Abstract:
Optical switches based on the balanced bridge interferometer design require precisely made (or half a coupling length) directional couplers to achieve minimum crosstalk for the two switch outputs. Precision 3 dB-directional couplers require the waveguide dimensions and fabrication parameters of the evanescent region to be tightly controlled making a low crosstalk switch difficult to manufacture and expensive. A new type of balanced bridge interferometer type switch is disclosed where the input and output directional couplers are asymmetrically biased to induce a certain difference in the propagation constants between the two waveguide in the directional couplers. By using the asymmetrically biased directional couplers with a certain tuning a bias voltage for the directional couplers. Low crosstalk switches can be achieved for a very wide range of directional coupler strengths, relaxing the precise half-coupling length directional couplers required in conventional design. This relaxation of the precise directional coupler waveguide regions allows a relaxation in the manufacturing tolerance of the devices and therefore make the switch much easier to make. Because low crosstalk switches can be a device with an extended operating range and broader directional coupler parameters, switches can be used for a much broader wavelength bandwidth. In one of the embodiments, this new design allows a device to switch both TE and TM mode optical signals simultaneously at low crosstalk levels to result in a polarization-independent optical switch.

Description:
This application claims priority to U.S. Provisional Application Ser. Nos. 60/204,774 and 60/204,775, both filed May 17, 2000, whose entire disclosure is incorporated herein by reference. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to electro-optic devices, and in particular, to polarization independent broadband optical modulators and switches for wideband fiberoptic networks. 
   2. Background of the Related Art 
   A balanced bridge optical switch has two input and two output waveguides. Two ½l c  (half a coupling length) 3-dB (i.e., 50:50 power splitter) directional couplers and a phase modulated interferometer waveguide pair are used. Note that “l c ” is the characteristic coupling length of a directional coupler, which is the length of the directional coupler necessary to transfer substantially all the power from a first waveguide to a second waveguide. The input 3-dB coupler is used to equally divide an input signal received by an upper input waveguide into both the upper and lower waveguides prior to entering an interferometer section of the balanced bridge optical switch. An output ½l c  directional coupler rejoins the electro-optical phase modulated signal from the interferometer section back into the upper output waveguide for a “straight-thru” path (i.e., “on” or (=) bar state) or the lower output waveguide in the “cross-over” path (i.e., “off” or switched (×) state). If the optical path lengths of the two waveguides are identical in the middle interferometer section, the two optical waves arrive at the output (½l c ) 3-dB coupler section and recombined coherently producing an optical signal that transfers all into the lower waveguide or crossover path. However, if there is a 180° phase difference between the two optical path lengths in the interferometer section, the two optical waves will recombine and transfer back to upper waveguides or the straight through path. Thus, electro-optical phase modulation of the two optical waves in the interferometer section results in an amplitude modulation at each of the output waveguides and the device can be used as a 1×2 or a 2×2 optical switch. 
     FIG. 1  illustrates a related art polarization-independent 2×2 electro-optic switch  100  based on a balanced-bridge interferometric waveguide structure. As shown in  FIG. 1 , the related art switch  100  includes upper and lower waveguide patterns  120 ,  130  formed in a X-cut Z-propagation lithium niobate (LiNbO 3 ) electro-optic substrate  110 . The switch  100  includes a 3 dB-directional coupler section  142  (50:50 power splitter) having an interaction length of L B =½L dc , an interferometer section of length L e , and an output 3 dB-directional coupler section  146  having an interaction length of L B =½L dc , where L B =½L dc , L dc  equals combined length of the two couplers, and l c  equals characteristic coupling length of the directional coupler. Note that “interaction length” and “effective coupling length” are used interchangeably to describe the actual length of the waveguides in a directional coupler over which a signal may couple from a first waveguide to a second waveguide. Also note that the effective coupling length may be described in terms or units of characteristic coupling length l c . Thus a range of effective coupling lengths or interaction lengths for a directional coupler can be indicated as 0.75l c  to 1.1l c . The input and output 3 dB-directional coupler sections operate as 50:50 power splitters and are preferably identical with a combined length where l c  is the characteristic coupling length of the switch  100 . As shown in  FIG. 1 , the upper waveguide  120  receives an input optical signal I in . Under straight-thru switch operations, the input signal I in  received by the upper waveguide  120  exits from the waveguide  120  as an output signal I upper  (=), and in cross-over switch operations, the input signal I in  enters the upper waveguide  120  but exits through the lower waveguide  130  as I lower  (×). 
   For the related art switch  100 , the upper and lower waveguides  120 ,  130  are single mode for each of two polarizations (TE, TM), and therefore support one TE mode and one TM mode each, where the “TE mode” is the transverse electric field mode, and the “TM mode” is the transverse magnetic field mode. A normalized applied voltage V applied in the interferometer section  144  is applied with an electric field in the Y-direction (E y ) that induces a differential propagation constant Δβ (“Δβ”) between the two interferometric sections of the upper and lower waveguides  120 ,  130  of length L e  via the linear electro-optic effect. The length L e  is the length of the electrodes  150 ,  152 , 154 . Electrodes  150 ,  152 ,  154  are arranged in a push-pull configuration to maximize the electro-optically induced Δβ between the upper and lower waveguides  120 ,  130  in the interferometer section  144 . Thus, the electrode  152  receives the normalized applied voltage V and the electrodes  150  and  154  receive a ground potential. As shown in  FIG. 1 , the placement of the electrodes  150 ,  152 ,  154  maximizes the E-field along the Y-axis inside the waveguides. 
   For the X-cut substrate  110 , when the waveguide propagation direction in the waveguides  120 ,  130  is along the Z-axis (optic axis), both the TE and TM modes see the same ordinary index (n o ). Thus, both the TE and TM polarization modes are nearly degenerated and will behave in approximately the same way. The electro-optic (“EO”) interaction for the TE and TM modes with the E y  field in the interferometer section are via EO coefficients that are equal but opposite in sign (i.e., r 22 , −r 22 ) in the lithium niobate substrate  110 . Therefore, the magnitudes of the Δβ i  for both the TM and TE modes are the same in the interferometer section  144  where Δβ i  is the difference in the propagation constants between the two waveguide pair in the middle “interference” section, and Δβ dc  is the difference in the propagation constants between the waveguide pair in the “input” and “output” directional coupler sections. In other words, the EO interactions in the interferometer section  144  in the TE mode is proportional to +r 22  (E y ) and the TM mode is proportional to −r 22  (E y ) as the corresponding change in the propagation constants is via the electric field in the Y-axis direction. 
   In  FIG. 2A , I cross-over  and I straight-thru  conditions are illustrated for the related art switch  100 , where optical power is a vertical axis and the ratio of normalized applied voltage to V π , which is the voltage required to cause a 180° phase shift between the two arms of the interferometer V/V π , is a horizontal axis. As shown in  FIG. 2A , the input signal I in  is output as I cross  when V/V π  is equal to −4, −2, 0, 2, 4 and I in  is output as I upper  (I  straight-thru ) when V/V π  is equal to −3, −1, 1, 3. 
   In  FIG. 2A , the optical power is illustrated from 0 to 1 corresponding to an on (=) or off (×) state of the switch  100 . For a high performance, low-crosstalk switching device, the input and output directional couplers  142 ,  146  of the switch  100  must behave as 3 dB-couplers for both the TE and TM modes simultaneously. In this case of zero (0) voltage, both the TE and TM modes entering an input port of the upper waveguide  120  will exit a lower output “cross-over” port (×) of the lower waveguide  130 . When voltage is applied to the interferometer section  144  of the switch  100  with an electric field in the Y-axis direction, the EO induced change in the waveguide indices for the TE and TM modes are exactly equal, but with opposite sign because of the r 22 , −r 22  linear EO coefficients. Because of the symmetric nature of the switching characteristics of the balanced bridge interferometer with respect to voltage, both the TE and TM modes would be switched to the upper output port as shown in  FIG. 2A  when a normalized applied voltage V=V π  (or V =−V π ) is applied. Thus, the related art optical switch  100  provides polarization independent switching. However, as shown in  FIG. 2B , for effective operation of the related art switch  100 , the length of each of the directional coupler sections  142 ,  144  L B (=½L dc ) must be very precisely manufactured to be equal to ½l c , which is the coupling length of the switch  100 . When L dc (=2 L B ) does not equal l c , light entering the upper input channel cannot be switched completely from the output port (=) of the waveguide  120  to the output port (×) of the other waveguide  130 . Note that L dc  equals 2×(L B ), and L B =length of each 3 dB coupler (input and output). Thus, L B  must precisely equal ½l c  for a low crosstalk switch. When L dc  does not equal l c , the crosstalk of the switch increases rapidly as L dc  deviates from l c . This is shown in  FIG. 2B , for L dc= 0.6l c , 0.8l c , 1.0l c  and 1.4l c . Accordingly, when L dc  does not equal 1.0l c  precisely, the high crosstalk can make the switch  100  a non-working switch. 
   As described above, the related art polarization independent optical switches have various disadvantages. Crosstalk of the switch depends on fabricating optimal 3 dB couplers. L dc  precision is limited by fabrication tolerances, and a precise length for the 3 dB couplers is hard to achieve. For example, a 10% variation in coupler length can render an optical switch defective. Thus, a low crosstalk (&lt;−25dB) switch is difficult to achieve. Further, an optimal fabrication parameter to achieve a 3 dB-coupler for the TE mode is often somewhat different than the optimal fabrication parameter required for a 3 dB-coupler for the TM mode. Thus, it is difficult to achieve an exact 3 dB coupling for both TE and TM modes simultaneously. This will result in an undesirable high crosstalk for either TE or TM modes or both. 
   The above references are incorporated by reference herein where appropriate for appropriate teachings of additional or alternative details, features and/or technical background. 
   SUMMARY OF THE INVENTION 
   An object of the invention is to solve at least the above problems and/or disadvantages and to provide at least the advantages described hereinafter. 
   Another object of the present invention is to provide an optical switch and method for operating same that substantially obviates one or more problems caused by disadvantages and limitations of the related art. 
   Another object of the present invention is to provide a polarization independent balanced-bridge interferometric waveguide switch and method for operating same that is a low crosstalk switch (less than −20 dB). 
   Another object of the present invention is to provide a polarization independent 1×2 or 2×2 electro-optic switch and method for operating same that provides polarization-independent switch operation over a broad wavelength. 
   Another object of the present invention is to provide a polarization independent 2×2 electro-optic switch and method for operating same that provides a reduced polarization mode dispersion. 
   Another object of the present invention is to provide a polarization independent 2×2 electro-optic switch and method for operating same that provides a reduced polarization dependent loss switch. 
   Another object of the present invention is to provide a polarization independent 2×2 electro-optic switch and method for operating same that uses differential propagation constant Δβ dc  coupling in the input and output couplers. 
   Another object of the present invention is to provide a polarization independent 2×2 electro-optic switch and method for operating same that uses tunable Δβ dc  directional couplers in the input and output power splitters. 
   Another object of the present invention is to provide a polarization independent 2×2 electro-optic switch and method for operating same that uses voltage induced linear electro-optic effect to induce Δβ dc  in the input and output directional couplers. 
   Another object of the present invention is to provide a polarization independent 2×2 electro-optic switch and method for operating same that uses asymmetric-waveguide widths to achieve the proper Δβ dc . 
   Another object of the present invention is to provide a polarization independent 2×2 electro-optic switch and method for operating same that uses directional couplers having different waveguide indices between the upper and lower waveguides that result in a Δβ dc  between the upper and lower waveguides. 
   In order to achieve at least the above-described objects of the present invention in whole or in part, there is provided a device including an optical input, a first coupler optically coupled to the optical input having a first +Δβ dc  mismatch, an optical interferometer optically coupled to the first coupler and having a first optical path and a second optical path, the interferometer having an input that receives a signal voltage, wherein an optical path length difference between the first and second optical paths is induced in response to the signal voltage, and a second coupler optically coupled to the optical interferometer and capable of having a second −Δβ dc  mismatch. 
   To further achieve the above-described objects of the present invention in whole or in parts, there is provided a device including an optical input a first coupler optically coupled to the optical input having a first +Δβ dc  mismatch, a first optical waveguide optically coupled to the first coupler and having a first path length, a second optical waveguide optically coupled to the first coupler and having a second path length, a control signal electrically coupled to at least one of the first and second optical waveguides, whereby an optical path length difference between the first and second optical paths is controlled in response to the control signal, and a second coupler optically coupled to the first and second optical waveguides and capable of having a second −Δβ dc  mismatch. 
   To further achieve the above-described objects of the present invention in whole or in parts, there is provided a device including at least one optical input, a first coupler optically coupled to the optical input having a first optical propagation constant Δβ mismatch, an optical interferometer optically coupled to the first coupler and having a first optical path and a second optical path, the interferometer having an input that receives a signal voltage, wherein an optical path length difference between the first and second optical paths is induced in response to the signal voltage, second coupler optically coupled to the optical interferometer and capable of having a second optical propagation constant Δβ mismatch, and at least one optical output optically coupled to the second coupler. 
   To further achieve the above-described objects of the present invention in whole or in parts, there is provided a device including at least one optical input, an input directional coupler optically coupled to the at least one optical input having a first optical propagation constant Δβ mismatch, a first optical waveguide optically coupled to the input directional coupler and having a first optical path length, a second optical waveguide optically coupled to the input directional coupler and having a second optical path length, a control signal electrically coupled to at least one of the first and second optical waveguides, whereby an optical path length difference between the first and second optical paths is controllable variable in response to the control signal, and an output directional coupler optically coupled to the first and second optical waveguides and capable of having a second optical propagation constant Δβ mismatch. 
   To further achieve the above-described objects of the present invention in whole or in parts, there is provided a balanced bridge optical switch including at least one input port, an input directional coupler having a first optical propagation constant Δβ mismatch coupled to the at least one input port, an interferometer optically coupled to the input directional coupler, an output directional coupler having a second optical propagation constant Δβ mismatch optically coupled to the interferometer, at least one output port optically coupled to the output directional coupler, whereby a first optical propagation constant Δβ mismatch is adjusted to provide an approximate 50% power split at the input directional coupler for a range of effective coupling lengths from approximately 0.75l c  to approximately 1.1l c , and a second optical propagation constant Δβ mismatch is adjusted to provide an approximate 50% power split at the output directional coupler for a range of effective coupling lengths from approximately 0.75l c  to approximately 1.1l c . 
   To further achieve the above-described objects of the present invention in whole or in parts, there is provided a balanced bridge optical switch including at least one input port, an input directional coupler having a first optical propagation constant Δβ mismatch coupled to the at least one input port, an interferometer optically coupled to the input directional coupler, an output directional coupler having a second optical propagation constant Δβ mismatch optically coupled to the interferometer, at least two output ports optically coupled to the output directional coupler, whereby the effective coupling length of the input directional coupler combined with the effective coupling length of the output directional coupler has a range from approximately 1.5l c  to approximately 2.2l c , and a first optical propagation constant Δβ mismatch is determined and a second optical propagation constant Δβ mismatch is determined such that crosstalk between the at least two output ports is below a desired amount. 
   Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and advantages of the invention may be realized and attained as particularly pointed out in the appended claims. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be described in detail with reference to the following drawings in which like reference numerals refer to like elements wherein: 
       FIG. 1  is a diagram that illustrates a related art polarization-independent 2×2 electro-optic switch based on a balanced-bridge interferometric waveguide; 
       FIG. 2A  is a diagram that illustrates optical output plotted against applied voltage for the related art optical switch of  FIG. 1 ; 
       FIG. 2B  is a diagram that illustrates normalized optical output plotted against normalized applied voltage for various ratios of length of the directional coupler over characteristic coupling length of the directional coupler (L dc /l c ); 
       FIG. 2C  is a diagram that illustrates a plot of optical output versus normalized applied voltage for an optical switch as shown in  FIG. 1 ; 
       FIGS. 3A and 3B  are diagrams that illustrates a schematic plan view of a preferred embodiment of a polarization-independent 2×2 electro-optic switch according to the present invention, and its output; 
       FIG. 4  is a diagram that illustrates a plot of optical output versus normalized applied voltage for the optical switch shown in  FIGS. 3A and 3B ; 
       FIGS. 5A-5C  are diagrams that illustrate plots of normalized optical output versus normalized applied voltage in the switch of  FIGS. 3A and 3B ; 
       FIGS. 6A-6G  are diagrams that illustrate output power contours of −10 dB, −20 dB and −30 dB for normalized optical output plotted against normalized applied voltage in a range of input/output bias voltages; 
       FIGS. 7A and 7B  are diagrams that illustrate a schematic plan view of another preferred embodiment of an optical switch according to the present invention, with an associated output signal; 
       FIGS. 8 and 9  are diagrams that illustrate a schematic plan view of another preferred embodiment of an optical switch according to the present invention, with a graph of its associated output signal; 
       FIG. 10  is a diagram that illustrates a schematic plan view of another preferred embodiment of an optical switch according to the present invention; 
       FIGS. 11A and 11B  are diagrams correlating the output port of a related art switch with the output signal; 
       FIGS. 12A-12E  shows the output of a related art switch for various coupling lengths of the directional couplers; 
       FIGS. 13A-13B  show a schematic of the invention with bias-able directional couplers, and contour plot showing the output power for both outputs of a single bias-able directional coupler; 
       FIGS. 14A through 14H  show optical outputs vs applied voltage for the present invention; and, 
       FIG. 15  shows contour plots of straight-thru and cross-over switch states for a related art balance bridge interferometer. 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 3A  is a diagram that illustrates a first preferred embodiment of a broad wavelength band polarization independent optical switch, in accordance with the present invention. “Broad wavelength band” includes the range of wavelengths from at least approximately 1530 nm (nanometer) to at least approximately 1610 nm. The switch&#39;s functioning wavelength range includes the C and L bands, where the C band spans approximately 1530 nm to 1565 nm, and the L band spans approximately 1565 nm to 1610 nm. However, the switch&#39;s functioning is not limited to the wavelength range encompassing the L and C band, and the switch will function substantially below and substantially above both those bands, inclusively. “Polarization independent” means that the switch may effectively switch any polarization or all components of an optical signal. The first preferred embodiment of the optical switch is a polarization-independent, broad-wavelength band 2×2 switch using a balanced-bridge interferometer with asymmetrically-biased (±Δβ dc ) directional couplers. 
   As shown in  FIG. 3A , an optical switch  300  includes upper and lower waveguide patterns  320 , 330  preferably formed in an X-axis cut, Z-axis propagation electro-optic substrate  310 . The electro-optic substrate is preferably lithium niobate (LiNbO 3 ). The switch  300  includes a first directional coupler section  342 , an interferometer section  344  and a second directional coupler section  346 . The first directional coupler  342  has an electrode length of L B , the interferometer section  344  has an electrode length L e  and the second directional coupler section  346  has an electrode length of L B . The first and second directional coupler sections  342 ,  346  preferably operate the same with opposite directivities and respectively couple an input and output of the interferometer section  344 . The first and second directional coupler sections  342 ,  346  have equal magnitude but opposite in sign differential propagation constants Δβ dc , i.e., the input coupler is +Δβ dc  biased and the output coupler is −Δβ dc  biased and vice versa. While it is perferable that the signs of the differential propagation Δβ dc  mismatches for the directional couplers are opposite, such a sign difference is not necessary. Additionally, when there is a sign difference between the differential propagation Δβ dc  mismatches for the directional couplers, either order will work. That is, the first directional coupler&#39;s differential propagation Δβ dc  mismatch may have a positive sign and the second directional coupler&#39;s differential propagation Δβ dc  mismatch may have a negative sign, or the first directional coupler&#39;s differential propagation Δβ dc  mismatch may have a negative sign and the second directional coupler&#39;s differential propagation Δβ dc  mismatch may have a positive sign. The first and second waveguide pair sections  342 ,  346  experience evanescent coupling while the interferometer section  344  does not. 
   Both the first and second directional couplers may have a differential propagation Δβ mismatch, and the interferometer may have Δβ mismatch. The differential propagation Δβ mismatch for the couplers may be referred to as either Δβ or Δβ dc , and the Δβ mismatch of the interferometer may be referred to as Δβ or Δβ E . When the mismatch is simply referred to as Δβ, whether it is the Δβ mismatch of a coupler or Δβ mismatch of an interferometer is determined by the context of the reference. “Coupler” refers to either directional coupler of the switch. “First coupler,” “first directional coupler,” “input coupler,” and “input directional coupler” and the like are synonymous. “Second coupler,” “second directional coupler,” “output coupler,” “output directional coupler,” and the like are also synonymous. Similarly, a “first optical propagation constant Δβ mismatch” refers to the Δβ in the first or input coupler, and “second optical propagation constant Δβ mismatch” refers to the Δβ mismatch in the second or output coupler. 
   The optical propagation Δβ dc  mismatch in a coupler may be achieved by having the propagation constant in the first waveguide of the coupler be a first value β 1 , and the optical propagation constant in the second waveguide of the coupler be a second value β 2 . Thus, β 1 −β 2 =+Δβ dc , and β 2 −β 1 =−Δβ dc . A coupler with an optical propagation Δβ dc  mismatch has a value of β 1  for one of its waveguides and a value of β 2  for another of its waveguides. 
   As shown in  FIG. 3A , the upper waveguide  320  of the switch  300  receives an input optical signal I in  that exits entirely from the waveguide  320  as an output signal I upper  in a “straight-thru” path or “bar (=)” state, and the input signal I in  enters the upper waveguide  320  but entirely exits through the lower waveguide  330  as I lower  in a “cross-over” path or “(×)” state. For the optical switch  300 , the upper and lower waveguides  320 ,  330  are single moded for both TE and TM polarizations, and therefore support one TE mode and one TM mode each. 
   A signal voltage V S  applied as a switching voltage in the interferometer section  344  is applied with an electric field in the Y-direction (E y ) that induces Δβ e  between the two interferometer arms of the upper and lower waveguides  320 , 330  via the linear electro-optic effect. The electrode length of the two interferometer arms is L e . The signal voltage can have various waveforms such as sinusoidal, stepped, chirped, sawtooth, DC, off/on, etc. Electrodes generating the electric fields are preferably arranged in a push-pull configuration to increase the electro-optically induced phase difference between the upper and lower waveguides  320 ,  330  in the interferometer section  344 . Thus, in the X-axis cut, Z-axis propagation substrate  310 , an electrode  352  receives the signal voltage V S  and electrodes  350  and  354  receives a ground potential. 
   As shown in  FIG. 3A , electrodes are placed to maximize an electric field in the Y-axis direction of the lithium niobate crystal  310 . In the X-axis cut substrate shown in  FIG. 3A , the electrodes are placed along side the waveguide so as to increase or maximize horizontal electric field (E y ) inside the optical waveguide. Alternatively, tor Y-axis cut Z-axis propagation substrates, the electrodes are preferably placed on top of the waveguides so as to increase or maximize the vertical electric field (E y ) inside the optical waveguide (as shown in FIG.  10 ). 
   To be polarization independent, the optical switch  300  orients the propagation direction of the waveguides  320 ,  330  along the Z-axis (optic axis) so that both the TE and TM modes see the same ordinary index (n o ). The EO interaction for the TE and TM modes with the E y  field are via electro-optic coefficients that are equal but opposite in sign (i.e., r 22 , −r 22  in a lithium niobate substrate). Thus, the EO interactions in the interferometer section  344  in the TE mode is +r 22  (E y ) and the TM mode is −r 22  (E y ) as the corresponding change in the propagation constants is via the electric field in the Y-axis direction. Thus, magnitudes of Δβ e  for both the TM and TE modes are the same, but opposite in sign in the interferometer section  344 . As shown in  FIGS. 5A-5C , optical power for the switch  300  is illustrated as a vertical axis and the ratio of voltages V/V π  is a horizontal axis. The optical power is measured by a ratio of an output optical power over an input optical power (e.g., I upper /I input ) Accordingly, the input signal I in  launched via the upper input channel is transmitted as I lower  (I cross-over ) via the waveguide  330  when V/V π  is equal to −4, −2, 0, 2, 4 and I in , launched via the upper input channel, is transmitted as I upper  (I straight-thru ) when the V/V π  is equal to −3, −1, 1, 3. 
     FIG. 3B  shows the same embodiment of the switch as shown in  FIG. 3A , with like numbers referring to like elements. The graph shows the output of the straight-thru port  320 , as a function of applied switching voltage. The maximums of the output labeled “=” correspond to when substantially all the signal exits the interferometer switch  300 , through the straight-thru port  320 , and the minimum labeled “×” corresponds to when substantially all the signal exits the interferometer through the cross-over port  330 . 
     FIG. 4  is a vertical two-dimensional slice of a three-dimensional plot of the power output of the upper waveguide  320  as a function of normalized applied voltage V/V π . When light is launched into the upper input channel of the switch  300 , where the X-axis is the ratio between L dc /l c  and the Y-axis is the ratio of the normalized applied voltage V/V π  in the interferometer section  344 . As shown in  FIG. 4 , crosstalk contour A, crosstalk contour B, and crosstalk contour C represent −10 dB, −20 dB and −30 dB crosstalk contour lines respectively.  FIGS. 5A-5C  show a particular case where electrodes  360 ,  362 ,  364  on the input and output couplers  342 ,  346  receive the normalized applied voltage bias of V dc =Δβ dc L dc /π of approximately ±1.6 (where Δβ dc =difference in the propagation constant of the two waveguides in the directional coupler). The characteristic coupling length of the switch  300  is represented as l c , and the combined length of the two directional coupler is L dc . 
     FIGS. 5A-5C  are two-dimensional plots that are horizontal slices through the three-dimensional plot of FIG.  4 .  FIGS. 5A-5C  each represent optical power output by the upper waveguide  320  while the ratio V/V π  varies for a fixed ratio of L dc /l c .  FIG. 5A  illustrates where L dc  is 2.2l c ,  FIG. 5B  illustrates the case where L dc  is 1.8l c , and  FIG. 5C  illustrates the case where L dc  is approximately 1.6l c . (L dc  is the total length of the two input and output directional couplers.) 
   In  FIGS. 5A-5C , the optical power is illustrated from 1 to 0, which correspond to an “ON” or “OFF” state of the switch  300 , respectively. The Δβ dc  (propagation difference between the directional waveguide pair) of the first and second directional couplers  342 ,  346  must be equal but opposite in sign. This means that the Δβ dc  of the second directional coupler  346  must be in the opposite direction of the Δβ dc  of the first input coupler  342  but of the same magnitude. This asymmetric Δβ dc  is achieved in the first preferred embodiment of the switch  300  by having an equal but opposite bias to the central electrodes  362  of the first and second directional couplers  342 ,  346  while the outer electrodes  360 ,  364  are coupled to the ground voltage. Further, the central electrodes  362  preferably have a length L E . The outer electrodes  360 ,  364  preferably have an equal length being L B . 
   When the signal voltage V S  is applied to the interferometer section  344  with an electric field in the Y-axis direction, the EO induced change in the waveguide indices for the TE and TM modes are exactly equal, but with opposite sign via the r 22 , −r 22  linear EO coefficients. Thus, because of the symmetric nature of the switching characteristics of the balanced bridge interferometer with respect to voltage, both the TE and TM modes of the input optical signal I in  would be switched to the upper output port as shown when a V S =V π  (or V S =−V π ) is applied. The dark band in the center of each contour on  FIG. 4  graphically shows an expanded “cross-over” switch region with very low (−30 dB) crosstalk for the switch when the input and output directional couplers are properly asymmetrically biased V dc =Δβ dc L dc /π of approximately ±1.6.  FIG. 4  also shows that an expanded −30 dB crosstalk contour (e.g., vertical slot) is achieved for an expanded range of L dc /l c  value from 1.5 to 2.2. This particular family of crosstalk contours illustrated by  FIG. 4  is achieved by applying a normalized bias voltage V dc =Δβ dc L dc /π of approximately ±1.6 to the first and second (input and output) directional couplers  342 ,  346 . 
     FIG. 5A  is a two-dimensional plot showing the output of the upper waveguide  320  when L dc =2.2l c . Again, the X-axis illustrates power of the signal coming out of the upper waveguide  320 , and the Y-axis shows the ratio of the switching voltage V/V π .  FIG. 4B  shows that even though L dc  is not equal to l c  and in fact is 2.2l c , the output of the upper waveguide  320  ranges from 0 to 1 thereby exhibiting very low crosstalk being &lt;−30 dB between the ON (upper) and the OFF (lower) outputs of the switch  300 .  FIG. 5B  is a two-dimensional graph for the special case of L dc =1.8l c . 
     FIG. 5B  shows that when L dc =1.8l c  the output from the upper waveguide  320  ranges from 0 to 1 through the range of normalized applied voltages even though L dc  does not equal l c  and in fact  FIG. 4C  shows that the switch  300  functions as well when L dc =1.8l c  as it does when L dc =2.2l c . Thus,  FIG. 5B  shows the switch  300  exhibits crosstalk being &lt;−30 dB for the ratio L dc =2.2l c . 
     FIG. 5C  is another two-dimensional plot showing the output of the upper waveguide  320  for the values of L dc ≈1.6l c  for a range of switching voltages. Once again  FIG. 5C  shows that the output of the upper waveguide ranges  320  from 0 to 1 for the range of normalized applied voltages V when L dc  is not equal to l c  but L dc ≈1.6l c . 
   Taken together,  FIGS. 5A-5C  graphically illustrate that the directional couplers  342 ,  346  can have a range of L dc  (or a range of ratios 1.5&lt;L dc /l c &lt;2.2) and the switch  300  still operates as a low −30 dB crosstalk switch. This is what is meant by the switch having expanded cross-over region and a −30 dB crosstalk contour (e.g., slot) for both the TE and TM modes. The switch  300  differs from the related art because the related art does not exhibit an expanded −30 dB crosstalk contour but merely has a −30 dB point when L dc =l c  as shown in FIG.  2 C. 
   According to the first preferred embodiment of the switch  300 , l dc  is the total length of the combined directional couplers, l c  is the characteristic coupling length for the directional coupler sections  342  and  346 . L B  is the electrode length of each directional coupler that is preferably equal to {fraction (1/2 )}L dc . The signal voltage V S  is preferably a normalized applied voltage, and is equal to Δβ e L e /π where L e  is the electrode length for the interferometer section  344 , and Δβ e  is the electron optically induced propagation difference between the two interferometric waveguide pair. Thus, normalized directional coupler bias voltage V dc =Δβ dc L dc /π where L B  (=½L dc ) is the electrode length for each of the input and output directional couplers, and Δβ dc  is the electro-optically induced Δβ dc  between the waveguide pair in the directional coupler region. 
   Thus, the first preferred embodiment of the optical switch  300  uses a balanced bridge interferometer waveguide structure with asymmetrically-bias Δβ dc -directional coupler structures  342  and  346 , with an equal magnitude, but an opposite sign for the directivity. The directional couplers  342  and  346 , are preferably designed such that the effective Δβ dc L dc /π is approximately equal to 1.6, which provides the favorable extinction ratios with an extended −30 dB crosstalk contour for a given coupling length ratio L dc /l c . Accordingly, to maintain a −30 dB optical switch, the total (including the input and output) directional coupler effective length (L dc ) can be in the range of ˜1.5 to 2.2 times the characteristic coupling length l c  of the directional coupler. Evanescent coupling occurs in the input and output directional couplers but not in the interferometer section. Light for both TE and TM polarizations is switched between the two outputs (e.g., I upper , I lower ) by applying a signal voltage V S  to the interferometer section equivalent to V π , which is the voltage required to electro-optically induce a phase mismatch of π (180°) between the two waveguides. 
   The first preferred embodiment generates the asymmetrically-biased Δβ dc  input and output directional couplers using an applied voltage to induce the Δβ dc  change using the linear electro-optic effect. However, the present invention is not intended to be so limited. 
   As shown in  FIGS. 6A-6G , the crosstalk contour plots of −10 dB, −20 dB and −30 dB for a vertical axis in units of L dc /l c  and a horizontal axis of a normalized applied voltage V/V π  are provided for a progressive directional coupler bias voltage V dc  applied to the switch  300 . A center of a bullseye is a low point in the optical power output of the waveguide, and represents low (−30 dB) crosstalk, and is shown being a cross-over (×) state  502  for the upper waveguide  320  (in  FIG. 3A ) in FIG.  5 A. For example, a cut on this contour plot along the line of L dc /l c =1 would be a horizontal cut through the center of the bullseye on V/V π =0. The bullseye is a low point and one can move horizontally to the right to where V/V π =1, which is a high point shown being the bar (=) state  504 , for the upper waveguide  320  (in  FIG. 3A ) in  FIG. 5A  occurs at V/V π =1. Moving horizontally, the next bullseye at V/V π =2 is a low point. Accordingly, a horizontal line cut along the L dc /l c =1 horizontal line would produce a sinusoidal varying linear switch line. Similar sinusoids are shown in  FIGS. 5A-5C . As another example, if a horizontal cut was taken along the L dc /l c =0 line along a bottom edge of the crosstalk contour plot in  FIG. 4 , there is no variation in the optical power as V/V π  goes from 0 to 2. Thus, there is no coupling to the lower waveguide and all the optical power remains in the upper waveguide output  320  of switch  300 . As V/V π  is varied there is no switching effect because there is no coupling in the interferometer section  344 . Similarly, at the L dc /l c =2 horizontal line in  FIG. 6A , each one of the directional couplers is 100% coupling in the bar (=) state. Thus, the first directional coupler  320  couples a portion of the input signal I in  to the bottom waveguide  320  and the first directional coupler  320  is exactly one coupling length l c  so all the input signal I in  power in the upper waveguide  320  will couple down to the lower waveguide  330  at V/V π =−2, 0, 2, etc. In the interferometer section  344 , a phase shift would be applied, but since there is no signal in the upper waveguide  320  all power is phase shifted to the bottom waveguide  330 . Upon passage through the output directional coupler  346 , which is again one coupling length l c , the input signal I in  is coupled back to the upper waveguide  320  and output as I upper . Thus, the result is similar. All the input power signal is transmitted out the upper waveguide output  320  independent of V/V π . As shown in the description of the related art, the bar state can generally be achieved by optical switches, but a −30 dB crosstalk cross-over (×) state is generally difficult to achieve. 
   When the cross-over (×) state (e.g., as indicated by a bullseye, peanut shape or slot in  FIGS. 6A-6G ) in the crosstalk contour plots cannot be reached, complete switching from 0 to 1 cannot be achieved by the optical switch and the switch would exhibit high crosstalk (e.g., greater than −20 dB, −30 dB outside the corresponding contours). As shown in  FIGS. 6A-6G , a −10 dB cross-over (×) state  610  is larger than a −20 dB cross-over (×) state  620 , which is larger than a −30 dB cross-over (×) state  630 . In fact, as shown in  FIG. 6A , where V dc =0, a −30 dB state can rarely be achieved since L dc  must be precisely 1l c  and such manufacturing tolerances are rarely achieved. However, as shown in  FIG. 6F , where V dc ≈±1.6, a −30 dB crosstalk contour extends from approximately from L dc /l c =1.5 to 2.2. Thus, a horizontal line across the crosstalk contour plot shown in  FIG. 6F  indicates that a −30 dB switch can achieve 100% switching from 0 to 1 for a large tolerance of L dc /l c  ratios and accordingly a very large tolerance of L dc  lengths. 
   The contour plots of  FIGS. 6A-6G  can be achieved by applying different bias voltages ±V dc  at the directional couplers  342 ,  346  in the switch  300  illustrated in FIG.  3 A.  FIG. 6A  is a diagram that shows a crosstalk contour plot with the bias voltage at 0,  FIG. 6B  is a diagram that shows the crosstalk contour plot with the bias voltage at 0.5, and  FIGS. 6C-6G  are diagrams that show crosstalk contour plots when ±V dc  is at 1.0, 1.4, 1.5, 1.6 and 1.7, note that V dc  is the normalized applied voltage in the unit of Δβ dc L dc /π where L dc  approximately equals the total length of the combined directional couplers (input and output), Δβ dc  equals the difference in propagation constant induced between the two directional coupler waveguide pairs.  FIG. 6F  is a crosstalk contour plot similar to that shown in  FIG. 4  for a bias voltage of approximately 1.6, where V dc  is a normalized voltage in the unit of Δβ dc L dc /π. 
   The advantage of looking at different bias voltages V dc  for the switch  300  illustrated in  FIG. 3A , is that an empirical understanding of the advantages according to preferred embodiments can be seen through the series of crosstalk contour plots.  FIG. 6A  is a crosstalk contour plot of an equivalent related art type switch where there is no asymmetric Δβ dc  coupling between the first and second directional couplers. As  FIG. 6A  illustrates, the cross-over state (×) occupies a very narrow region on the L dc /l c  axis. This indicates that the ratio of L dc  to l c  must be tightly controlled in order for a low crosstalk switch to be achieved.  FIG. 6B  is a crosstalk contour plot showing the output when the normalized bias voltage in the unit of Δβ dc L dc /π, V dc  at the directional couplers  342 ,  346  is 0.5. The crosstalk contours shown in  FIG. 6B  are very similar to the contours shown in FIG.  6 A. The primary difference being that the −10 dB regions  620  in  FIG. 6B  have moved closer to each other along the axes L dc /l c . Turning to  FIG. 6C  where the bias voltage V dc  at the directional couplers  342 ,  346  is 1, the plot illustrates how the −30 dB contours  610 ,  620 ,  630  are closer yet along the axis represented by L dc /l c .  FIG. 6D  shows the crosstalk contour plot where the bias voltages V dc  is 1.4. This contour plot shows yet again how the contours  610 ,  620 ,  630  have moved closer to each other due to the bias voltage V dc  and that there is some overlap in the −10 dB region  610  of the crosstalk contour plot. 
     FIG. 6E  shows the crosstalk contour plot for a bias voltage V dc  of 1.5 where the contours  610 , 620 , 630  have moved even closer and there is almost overlap in the −20 dB region  620 .  FIG. 6F  shows the crosstalk contour plots for the bias voltage 1.6 where the 30 dB contours  630  have merged along the Y-axis representing the L dc /l c  ratio. This elongated crosstalk contour along the Y-axis indicates that for a wide range of ratios of L dc /l c , a cross-over state at −30 dB can be achieved. This indicates that the switch can be manufactured with a wide range of ratios of L dc /l c  and the switch will still function as a low crosstalk switch.  FIG. 6G  shows contours for a bias voltage V dc  of 1.7 at the directional couplers  342 ,  346 .  FIG. 6G  shows how as the bias voltage V dc  is increased above 1.6, the −30 dB crosstalk contours  630  come even closer to one another so that there is less of a range for the ratio of L dc  to l c  where the switch  300  will operate with about −30 dB of crosstalk.  FIG. 6G  is an example whereby the bias voltage V dc  has been increased beyond an optimal amount.  FIGS. 6A-6G  show that as the bias voltage V dc  at the directional couplers  342  and  346 , is increased, the switch  300  becomes more and more tolerant of a range of ratios of L dc  to l c  with an optimal range being reached at about V dc  being equal to approximately 1.6 yet still exhibit low crosstalk. 
   Looking at the difference in the cross-over contours between  FIG. 6A  which illustrates equivalent operations of a related art switch and  FIG. 6F  which illustrates operations of a preferred embodiment of the present invention, it is clear that the switch in  FIG. 6F  allows a much wider range of L dc  over l c , which translates into at least a larger tolerance for error in the manufacturing process for the length L dc . 
   In the Z-propagation waveguide switches, even if the TE and TM modes have slightly different characteristics in their respective coupling behavior, or the waveguides using the +r 22 , −r 22  EO coefficients, that slight difference would merely be represented as a small vertical offset between close horizontal slices in the crosstalk contour plot of FIG.  6 F. Thus, the TE and TM modes can be designed to be completed completely within the large available −30 dB crosstalk contour  630  and thus, an effective polarization independent switch is achieved. 
   In addition, as coupling length is a function of wavelength (λ) of the input signal I in , a broad band light source can be used while the optical switch still performs at a −30 dB crosstalk level. Directional coupling length (l c ) is a function of the operating wavelength. Therefore, a change in wavelength λ simply means a change in the effect directional coupling length (L dc /l c ). Since the switch can be operated with very low crosstalk for an expanded range of (L dc /l c ) when V dc ˜1.6, a switch can be operated with very low crosstalk for an expanded range of wavelength as compared to conventional switch. 
   For example, a broad band light source having wavelengths between 1.4 and 1.7 microns can be permitted for operating an input signal to the optical switch  300 . 
     FIG. 7A  is a diagram that illustrates a second preferred embodiment of the optical switch in accordance with the present invention. The second preferred embodiment is a polarization independent broad wavelength 2×2 switch relying on a balanced bridge Mach-Zender interferometer constructed on an X-axis cut Z-propagation lithium niobate waveguide (LiNbO 3 ) structure with asymmetrically biased directional couplers. In the second preferred embodiment, the asymmetric waveguide function is achieved by designing the waveguides to have different widths in the directional coupler section that result in a selected Δβ dc  between the waveguides. 
   As shown in  FIG. 7A , an optical switch  700  is formed in an X-axis cut Z-axis propagation electro-optic substrate  710 . The EO substrate is preferably lithium niobate LiNbO 3 , however, it may be made of other suitable electro-optic substrates. The switch  700  includes a lower waveguide input  712  and an upper waveguide input  714 , and the switch  700  also includes a first directional coupler  720 , an interferometer section  722  and a second directional coupler  724 . The output end of the switch  700  has a lower output waveguide  732  and an upper output waveguide  734 . The first and second directional couplers  720  and  724  are close enough so that the two waveguides experience evanescent coupling. The interferometer section  722  of the switch  700  does not experience evanescent coupling between the waveguides. In the interferometer section  722  of the switch  700  are three electrodes  746 ,  744  and  742 . The electrodes  746 ,  744 ,  742  parallel the waveguides in the interferometer section  722  with the electrode  746  being along one side of the waveguides, the electrode  742  along the opposite side of the waveguides and the electrode  744  located between the waveguides. Electrodes  742  and  746  are preferably electrically connected to ground potential and the center electrode  744  is connected to the signal voltage V S . Referring to the first and second directional couplers  720  and  724 , the total length of the two directional couplers  720 , 724  is L dc , and L dc  can be anywhere in the range of 1.5 to 2.2 times the characteristic coupling length l c . The directional coupler effective length L dc  is preferably divided between each directional coupler  720  and  724  as L B  and L B . The asymmetric (Δβ dc ) nature of the couplers is achieved by the un-equal width of the waveguides in the coupler regions. 
   The asymmetrically biased nature of the directional couplers  720 ,  724  is achieved in the second embodiment by using asymmetric waveguide widths for the two waveguides in each directional coupler section  720  and  724 , which effectively results in a Δβ dc  between the waveguides. The two waveguides with different widths are designed so that Δβ dc  is equal but opposite in sign, where the propagation difference between them is Δβ dc L dc /π˜1.6 for the output directional coupler. For example, that portion of the waveguide  714  in the first directional coupler  720 , is wider, w 1 , than the corresponding narrower, w 2 , portion of the waveguide  712  in the first directional coupler  720 , and that portion of the waveguide  714  in the second directional coupler  724 , is narrower, w 2 , than the corresponding wider, w 1 , portion of the waveguide  712  in the second directional coupler  724 . Δβ dc L dc /π≈1.6 is achieved by fabricating the appropriate Δw, where Δw=(w 1 −w 2 ). 
   All the switch operations are similar to the first case where Δβ dc L dc /π˜1.6 using bias voltage. In operation, the switch  700  receives an optical signal into the input waveguide  714 , the first directional coupler  720  divides the optical signal between the two arms of the interferometer section  722 , the signal voltage V S  then controls whether the divided optical signal couples into the upper output  734  or the lower output  732  at the second directional coupler  724 . The interferometer section  722  controls which waveguide the optical signal couples into using the signal voltage V S  by relying on the EO effect of the lithium niobate substrate. The propagation constant of the lithium niobate substrate is altered based on the direction and the magnitude of the electric field applied by the signal voltage V S . The electrodes  746 , 744  and  742  are arranged to maximize the difference in Δβ i  when the signal voltage is applied. For an X-cut lithium niobate substrate with waveguide propagation direction along the Z-axis, the electrodes  746 , 744  and  742  are placed alongside the waveguides in order to maximize the horizontal electric field, E y , inside the two arms of the interferometer section  722 . 
   When the switch  700  is in the bar state (=), the optical signal entering the input waveguide  714  exits the switch  700  at output waveguide  734 . When the switch  700  is in the crossover state (×), an input signal at input waveguide  714  exits the switch at output waveguide  732 . Because the waveguides are arranged on the lithium niobate substrate so that the propagation direction is along the Z-axis, both the TE and TM modes see the same ordinary index n 0 . Similar to the first case, when Δβ dc L dc /π˜1.6 using asymmetric waveguide widths, rather than an applied voltage, switch operation with low crosstalk can be achieved for a very wide range of directional coupler parameters (L dc /l c ˜1.5 to 2.2). Therefore a broad wavelength, polarization independent switch can be achieved. 
   As shown in  FIG. 7B  shows the same embodiment of the switch as shown in  FIG. 7A , with like numbers referring to like elements. The graph of  FIG. 7B  shows the output of the straight-thru port  734 , as a function of applied switching voltage. The maximums of the output labeled “=” correspond to when substantially all the signal exits the interferometer switch  700 , through the straight-thru port  734  and the minimum labeled “×” corresponds to when substantially all the signal exits the interferometer switch through the cross-over port  732 . 
   A third preferred embodiment of an optical switch according to the present invention will now be described. As shown in  FIG. 8 , a third preferred embodiment of a polarization independent broad wavelength band 2×2 switch  800  uses a Mach-Zender type balanced bridge interferometer waveguide structure with asymmetrically biased directional couplers. The asymmetrically biased nature of the directional couplers is achieved by manufacturing the waveguide with different propagation indices, n 1  and n 2 , between the waveguides in the directional couplers. Different propagation indices for the waveguides can be achieved, for example, by changing the thickness of the initial metal to be diffused or by using material loading effects on the waveguides in the coupler region. Either one of these methods achieves a selected difference in Δβ dc  between the waveguides. 
   Turning to the switch  800  shown in  FIG. 8 , the waveguide substrate material  810  is made preferably out of lithium niobate. The substrate material is X-cut with a preferred propagation direction along the Z-axis. There are two waveguide inputs  812  and  814 . There is a first directional coupler  820  followed by an interferometer section  822 , followed by a second directional coupler  824 , and on the output end of the switch  800  are two output waveguides  832  and  834 . In the interferometer section  822  of the switch  800 , are three electrodes  842 ,  844  and  846 . For the optical switch  800 , the upper and lower waveguides  814  and  812  are single moded for both the TE and TM modes. For the X-cut lithium niobate substrate, the electrodes  842 ,  846  are preferably arranged on the outside along opposite sides of the waveguides and the electrode  844  is positioned between the interferometer arms. The electrodes  846  and  842  are electrically connected to ground potential. A signal voltage V S  can be applied to the electrode  844  to alter the propagation constant in the same amount but in different directions for each arm of the interferometer section  822 . The first and second directional couplers  820  and  824  are asymmetrically biased directional couplers. 
   In the third preferred embodiment shown in  FIG. 8 , the difference in propagation constant (Δβ dc ) of the directional couplers is achieved by how the waveguides are constructed. In general, a waveguide is constructed on a lithium niobate substrate or other dielectric material by diffusing other materials into the substrate during the manufacturing process to change the optical index locally so that light will then propagate preferentially along the path created by the diffused material. By varying the amount of material diffused into the substrate, the propagation constant of a particular waveguide can be altered. In the third preferred embodiment, a Δβ dc  between the first and second directional couplers  820 ,  824  for each waveguide is achieved by starting with a different amount of metal to be diffused into the substrate. Otherwise known as differential optical loading, the differential propagation constant can also be achieved by asymmetric layering of a dielectric or metal over the waveguide. 
   By diffusing into, or layering upon, different amounts of metal or dielectric, different indexes of refractions and the corresponding waveguide indexes, n 1  and n 2 , are achieved for each waveguide section in the coupler region. ±Δn is the waveguide&#39;s difference in the index of refraction in the coupler region, where Δn=n 1 −n 2 , and the sign indicates the direction of the change. Δn is the same but opposite in sign between the input (first)  820 , and output (second)  824 , directional couplers. Δn is chosen so that Δβ dc L dc /π≈±1.6. 
   Alternatively, one can also change the optical waveguide index by using material such as a dielectric or metal loading effect to change the waveguide propagation index. By properly selecting a Δn designed to achieve Δβ dc L dc /π to be approximately ±1.6 (equal but opposite in sign between the input and output couplers), a switch with low crosstalk can be achieved for an extended range of directional coupler parameters L dc /l c ˜1.5 to 2.2. 
   In operation, the switch  800  as shown in  FIG. 8  performs similar to the other preferred embodiments. Accordingly, a detailed description is omitted. Further, the switch  800  receives an input signal into input waveguide  814 . The input signal is divided between the two waveguides at the first directional coupler  820 . The divided signal travels through the upper and lower arms of the interferometer section  822 . The upper and lower arms of the interferometer section receive a signal voltage V S  at the center electrode  844  while the outer electrodes  842  and  846  are held at ground. The signal voltage causes an electric field between the electrodes which changes Δβ i  for the interferometer section. This causes a phase shift between the optical signals in the upper and lower arms so that when both signals arrive at the second directional coupler  824 , the optical signal is either coupled entirely into output waveguide  834  or output waveguide  832 . If the signal couples into waveguide  834 , the switch is in a bar state which is a straight-thru configuration. If the signal is coupled into waveguide  832 , the switch is in a cross-over state, when the Δβ dc L dc /π˜1.6, and the directional couplers  820  and  824  have a total coupling length of L dc  equal to about 1.5 to 2.2 times the characteristic coupling length l c . Thus, the total directional coupler length L dc  can be anywhere in the range of about 1.5 to 2.2 times the characteristic coupling length l c  of the directional couplers  820 ,  824 . 
     FIG. 9  shows the same embodiment of the switch as shown in  FIG. 8 , with like numbers referring to like elements. The graph of  FIG. 9  shows the output of the straight-thru port  834 , as a function of applied switching voltage. The maximums of the output labeled “=” correspond to when substantially all the signal exits the interferometer switch  800 , through the straight-thru port  834  and the minimum labeled “×” corresponds to when substantially all the signal exits the interferometer switch through the cross-over port  832 . 
   In the first, second and third embodiments of the optical switch, an X-cut, Z-propagation LiNbO 3  crystal was used as the substrate. In addition to not being limited to LiNbO 3  as the substrate material, the invention is not intended to be limited to an X-cut crystal orientation. It is contemplated that other orientations will work for the switch substrate. For example,  FIG. 10  shows a Y-cut, Z-propagation optically active crystal as the substrate. In  FIG. 10 , the interferometer switch  1000  has an upper and lower input port,  1002  and  1004 , respectively, and an input and an output directional coupler  1006  and  1010 , respectively. The input directional coupler  1006 , has an upper input electrode  1012  and a lower input electrode  1014 . The second directional coupler  1010 , has an upper output electrode  1016  and a lower output electrode  1018 . In the interferometer section  1008 , there is an upper switch electrode  1020 , and a lower switch electrode  1022 . 
   In  FIG. 10 , because the crystal&#39;s X and Y axes are rotated about the Z axis by 90° from the X-cut examples, the electrodes  1012 ,  1014 ,  1016 ,  1018 ,  1020 , and  1022  must be placed in different positions relative to the waveguides in order to induce the change in propagation constant, Δβ, in the Y-direction. As  FIG. 10  illustrates, the electrodes must be placed above the waveguides to induce a Δβ in the Y direction. Also contemplated for the Y-cut crystal is placing some or all of the electrodes under the waveguides. 
   After a switch made according to the preferred embodiments has been installed, the aforementioned tuning feature of the switch (e.g., the switch  300  shown in  FIG. 3A ) can be used to optimize the switching function if the switch is degraded by local conditions such as for example, temperature, pressure, mechanical stresses such as bending or twisting, and chemical environment. The switch&#39;s tuning characteristics can also be used to optimize the switching function if it degrades over time. For example, switching degradation can be caused by substances diffusing into the switch substrate and waveguides, or by the frequency of the optical signal changing, etc. Virtually any change in the switching characteristics based on altered directional coupler functionality can be compensated by tuning the directional couplers using their associated electrodes. 
     FIG. 11A  shows related art balanced-bridge interferometer  1100 , with a graph of the signal output of the straight-thru port.  1110  and  1120 , are the top and bottom input ports, respectively.  1130  and  1140 , are the first and second directional couplers.  1150  is the interferometer section, and includes an upper and lower electrode  1160  and  1180 , respectively, which are held at ground potential, and a middle electrode  1190 , which receives a controlling signal.  1195  and  1197  are the straight-thru and cross-over outputs, respectively. All the waveguides are single-moded. 
   For the related art balanced-bridge interferometer switch  1100 , to function with low cross-talk, each directional coupler  1130  and  1140 , should have an effective length of one-half the characteristic coupling length. In operation, a differential phase shift is induced within the interferometer section  1150 , by application of a switching signal to the middle electrode  1190 . 
   The output of the straight-thru port as a function of applied switching voltage for coupler lengths of one-half the characteristic coupling length is shown in FIG.  11 B. The maximums of the output labeled “=” correspond to when substantially all the signal exits the interferometer  1100 , through the straight-thru port  1195 , and the minimum labeled “×” corresponds to when substantially all the signal exits the interferometer through the cross-over port  1197 . When the lengths of the first and second directional coupler  1130  and  1140 , respectively, are one-half the characteristic coupling length, the interferometer exhibits low cross-talk as indicated by the minima of  FIG. 11B  being substantially equal to 0. 
     FIGS. 12A through 12E  show the output of the straight-thru port  1195 , as a ratio between input signal and output through the straight-thru port, of the interferometer switch  1100 , for a range of directional coupler  1130  and  1140 , lengths from 0.6l c  to 1.4l c . When the ratio is close to one, substantially all the signal exits through the straight-thru port, and when the ratio is close to 0, substantially all the signal exits through the cross-over port. In  FIG. 12C , where the minimum represented by the reference letter “A” is close to 0, the interferometer switch  1100  is exhibiting low cross-talk, and has a minimum of cross-talk when L dc =1.0l c . The interferometer switch  1100  exhibits increasing cross-talk as indicated by the minimum at A increasing in value as L dc  deviates from 1.0l c .  FIGS. 12A ,  12 B,  12 D, and  12 E are for L dc =0.6l c , L dc =0.8l c , L dc =1.2l c , L dc =1.4l c    
     FIG. 13A  is an example of a balanced bridge interferometer switch  1300 , with an input directional coupler  1302 , an interferometer section  1304 , and an output directional coupler  1306 . The input directional coupler  1302 , has a pair of electrodes  1308  and  1310 . The output directional coupler  1306 , has a pair of electrodes  1312  and  1314 . The interferometer section has a pair of electrodes  1316  and  1318 . The interaction lengths L B , of the input and output directional couplers,  1302  and  1306 , respectively are each equal to one-half the characteristic coupling length l c . 
   Via the electrodes  1308 ,  1310 ,  1312 , and  1314 , associated with the directional couplers  1302  and  1306 , a difference in the propagation constant Δβ dc , of the waveguides in the couplers can be induced. A normalized applied voltage of Δβ dc L B /π=±0.8 is the preferred voltage to be applied between the electrodes  1308  and  1310 , as well as between  1312  and  1314 . It is further preferred that the each directional coupler be biased the same amount but with an opposite sign, and this would be achieved by suitably controlling the polarity of the bias voltages. By applying a normalized voltage of Δβ dc L B /π=±0.8, the widest range of coupler interaction length L B  is allowed for a coupler to function as a 3 dB coupler. 
     FIG. 13B  is a contour plot for a single directional coupler which could be used as either the input directional coupler  1302  or the output directional coupler  1306  of the balanced bridge interferometer switch  1300 . The horizontal axis is the induced change in propagation constants between the waveguides of a directional coupler as expressed in units of Δβ dc L B /π, where Δβ dc  is the difference in the propagation constant between the waveguides and L B  is the interaction length of the coupler. The vertical axis is the normalized interaction length between the couplers as expressed in units of L B /l c , where L B  is the same as for the horizontal axis and l c  is the characteristic coupling length. Characteristic coupling length is the interaction length between the two waveguides sufficient to transfer all the power in one waveguide into the other. Reference letter “A” indicates the locus of the 3 dB half power points. Reference letter “D” is where the locus of the 3 dB half power point crosses the zero vertical axis. Reference letter “C” is that section of the 3 dB locus corresponding to where Δβ dc L B /π is approximately equal to 0.8. Reference letter “D” indicates the contour for when all of the output power exits from the straight through output with less than 30 dB power exiting through the crossover output. Reference letter “E” indicates the power contour region when all the output power exits through the cross-over output with less than 30 dB power exiting through the straight-thru output. 
   The line where the normalized applied voltage bias equals zero on the horizontal axis corresponds to the 0 bias state of related art directional couplers. Hence  FIG. 13B  indicates that, with a normalized applied voltage bias equal to zero, the line associated with the interaction length of a coupler bisects the locus of the 3 dB half power point near 0, and consequently intersects the locus in a region corresponding to a point. 
   The physical implication of  FIG. 13B  is that the interaction length of the coupler must be precisely controlled in order to achieve the 3 dB coupler. When the normalized applied voltage bias (Δβ dc L B /π) equals either negative 0.8 or positive 0.8, the edge of the locus of the 3 dB point is intersected. Consequently, the coupler interaction length can have a much greater variation, and 3 dB coupling would still being achieved. Corresponding to ±0.8 normalized voltage bias, the 3 dB coupling length of the coupler ranges from 0.75 to 1.1 in units of l c . In other words, at the bias point of Δβ dc L B /π˜±0.8, 3 dB splitting can be achieved for an extended range of L B /l c ˜0.75 to 1.1 (i.e. L dc /l c ˜1.5 to 2.2), not a singular point as in the conventional design. 
   The 3 dB locus in the regions of Δβ dc L B /π=+0.8 and −0.8 normalized voltage bias has an opposite curvature. The bias of the input and output directional couplers for the balanced bridge interferometer switch are chosen to have the same magnitude, but opposite polarity to balance out this slight asymmetry. 
   The contour plot of  FIG. 13B  is derived using standard coupled wave formula. The derivation and starting equations can be found, for example, in the “Handbook of Microwave and Optical Components,” Vol. 4, Chapter 4, “Optical Modulation, Electro-Optic devices,” by Suwat Thaniyavarn, which is incorporated herein by reference. 
     FIGS. 14A through 14H  show the output of the switch  300  shown in  FIG. 3A  for various coupling lengths ranging from 1.2l c  to 2.6l c . When the ratio shown in  FIGS. 14A through 14H  is close to one, substantially all the signal exits through the straight-thru port, and when the ratio is close to 0, substantially all the signal exits through the cross-over port. In  FIGS. 14B through 14G , which corresponds to L dc =1.4l c  to 2.4l c , reference letter “A” indicates that there is substantially 0 cross talk. This is a much wider operational range than the related art interferometer switch represented by  FIGS. 12A through 12E . 
     FIG. 15  shows contour plots of straight-thru and cross-over switch states for a related art balanced bridge interferometer. The “×” corresponds to the cross-over switch state with three levels of cross-talk of &lt;−30 dB, &lt;−20 dB, and &lt;−10 dB. The “=” corresponds to straight-thru switch states with three levels of cross-talk of &lt;−30 dB, &lt;−20 dB, and &lt;−10 dB. 
   As described above, the present invention provides various advantages. According to the preferred embodiments, polarization independent switching over a broad wavelength can be realized because of relaxed coupler length tolerances. Further, the polarization independent switching has a very low polarization mode dispersion (PMD) and polarization dependent loss (PDL) through the use of Z-axis (i.e., optic-axis) propagation waveguide orientation on an electro-optic substrate where TE and TM see an identical ordinary index. 
   A low crosstalk switch (less than −25 dB) can be achieved for a very large range of L dc  values (first preferred embodiment 1.5l c  to 2.2l c ). In accordance with the large range of the directional coupler effective coupling length L dc , a fabrication tolerance of L dc  equal to 1.5l c  to 2.2l c  can be achieved, which creates an increased production yield. Further, since the characteristic coupling length l c  of the directional coupler is a function of an optical wavelength and polarization (and to a small degree a function of environmental parameters such as waveguide loading effects from a dielectric layer, electrode layer, stress, temperature, etc.), the switch can be designed to operate in a very broad range of wavelengths for both TE and TM polarizations. 
   The foregoing embodiments and advantages are merely exemplary and are not to be construed as limiting the present invention. The present teaching can be readily applied to other types of apparatuses. The description of the present invention is intended to be illustrative, and not to limit the scope of the claims. Many alternatives, modifications, and variations will be apparent to those skilled in the art. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not only structural equivalents but also equivalent structures.