The invention relates to the field of integrated optics, and in particular to a spatial diversity scheme particularly suitable for a hitless switch for integrated optics.
A distinct advantage of Integrated Optical Circuit (IOC) devices is that they are suitable for direct coupling to optical fibers since the guided light wave is well confined in both transverse dimensions. An electro-optic directional coupler switch comprises two parallel strip line waveguides forming a passive directional coupler with an electro-optic pad at the edge of each waveguide. Initially, light is focused onto one of the waveguides and the amount of light coupled to the adjacent channel can be controlled electro-optically. This scheme not only permits direct amplitude modulation of the light propagating in one channel, but allows light to be switched from one channel to another.
Wavelength-division-multiplexed (WDM) optical transmission systems carry multiple wavelength channels simultaneously on a single guiding optical line. Dynamic reconfiguration of functional optical components that operate on a subset of the used WDM spectrum may be employed to reroute one or more WDM signals around a broken link in the network, to add/drop one or more wavelength channels at a network node, or to perform other signal processing operations on a wavelength-selective basis. It is preferable that during the dynamic reconfiguration of such optical components, which operate on a subset of the WDM spectrum, the data flow on other wavelength channels not be interrupted or deteriorated during the reconfiguration operation. This is referred to as hitless switching or hitless reconfiguration of the optical component.
According to one aspect of the invention, there is provided an optical device. The optical device includes a first and a second splitting device. Each of the first and second splitting devices have respective first and second input ports, respective first and second output ports, and a respective transfer matrix. A first optical waveguide is optically coupled to the first output port of the first splitting device and the first input port of the second splitting device. A second optical waveguide is optically coupled to the second output port of the first splitting device and the second input port of the second splitting device. The first and second optical waveguides are configured to introduce a phase shift of π radians to the optical radiation propagating through the first optical waveguide with respect to the optical radiation propagating through the second optical waveguide. The transfer matrix of the second splitting device is the diagonal transpose of the transfer matrix of the first splitting device and the transfer matrix of the second splitting device is substantially different from the transfer matrix of the first splitting device.
According to another aspect of the invention, there is provided a method of propagating optical radiation in an optical device. The method includes providing a first and a second coupler, each of the first and second coupler having a respective transfer matrix, and providing that the transfer matrix of the second coupler is the diagonal transpose of the transfer matrix of the first coupler. A first optical waveguide is optically coupled to the first coupler and the second coupler. A second optical waveguide is optically coupled to the first coupler and the second coupler. Also, the method includes configuring the first and second optical waveguide to introduce a phase shift of π to the optical radiation propagating through the first optical waveguide with respect to the optical radiation propagating through the second optical waveguide.
According to another aspect of the invention, there is provided an optical device. The optical device includes a first and a second splitting device, each of the first and second splitting device having respective first and second input port, respective first and second output port and a respective transfer matrix. A first optical waveguide is optically coupling to the first output port of the first splitting device and the first input port of the second splitting device. A second optical waveguide is optically coupled to the second output port of the first splitting device and the second input port of the second splitting device. The first and second optical waveguide are configured to introduce a phase shift of π radians to the optical radiation propagating through the first optical waveguide with respect to the optical radiation propagating through the second optical waveguide. The transfer matrix of the second splitting device is the full transpose of the transfer matrix of the first splitting device. The transfer matrix of the second splitting device is substantially different from the transfer matrix of the first splitting device and the transfer matrix of the first splitting device has the off-diagonal elements equal.
According to another aspect of the invention, there is provided an optical single layer MEMS device. The optical single layer MEMS device includes a first and a second coupler. A first optical waveguide is optically coupled to the first coupler and the second coupler. A second optical waveguide is optically coupled to the first coupler and the second coupler. Sideways perturbations by the MEMS device are used to perform operations of an optical switch.
Advantage could be derived for integrated optical devices from a simple integrated-optical “spatial diversity” scheme, that would provide for a broadband input signal on one waveguide (such as a collection of channels on a WDM optical signal) to be divided and routed along a number of physical waveguide paths, before being perfectly recombined in one output waveguide. The input signal may be split among the several paths according to a set splitting ratio, preferably controllable by a switch, and in a broadband or wavelength-dependent manner over the wavelength range of interest.
The separated physical paths provide a simple way to operate on only part of the optical input signal, the part in one of the paths, by inserting a particular optical device in that path. For example, hitless reconfiguration of a channel add-drop filter can be obtained by placing the filter in one path, and then directing all input light through the filter path under normal operation, or through the second bypass path during filter reconfiguration (e.g. wavelength tuning), as is to be described herein.
The challenge in producing such a spatial diversity scheme is the difficulty of ensuring perfect recombination of the spatially divided signals at the output independently of wavelength, and, for reconfigurable schemes involving switches, even during switch reconfiguration.
The invention provides a design for 2-way spatial diversity schemes that take a broadband input signal entering via one waveguide, split it among two paths in a fixed or controllable, broadband or wavelength-dependent way (over the wavelength range of interest), and identically recombine all signal (at all wavelengths) into a single waveguide again at the output. A specific symmetry is employed to guarantee broadband recombination, so the scheme works for a large class of devices, with various possible applications. The signal splitting ratio among the two paths within the spatial diversity scheme may be substantially wavelength dependent or substantially wavelength independent over the wavelength range of interest. The splitting ratio may be fixed or controllable. The invention achieves spatial diversity for a large class of signal splitting device designs by employing low-loss 4-port devices and time-reversal symmetry.
The general design scheme of the present invention, shown in
In the particular case wherein the first splitting device A is invariant for mirror reflection about a vertical symmetry axis, the two operations above reduce to just mirror reflection about a horizontal axis.
The splitting device A, A′ may comprise any arbitrary device that meet the above requirements including waveguide directional couplers and switches, Mach-Zehnder interferometers (MZIs), multi-mode interference couplers (MMIs), ring-resonator filters or other optical elements. A switch is a splitting device configured to assume alternatively a first and a second state, wherein in the first state an optical radiation input only in the first input port is directed substantially solely to the first output port and in the second state an optical radiation input only in the first input port is directed substantially solely to the second output port. The splitting device A, A′ may be wavelength-dependent over the wavelength band of interest. They may be controllable in their splitting operation (i.e. contain switches, tunable elements, etc.).
In the case of non-reciprocal devices A, A′ (i.e. optical devices comprising non-reciprocal media that support Faraday rotation), A′ deviates from being structurally identical to A only in the aspect that any built-in or applied DC magnetic fields are reversed (i.e. opposite orientation of aligned magnetic dipoles) in A′ with respect to optical device A, as symbolically shown in
The pair of waveguides 82, 84, or more generally a pair of provided optical modes, provides ideally a π radians phase shift difference between the two waveguides 82, 84 or optical modes, over the propagation length from optical device A to optical device A′, over the wavelength spectrum of interest.
All designs with the above characteristic put all signals entering port a1 into output port b1′, or alternatively, all signals entering a2 into port b2′. This does not depend on the particular type of splitting devices A and A′, nor on their wavelength dependence, if any. The signal recombination is perfect for all wavelengths at the output if: the devices A, A′ are lossless and are a “time-reversal pair”, they are connected by two waveguides in the manner described herein and illustrated in
The spatial diversity scheme described herein becomes useful, for example, for creating designs for hitless switching of integrated channel add-drop filters or hitless bypass of another type of optical device, when a functional optical device, 86 or 87, is inserted into one arm 82 or 84, respectively. Optionally, several functional optical devices (86, 87 in
This spatial diversity scheme described herein is superior to approaches in prior art in that: (a) recombination of all input light at the output of the diversity scheme is not dependent on the particular type of input splitting device A and output recombiner device A′ used. The described configuration guarantees wavelength-independent and parameter-independent ideal recombination. Thus, the property of the scheme to fully recombine all input radiation from one input port into one output port is also not sensitive to wavelength dependence or fabrication error in parameters of the elements A and A′, so long as they remain structurally substantially identical, which is very often the case for lithographic fabrication errors; (b) in case A and A′ are variable, controllable optical devices (such as switches) the scheme here requires only symmetric (in unison) actuation of A and A′, such that they remain structurally identical at all times, to achieve hitless switching of the light path between one arm 82 and the other arm 84. This is superior to some schemes in prior art that require a different and dependent adjustment of the output recombination element A′ in response to the particular setting of the input splitter element A, in order to ensure perfect recombination into one output port. Such active control schemes are difficult to implement in that the feedback and control problem can be complex. The scheme described herein is considerably simpler in that one must only ensure that A and A′ are identically actuated at any one time, making the control problem much simpler and more tractable.
The derivation of the concept design that follows is general, and encompasses a large class of splitting devices A and A′, because it relies only on losslessness of the elements A, A′ in the sense defined, and time-reversibility, which is a known property of the Maxwell's equations that govern behavior of integrated optical devices (true even for non-reciprocal devices, if reversing DC magnetic fields is permitted). This is the reason why the presented scheme holds for both reciprocal and non-reciprocal devices A and A′, as shown below.
Optical splitting devices A, A′ are preferably to be identical lossless 4-ports (except for having opposite DC magnetic fields if non-reciprocal media are used), where a port is defined to correspond to a single guided optical mode that is coupled to the respective optical device A or A′, and where the ports may be chosen in pairs such that all power sent into any one port (belonging to one pair) is fully transmitted to two of the four ports (the other pair) with no reflection to the input port or to the second port in the pair including the input port. Low loss in transmission of A and A′ is important only insofar as the phase relationship between the output ports is not significantly altered in comparison to that restricted by the lossless condition, as discussed further later in the text. In practice, errors up to ˜30% in the phase produce tolerable hit loss of <1 dB. Depending on the particular choice of device A, A′, losses of the order of 50% (3 dB) may be tolerable, but for practical applications losses <10% are more preferable, and substantially lower losses <1% are even more preferable. In terms of reflection, for proper operation reflection levels less than −10 dB should be acceptable, although greater reflection suppression of >20 dB is more preferable. Preferably, each port is accessed by a single-mode waveguide, such that two input waveguides and two output waveguides are present. More generally, any structure may be used that provides the guided modes to serve as the two input or output ports, such as, for example, a two-moded waveguide for each of the input and output port sets.
The transmission response of a 2×2 4-port optical device A (and analogously A′) with no reflection to input ports can be represented by a 2×2 matrix,
where umn≡|umn|eiφ
where there are four free parameters represented by real numbers κ, θo≡(φ11+φ22)/2, θ1≡(φ11−φ22)/2 and θ2≡(φ12−φ21)/2. For any choice of these parameters the total output power equals the total input power, {overscore (b)}†{overscore (b)}={overscore (a)}†{overscore (a)} (i.e. |b1|2+|b2|2=|a1|2+|a2|2).
The number of parameters in {double overscore (U)}, as shown in equation (2), that may be freely chosen was restricted to four (κ, θo, θ1, and θ2) by using the requirement of unitarity that φ11+φ22−φ12−φ21=±π. The π phase in the previous relationship is important, and is related to the customary 90° phase lag of waves coupling each way across standard directional couplers. In fact, any general 2×2-port device with a particular set of the four parameters κ, θo, θ1, and θ2 can be modeled at any one optical frequency as a particular ideal directional coupler.
In the following, the transfer matrix of the first optical splitting device A will be represented by the matrix {double overscore (U)}. According to the requirements set out above for the devices A and A′, the analogous transfer matrix {double overscore (U′)} of device A′ (defined by equation (1) with all variables primed) is found to be directly related to the matrix {double overscore (U)} of device A as,
The transfer matrix {double overscore (U′)} of A′ in equation (3) is the same as {double overscore (U)}, but with the diagonal elements swapped—let us call {double overscore (U′)} the “diagonal transpose” of {double overscore (U)}. The term “diagonal transpose” of a 2×2 matrix {double overscore (U)}, for purposes of this document, refers to a matrix whose diagonal elements, u11 and u22, are swapped. The equivalence of the specified configuration requirements for devices A and A′ in the inventive scheme with the stated relationship between their matrices {double overscore (U)} and {double overscore (U′)} is rigorously justified later on in the text.
The total transfer matrix of the device providing the spatial diversity scheme of
The transfer matrix {double overscore (T)} is defined to relate outputs {overscore (c)}=[c1,c2]T and inputs {overscore (a)}=[a1,a2]T, as {overscore (c)}={double overscore (T)}·{overscore (a)} (as shown in
Since the magnitude of matrix elements T11 and T22 is unity and T12=T21=0, where we have made minimal assumptions (unitarity) about the matrix {double overscore (U)} describing element A, this shows that the scheme described is a general 2-way spatial diversity scheme that intrinsically recombines all input to one final output, independent of the particular type of 2×2 optical elements A and A′ used, and independent of wavelength. Signal entering port a1 is recombined in c1 (i.e. b1′), while that entering a2 is recombined in c2 (i.e. b2′), according to equation (5). The perfect signal recombination at the output is as broadband as the π phase shift realization employed. The details of signal splitting between the two arms, 82 and 84 in
The parameters of matrix {double overscore (U)} describing the 2×2 optical splitting device A may be wavelength-dependent over the wavelength range of interest and/or controllable (e.g. a switch), i.e. {double overscore (U)}={double overscore (U)}(λ, p), where p parameterizes possible configurations for a dynamic element such as a switch (range of states). Namely, |T11|2=|T22|2=1 for all λ and p.
The complete recombination of light input in one port into one output port that is guaranteed by this scheme will not be affected by arbitrary phase factors applied to each output port of the element A′, since such phase factors do not affect the unity magnitude of the elements T11 and T22 of the total transfer matrix of the scheme as shown in equation (5). Although in cases where devices A and A′ are an exact “time-reversal pair” connected as in
where ψ1, ψ2 are arbitrary real numbers and may depend on (be a function of) wavelength. Since matrix {double overscore (V′)} is the same as {double overscore (U′)} except for arbitrarily different phase applied at output ports, one can call {double overscore (V′)} to be “output-phase-equivalent” to matrix {double overscore (U′)}. Thus, the scheme of the present invention more generally comprises a first element A described by a matrix {double overscore (U)} with arbitrary choice of its 4 free parameters κ, θo, θ1, θ2 as specified in equation (2), a π differential phase shift in the waveguide arms 82, 84, and a second element A′ with a matrix {double overscore (V′)}, shown in equation (6), that is the “diagonal transpose” of chosen matrix {double overscore (U)} of first element A, but with additional arbitrary phases ψ1 and ψ2 applied to the top and bottom rows of the matrix, respectively. This general scheme gives |T11|=|T22|=1, T12=T21=0, for all wavelengths and all choices of parameters κ, θo, θ1, θ2 for splitting device A, and any additional arbitrary phases ψ1, ψ2 that may be chosen for A′. In the remainder of the document, the preferable configuration using matrices {double overscore (U)} and {double overscore (U′)} will be used, with the understanding that in the more general case, the more general matrix {double overscore (V′)} replaces {double overscore (U′)}, i.e. a more general device A′ is permitted.
In view of the described configuration of the inventive spatial diversity scheme in terms of transfer matrices, there are several equivalent ways to state the corresponding desired physical configuration of the scheme. In the transfer matrix description above, the spatial diversity scheme of the present invention provides a first 4-port optical element A, with 2 input ports and 2 output ports, such that substantially all power sent into the input ports exits the output ports; in other words an element A described by a matrix of the form {double overscore (U)} in equation (2) with any choice of the 4 free parameters κ, θo, θ1, θ2; where these parameters can vary with wavelength and, if the optical device A is reconfigurable, with time. It is further required to provide a second 4-port optical element A′, with 2 input ports and 2 output ports, and described by a matrix {double overscore (V′)}, where the matrix {double overscore (V′)} is equal to {double overscore (U′)}, the “diagonal transpose” of matrix {double overscore (U)} that describes the first element A, or be alternatively any matrix that is “output-phase-equivalent” to {double overscore (U′)}. Further, it is required to connect output b1 of device A to input a1′ of device A′, and output b2 of A to input a2′ of A′ whereby the two previously described connecting paths must introduce a π differential optical propagation phase between them. Inputs and outputs are numbered in the present document such that the subscript 1 and 2 indicate respectively the top and bottom component of the input and output vector (see equation (1)), and in the presented figures,
A second equivalent physical description may be made. In the case where reciprocal devices A and A′ are used, A and A′ are preferably structurally identical (setting the additional arbitrary phases ψ1=ψ2=0). Then, the scheme simplifies to: a first 4-port substantially lossless 2×2 optical element A (one described by a matrix of form {double overscore (U)}) with ports P, Q, R, S, where P, Q are inputs and R, S are outputs; a second element A′ that is identical to A with the corresponding ports P′, Q′, R′, S′, but where now R′, S′ are used as input ports and P′, Q′ are used as output ports (corresponding to vertical-axis mirror reflection of A′ with respect to A in FIGS. 1,2); elements A and A′ being connected by waveguides connecting port R to port S′, and port S to port R′ (corresponding to horizontal-axis mirror reflection of A′ with respect to A in FIGS. 1,2); finally, the optical connection paths R-S′ and S-R′ imposing a π relative phase difference in propagation. The two mirror reflections (vertical and horizontal) implied in the context of the arrangement of A′ and A in
The required “diagonal transpose” relationship of matrix {double overscore (U′)} of element A′ to matrix {double overscore (U)} of element A, stated in equation (3), can be derived as follows, without any loss of generality for the claimed invention.
An element A that splits radiation entering a single port into two arbitrary parts, if viewed with time running backwards, may intuitively be seen as having radiation propagating in the opposite direction and retracing its path to recombine the two separated parts back into the single input. This “time-reversed” operation is permitted by Maxwell's equations which govern the device operation, if the magnetic fields are reversed. The time-reversed solution of the device A (with a transfer matrix subscripted by tr), is analogous to “running the movie” of the propagating electric and magnetic fields backwards. In that solution, the outputs become the inputs ({overscore (b)}*→{overscore (a)}tr), the inputs become the outputs ({overscore (a)}*→{overscore (b)}tr) and the time-reversed transfer matrix is {double overscore (U)}tr=[{double overscore (U)}*]−1. In addition, in the time-reversed solution, just as the mode amplitudes {overscore (a)}, {overscore (b)} are conjugated (so that a relative phase delay between ports in forward operation becomes reversed in time-reversed operation, as required), so the material properties (respective dielectric permittivity and magnetic permeability tensors) must be conjugated as {double overscore (ε)}→{double overscore (ε)}* and {double overscore (μ)}→{double overscore (μ)}*. It is known that for lossless media {double overscore (ε)}={double overscore (ε)}†, {double overscore (μ)}={double overscore (μ)}†, and for reciprocal media {double overscore (ε)}={double overscore (ε)}T, {double overscore (μ)}={double overscore (μ)}T. Thus, for optical components composed of lossless, reciprocal media {double overscore (ε)} and {double overscore (μ)} are real tensor functions of space, giving the material spatial distribution representing the device, and the time-forward and time-reversed solution are supported by one and the same structure. For non-reciprocal lossless media, the time-reversed solution is supported by a structure with reversed orientation of the built-in (and any applied) DC magnetic fields in the material.
The above suggests that cascading a splitting device A and its time-reverse structure (in the context of
in the two output ports, in comparison to
when the first input is excited. Therefore, the time-reversed version of the first device A with the second input port excited, when cascaded after the first device A with its first input port excited, cancels the variable phases θ1,θ2 to yield a total phase difference of π. This remaining difference of π is independent of the particular device A and is compensated in the inventive scheme by a proper design of the waveguide pair connecting the two devices A and A′ to compensate the π phase shift difference between the ports over the wavelength band of interest. From equation (2), one also notes that the splitting ratio is the same when the first or second input port is excited, but that the fraction of light in each output port is opposite in the two respective cases. Therefore, in order for the time-reversed structure A′ to recombine the signals split by structure A, the ports 1 and 2 of the second structure A′ must further be reversed with respect to the first structure A. This is the reason for the additional mirror reflection of with respect to a horizontal axis of A′ in relation to A, in
Thus, the spatial diversity scheme presented herein is built from one 2×2 optical element A, followed by a differential π phase shift in the output arms, and a time-reversed version A′ of the first element A such that, in addition, the outputs b1,2 of the first element are connected to their respective equivalents in A′ in swapped order, that is to the time-reversed inputs a′1,2, respectively in that order (as shown in
This is the same transfer matrix {double overscore (T)} as that in equation (4), and thus the first three matrices represent the total transfer matrix {double overscore (U′)} of element A′. Matrix {double overscore (U)}tr represents the mirror reflection about the vertical axis of element A′ with respect to element A, while the pre- and post-multiplication [0,1; 1,0] matrices represent the additional mirror reflection about the horizontal axis of A′ with respect to A. Using unitarity of {double overscore (U)}, the time-reverse transfer matrix {double overscore (U)}tr is found to be the transpose of {double overscore (U)}, {double overscore (U)}tr≡[{double overscore (U)}*]−1={double overscore (U)}T, and by comparing equations (4) and (7), the transfer matrix {double overscore (U′)} for A′ is
Thus, the transfer matrix {double overscore (U′)} for A′ is shown to be the diagonal transpose of the matrix {double overscore (U)} for element A, as previously stated.
It is noted that in the case where the first splitting device A, together with the reference planes used to define its ports, is invariant for vertical symmetry mirror reflection, its associated transfer matrix has the two off-diagonal elements equal, so that the transposed matrix is the same as the starting matrix. In this case, following equation (8), according to the invention the transfer matrix of the second splitting device A′ is simply obtained by pre- and post-multiplication of {double overscore (U)} by [0,1; 1,0] matrices (defined as the ‘full transpose’, wherein the two elements of the diagonal are swapped and also the the two elements of the off-diagonal are swapped), which is equivalent to doing a mirror reflection with respect to a horizontal axis (A′ is up-side-down with respect to A).
Applications of the inventive spatial diversity scheme, as described, include schemes for the hitless reconfiguration of optical components. For hitless reconfiguration of channel add-drop filters, the spatial diversity scheme can be used to switch the entire broadband input signal between one arm that contains the filter, and the other arm that does not, to permit wavelength reconfiguration of the filter without disturbing other wavelength channels during the reconfiguration. The present invention provides hitless switching because the output c1 contains the signal exciting input a1 before, during and after the devices A, A′ are actuated in unison to switch light propagation fully from one arm, e.g. 82 in
By symmetrically actuating the switches (i.e. in unison, ΔβA=−ΔβA′=Δβ), input optical signal is seamlessly transferred between the two arms 82, 84 of the interferometer, while ensuring all light recombines in one output before, during and after the switching operation. By inserting, for example, a tunable optical channel add-drop filter 108 in one arm 82 of the interferometer in
Standard Δβ switches can be sensitive to fabrication tolerances, particularly in the configuration where the cross-state is to be maximized. Since the inventive design provided works for any 4-port device A, A′ that satisfies the constraints described, other types of switch may be used for A, A′. Alternating Δβ switches are known to provide better tolerances with respect to extinction in both the on and off states, and can equally well be used. Mach-Zehnder-interferometer switches may also be used that can be more suitable for switching using the thermo-optic effect.
While any wavelength dependence of switches A and A′ of
When no Δβ actuation is applied, the directional couplers 130, 134 are identical to those of the static broadband coupler and all light is transferred across to the cross-state waveguide 84 (e.g. from a1 to b2). When a Δβ perturbation is applied to each coupler 130 and 134, broadband coupler 128 may be tuned to bring transfer to a null. Because the transfer is identically zero for only particular values of detuning, wavelength dependent coupling can mean that one does not disable the coupling fully at all wavelengths. However, if a large Δβ detuning can be applied, the transfer goes invariably toward zero. Thus, with a large Δβ detuning a broadband on and off state can be achieved. Use of such broadband switches as elements 128 and 136, with element 136 structurally identical to element 128, and identically actuated, but in 180-degree-rotated orientation with respect to 128, as required by the invention, permits broadband hitless switching.
A π differential phase shift is required. An optical functional device 86 such as a filter is included in at least one of the intermediate waveguide arms 82, 84. Note that the switches 128 and 136 need to be broadband for the wavelength range of interest only in the on and off states—the splitting ratio in the intermediate states may be wavelength dependent because the geometry of the spatial diversity scheme, with element 136 rotated by 180 degrees with respect to element 128 and with the π phase shift, guarantees broadband perfect recombination of the input light in the output, irrespective of the wavelength dependence of elements 128 and 136. And, the broadband character of the switches 128, 136 in the case of a hitless bypass application for optical filters is only of interest in the fully-coupled state to either the filter waveguide arm 82 (during normal filter operation) or to the second bypass waveguide arm 84 (during filter reconfiguration).
One advantage of the MZI-based switches is that they are particularly suitable for switching using the thermo-optic effect, which is weak and thus difficult to use for Δβ-type switches. Larger arm lengths permit small thermo-optic material index changes to permit a sufficient phase Δθ to accumulate. This example shows an arbitrary filter device 86 in one of the two waveguide arms 82.
Thermo-optically-actuated, cascaded MZI-based switches for hitless switching of filters are known in prior art. Those approaches employ configuration where elements 148 and 150 are not 180° degree rotated in orientation or reflected about a horizontal axis with respect to one another as according to the present invention design, and do not require a π phase shift difference to be imposed by the two arms 82, 84 connecting the elements 148 and 150 or 128 and 136, but rather use balanced, i.e. zero phase shift, configuration. These configurations, with identically oriented switches 148 and 150 connected by balanced arms, work only with the limited set of signal splitting switches for which a pair of output reference planes can be found such that exactly 0 or π phase difference between the two outputs is maintained for excitation from one input, for all wavelengths in the spectrum of interest and for all settings of the switch. MZI switches using ideal 3 dB couplers at all wavelengths would be in this category, and hence would permit the cited schemes to work over a wavelength range where the MZI has substantially ideal 3 dB couplers.
The designs of the present invention show the following advantages. First, they allow a spatial diversity scheme with complete recombination of the signal from one input waveguide into one output final waveguide for all 2-input, 2-output low-loss optical signal splitting/recombining devices A, A′ (e.g. switches), even if those devices A and A′ do not guarantee 0 or π phase difference between the two outputs for all states, and/or the phase difference changes with wavelength or depending on the state of the switch. This more general case includes Δβ switches and resonant filters. Secondly, MZI switches with couplers which deviate from the ideal 3 dB condition will not yield perfect recombination of all input light in the cited schemes, and thus fabrication errors in creating the couplers will result in non-ideal recombination. Further, wavelength dependence of couplers means that they generally are not 3 dB at all wavelengths. This would further deteriorate, in the intermediate and in some cases also the final states of the switches A and A′, the complete, hitless recombination in the output port (port c1 in
The scheme of the present invention, which requires that switches 148 and 150 be in opposite orientation as described (i.e. actuated at opposite sides—top for 148 (A), bottom for 150 (A′)—in this example,
In the following, the hitless switching scheme described in
A single Δβ-type optical switch is based upon a directional coupler, where power transfer is governed by the strength of evanescent coupling and a controllable propagation constant mismatch. The couplers 172, 174 of the interferometer can be described by the solutions of the coupled-mode equations,
where u1,2 are the guided mode envelope amplitudes in the two waveguides, normalized so that power in each guide is |u1,2|2. Here, {overscore (β)}≡(β1+β2)/2, δ≡(β1−β2)/2=Δβ/2 is the propagation constant mismatch between the two waveguides, and |κ| is the strength of evanescent coupling. Free choice of normalization allows κ=κ*, real. The solution for propagation through a distance l is found as (convention: j=−i, where j2=i2=−1)
where r, t, φ are real, {overscore (a)}≡{overscore (u)}(z=0) are the incident waves and {overscore (b)}≡{overscore (u)}(z=l) are the transmitted waves, and
Note that r2+t2=1, and that transfer is controlled only by κl and δ/κ. Now consider the interferometer formed by coupler 172, two waveguides 176 and 178 dephased by ±Δθ/2, and a second coupler 174, as shown in
Hitless operation requires that two elements of the matrix remain at unity magnitude at all times during reconfiguration, i.e. at all, including intermediate, settings of the Δβ switches. It is desirable to make the switches identical and actuated in unison, to improve tolerability to fabrication errors and simplify control. In this case, ra=rb≡r, ta=tb≡t. During the actuation of the switches, r, t, φa and φb change. For the switch to operate as desired and guarantee hitless transfer of power from one arm to another, two features are required: the inputs of second coupler b must be reversed relative to first coupler a, so that φa=−φb≡φ, and a differential phase shift of a radians in the intermediate arms must be introduced (i.e. Δθ=π). Observing the form of the transfer matrix of the first switch in equation (10), this requirement is seen to be consistent with the earlier stated requirement that the second switch have a transfer matrix that is the diagonal transpose of that of the first switch. Note that equation (10) is the particular case of transfer matrix with off-diagonal elements equal.
The result, seen from equation (11), is that matrix elements T11 and T22 have unity magnitude, while the other two are zero, in all states of the compound switch. On the other hand, the operation changes the fraction of total power in waveguide 176 as r2.
To further enable full transfer of power between one arm and the other, κl=π/2, and δ/κ which controls the switching, varies from 0 for full transfer to {square root}{square root over (3)}, higher nulls, or asymptotically high values for null transfer.
To form a hitless switchable device, the device 180 is inserted in one arm of the described switch, such that it does not disturb the phase of those signals that are to be switched in a hitless manner. For a channel add/drop filter, these signals would be the adjacent/express channels.
Ideal operation of the switch, taken to mean that all input signal can be ideally recombined at the output, depends only on lossless (or substantially low loss) operation of the Δβ switches, their antisymmetric arrangement and symmetric actuation, and the introduced π phase differential.
The character of the function to recombine all input light at one output of the proposed hitless switching scheme is broadband independent of the frequency dependence of the constituent switches, and depending only on the bandwidth of the required π phase shift, which depends on the particular realization chosen for the shift.
To realize a hitless switch of this kind, one can consider some physical realizations of Δβ switches and the π phase shift that were idealized in the presented model. One first addresses the phase shift. The simplest realization is a half-guided-wavelength (at center-band) extra-length of waveguide section, e.g. in arm 176 relative to arm 178. The guided wavelength of the propagating mode is related to its propagation constant β as λguide=2π/β. A half guided-wavelength is equivalent to a π phase shift. Waveguide dispersion causes the phase shift to vary with wavelength, but the short length guarantees a reasonably large bandwidth. For example, identical cross-section slab waveguide arms with core index 2.2, cladding index 1.445 and thicknesses of 0.5 μm (TE) give less than 5% deviation in the π shift over 140 nm bandwidth, as shown in
For wider bandwidths or lower hit loss, the dispersion of the waveguides in the two interferometer arms may be engineered by using non-identical cross-sections. If the two waveguides 1 and 2, i.e. 176 and 178 in FIGS. 8A,B, have lengths L1 and L2, then in the ideal case, β1(ω)L1−β2(ω)L2=π2πm. In a band of interest near ωo, a first-order Taylor-series expansion of β(ω) in frequency detuning δω yields two requirements:
Such waveguide designs are realizable. For example, a pair of slabs as above, this time of identical length L1=L2=6.5 μm, but widths of 0.5 μm and 0.91 μm, yields a differential π phase shift within 5% over more than 900 nm, as shown in
The implementation of a Δβ switch is typically electro-optic. MEMS-actuated switches based on dielectric perturbation can provide fast, strong perturbation enabling small-footprint switches. Here, a high-index-contrast (HIC) waveguide switch is presented with MEMS-actuated dielectric slab β perturbation. HIC enables compact-footprint photonic components. Due to the exponentially vanishing evanescent field of a guided mode, for a particular waveguide, short, strong couplers are more broadband than long, weakly-coupled ones. To maintain κl=π/2 in a short coupler, strong coupling κ is required. For switching to be achieved, therefore, large Δβ is also required.
In the following example, operation of one such switch is described, in a vertical geometry where the coupler waveguides 184, 186 are in different lithographic layers and the slab 190 moves up and down, as shown in
In addition to a strong Δβ detuning due to the effective index change induced in the top waveguide 184 by the lowered high-index dielectric slab 190, the slab also “pulls” the guided mode of the top waveguide closer waveguide toward it, thus also reducing the coupling κ and further increasing the δ/κ ratio that is relevant for switching. Eigenmode-expansion-method simulation results showing the bar-state transmission (fraction of light entering bottom waveguide 186 that stays in that waveguide) as a function of the slab separation s are depicted in
Embodiment variants of the hitless switch scheme provided by the present invention are demonstrated using the vertical MEMS-based Δβ switches of
The vertically-actuated two-layer configuration in
From FIGS. 11A,B it is seen that for the hitless switching configurations in
Alternatively, single-layer MEMS-perturbation schemes may be pursued akin to similar applications of MEMS perturbation used for ring tuning. Of course, for the scheme presented, any realization of Δβ switch or π phase shift will work, including both single-layer and multiple-layer switch implementations.
Note the directional couplers 4, 6 include microelectromechanical perturbations to perform their processing. Moreover, the microelectromechanical dielectric slab perturbs the waveguide mode on the same vertical plane, through a sliding motion of the dielectric slab. The microelectromechanical (MEMS) dielectric perturbation gives a phase mismatch, and hence detuning, of the directional coupler. The inventive designs described herein permit a hitless switch to be constructed in a single-level, permitting reductions in device micro- and nano-fabrication complexity. This translates to improvements in device yield, reduction in costs and manufacturing completion time.
Other alternatives for an integrated hitless switch include an alternating-Δβ optical waveguide coupler. In these alternatives, the directional couplers are typically electro-optically switched. The switched directional couplers can also be surface waves generated through a transducer, differing from the usage of dielectric slab perturbation. Finally, bypass switches in free-space optics with MEMS micromirrors have been suggested for optical fiber data distribution, though these developments do not use the switched directional couplers discussed herein and are not feasible for high-density integrated optics.
a3(z)/e−{overscore (iβ)}z=a1(cosβoz−i(δ/βo)sinβoz)+a2(κ12/βo)sinβoz (14)
a4(z)/e−{overscore (iβ)}z=a1(κ21/βo)sinβoz+a2(cosβoz+i(δ/βo)sinβoz) (15)
where a1, a2=the field amplitudes at the two input guides 32, 34, κ12=−κ21*=κ, βo=(δ2+κ2)0.5, δ=(β1−β2)/2, {overscore (β)}=(β1+β2)/2, and β1 and β2 are the propagation constants in waveguide 32 and 34, respectively, in optical coupler 40.
The coupling coefficient κ is estimated through a mode solver, and the design verification is done through finite-difference time-domain numerical computations. The signals a5, a6 in the through port 36 and tap port 38 can be found by repeating equations (14) and (15) for the second directional coupler 42, with a3 and a4 replacing a1 and a2 as the inputs and δ′=(β3−β4)/2=−(β1−β2)/2=−δ, {overscore (β)}=(β3+β4)/2=(β1+β2)/2, β3 and β4 the propagation constants in waveguide 32 and 34 respectively, in optical coupler 42. The extinction ratio is defined as |a4|2/|a3|2. With the MEMS perturbation such that δ=31/2 κ, there is zero net crossover of signal from signal bus waveguide to the coupled waveguide.
The calculated signal power, normalized by the input power |a1|2, is shown in
Note that the coupled mode theory formalism predicts zero crosstalk for δ=0 when switching in one designed directional coupler. However, a very low, but finite, crosstalk is expected due to the index perturbation necessary for switching. Design for low crosstalk is, therefore, desirable in the adiabatic separation region of the couplers. Scattering losses in the waveguides could also contribute to the crosstalk degradation.
In the matrix formalism, eq. (14) and (15) for the first coupler 40, disregarding the common propagation factor e−{overscore (iβ)}z, assume the form:
while for the second coupler 42 (opposite-sign detuning δ′=−δ) they assume the form:
wherein {double overscore (U′)} is seen to be the diagonal transpose of {double overscore (U)} for any value of δ. This result is consistent with the fact that, as shown in
As an example, a SiNx material system is chosen (refractive index n˜2.2) to form two signal bus waveguides 50, 52 shown in
As shown in
An in-plane sliding actuator mechanism 60, as shown in
The supporting beams 64 can be designed for sufficient stiffness on order of 0.5 N/m, cantilever lengths of order 150 μm, widths of order 5 μm, and thickness of order 0.3 μm, for order 1 nm displacement resolution of the perturbing dielectric slab. Following this example, the number of comb-drive finger pairs 62 is on order of 50, with a gap of 1 μm between the fingers, and applied voltages between 1 V for a 1 nm displacement and 50V.
During actual device fabrication and operation, the device geometry and perturbation deviates from ideal theoretical design. The sensitivity from imperfect fabrication and operation, caused by: (i) asymmetric MEMS perturbation, (ii) variation in π-phase shift, and (iii) asymmetric directional couplers are described in the following. These variations results in a loss in through port signal in at least some switch states, leading to insertion loss and/or “hit loss” during reconfiguration.
Asymmetric MEMS perturbation arises when the two dielectric slabs do not arrive at exactly the same time and position.
Secondly, the effect of variations in the π-phase shift is illustrated in
In addition, each directional coupler has a frequency dependence between 1530 to 1570 nm, ranging from 5-10% variation of the coupling κ at 1550 nm. However, even if conversion lengths are designed only for operation at 1550 nm, the two cascaded directional couplers as a whole are broadband, as demonstrated by equation (5). Operating away from 1550 nm, there is incomplete crossover (“leakage”) at the first directional coupler but this leakage is destructively interfered at the output of the second directional coupler.
Thirdly, the effects of asymmetric couplers are described in
Finite-difference time-domain (FDTD) calculations, as shown in
By removing the need to switch lithographic layers for inputs of DCM2 (directional-coupler MEMS 42 in
The fabrication process flow, showing the top view and side profile of the invention, is illustrated in
Although the present invention has been shown and described with respect to several preferred embodiments thereof, various changes, omissions and additions to the form and detail thereof, may be made therein, without departing from the spirit and scope of the invention.
This application is a continuation-in-part of U.S. patent application Ser. No. 11/012,769 filed Dec. 15, 2004, which is a continuation of U.S. patent application Ser. No. 10/833,453 filed Apr. 28, 2004, which claims priority from provisional application Ser. No. 60/538,736 filed Jan. 23, 2004, all of which are incorporated herein by reference in their entireties.
Number | Date | Country | |
---|---|---|---|
60538736 | Jan 2004 | US |
Number | Date | Country | |
---|---|---|---|
Parent | 10833453 | Apr 2004 | US |
Child | 11012769 | Dec 2004 | US |
Number | Date | Country | |
---|---|---|---|
Parent | 11012769 | Dec 2004 | US |
Child | 11041350 | Jan 2005 | US |