  and the negative electrode S−  55 , thereby being placed in a substantially horizontal electric field  59  which exists between the positive electrode S+  54  and the negative electrode S−  55 . 
     Preferably, the optical waveguide (WG)  57  is placed in a center of and underneath a gap between the positive electrode S+  54  and the negative electrode S−  55 . However, one of ordinary skill in the art should recognize that the optical waveguide (WG)  57  can be shifted to toward the left and closer to the positive electrode S+  54  or toward the right and closer to the negative electrode S−  55 , or aligned to the right edge of the positive electrode S+  54  or the left edge the negative electrode S−  55 . The optical waveguide  57  can be doped or diffused with a material that has a slightly higher refractive index than the surrounding material. For example, if LiNbO, a Ti that is diffused into the material and that caused a higher index of refraction that guides a wave. 
     A negative signal is introduced into the electrode S−  53  that travels with the positive signal S+  54  to provide significant enhancement of the electrical field. The field enhancement is provided by the superposition of the fields created by each electrode giving better performance. The material  51  can be made of any compound having linear electro-optic properties. Lithium Niobate has a preferred direction, depending on the direction of a crystal. 
     FIG. 6 is a circuit diagram illustrating a tri-electrode phase-shifter  60  utilizing a horizontal electric field. An amplifier  63  receives an input  62  and generates three electrical outputs through a transmission line S 1   64   a , a transmission line S 2   64   b , and a transmission line S 3   64   c . The transmission line S 1   64   a  extends through the electrode  53  to a load L 1  or termination resistor  65   a  and a ground  66   a . The transmission line S 2  extends through the electrode  54  to a load L 2  or termination resistor  65   b  and a ground  66   b . The transmission line S 3   64   c  extends through the electrode  55  to a load L 3  or termination resistor  65   c  and a ground  66   c . Between the negative electrode  53  and the positive electrode  54 , a traveling electrical wave ω 1   67  is created due to the proximity of the S 1   64   a  transmission line and the S 2   64   b  transmission line. Between the positive electrode  54  and the negative electrode  55 , a traveling electrical wave ω 2   68  is created due to their proximity. In this embodiment, an optical wave λin  61  received from, for example, an optical fiber, travels between the negative electrode S−  53  and the positive electrode S+  54 , in generating an output λout  69 . The optical signal λin  61  travels co-spatially with the electrical signal ω 1   67  and ω 2   68 . Preferably, the traveling wave ω 1   67  is symmetrical or substantially symmetrical to the traveling electrical wave ω 2   68 . 
     The amplifier  63  matches the impedance of the transmission lines S 1   64   a , S 2   64   b  and S 3   64   c , and matches the impedance of the loads Li  65   a , L 2   65   b , and L 3   65   c . In the preferred mode, the amplitudes of the negative electrodes S− 53  and S−  55  have the same amount of amplitude as the amplitude of the positive electrode S+  54 . 
     The amount of signal amplitude applied affects the amount of phase shift. The amount of phase shift is linearly proportional to the signal amplitude generated from the amplifier  63 . For example, if apply 1-volt, it may result in a 45 degree phase shift, and if apply 2-volt, it may result in a 90 degree phase shift. 
     Optionally, a direct current (DC) bias field can be applied to each of the electrodes S−  53 , S+  54 , and S−  55 , by direct or indirect coupling. 
     A reduction of Vπ×L is caused by the superposition of the field induced by the electrodes, resulting in the enhancement in the electrical field. In one embodiment, the amplitude of the traveling electrical wave ω 1   67  is doubled due to the field excitation between the electrodes  53  and  54 . However, the increase can be more than 2 times, or less than 2×, depending on the distance between the electrodes  53  and  54 , the height and shape of each electrode  53  or  54 , and the thickness of a buffer layer. Preferably, the ω 1   67  modulation is symmetrical to the traveling electrical wave ω 1   68  modulation. One of ordinary skill in the art, however, should recognize that the traveling electrical wave ω 1   67  and the traveling electrical wave ω 1   68  can be designed to by asymmetrical. 
     The electrodes of the optical phase-shifter would be driven as in FIG. 5, where a driver amplifier would provide the signal to the three electrodes, the outer two driven with the same polarity and the center with opposite polarity of the outer. The electrical signal propagates from left to right, where the signal is terminated into matched loads. 
     FIG. 7 is a circuit diagram illustrating a single a modulator  70  with a tri-electrode phase-shifter utilizing a horizontal electric field. The light signal input λin  71  is split into two optical paths, a λ 1   72  and a λ 2   73 . The λ 1   72  travels in an optical waveguide (not shown) that is routed away from the electrodes S−  53 , S+  54  and S−  55 , while the λ 2   73  travels between the electrode S−  53  and the electrode S+  54 . λ 1   72  and a λ 2   73  are combined to generate a single optical output λout  741 . The amplifier  63  receives the input  62  and generates three electrical outputs through the transmission line S 1   64   a , the transmission line S 2   64   b , and the transmission line S 3   64   c . The transmission line S 1   64   a  extends through the electrode  53  to the load L 1  or termination resistor  65   a  and a ground  66   a . The transmission line S 2  extends through the electrode  54  to the load L 2  or termination resistor  65   b  and the ground  66   b . The transmission line S 3   64   c  extends through the electrode  55  to the load L 3  or termination resistor  65   c  and the ground  66   c . Between the negative electrode  53  and the positive electrode  54 , a traveling electrical wave ω 1   67  is created due to their proximity. Between the positive electrode  54  and the negative electrode  55 , a traveling electrical wave ω 2   68  is created due to their proximity. In this embodiment, an optical wave λin  71  received from, for example, an optical fiber (not shown), travels between the negative electrode S−  53  and the positive electrode S+  54 , in generating an output λout  69 . The optical signal λin  61  travels co-spatially with the electrical signal ω 1   67  and ω 2   68 . Preferably, the traveling wave ω 1   67  is symmetrical or substantially symmetrical to the traveling electrical wave ω 2   68 . 
     FIG. 8 is a circuit diagram illustrating a first embodiment of two optical phase shifters  80  in constructing an optical switch, a modulator, or a Mach-Zehnder type interferometer. The two phase-shifters  80  has an upper phase shifter  81  and a lower optical phase shifter  70 . The light signal input λin  82  is split into two paths, the λ 1    83  and the λ 2    84 , which are re-combined to generate a the λout  85 . In this embodiment, the light signal λ 1    82  travels between a positive electrode  45   b  and a negative electrode  45   c , while the light signal λ 2    83  travels between the positive electrode  13  and the negative electrode  14 . The amplifier  42  receives the input  41  and generates a first output to an amplifier  43 , and a second output to the amplifier  23 . The amplifier  43  receives then generates three electrical outputs through a transmission line S 1   44   a , a transmission line S 2   44   b , and a transmission line S 3   44   c . The transmission line S 1   44   a  extends through a first electrode  45   a  to the load L 1  or termination resistor  46   a  and the ground  47   a . The transmission line S 2   44   b  extends through the electrode  45   b  to the load L 2  or termination resistor  46   b  and the ground  47   b . The transmission line S 3   44   c  extends through the electrode  45   c  to the load L 3  or termination resistor  46   c  and the ground  47   c . Between the positive electrode  45   b  and the negative electrode  45   a , a traveling electrical wave ω 48   a  is created due to the close proximity of a gap between them. Between the negative electrode  45   c  and the positive electrode  45   b , the traveling electrical wave ω 48   b  is created due to the close proximity of the gap between them. 
     FIG. 9 is a circuit diagram illustrating a second embodiment of a two phase-shifters in constructing an optical switch, a modulator, or a Mach-Zehnder type interferometer. The light signal input λin  91  is split into two paths, the λ 1    92  and the λ 2    93 , which are re-combined to generate a the λ out    94 . In this embodiment, the light signal λ 1    82  travels between a negative electrode  45   a  and a positive electrode  45   b , while the 
     FIG. 10 is a circuit diagram illustrating a third embodiment of two optical phase shifters  100  in constructing an optical switch, a modulator, or a Mach-Zehnder type interferometer. The light signal input ωin  101  is split into two paths, the ω 1   102  and the λ 2   103 , which are re-combined to generate a λout  104 . In this embodiment, the light signal λ 1   102  travels between the negative electrode  45   a  and the positive electrode  45   b , while the light signal λ 2   103  travels between the negative electrode  13  and the positive  15  electrode  14 . 
     FIG. 11 is a circuit diagram illustrating a fourth embodiment of two optical phase-shifters  110  in constructing an optical switch, a modulator, or a Mach-Zehnder type interferometer. The light signal input λin  111  is split into two paths, the λ 1   112  and the λ 2   113 , which are re-combined to generate a λout  114 . In this embodiment, the light signal λ 1   102  travels between the positive electrode  44   b  and the negative electrode  44   c , while the light signal λ 2   113  travels between the positive electrode  14  and the negative electrode  15 . 
     FIG. 12 is a structural diagram illustrating a first embodiment of a cross-sectional view of an optical phase-shifter  120  with a buffer layer utilizing a vertical electric field in the optical waveguide. A buffer layer  121  is placed between the substrate  11 , and the ground electrode  12 , the negative S− electrode  13 , the positive S+ electrode  14 , the negative electrode S−  15 , and the ground electrode  16 . The width of the buffer layer  121  extends all the way from the ground electrode  12 , through the negative S− electrode  13 , the positive S+ electrode  14 , the negative electrode S−  15 , to the ground electrode  16 . 
     The buffer layer  121  preferably has a significantly lower dielectric constant than that of the substrate  11 . The use of the buffer layer  121  helps to improve the phase matching between an electrical signal and an optical signal, as well as increasing the electrode impedance. 
     If the substrate  11  uses lithium niobate, the preferred material for the buffer layer  121  is silicon oxide, with a thickness of, for example, 1 microns. With the buffer layer  121 , the design of a phase shifter is significantly simpler due to the more electric field in the air. Optionally, the thickness of the buffer layer  121  can be reduced to enhance the electrical field. 
     FIG. 13 is a structural diagram illustrating a second embodiment of a cross-sectional view of a tri-electrode optical shifter  130  with a buffer layer utilizing a vertical electric field. The width of a buffer layer  131  extends underneath the negative S− electrode  13 , the positive S+ electrode  14 , and the negative electrode S−  15 . The buffer layer  131  does not extend to underneath of the ground electrode  12  and the ground electrode  16 . The buffer layer  131  preferably has a significantly lower dielectric constant than that of the substrate  11 . 
     FIG. 14 is a structural diagram illustrating a third embodiment of a cross-sectional view of an optical phase-shifter with a buffer layer utilizing a horizontal field in the optical waveguide. A buffer layer  141  is placed between the substrate  51 , and the ground electrode  52 , the negative S− electrode  53 , the positive S+ electrode  54 , the negative electrode S−  55 , and the ground electrode  56 . The width of the buffer layer  141  extends all the way from the ground electrode  52 , through the negative S− electrode  53 , the positive S+ electrode  54 , the negative electrode S−  55 , to the ground electrode  56 . The buffer layer  141  preferably has a significantly lower dielectric constant than that of the substrate  51 . The optical waveguide  57  is positioned in a gap underneath and in between the positive S+ electrode  54  and the negative electrode S−  55 . 
     FIG. 15 is a structural diagram illustrating a fourth embodiment of a cross-sectional view of a tri-electrode optical phase shifter with a buffer layer utilizing a horizontal electric field. A buffer layer  151  is placed between the substrate  51 , and the ground electrode  52 , the negative S− electrode  53 , the positive S+ electrode  54 , the negative electrode S−  55 , and the ground electrode  56 . The width of the buffer layer  151  extends all the way from the ground electrode  52 , through the negative S− electrode  53 , the positive S+ electrode  54 , the negative electrode S−  55 , to the ground electrode  56 . The buffer layer  141  preferably has a significantly lower dielectric constant than that of the substrate  51 . An optical waveguide  152  is positioned in a gap underneath and in between the positive S+ electrode  54  and the negative electrode S−  53 . 
     FIG. 16 is a process diagram illustrating a first embodiment of a cross-sectional view of an optical modulator  160  with a tri-electrode utilizing a horizontal electric field in the optical waveguide. The tri-electrode modulator  160  has three electrodes, a negative electrode S−  163 , a positive electrode S+  164 , and a negative electrode S−  165 . The center electrode, the positive electrode S+, has one polarity, and the outer electrodes, the negative electrode S−  163  and the negative electrode S−  165 , have an opposite polarity of the center. One of ordinary skill in the art should recognize that the center electrode could have a negative electrode, while the outer electrodes have positive electrodes. Optical waveguides  167  and  168  are shown in a region of large horizontal field E field  169   a  and  169   b . The optical waveguide (WG)  167  is positioned in a gap underneath and in between the negative electrode S−  163  and the positive electrode S+  164 , thereby being placed in a substantially horizontal field. Similarly, the optical waveguide (WG)  168  is positioned in a gap underneath and in between the positive electrode S+  164  and the negative electrode S−  165 , thereby being placed a substantially horizontal field. An electrical field E  169   a  exists between the positive electrode S+  164  and the negative electrode S−  163 , and an electrical field E  169   b  exists between the positive electrode S+  164  and the negative electrode S−  165 . 
     A first negative signal is introduced into the electrode S−  163  that travels with the positive signal S+  164  so to significantly enhance the electrical field in the optical waveguide  167 . A second negative signal is introduced into the electrode S−  165  that travels with the positive signal S+  164  so to significantly enhance the electrical field in the optical waveguide  168 . The field enhancement is provided by the superposition of the fields created by each electrode giving better performance. The material  161  can be made of any compound having linear electro-optic properties. Lithium Niobate has a preferred x-cut orientation. 
     FIG. 17 is a circuit diagram illustrating the first embodiment of an optical modulator  170  with a tri-electrode utilizing a horizontal electric field. An amplifier  23  receives an input  22  and generates three electrical outputs through a transmission line S 1   24   a , a transmission line S 2   24   b , and a transmission line S 3   24   c . The transmission line S 1   24   a  extends through the electrode  13  to a load L 1  or termination resistor  25   a  and a ground  26   a . The transmission line S 2   24   b  extends through the electrode  54  to a load L 2  or termination resistor  25   b  and a ground  26   b . The transmission line S 3   24   c  extends through the electrode  55  to a load L 3  or termination resistor  25   c  and ground  26   c . Between the negative electrode  53  and the positive electrode  54 , a traveling electrical wave ω 1   57  is created due to their proximity. Between the positive electrode  54  and the negative electrode  55 , a traveling electrical wave ω 2   58  is created due to their proximity. In this embodiment, an optical wave λin  171  is received from, for example, an optical fiber (not shown). The optical signal λin  171  splits into two light signals λ 1   172  and λ 2   173 , before re-combination at the output λout  174 . Preferably, the traveling wave ω 1   57  is symmetrical or substantially symmetrical to the traveling electrical wave ω 2   58 . 
     The amplifier  23  matches the impedance of the transmission lines S 1   24   a , S 2   24   b , and S 3   24   c , and matches the impedance of the loads L 1   25   a , L 2   25   b , and L 3   25   c . In the preferred mode, the amplitudes of the negative electrodes S−  53  and S−  55  have the same amount of amplitude as the amplitude of the positive electrode S+  54 . The amount of signal amplitude applied affects the amount of phase shift. The amount of phase shift is linearly proportional to the signal amplitude generated from the amplifier  23 . For example, if applying 1-volt, a 45 degree phase shift can result, and if applying 2-volts, a 90 degree phase shift can result. 
     A reduction of Vπ×L is caused by the superposition of the field induced by the electrodes, resulting in the enhancement in the electrical field. In one embodiment, the amplitude of the traveling electrical wave ω 1   57  is doubled due to the field excitation between the electrodes  53  and  54 . However, the increase can be more than 2 times, or less than 2×, depending on the distance between the electrodes  53  and  54 , the height of each electrode  53  or  54 , and the thickness of a buffer layer. Preferably, the ω 1   57  is symmetrical to the traveling electrical wave ω 1   58  modulation. One of ordinary skill in the art, however, should recognize that the traveling electrical wave ω 1   57  and the traveling electrical wave ω 2   58  can be designed to be asymmetrical. 
     The electrodes of the optical phase-shifter would be driven as in FIG. 17, where a driver amplifier would provide the signal to the three electrodes, the outer two driven with the same polarity and the center with opposite polarity of the outer. The electrical signal propagates from left to right, where the signal is terminated into matched loads. 
     Optionally, a direct current (DC) bias field can be applied to each of the electrodes S−  53 , S+  54 , and S−  55 , by direct or indirect coupling. 
     FIG. 18 is a process diagram illustrating a first embodiment of a cross-sectional view of an optical modulator  180  with a tri-electrode utilizing a horizontal electric field. Optical waveguides  181  and  182  are shown in a region of large vertical field E field  183  and  184 . The optical waveguide (WG)  181  is positioned directly underneath the positive electrode S+  54 . Similarly, the optical waveguide (WG)  182  is positioned directly underneath the negative electrode S−  55 , thereby creating a vertical field. An electrical field E  183  exists between the positive electrode S+  54  and the negative electrode S−  53 , and an electrical field E  184  exists between the positive electrode S+  54  and the negative electrode S−  55 . 
     FIG. 19 is a circuit diagram illustrating the second embodiment of an optical modulator  190  with a tri-electrode utilizing a horizontal electric field. In this embodiment, the optical signal λin  191  splits into two light signals λ 1    192  and λ 2    193 , before re-combination at the output λout  194 . The λ 1    192  travels underneath the positive electrode  54  and the λ 2    193  travels underneath the negative electrode  55 . Preferably, the traveling wave ω 1   27  is symmetrical or substantially symmetrical to the traveling electrical wave ω 2   28 . 
     FIG. 20 is a process diagram illustrating a phase shifter  200  employing dual-electrodes with a horizontal electric field in the optical waveguide. The phase shifter  200  has two electrodes, a first electrode  201  and a second electrode  202 , where the first electrode  201  has an opposite polarity as the second electrode  202 . An optical waveguide  203  is placed in a gap underneath and in between the first electrode  201  and the second electrode  202 , in generating a horizontal electric field. Ground electrodes  204  and  205  are used to suppress the couplings to parasitic modes at high frequencies. A substrate  206  can be selected from a material such as like GaAs, KDP, or LiNbO3, which demonstrates a linear electro-optic effect. 
     A negative signal is introduced into the electrode S−  201  that travels with the positive signal S+  202  to enhance an electrical field significantly. The field enhancement is provided by the superposition of the fields created by each electrode giving better performance. The material  206  can be made of any compound having linear electro-optic properties. 
     FIG. 21 is a process diagram illustrating a phase shifter  210  employing dual-electrodes with a horizontal electric field in the optical waveguide with a buffer layer. A buffer layer  211  is placed between the substrate  206 , and the ground electrode  204 , the negative S− electrode  201 , the positive S+ electrode  202  and the ground electrode  205 . The width of the buffer layer  211  extends all the way from the ground electrode  204 , through the negative S− electrode  201 , the positive S+ electrode  202 , to the ground electrode  205 . The buffer layer  211  preferably has a significantly lower dielectric constant than that of the substrate  206 . The use of the buffer layer  211  helps to improve the phase matching between an electrical signal and an optical signal, as well as increasing the electrode impedance. 
     If the substrate  206  uses lithium niobate, the preferred material for the buffer layer  211  is silicon oxide, with a thickness of, for example, 1 microns. With the buffer layer  211 , the design of a phase shifter is significantly simpler due to the more electric field in the air. Optionally, the thickness of the buffer layer  211  can be reduced to enhance the electrical field. 
     FIG. 22 is a circuit diagram illustrating a phase-shifter  220  employing dual-electrodes with a horizontal electric field. An amplifier  222  receives an electrical input  221 , generates a first output to a transmission line  223  to the negative electrode  201 , a loading or termination resistor  224 , and a ground  225 , generates a second output to a transmission line  226  to the positive electrode  202 , a loading or termination resistor  227 , and a ground  228 . A input light signal λ in    229   a  travels underneath and between the negative electrode  201  and the positive electrode  202  in generating an output light signal  229   b . In this embodiment with dual electrode traveling wave optical phase-shifter, a distance D electrode width  226  is relatively short in distance between the negative electrode  201  and the positive electrode  202 , preferably less than or equal to 20 microns. 
     FIG. 23 is a circuit diagram illustrating a single arm modulator  230  employing dual-electrodes with a horizontal electric field in the optical waveguide. The single end or single arm modulator  230  receives a light sign input λin  231  and splits the light signal λin  231  into two optical paths, a λ 1   232  and a λ 2   233 . The λ 1   232  travels in an optical waveguide that is routed away from the negative electrode S−  201  and the positive electrode S+  202 , while the λ 2   233  travels between the negative electrode S−  201  and the positive electrode S+  202 . λ 1   232  and a λ 2   233  are combined to generate a single optical output λout  234 . The amplifier  222  receives the electrical input  221 , generates the first output to a transmission line  223  to the negative electrode  201 , a loading or termination resistor  224 , and the ground  225 , and generates a second output to a transmission line  226  to the positive electrode  202 , a loading or termination resistor  227 , and the ground  228 . Between the negative electrode  201  and the positive electrode  202 , a traveling electrical wave ω 1   235  is created due to their proximity. In this embodiment with dual-electrode traveling wave optical phase-shifter, the distance D electrode width  229  between the negative electrode  201  and the positive electrode  202  is relatively short in distance, preferably less than or equal to 20 microns. 
     FIG. 24 is a circuit diagram illustrating two phase-shifters  240  connected in parallel to form a MZ modulator utilizing a horizontal electric field in the optical waveguides, having an upper phase-shifter  241  and the lower optical phase-shifter  230 . The light signal input λin  247  is split into two paths, the λ 1   248   a  and the λ 2   248   b , which are re-combined to generate a λout  249 . An amplifier  243   a  receives the input  242  and generates a first output  244   a  to an amplifier  243   a , and a second output  244   b  to the amplifier  222 . The amplifier  243   b  then generates two electrical outputs through a transmission line S 1   245   a , and a transmission line S 2   246   a . The transmission line S 1   245   a  extends through a first electrode  245   b  to the load L 1  or termination resistor  245   c  and the ground  245   d . The transmission line S 2   246   a  extends through the electrode  246   b  to the load L 2  or termination resistor  246   c  and the ground  246   d . Between the negative electrode  201  and the positive electrode  202 , a traveling electrical wave ω 1   235  is created due to their proximity. Preferably for wide band applications, the electrical wave ω 1   235  matches or substantially matches the electrical wave ω 2   243   c . In addition, the light wave λ 1    248   a  matches or substantially matches the light wave λ 2    248   b . Optionally, the electrodes  245   b ,  246   b ,  201 , and  202  can be connected to a voltage supply (not shown), to generate a DC bias field in the optical waveguides. FIG. 25 is a process diagram illustrating a phase shifter  250  employing dual-electrodes with a vertical electric field. The phase shifter  250  has two electrodes, a first electrode  201  and a second electrode  202 , where the first electrode  201  has an opposite polarity as the second electrode  202 . An optical waveguide  251  is placed directly underneath the second electrode  202 , thereby being placed in a substantially vertical electric field. Ground electrodes  204  and  205  are used to suppress the couplings to parasitic modes at high frequencies. A substrate  206  can be selected from a material such as like GaAs, KDP, or LiNbO3, which demonstrates a linear electro-optic effect. 
     A negative signal is introduced into the electrode S−  201  that travels with the positive signal S+  202  to enhance an electrical field significantly. The field enhancement is provided by the superposition of the fields created by each electrode giving better performance. The material  206  can be made of any compound having linear electro-optic properties. 
     FIG. 26 is a circuit diagram illustrating a phase shifter  260  employing dual-electrodes with a vertical electric field with a buffer layer. A buffer layer  261  is placed between the substrate  206 , and the ground electrode  204 , the negative S− electrode  201 , the positive S+ electrode  202  and the ground electrode  205 . The width of the buffer layer  261  extends all the way from the ground electrode  204 , through the negative S-electrode  201 , the positive S+ electrode  202 , to the ground electrode  205 . The buffer layer  261  preferably has a significantly lower dielectric constant than that of the substrate  206 . The use of the buffer layer  261  helps to improve the phase matching between an electrical signal and an optical signal, as well as increasing the electrode impedance. 
     If the substrate  206  uses lithium niobate, the preferred material for the buffer layer  261  is silicon oxide, with a thickness of, for example, 1 microns. With the buffer layer  261 , the design of a phase shifter is significantly simpler due to the more electric field in the air. Optionally, the thickness of the buffer layer  261  can be reduced to enhance the electrical field. 
     FIG. 27 is a circuit diagram illustrating a phase shifter  270  employing dual-electrodes with a vertical electric field in the optical waveguide. The amplifier  222  receives the electrical input  221 , generates a first output to a transmission line  223  to the negative electrode  201 , a loading or termination resistor  224 , and a ground  225 , and generates a second output to a transmission line  226  to the positive electrode  202 , a loading or termination resistor  227 , and a ground  228 . An input light signal λin  271  travels underneath the positive electrode  202  in generating an output light signal  272 . Between the negative electrode  201  and the positive electrode  202 , a traveling electrical wave ω 1   273  is created due to their proximity. In this embodiment with dual-electrode traveling wave optical phase-shifter, a distance D electrode width  274  between the negative electrode  201  and the positive electrode  202  is relatively short in distance, preferably less than or equal to 20 microns. 
     FIG. 28 is a circuit diagram illustrating a single arm modulator  280  employing dual-electrodes with a vertical electric field in the optical waveguide. The single arm modulator  280  receives a light signal input λin  181  and splits the light signal λin  281  into two optical paths, a λ 1   282  and a λ 2   283 . The λ 1   282  travels in an optical waveguide that is routed away from the negative electrode S−  201  and the positive electrode S+  202 , while the λ 2   283  travels underneath the positive electrode S+  202 . λ 1   282  and λ 2   283  are combined to generate a single optical output λout  284 . The amplifier  222  receives the electrical input  221 , generates the first output to a transmission line  223  to the negative electrode  201 , a loading or termination resistor  224 , and the ground  225 , and generates a second output to a transmission line  226  to the positive electrode  202 , a loading or termination resistor  227 , and the ground  228 . Between the negative electrode  201  and the positive electrode  202 , a traveling electrical wave ω 1   273  is created due to their proximity. In this embodiment with dual-electrode traveling wave optical phase-shifter, the distance D electrode width  274  between the negative electrode  201  and the positive electrode  202  is relatively short in distance, preferably less than or equal to 20 microns. 
     FIG. 29 is a circuit diagram illustrating two phase-shifters  290  connected in parallel to form a MZ modulator utilizing a vertical electric field, having an upper phase-shifter  241  and the lower optical phase-shifter  230 . The light signal input λin  291  is split into two paths, the λ 1   292  and the λ 2   293 , which are recombined to generate a Bout  294 . The λ 1   292  light signal travels underneath a positive electrode  245   b , while the λ 2   293  light signal travels underneath the negative electrode  201 . The amplifier  243   a  receives the input  242  and generates a first output  244   a  to an amplifier  243   a , and a second output  244   b  to the amplifier  222 . The amplifier  243   b  then generates two electrical outputs through a transmission line S 1   245   a , and a transmission line S 2   246   a . The transmission line Si  245   a  extends through a first electrode  245   b  to the load L 1  or termination resistor  245   c  and the ground  245   d . The transmission line S 2   246   a  extends through the electrode  246   b  to the load L 2  or termination resistor  246   c  and the ground  246   d . Between the negative electrode  201  and the positive electrode  202 , a traveling electrical wave ω 1   273  is created due to the close proximity of a gap between them. Between the negative electrode  246   b  and the positive electrode  245   b , a traveling electrical wave ω 2   295  is created due to their proximity. 
     Preferably, the light wave λ 1    292  matches or substantially matches the light wave λ 2    293 . Optionally, the electrodes  245   b ,  246   b ,  201 , and  202  can be connected to a voltage supply (not shown), to generate a DC bias field in the optical waveguides. 
     FIG. 30 is a structural diagram illustrating a dual-electrode modulator  300  where two optical waveguides  306  and  307  are placed in regions of a vertical electric field. The dual-electrode modulator  300  has two electrodes, a negative electrode S−  303 , and a positive electrode S+  304 . The two electrodes, the negative electrode S−  303  and the positive electrode S+  304 , have opposite polarity from one another. It is apparent to one of ordinary skill in the art that the polarity of the two electrodes can be swapped. The optical waveguide (WG)  306  directly is underneath the negative electrode S−  303 , thereby experiencing a substantially vertical electric field. Similarly, the optical waveguide (WG)  307  is directly underneath the positive electrode S+  304 , thereby experiencing a substantially vertical electric field. 
     A first negative signal is introduced into the electrode S−  303  that travels with the positive signal S+  304  for significant enhancement of the electrical field in the optical waveguides. The field enhancement is provided by the superposition of the fields created by each electrode giving better performance. Ground electrodes  302  and  305  are used to suppress the couplings to parasitic modes at high frequencies. A substrate  301  can be selected from a material such as like GaAs, KDP, or LiNbO3, which demonstrates a linear electro-optic effect. 
     FIG. 31 is a circuit diagram illustrating a dual-electrode modulator  310  driven from an amplifier with two optical waveguides utilizing a vertical electric field. An amplifier  312  receives an electrical signal input  311  and generates a first output to a transmission line S 1   313   a  and a second output to a transmission line S 2   314   b . The transmission line S 1   313   a  extends through the negative electrode  303 , to a load or termination resistor  313   b  and a ground  313   c . The transmission line S 1   314   a  extends through the positive electrode  304 , to a load or termination resistor  314   b  and a ground  314   c.    
     The dual-electrode modulator  310  receives a light signal input λ in    315  and split the light signal λ in    315  into two optical paths, a λ 1    316   a  and a λ 2    316   b . The λ 1    316   a  travels underneath the negative electrode S−  303 , while the λ 2    316   b  travels underneath the positive electrode S+  304 , for generating a single optical output λ out    319 . Between the negative electrode  303  and the positive electrode  304 , a traveling electrical wave ω 1   317  is created due to the close proximity of a gap between them. In this embodiment with dipole-enhanced traveling wave optical phase-shifter, the distance D electrode width  318  is relatively short in distance between the negative electrode  303  and the positive electrode  304 , preferably less than or equal to 20 microns. 
     FIG. 32 is a process diagram illustrating a ridge structure  320  employing tri-electrodes utilizing a vertical electric field. A ridge layer  321  is added above the element  11 , with an optical wave guide  322  internal to the ridge layer  321  and underneath a positive electrode  323 . The ridge is layer typically built of the same materials as the element  11 , which has a linear electro-optic coefficient. 
     FIG. 33 is a process diagram illustrating a ridge structure  330  employing double-electrodes with a horizontal electric field. A ridge layer  331  is added above the layer  206 , with an optical wave guide  332  underneath the buffer layer  261 , as well as in gaps underneath and in between the negative electrode  201 , and the positive electrode  202 . The ridge layer is typically built of the same materials as the element  11 , which has a linear electro-optic coefficient. 
     FIG. 34 is a structural diagram illustrating a tri-electrode modulator  340  where two optical waveguides  346  and  347  are placed in regions of a horizontal electric field. The tri-electrode modulator  340  has three electrodes, a negative electrode S−  341 , and a positive electrode S+  343  and a negative electrode S−  342 . The three electrodes, the negative electrode S−  341  and S−  342 , and the positive electrode S+  343 , have opposite polarity from one another. It is apparent to one of ordinary skill in the art that the polarity of the three electrodes can be swapped. The optical waveguide (WG)  346  is placed directly in the ridge  348  between the negative electrode S−  341  and the positive electrode S+  343  in a substantially horizontal electric field. Similarly, the optical waveguide (WG)  347  is placed directly in the ridge  349  between the negative electrode S−  342  and the positive electrode S+  343 , thereby experiencing a substantially horizontal electric field. 
     A first negative signal is introduced into the electrode S−  341 , and a second negative signal is introduced into the electrode S−  342 , that travels with the positive signal S+  343  for significant enhancement of the electrical field in the optical waveguides. The field enhancement is provided by the superposition of the fields created by each electrode giving better performance. Ground electrodes  344  and  345  are used to suppress the couplings to parasitic modes at high frequencies. A substrate  406  can be selected from a material such as like GaAs, KDP, or LiNbO3, which demonstrates a linear electro-optic effect. The ridge  348  and ridge  349  typically are built of the same material as substrate  406 . 
     In all the preceding diagrams, FIGS. 1-34, the electrodes have been labeled either positive or negative in order to indicate that they are driven with opposite polarity modulation signals. Another suitable notation is to use S and S, where the symbol S has an opposite polarity from {overscore (S)}. In one embodiment, the polarity referred to is that of the modulation component of the signal applied to the electrode, and is not meant to refer to the absolute polarity of field between the electrodes. For example, applying a large DC offset to one of the electrodes could make the absolute polarity of electric field between the electrodes constant, but the polarity of the modulation components of the signals applied to S+ and S− would still be of opposite polarity. 
     It should be clear to one of ordinary skill in the art that the actual drive waveform applied to the positive electrode may be either positive or negative at a given point in time, and the actual drive waveform applied to the negative electrode will be of opposite polarity. For example, FIG. 35A is a diagram illustrating one example of a pair of time-varying signals with opposite modulation polarity. At time slice t 1 , the signal applied to the positive electrode S+ has a higher voltage than the signal applied to the negative electrode S−. At time slice t 2 , the signal applied to the positive electrode S+ has a lower voltage than the signal applied to the negative electrode S−. 
     FIG. 35B is a graphical diagram illustrating electric field lines between the positive electrode S+ and negative electrode S− at time t 1 . The electric field between the electrodes flows from S+ to S−. FIG. 35C is a graphical diagram illustrating electric field lines between the positive electrode S+ and negative electrode S− at time t 2 . The electric field between the electrodes flows from S− to S+. 
     If a large DC offset voltage were added to the modulation signal applied to S+, then at time slice t 1 , the signal applied to the positive electrode S+ would have a higher voltage than the signal applied to the negative electrode S−, and at time slice t 2 , the signal applied to the positive electrode S+ would be reduced by the modulation component of the signal, but would still have a higher absolute voltage than the signal applied to the negative electrode S−. In this case, with a large DC voltage applied to S+, the electric field lines would flow from S+ to S− as shown in FIG. 35B, but the necessary condition of applying opposite polarity modulation signals to S+ and S− would still be satisfied. 
     The above embodiments are only illustrative of the principles of this invention and are not intended to limit the invention to the particular embodiments described. For example, although the tri-electrodes have been specified as the negative electrode S−  13 , the positive electrode S+  14 , and the negative electrode S−  15 , one of ordinary skill in the art should know that the polarities can be altered, such as having a positive electrode S+  13 , a negative electrode S−  14 , and a positive electrode S+  15 . The concept is to have the electrode  13  and electrode  15  having one polarity, and the electrode  14  having an opposite polarity from the electrodes  13  and  15 . Alternatively, the electrode  13  and the electrode  14  can have the same polarity but with a different amplitude where the difference in amplitude is equal or substantially similar to the amplitude difference between a positive electrode and a negative electrode. Accordingly, various modifications, adaptations, and combinations of various features of the described embodiments can be practiced without departing from the scope of the invention as set forth in the appended claims.