HIGH-SPEED HITLESS SWITCHES FOR FIBER OPTICS
Cross-Reference to Related Application This application claims the benefit of United States Provisional Patent Application Nos. 60/559,717, filed April 5, 2004, and 60/560,356, filed April 6, 2004, which are both hereby incorporated by reference herein in their entireties.
Field of the Invention This invention relates to apparatuses and methods for switching in fiber optic transmission systems. More particularly, this invention relates to apparatuses and methods for switching in fiber optic transmission systems in which it is desirable to minimize data lost during switching.
Background of the Invention Fiber optic switches are widely known in the prior art. Many such switches have been developed for the purpose of changing the path traveled by an optical beam upon a command or instruction. Switches in optical systems are necessary for a number of reasons. One reason may be to switch around or bypass an optical device, such as an add/drop multiplexer, when the optical device needs to be reconfigured. A switch could be needed in this instance because the finite reconfiguration time necessary for tuning or otherwise calibrating an optical device can disrupt data flow and possibly corrupt optical signals on the fiber. As fiber optic technologies continue to improve the bandwidth on fiber optic cables and as Internet data traffic continues to grow, the issue of lost or corrupted data during optical device reconfigm-ation will become more and more problematic. It is, therefore, desirable to provide a switch for fiber optics that can operate without the loss of data when moving the optical beam from one path to another path.
Summary of the Invention In accordance with the present invention, switches for hitless switching of an optical beam between paths are provided. In preferred embodiments, the switches operate by placing two optical paths within a certain proximity to one anther so that the paths may be within a field coupling distance. Then, by changing a parameter that controls how the optical signal
travels through one of the paths, the optical signal can be switched between the paths because the paths are within the field coupling distance. For example, this parameter may be a refractive index of the path. The switches can additionally be cascaded and two routes can be placed between the cascaded switches. Additionally, in certain embodiments, an optical device can be placed on one of the routes so that the signal can be switched around the optical device when desired. Thus, in accordance with the present invention, certain embodiments comprise a first waveguide and a second waveguide that is in a coupling proximity to the first waveguide. The second waveguide comprises a material that causes light to pass into the first waveguide based upon an electric field present in the material. In accordance with some embodiments of the present invention, the waveguides may be composed of a semiconductor material. In other embodiments, this apparatus may also be cascaded and used on either end of a Mach- Zehnder configuration. In yet other embodiments, this apparatus may also comprise the use of a capacitive phase shifter in the pi shift region of the Mach-Zehnder configuration. In some embodiments, this apparatus may also comprise an optical device in one of the two waveguides of the Mach-Zehnder configuration. Further, in accordance with the present invention, certain embodiments comprise a first waveguide and a second waveguide that is within coupling range of the first waveguide. The second waveguide comprises a plurality of regions each having its own electric field that causes light to pass into the first waveguide based upon an electric field present in the material. In accordance with some embodiments of the present invention, the waveguides may be composed of a semiconductor material. In other embodiments, this apparatus may also be cascaded and used on either end of a Mach-Zehnder configuration. In still other embodiments, this apparatus may also comprise the use of a capacitive phase shifter in the pi shift region of the Mach-Zehnder configuration. In some embodiments, this apparatus may also comprise an optical device in one of the two waveguides of the Mach-Zehnder configuration. Still further, in accordance with the present invention, certain embodiments comprise changing the refractive index of a first waveguide that is within coupling distance of a second waveguide in response to an induced change in free charge carriers in the first waveguide and using the induced change in the refractive index to detune an optical signal in the first waveguide to direct the optical signal into the second waveguide. In accordance with some embodiments of the present invention, this method may comprise using a controller that
regulates the electric fields in multiple sections of the first waveguide. In other embodiments, perturbed directional couplers may be cascaded and placed on either end of a Mach-Zehnder configuration. In some embodiments, the method may also comprise the use of a capacitive phase shifter in the pi shift region of the Mach-Zehnder configuration. In other embodiments, the method may also comprise the use of an optical device in one of the two waveguides of the Mach-Zehnder configuration. Yet further, in accordance with the present invention, certain embodiments comprise an optical switch which uses an electric field to control switching and may be made using complementary metal-oxide-semiconductor manufacturing techniques. In accordance with some embodiments of the present invention, this apparatus may also comprise two waveguides within coupling distance of one another. In other embodiments, this apparatus may also comprise a plurality of contacts along one of the waveguides, wherein each contact can be controlled separately.
Brief Description of the Drawings The above and other objects and advantages of the present invention will be apparent upon consideration of the following detailed description, taken in conjunction with accompanying drawings, in which like reference characters refer to like parts throughout, and in which: FIG. 1 is a schematic diagram of a high-speed hitless switch in accordance with certain embodiments of the present invention; FIG. 2 is a schematic diagram of how an optical signal might flow around an optical device in accordance with certain embodiments of the present invention; FIG. 2B is a picture of how an optical signal might look crossing from one waveguide to another in accordance with certain embodiments of the present invention; FIG. 3 is a picture of how an optical signal might look remaining in the same waveguide in accordance with certain embodiments of the present invention; FIG. 3B is a schematic diagram of how an optical signal might flow through an optical device in accordance with certain embodiments of the present invention; FIG. 4 is a cross-sectional view of a coupler in accordance with certain embodiments of the present invention; FIG. 4B is a cross-sectional view of a coupler with free charge carriers present in accordance with certain embodiments of the present invention;
FIG. 5 is a schematic diagram of an illustrative embodiment of a metal-oxide- semicoήductor capacitor phase shifter introduced on π shift Mach-Zehnder configuration in accordance with certain embodiments of the present invention; FIG. 6 is a schematic diagram of a multi-section metal-oxide-semiconductor capacitor phase shifter in accordance with certain embodiments of the present invention; FIG. 6B is schematic diagram of a multi-section metal-oxide-semiconductor capacitor phase shifter with a controller in accordance with certain embodiments of the present invention; FIG. 7 is a graph illustrating the relationship between coupling length and ΔβlJπ for a single-section directional coupler in accordance with certain embodiments of the present invention; and FIG. 8 is a graph illustrating the relationship between coupling length and ΔβLJπ for a multi-section directional coupler in accordance with certain embodiments of the present invention.
Detailed Description of the Invention In accordance with the present invention, apparatuses and methods for switching optical signals at high speeds with minimal or no data loss are disclosed. The switches generally work by placing two optical paths within a coupling distance of one another, and then actively altering how the optical signal travels through one of the paths so that the optical signal can be switched between the paths. The switches can additionally be cascaded and two pathways can be placed between the cascaded switches. Additionally, in certain embodiments, an optical device can be placed on one of the paths so that the signal can be switched around the optical device as desired. One need for a hitless switch stems from the finite reconfiguration time necessary for tuning optical devices, e.g. an optical add/drop multiplexer. Within this finite time - order of milli- to micro-seconds - information bits can be lost or distorted in the high-bandwidth optical channel. Therefore, a solution presented by some embodiments of the invention is to switch information from a signal bus waveguide to another "bypass" waveguide, without any loss of bits, while the reconfiguration is being performed on a device or devices attached to the signal bus waveguide. FIG. 1 illustrates an embodiment of the invention where switches are cascaded and there is an optical device present in one of the routes. A configuration where there are two
paths coupled at two distinct points may be referred to as a Mach-Zehnder configuration. In the embodiment shown in FIG. 1, a Mach-Zender configuration is composed of waveguides 14, 15, 16, 17, 18 and 20 and is coupled at points 10 and 12. However, unlike a typical Mach-Zehnder Interferometer (MZI), the optical signal is not split in half at the first couple 10 and the waveguides are not fused together at points 10 and 12. Typically, in a Mach-Zehnder configuration, a phase delay is induced in an optical signal traveling in one arm relative to the optical signal traveling in another arm. Conventional Mach-Zehnder interferometers shift the phase of light in one of the arms by one of several ways, such as using an electro-optic effect, an electro-thermal effect, or an arm length difference. The first two methods change the index of refraction in the waveguide thereby slowing the propagation of light in one arm relative to the light in the other arm. Changing the index of refraction can be thought of, for example, as analogous to changing the optical length of the arm. In the conventional Mach-Zehnder Interferometer, the induced phase delay between the two optical signals can cause intensity changes when the two signals are recombined at the second couple by destructively or constructively modifying the signal. In the preferred embodiment, π shift 19 on FIG. 1 refers to a half wavelength phase shift that occurs in waveguide 20. As one skilled in the art will appreciate, the π shift in waveguide 20 is measured relative to the phase of an optical signal in waveguide 18. In a preferred embodiment, a metal-oxide-semiconductor (MOS) technology forms the basis of switches 10 and 12. A MOS configuration can provide the change needed to move the optical signal from one waveguide to another as follows. The capacitive behavior of the MOS, when the semiconductors are biased into accumulation, alters the characteristics of the MOS semiconductors by introducing free charge carriers. If one of the MOS semiconductors is used as a section of the waveguide in a switch, then the optical beam can polarize the free charge carriers and can subsequently perturb the local dielectric constant of the medium. This may lead to a perturbation of the propagation velocity of the optical beam, which can change the index of refraction. The index of refraction can be changed in such a manner because the index is based upon the ratio of the speed of light in a vacuum to the speed of light in a second material. Another effect that may occur, as a result of the free charge carriers present in the material, can be the absoφtion of optical beam energy as the optical beam field accelerates the free charge carriers. In one embodiment, the MOS device may be a majority-carrier semiconductor with no stored charge injected into or removed from the device. This embodiment may allow
faster switching because the free charge carrier levels in the semiconductor can be modified without having to wait for recombination as may be the case in other devices. More particularly, in certain embodiments, a configuration of semiconductor material called an asymmetric metal-oxide-semiconductor capacitor phase shifter (ACPS) may be used to implement the functionality of perturbed directional couplers (PDC) 10 and 12. The ACPS derives its name from being a device where the waveguides are not equally perturbed in the operation of shifting the phase of an optical signal through modification of the capacitance of the device. PDCs, which in one embodiment can be composed of ACPS, can be thought of as comprising the concepts of coupling distance, with the waveguides placed in a certain proximity to one another, and phase shifting occurring in the waveguide. The combination of the two concepts can allow optical switching to occur. When an optical signal passes through one waveguide, at least some energy may be transferred to a second waveguide. However, if the light passes through the waveguide at the correct phase, then it can cause a complete, or nearly complete, transfer of energy to the second waveguide. In another example, if the light is in completely the wrong phase, it can lead to little or no energy being transferred to the second waveguide. As stated above, there are two waveguides 14 and 16 that pass through PDCs 10 and 12. These waveguides can remain separated and, in certain embodiments, the waveguides in the PDC may be separated by silicon oxide (SiO2). Moreover, because the waveguides do not cross, waveguide 14 continues as waveguide 20 and waveguide 16 continues as waveguide 18 after PDC 10. In some embodiments, waveguides 16 and 17 can be eliminated so that one waveguide goes into PDC 10 and one waveguide leaves PDC 12. As shown in box 22, an optical signal can be switched into or out of an optical device 24, which may be for example an optical add/drop multiplexer, depending on the configuration of PDCs 10 and 12. In some embodiments, for switching to occur, one of the two waveguides in the coupler may be altered so that the light undergoes a phase shift. In other embodiments, the PDC may be composed of a capacitive phase shifter wherein both waveguides can undergo a phase shift. In yet other embodiments, the PDC may be composed of a plurality of waveguides and at least one of a plurality of waveguides may be altered so that the corresponding waveguide undergoes a phase shift. The phase mismatch or detuning, δ, in the PDC determines how the signals further propagate in waveguides 18 and 20. The detuning can be explained by the equation
δ = (βi - β )/2, where \ and β2 are propagation constants in each of the waveguides. In one embodiment, the detuning, δ, is designed to be initially zero, permitting an input signal in waveguide 14 to cross-over to waveguide 18 as shown in FIGS. 2 and 2B. FIG. 2 illustrates the switch in the cross-state and shows an embodiment where an optical signal would flow through optical device 24, e.g. optical add/drop multiplexer, in waveguide 18. The state when the optical signal changes waveguides is called the cross-state of the PDC. Another illustration of the cross-state is FIG. 2B whereby the coupling effects of a properly tuned optical signal can clearly be seen. The PDC, in some embodiments, can be designed so that the input signal is tuned to cross-over without any applied voltage in the ACPS. In another embodiment, the switch can be implemented were the input signal is tuned to remain in the bar state (i.e., the state with no cross-over) without any applied voltage. The cascaded setup of PDCs 10 and 12, where the two PDCs perturb opposite waveguides, may be used to ensure that the signal is properly re-routed after being routed through waveguides 18 or 20. When the detuning, δ, from the phase shift in the perturbed waveguide in the PDC is equal to 31/2 K (where K is the coupling coefficient), an input signal in waveguide 14 remains in the same waveguide and continues in waveguide 20 as shown in FIG. 3 and FIG. 3B. An input signal that remains in the same waveguide is defined as being in the bar-state of the PDC. FIG. 3 illustrates how an optical signal can be tuned so that at the end of the PDC effectively little or no energy is transferred to the other waveguide. Although there is some interaction between the waveguides in the bar-state, if the optical signal is properly detuned the signal can remain in the same waveguide. FIG. 3B illustrates the PDC in the bar-state and shows an embodiment where an optical signal is switched around optical device 24, for example, optical add/drop multiplexer, in waveguide 20. In FIG. 3B, the optical signal would move from waveguide 14 to waveguide 20, essentially staying in the same waveguide. An explanation of how PDCs 10 and 12 work in certain embodiments of the invention is now provided. As stated above, the waveguides within the PDCs need to be placed within a certain proximity of one another so that the fields of the waveguides can interact. One of the effects experienced by the waveguides at a coupling distance is that of fringing fields. Fringing fields can be thought of, for example, as the edge effects in capacitive structures that increase the effective area of the capacitor. Fringing fields can lead to capacitive coupling, which can lead to the transfer of energy from one waveguide to another by means of the mutual capacitance between the waveguides. In certain embodiments of the invention, the
waveguides in the PDCs may be coupled in space via fringing fields, allowing the optical signal to move from one waveguide to another waveguide in the couple. To explain how the switching may be implemented, field amplitudes a in waveguide 14 and a2 in waveguide 16 are introduced for use in the following equations: a. = -jβ1al + κl2 a2 dz (1)
where z is the direction along the waveguide propagation, βj and fa are the waveguide propagation constants for waveguides 14 and 16, and Kn and κ_
\ the complex coupling coefficients for waveguides 14 and 16. For energy conservation, Kn = - κ_ι for co- propagating waves, and Kn = κ_ι for counter-propagating waves. The coupling coefficients can be evaluated from equations: jω
r κ,
2 = - — )
G, (εi - ε ) e
2 • e,
* dx dy (3) jω r *ii = - — JG2 (ε
2 - ε ) e,
• e
2 dx dy ^
where ei and e
2 are the normalized field amplitudes in waveguides 14 and 16 respectively, x and y are directions in the cross-sectional plane of the waveguides, ε
\ and ε
2 are the permittivities in waveguides 14 and 16, respectively, and Gl and G2 the cross-sectional areas of waveguides 14 and 16, respectively. An effective propagation constant of the coupled waveguides, β, may be found from the determinantal solution of Equations (1) and (2) as
or: β = β ± (δ
2 + κ
12 κ
2I) = β ± β
0 (5)
where β = (βι + βi)l2 and β0 = (δ2 + K K2i)m . δis the detuning parameter and can be defined as (βi - >2)/2. In the weak-coupling assumption, the following may hold: \κ \ « \βι\ and \β_\. From Equation (5), though, it is preferable to have <?on order of K for appreciable coupling. Thus, for appreciable coupling, βi ≡ βi. To perturb a directional coupler, βi is preferably significantly different from β . The difference can be achieved with a CMOS
asymmetric metal-oxide-semiconductor capacitor phase shifter as detailed for some embodiments of the invention. In addition, if waveguides 14 and 16 are identical or nearly identical, then κi2 can equal (β+ - β.)l2, where β. = β - β0 and β+ = β + β0 . β. and β+ are the lowest symmetric and anti-symmetric eigenmodes of the coupled identical waveguides. The field profiles at any arbitrary position z for co-propagating waves can be derived from Equations (1) and (2) as the following: a,(ζ) / e" ■^jβ2z == a,(0) [cos βoZ -j g sin &ζ] + a2(0) [ jξ sin βH (6) a2(z) I e" ■j ■"β'z* _ = a,(0) [ ξ sin βΛ] + a2(0) [cos βΛ +j sin ] (?)
where a^O) and a (0) are the input fields to waveguides 14 and 16 at the z = 0 frame of reference. In some embodiments, these field profiles can be cascaded into the second coupler, with a π-phase shift at one of the arms of the Mach-Zehnder configuration. These π- imbalanced Mach-Zehnder configurations can then be cascaded in a variety of geometries for multiple functionalities, in various other embodiments of the design. The resultant transfer matrix can be derived from scattering matrix calculations, or direct repeated application of Equations (6) and (7). For the puφoses of switching, in some embodiments, the coupling length for full signal power transfer is of interest. For symmetric waveguides (δ = 0) in a single directional coupler with single excitation (ai = 1 and a2 = 0), the coupling length may be found as:
_ π _ _ it ZcoupUng - 2β0 ~ β+ - β_ ~ 2κ (8) For completely detuned waveguides (δ = -J K) with single excitation (ai = 1 and a =
0) in a single directional coupler, the power transfer can be periodic and may have a maximum of 0.25, occurring at half the unperturbed coupling length, z = zCouPiing/2 as shown in FIG. 3. At the full unperturbed coupling length, z = Zco pUng, the power may stay in the excitation waveguide as shown in FIG. 3 instead of crossing-over into the coupled waveguide as shown in FIG. 2B. FIG. 4 illustrates how the cross section of a PDC implemented using an ACPS might appear. In some embodiments, silica, SiO2, 30 is ribbed between p-polysilicon waveguides 32 and 34. Silica is a pure form of glass that is typically an insulator when used in electronics and is also a major component in fiber optic cables. Aluminum contact 36 where a drive
voltage, VD, can be applied is provided. The phase shift magnitude in waveguide 34 may vary with driving voltage, VD, and the active length of the phase shifter, L 26 (shown in FIGs. 1, 2 and 3B). A controller 45 may be used to manage the switching in the PDC. Controller 45 may be, for example, a microprocessor based controller, a logical circuit, an analog circuit or even a digital circuit. In some embodiments of the invention, for an applied voltage of 10 V, the refractive index change in terms of phase shift induced, Δneff,ps, can be estimated at ~ 315(λ/2π) m"1 based on the charge-carrier effects from the capacitor. Metal contact 36, separated by highly-doped surface 44, can be placed on one side of perturbed waveguide 34. Highly-doped surface 38 may be where a ground voltage (Vground) is applied. As described above, controller 45 connected to contact 36 and surface 38 may be used to manage the switching. There may also be gate oxide 42 sandwiched between the bottom of p-polysilicon 34 and the top of n-silicon 40 in the some embodiments. When a drive voltage is applied to between contact 36 and surface 38, majority charges may accumulate on both sides of the gate in waveguide 34 and n-silicon 40 as a thin charge layer, causing a change in the free charge densities Nelectrons and N 0ιes in p-polysilicon 34 and n- silicon 40 as shown in FIG. 4B. The applied voltage may cause absoφtion and refractive index changes in waveguide 34 through the charge-carrier effects, which alter the phase of the signal. The free charge density may be a small change, with the charge layer covering less than one percent of the fundamental transverse electric mode area. The required index change, Δneff,req. may be linearly dependent on the coupling coefficient K and hence be exponentially dependent on the gap separation between the directional couplers. In some embodiments, for a gap separation of 800 nm, for example, in single-mode silicon waveguide directional couplers K turns out to be around 144 m"1 which can translate to a Δneffιreq of about 498(λ/2π) m"1. This order of magnitude can be achieved with the single ACPS embodiment as described above. However, a difficulty in the design might be the estimation of K at relatively large gap separations when having to take into account manufacturing imperfections. To improve estimation, the gap separation may be decreased (and hence K increased) so that larger phase shifting will be needed from the ACPS to detune the waveguides. Another solution may be through an alternate embodiment of a multi-section phase shifters as described in connection with FIG. 6. In one embodiment, insulating region 44 shown in FIG. 4, which may be composed of SiO2, allows attachment of the device to a silicon substrate. The design of the metal-oxide- semiconductor capacitor phase shifter may be made entirely in a complementary metal oxide
semiconductor (CMOS) foundry, laying the ground for silicon microphotonics. A primary source of optical losses is the polysilicon 32 and 34 in the "rib" section (i.e., made up of sections 30, 32, and 34) of the waveguide. The losses in the "rib" section may be reduced using sequential lateral solidification to form single-crystal Si from amoφhous Si regions in this section. The thermal insulation layers for the single-crystal Si formation are SiO2 30 in the "rib" section and SiO2 44 underneath single-crystal n-Si 40 shown in FIG. 4. FIG. 5 illustrates the addition of metal-oxide-semiconductor-capacitor phase shifter (CPS) 50 to π shift region 60 of the Mach-Zehnder configuration. The reason it may be desirable to add CPS 50 is because CPS 50 may reduce some of the optical energy losses that can occur with the uses of the PDCs. More particularly, as described above, different refractive indexes in a waveguide can create a frequency dependence which can lead to optical signal spreading and attenuation. The frequency dependence can be, for example, a ~ 2.5% fractional dependence for a 40 nm spectrum in the 1530 - 1570 nm band. The dependence can result in a 0.01 dB drop in transmission for the 40 nm bandwidth. However, designing the PDCs cascaded in the π-shifted asymmetric Mach-Zehnder configuration, can reduce the associated frequency dependent losses introduced by the refractive index changes in each of the directional couplers. Thus, it may be desirable to introduce a π shift, or half wavelength shift of the signal, was introduced to obtain the hitless switching behavior and to help reduce frequency dependence. The π shift in conjunction with the PDCs, may prevent the optical signal from "leaking" or partially switching to the other waveguide. For example, if a π shift is not specifically obtained in waveguide 54, and the phase shift is around 23% off, then the signal losses may be around 5%. In some embodiments, waveguide 54, may be lengthened to create the π shift. In other embodiments, an electro-optic effect or an electro-thermal effect may be used to obtain the π shift. In yet other embodiments, the corrective phase shift required can be achieved with the use of an integrated MOS-capacitor. Moreover, the integration of a CPS in the π shift region can also allow the adjustment of the phase of the optical signal to correct any manufacturing imprecision the waveguide length. FIG. 6 illustrates a multi-section MOS-capacitor phase shifter of the ACPS design. The multi-section ACPS design may be similar to the single section ACPS design in terms of the waveguide proximity and the placement of contacts on the perturbed waveguide, but the difference arises in there being multiple regions where the waveguide can be independently
perturbed. The capability to independently perturb different sections in the same PDC can provide the ability to better tune the phase shift of the optical signal. In the some embodiments of the multi-section ACPS, one waveguide may feature multiple contacts along its length in the PDC. The contacts may be separated from one another by distances that can be around 50 times the width of the waveguide. The separation should be enough to avoid sustained free carrier migration from one contact to another, which may then form an electrical current in the waveguide.
As one skilled in the art will appreciate, various designs of the multi-section ACPS design exist. In some embodiments, the multi-section MOS-capacitor phase shifter may be designed so that materials used in the ACPS have different propagation constants. In other embodiments, the multi-section MOS-capacitor phase shifter allows control over each section so the free charge density of each region can be precisely tuned. In yet other embodiments, the sections can be composed of all the same waveguide material and just the electric fields induced in each section can vary. The waveguide may also be doped differently, in some embodiments, to modify how the phase shifting can occur or possibly reduce energy losses in the waveguide. In the certain embodiments, the multi-section ACPS may employ an alternating-Δβ configuration with two or more sections to provide tunability in the cross-over states.
The multi-section design can further reduce transmission losses due to asymmetries in the directional couplers. Asymmetries in the PDCs may be used to reduce the cancellation of the frequency dependence, as mentioned above, in the π-shift cascaded directional couplers. Frequency dependence transmission losses can arise, when the first directional coupler is slightly different in geometrical dimensions - from real-world fabrication deviations - than the second directional coupler. The effect of the dimension mismatch can be described using coupled-mode theory approximations. However, the effect is typically small and the result can be controlled within a 0.5 dB transmission loss with a single section MOS-capacitor phase shifter. The multi-section MOS-capacitor phase shifters can be used to further reduce transmission losses by providing tuning capacity through the use of external voltages. In some embodiments, a controller 70 as shown in FIG. 6B can regulate the multi-section MOS- capacitor phase shifters. Controller 70 may be, for example, a microprocessor based controller, a logical circuit, an analog circuit or even a digital circuit for the puφose of managing the phase shifting in the PDC.
Moreover, with multi-section MOS-capacitor phase shifters incoφorated into a directional coupler, the mismatch of the change in propagation constant, Δβ, needed to achieve the bar states may be reduced. FIG. 7 illustrates the relationship between coupling length and ΔβlJπ for a single-section directional coupler. Incomplete cross-over due to manufacturing imperfections can result in a power "leak" that typically cannot be changed in a single-section directional coupler because of a lack of range in the cross states as seen in FIG. 7.
FIG. 8 illustrates the relationship between coupling length and ΔβlJπ for a multi- section directional coupler. In a multi-section MOS-capacitor phase shifter, the cross states can be varied by an external voltage or voltages to achieve the non-zero cross-states in FIG. 8. In some embodiments, a controller 70 (FIG. 6B) can regulate these voltages. Moreover, with multi-section MOS-capacitor phase shifters incoφorated into a directional coupler, the mismatch of the change in propagation constant, Δβ, needed to achieve the bar states can be reduced. For example, as seen in FIG. 8, the minimum ΔβL to switch from the cross-state to the bar remains approximately the same between a three-section directional coupler and a single-section directional coupler. However, with L 26 approximately three times larger than before, Δβ may be proportionally reduced. That is, with a w-section Asymmetric MOS- Capacitor Phase Shifter (ACPS) design, the required Δβ mismatch for complete cross-over is roughly linearly reduced by n. Other embodiments, extensions, and modifications of the ideas presented above are comprehended and should be within the reach of one versed in the art upon reviewing the present disclosure. Accordingly, the scope of the present invention in its various aspects should not be limited by the examples presented above. The individual aspects of the present invention, and the entirety of the invention should be regarded so as to allow for such design modifications and future developments within the scope of the present disclosure. The present invention is limited only by the claims which follow.