Theoretical Analysis Of Multi-electrodes Directional Coupler Polymer Electro-optic Switches

As the foundation and development of integrated electro-optics (EO) and technique of density wavelength divided multiplex (DWDM), the information in communicating field has been greatly increased day by day. People not only need large information transform capacity but also need a much fast signal transforming speed (up toμs) according with the capacity. Because of the electro choke point of traditional electric networks, the transforming speed can't achieve such a high speed. So networks based on optic can be a better solution to this problem. Development of the synthetic technique of electro-optic materials especially the electro-optic polymer and the facture technique of electro-optic devices provide material and technique assuredness to the development of all-optic networks.Optic switches are basic devices in WDM communication networks. They can be widely used in space, time and wavelength divided multiplex systems. Integrated optic switch arrays are also key devices in realizing wavelength multiplex and optic cross connections. Electro-optic switches are switches based on electro-optic, or better-known Pockels effect. Such kind of switches is known as their advantages of fast speed, low insertion loss, high extinction ration and longevity. As waveguide and substrate materials of macromolecule electro-optic switches, macromolecule polymer takes advantages of high electro-optic coupling coefficient, low dielectric constant, short response time, low loss and low driving voltage compared with traditional inorganic compound. And also they can be made to be complicated electro-optic devices only by coating and photolithography and need not by heating in high temperatures. Because of such advantages, macromolecule polymer based devices has been paid more and more attentions in research.A kind of directional coupler (DC) polymer switches is discussed in this paper. The whole design theory and method are proposed. The switching characteristics of such switches with multi-electrodes are analyzed. The switch characteristics curves of single, double, triple, and for electrodes switches are detailed described, and alsothe switching voltages are calculated and a fully comment is given in this paper. In the end, the relationship between multi-electrodes is presented.Firstly, the basic theory, electro-optic effect is discussed, and the relationship between refraction index ellipsoid and electro-optic coefficient of the crystal in electric field is described. Through examples, principles of electro-optic crystal phase modulator and amplitude modulator are analyzed in detail. And working principle, performance perimeters and problems considered in designing of Ti: LiNbO₃ electro-optic modulators are also analyzed. Performance perimeters expressions of electro-optic DC switches are given in this essay. These are important content which should be theoretically analyzed and numerically calculated in this thesis.Then this paper fully discussed the mode analytical method of rectangle waveguides, and offers a relatively practical method-the Marcatili method. This method firstly breaks the rectangle waveguide into two flat waveguides in x-dimension and y-dimension. Then the two flat waveguides are analyzed. And in the end, the analytical results from the two waveguides are combined together. So we can get the field distribution functions and characteristic equations of E mynand E_mn^x modes. This method provided a theory basis of designing single mode waveguide. At the same time, another method– the effective refractive index method is also discussed. The basic principle of this method is similar with the former method. The analytical course of this method is simpler, and the results are also more accurate. So the mode analytical method taken in this paper is this method. In the end,the bend mode analytical method, the Melloni method is given, which can be used to analyze the mode characteristics of bending waveguide. This method provides theories of analyzing the bending waveguide of DC switches for our succession job.At the following part of this paper, the electric field distribution of symmetric coplanar electrodes is analyzed and presented using conformal mapping method and Schwarz mapping method. Considered the buffer layer with a certain thickness, another electric field analytical method is given, which is called Image Method. Meanwhile, the electrode perimeters including conductance, capacity, inductance and resistance of unit length are described. The structure with reserved phase electrodes is analyzed in detail and can bring advantages of broadband, low voltage and large modulation index. Similarly, electro-optic switch with such structure will not affect the modulation index and the coupling coefficient. And also the waveguide length will not be acquired so accurate with supplemented voltage.Characteristics of EO switches with multi-electrodes are analyzed in the core parts of this paper. First, the designing principle, method and theory of EO switches are expatiated. Then curves and voltage of single electrode are calculated. According to the calculating results, the waveguide length must be exactly integral times of coupling length in order to realize cross status. This can bring troubles in facture. Here are the calculating results: the switching voltage is 17.7V at the coupling length of L₀ = 1.90mm for single electrode EO switches.According to the calculating results of DC EO switches with double, triple and four electrodes, we can get conclusions as follows. In the situation of multi-electrodes, there are many status curves. We can exchange status of the DC switch by applying different voltages for waveguide with any length. This is different from single electrode switches. The minimum distance between the two abscissas of status curves corresponds to the switching voltage. Here we use computer-searching method. There needn't be so accurate waveguide length when not taking the isolating point as status point. It can be implemented by applying voltages in a small range. So it is an advantage of this structure, and superior to single electrode. Meanwhile, according to the status curves, voltages U×andU= of cross and bar state may be not zero. The subtraction result between U×andU= equals to the switching voltage. Calculation results of switching voltages show that the switching voltage has a relation of inverse proportion with waveguide length.The greater the length is, the lower the voltage is but the lower the integrity is. In the other hand, the smaller the length is, the larger the integrity is but the higher the voltage is. So we must choose the two appropriately. The calculation results are as follows. The switching voltage is 7.82V at the waveguide length of L = 2. 35L0 for double electrodes EO switches, 5.30V at length of L = 3 .18L0 for triple electrodes, and 1.72V at length of L = 5 .50L0 for four electrodes. Additionally, switching voltages at waveguide length of integral times (1,2,3)of coupling length are calculated and presented in this paper. The theoretical analysis results show that we can get low status voltages and low switching voltages of switches with multi-electrodes. When the number of electrodes increases to infinity, the switching voltage can be down to zero. This is decided by the number of status curves. But the reducing speed of switching voltage can get be more placid as the number increases. The relationship between transforming matrixes of multi-electrodes is discussed inthe end, which can be used as theory basis for our further research.Currently more and more attentions have been paid to research of DC electro-optic switches. But structures with more than three electrodes are rarely researched. A kind of DC polymer EO switches is researched and designed in this paper. The theory basis and practical method are discussed. The relation between important perimeter of switches, switching voltage and number of electrodes are obtained through theoretical analysis of switches with multi ?βreversed electrodes. Some novelties of this thesis are as follows:(1) We have proposed series of theory basis, computing methods and design flows in DC EO switches'designing. The MATLAB programs are compiled to realize this design course. A method in optimizing perimeters of symmetric coplanar electrodes is proposed. This method combines theoretical computing and computer searching together.(2) Perimeters and characteristics of DC EO switches with triple and four electrodes are detailed analyzed. The inducing courses are given. From the conclusion, we can see that these electrodes structure can obtain even low switching voltage, and needn't so accurate waveguide length. This not only reduces device power assumption but also bring more convenience in facture.(3) The relationship between transforming matrixes of multi-electrodes is induced in this paper. The expressions are given, which can be used as theory basis for our further research in switches with even more electrodes.(4) Many analytical methods are discussed and made conclusions in this thesis, such as Marcatili method and effective refractive index method on rectangle waveguides, IM method, conformal mapping method and Schwarz mapping method on electric field distribution and Melloni analytical method on mode of bending waveguide.(5) The analytical methods, optimizing methods, relative computing formulas and computing programs proposed in this paper have advantages of formal and short structure, practical in use, high accuracy and so on. These can bring certain referring values in design and factures of switches and simple devices.