Contradirectional-Filter Architecture Having Low Back-Reflection

Abstract

The teachings of the present disclosure enable wavelength-agile WDM systems comprising wavelength drop ports based on contra-DC wavelength filters, where back-reflections at each drop port are mitigated by virtue of the system architecture. The contra-DC filters are arranged in a series along a common bus waveguide such that the operating wavelengths of the filters change in monotonic fashion through the series. As a result, back-reflections arising at each filter is suppressed by the contra-DC filter that precedes it in the series. In some embodiments, each contra-DC filter is configured such that its filter bandwidth is large enough to accommodate both its drop signal and back-reflections arising from the grating element of the preceding contra-DC filter in the series. In some embodiments, conventional back-reflection approaches are used in concert with the system-architecture approach of the present disclosure.

Claims

1. A wavelength division multiplexed (WDM) system comprising: a bus waveguide for receiving a WDM signal that includes a plurality of wavelength signals, wherein the bus waveguide includes a plurality of bus-waveguide portions; and a plurality of contra-directional coupler (contra-DC) filters that is optically coupled with the bus waveguide, wherein each contra-DC filter of the plurality thereof is characterized by a different filter bandwidth and different drop signal that includes a drop wavelength, and wherein the plurality of contra-DC filters is arranged in a series along the bus waveguide such that the plurality of filter bandwidths are non-overlapping and the plurality of drop wavelengths changes monotonically along the series; wherein each contra-DC filter includes a grating element that is optically coupled with a different bus-waveguide portion of the plurality thereof, the grating element comprising a periodic arrangement of teeth and a grating waveguide that extends through the entire length of the grating element, the grating waveguide including a drop port.

2. The WDM system of claim 1 wherein the plurality of drop wavelengths increases monotonically along the series.

3. The WDM system of claim 1 wherein a first contra-DC filter of the plurality thereof gives rise to a first reflected signal on the bus waveguide, and wherein the first reflected signal has a first reflected spectrum that is within the filter bandwidth of a second contra-DC filter of the plurality thereof, and further wherein the first and second contra-DC filters are adjacent in the series.

4. The WDM system of claim 3 wherein the plurality of filter bandwidths collectively defines a composite bandwidth, and wherein each contra-DC filter of the plurality thereof gives rise to a second reflected signal on its respective grating waveguide, and further wherein each of the plurality of second reflected signals has a reflected spectrum that is outside the composite bandwidth.

5. The WDM system of claim 3 wherein the first contra-DC filter of the plurality thereof gives rise to a second reflected signal on its respective grating waveguide, and wherein the second reflected signal has a second reflected spectrum that is between the filter bandwidth of the first contra-DC filter and the filter bandwidth of a second contra-DC filter that is adjacent to the first contra-DC filter in the series.

6. The WDM system of claim 3 wherein each filter bandwidth of the plurality thereof includes a pad region, and wherein the first contra-DC filter of the plurality thereof gives rise to a second reflected signal on its respective grating waveguide, and wherein the second reflected signal has a second reflected spectrum that is within the pad region of a second contra-DC filter that is adjacent to the first contra-DC filter in the series.

7. The WDM system of claim 1 wherein each contra-DC filter includes a different portion of the bus waveguide, and wherein, at each contra-DC filter of the plurality thereof, its respective bus-waveguide portion and grating element are configured to define first and second taper regions and a mirror region located between the first and second taper regions, the mirror region being a strongly coupled region for a first light signal, the grating waveguide being included in each of the first and second taper regions and the mirror region, and wherein the first taper region includes a first adiabatic coupler for adiabatically transitioning the first light signal between a first weak coupling region and the mirror region, and further wherein the second taper region includes a second adiabatic coupler for adiabatically transitioning a second light signal between the mirror region and a second weak coupling region, the second light signal including at least a portion of the first light signal.

8. The WDM system of claim 7 wherein each bus-waveguide portion of the plurality thereof has a first core having a first width at an input port and a second width at the mirror region of its respective contra-DC filter, the first width being larger than the second width.

9. The WDM system of claim 1 wherein each tooth of the periodic arrangement of teeth has a tooth length that varies according to its position within the periodic arrangement.

10. The WDM system of claim 1 wherein at least one drop signal of the plurality thereof includes a wavelength channel that is a CWDM channel, and wherein the CWDM channel includes a plurality of DWDM signals.

11. A method for dropping at least one wavelength signal from a wavelength divisional multiplexed (WDM) signal that includes a first plurality of wavelength signals, the method comprising: providing the WDM signal on a bus waveguide that is operatively coupled with a plurality of contra-directional coupler (contra-DC) filters, wherein each contra-DC filter of the plurality thereof is characterized by a different filter bandwidth and different drop signal that includes a drop wavelength, and wherein the plurality of contra-DC filters is arranged in a series along the bus waveguide such that the plurality of filter bandwidths are non-overlapping and the plurality of drop wavelengths changes monotonically along the series; dropping a first drop signal to a first drop port of a first contra-DC filter of the plurality thereof; and dropping a second drop signal at a second drop port of a second contra-DC filter of the plurality thereof.

12. The method of claim 11 further comprising providing the plurality of contra-DC filters such that the plurality of drop wavelengths increases monotonically along the series.

13. The method of claim 11 wherein the first contra-DC filter gives rise to a first reflected signal on the bus waveguide, the first reflected signal having a first reflected spectrum, and wherein the method further includes: providing the first and second contra-DC filters such that they are adjacent in the series, wherein the second contra-DC filter is provided such that its respective filter bandwidth includes the first reflected spectrum; and suppressing the first reflected signal at the second contra-DC filter.

14. The method of claim 13 wherein the first contra-DC filter gives rise to a second reflected signal on its respective grating waveguide, the second reflected signal having a second reflected spectrum, and wherein the method further includes: providing the plurality of contra-DC filters such that the plurality of filter bandwidths defines a composite bandwidth that is non-inclusive of the second reflected spectrum.

15. The method of claim 13 wherein the first contra-DC filter gives rise to a second reflected signal on its respective grating waveguide, the second reflected signal having a second reflected spectrum, and wherein the method further includes: providing the first and second contra-DC filters such that they are adjacent in the series and such that second reflected spectrum is between their respective filter bandwidths.

16. The method of claim 13 wherein the first contra-DC filter gives rise to a second reflected signal on its respective grating waveguide, the second reflected signal having a second reflected spectrum, and wherein the method further includes: providing the plurality of contra-DC filters such that each filter bandwidth includes a pad region, wherein the pad region included in the filter spectrum of the second contra-DC filter includes the second reflected spectrum.

17. The method of claim 11 wherein each contra-DC filter of the plurality thereof is provided such that it includes a different bus-waveguide portion of the bus waveguide, and wherein, at each contra-DC filter of the plurality thereof, its respective bus-waveguide portion and grating element are configured to define first and second taper regions and a mirror region located between the first and second taper regions, the mirror region being a strongly coupled region for a first light signal, the grating waveguide being included in each of the first and second taper regions and the mirror region, and wherein the first taper region includes a first adiabatic coupler for adiabatically transitioning the first light signal between a first weak coupling region and the mirror region, and further wherein the second taper region includes a second adiabatic coupler for adiabatically transitioning a second light signal between the mirror region and a second weak coupling region, the second light signal including at least a first portion of the first light signal.

18. The method of claim 17 wherein each contra-DC filter of the plurality thereof is provided such that its respective bus-waveguide portion has a core having a first width at an input port and a second width at the mirror region of its respective contra-DC filter, the first width being larger than the second width.

19. The method of claim 11 wherein at least one contra-DC filter of the plurality thereof is provided such that its respective drop signal includes a wavelength channel that is a CDWM channel, and wherein the CWDM channel includes a plurality of DWDM signals.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] FIG. 1A depicts an operational schematic drawing of a contra-DC filter in accordance with the present disclosure.

[0026] FIG. 1B depicts an exemplary spectral response of a contra-DC filter in accordance with the present disclosure.

[0027] FIG. 2 depicts a schematic drawing of an illustrative embodiment of a WDM architecture in accordance with the present disclosure.

[0028] FIG. 3 depicts the spectral response of a first exemplary approach for addressing backward propagating modes in the grating elements of a system architecture in accordance with the present disclosure.

[0029] FIG. 4 depicts the spectral response of a second exemplary approach for addressing backward propagating modes in the grating elements of a system architecture in accordance with the present disclosure.

[0030] FIG. 5 depicts the spectral response of a third exemplary approach for addressing backward propagating modes in the grating elements of a system architecture in accordance with the present disclosure.

[0031] FIG. 6 depicts the spectral response of an exemplary approach for addressing backward propagating modes in the grating elements of a system architecture comprising contra-DC filters arranged in a longest-wavelength to shortest-wavelength order in accordance with the present disclosure.

DETAILED DESCRIPTION

[0032] Basic Operation of a Contra-DC Filter in Accordance with the Present Disclosure

[0033] FIG. 1A depicts an operational schematic drawing of a contra-DC filter in accordance with the present disclosure. Filter 100 includes bus waveguide 102, grating element 104, input port IP, through port TP, and drop port DP.

[0034] Bus waveguide 102 and grating element 104 are integrated-optics waveguide-based elements arranged on a suitable substrate 106 to define a central mirror region located between symmetric taper regions. In the depicted example, substrate 106 is a conventional silicon-on-insulator wafer; however, any substrate suitable for planar processing can be used without departing from the scope of the present disclosure.

[0035] Bus waveguide 102 includes input port IP and through port TP. In the depicted example, bus waveguide 102 comprises a waveguide core that is made of silicon nitride and has a shape and interaction geometry that are configured to provide good filtering response for the coupled waveguide-grating system. Given the generally good confinement of the fundamental mode of a light signal in a single-mode optimized geometry, the width of the bus waveguide is modified along the z-axis such that the optical mode of a light signal propagating through the bus waveguide is less confined in the mirror region.

[0036] It is an aspect of the present disclosure that the core of bus waveguide 102 is tapered such that it enables an adiabatic transformation of the optical mode of a light signal propagating through the filter from input port IP, to its state in the mirror region, to though port TP and drop port DP. As will be apparent to one skilled in the art, an adiabatic transition is one that occurs without significant optical loss, as well as to realize equal suppression of sidelobes on both sides of the filter band and mitigation of scattering losses. Furthermore, equal suppression of sidelobes and, as a result, a more symmetric filter spectrum, is achieved by maintaining phase-matching at the desired drop wavelength throughout the entire length of the device. For embodiments in accordance with the present disclosure, to maintain phase-matching, the propagation constants of the supermodes are adjusted as the device transitions between the weakly coupled and strongly coupled regions via implemented S-bends (or other transition shape chosen to facilitate an adiabatic transition) as well as the tapering of the core of the bus waveguide.

[0037] It should be noted that, typically, the functional form of the tapering of the width of bus waveguide 102 is highly important so as to facilitate this adiabatic transformation of the optical mode through the filter, as well as to maintain phase-matching between the bus waveguide and grating modes throughout the taper. Examples of suitable bus waveguide tapers are provided in U.S. patent application Ser. No. 18/414,727, filed Jan. 17, 2024, which is incorporated herein by reference.

[0038] Grating element 104 includes grating waveguide 114 and a periodic arrangement of teeth 116 that are optically coupled with the grating waveguide. In the depicted example, grating waveguide 114 is a single-mode silicon nitride waveguide that runs through the entire length, LGE, of grating element 104 and includes drop port DP. Teeth 116 are also regions of silicon nitride that project outward from the grating waveguide along the x-direction. Typically, the amount any specific tooth extends outward from the grating waveguide (i.e., its tooth length) is dependent upon the specific location of that tooth within the grating structure, as discussed in U.S. patent application Ser. No. 18/414,727. In the depicted example, teeth 116 have uniform width (i.e., dimension along the longitudinal axis of grating element 104the z-axis, as shown in FIG. 1) and are separated from one another by uniform gaps 118 such that grating element 104 has a uniform grating period, A; however, in some embodiments, at least one of teeth 116 and gaps 118 have non-uniform width.

[0039] It should be noted that, although the depicted example employs silicon nitride waveguides, the teachings of the present disclosure are applicable to waveguides of any suitable material (e.g., silicon, silicon oxide, germanium, lithium niobate, compound semiconductors, etc.).

[0040] The silicon nitride elements of filter 100 are encased in cladding material. In the depicted example, the cladding material is silicon dioxide; however, any suitable cladding material can be used without departing from the scope of the present disclosure.

[0041] In operation, filter 100 receives light signal 108 as a multiwavelength signal at input port IP of bus waveguide 102, redirects those wavelength components of light signal 108 within its filter bandwidth to drop port DP as drop signal 110, and provides the remaining wavelength components of light signal 108 to through port TP as through signal 112.

[0042] As will be apparent to one skilled in the art, a contra-DC filter is normally configured such that the bus waveguide and grating element are characterized by three distinct Bragg conditions. A primary condition associated with the coupled system and two secondary conditions associated with the individual elements (bus waveguide and grating separately), which can be expressed as:

[00001]${?}_{\mathrm{drop}}=?\left(n_{\mathrm{wg}}+n_{\mathrm{gr}}\right)\left(\mathrm{primary}\right)$${?}_{\mathrm{BrWg}}=2n_{\mathrm{wg}}?\left(\mathrm{secondary}\right)$${?}_{\mathrm{BrGr}}=2n_{\mathrm{gr}}?\left(\mathrm{secondary}\right)$

[0043] The primary reflection is taken to be the one which is utilized for the filter bandwidth of the contra-DC filter, which determines the drop wavelengths, ?.sub.drop, included in drop signal 110. As is common with contra-DC filters, the filter bandwidth can be relatively large (>10 nm), provided satisfactory design.

[0044] The two secondary reflections are a byproduct of the grating element diffracting the forward propagating mode in the bus waveguide into reflection signals 120 and 122, where the reflected spectrum of reflection signal 120 manifests as a backward propagating mode, {right arrow over (E)}.sub.?.sub.BrWg, in bus waveguide 102 and the reflected spectrum of reflection signal 122 manifests as a backward propagating mode, {right arrow over (E)}.sub.?.sub.BrGr in grating waveguide 114.

[0045] In highly integrated photonic circuits, backward propagating mode, {right arrow over (E)}.sub.?.sub.BrWg, is of primary concern, since it propagates backward along the main optical path that potentially contains active elements. While the backward propagating mode in the grating element at {right arrow over (E)}.sub.?.sub.BrGr, is similarly undesirable, it is more easily mitigated than {right arrow over (E)}.sub.?.sub.BrWg in the main circuit path.

[0046] FIG. 1B depicts an exemplary spectral response of a contra-DC filter in accordance with the present disclosure. Spectrum 124 shows the filter bandwidth, FBW, of filter 100 and its respective drop signal 110 at drop wavelength, ?.sub.drop, as well as reflection signals 120 and 122 (at ?.sub.BrWg, and ?.sub.BrGr, respectively), which are spectrally located on either side of drop signal 110.

[0047] For the purposes of this Specification, including the appended claims, filter bandwidth, is defined as the spectral band within which the drop signal of a filter is at most 1 dB below the nominal, peak signal strength.

[0048] It should be noted that the spectral response of each drop filter includes a central filter bandwidth (as defined above), as well as spectral wings on either side of the filter bandwidth. Typically, it is desirable that these spectral wings are extremely narrow (i.e., the spectral response of the filter has a sharp roll off) such that they do not substantially contribute to the operational behavior of the filter. Furthermore, spectrally narrow spectral wings enable denser packing of the filter bandwidths of a plurality of drop filters.

[0049] The de-tuning, ?, between ?.sub.drop and ?.sub.BrWg (and simultaneously ?.sub.BrGr) can be adjusted through the appropriate design of the device geometry. In practice, positioning ?.sub.BrWg on the blue side (i.e., the shorter-wavelength side) of ?.sub.drop and ?.sub.BrGr on the red side (i.e., the longer-wavelength side) of ?.sub.drop is a more straight-forward approach; however, these spectral positions can be reversed without departing from the scope of the present disclosure.

[0050] FIG. 2 depicts a schematic drawing of an illustrative embodiment of a WDM architecture in accordance with the present disclosure. System 200 includes filters 202-1 through 202-N and filter 204.

[0051] Each of filters 202-1 through 202-N (referred to, collectively, as filters 202) is analogous to filter 100 described above and are configured such their filter bandwidths are non-overlapping (although there can be some overlap of the spectral wings of adjacent filters). Filters 202 are arranged in series along common bus waveguide 102 such that each filter 202-i includes a grating element 104-i that is optically coupled with a different bus-waveguide portion BWP-i of the bus waveguide. Bus waveguide 102 receives input signal 208 at system input port 206, passes it through filters 202, and provides output signal 210 at output port 212. As will be apparent to one skilled in the art, the spectrum of output signal 210 is characterized by notches due to the drop signals that manifest at each of filters 202. In the depicted example, each of filters 202 also includes an optional conventional beam dump 214 for removing unwanted light from its grating waveguide.

[0052] Input signal 208 is a conventional WDM signal that includes a plurality of wavelength channels. In the depicted example, input signal 208 is a standard CWDM signal containing N CWDM channels, L1 through LN, where each CWDM channel includes a plurality of DWDM channels. In some embodiments, however, input signal 208 is other than a standard CWDM signal and N can be any practical number. In some embodiments, each CWDM channel is an information-carrying channel that includes a plurality of wavelength signals. In some embodiments, the CWDM channels are spaced apart by 20 nm (in accordance with the ITU-T G.649.2 standard); however, other CWDM channel spacings that are commensurate with a set of desired contra-DC filters bandwidths can be used without departing from the scope of the present disclosure.

[0053] Furthermore, in some embodiments, the wavelength signals included in at least one CWDM channel are DWDM signals in accordance with the ITU-T G.649.1 standard; however, other sets of wavelength signals can be used one or more of the CWDM channels without departing from the scope of the present disclosure.

[0054] Filters 202 are arranged along the bus waveguide such that their drop wavelengths (?.sub.drop1 through ?.sub.dropN) are in a shortest-wavelength to longest-wavelength order. In other words, the center wavelengths of the filter bandwidths increase monotonically through the series of filters such that filters 202-1 through 202-N are configured to drop wavelength channels L1 through LN, respectively, where ?.sub.L1<?.sub.L2< . . . <?.sub.LN-1<?.sub.LN. In some embodiments, filters 202 are arranged in a longest-wavelength to shortest-wavelength order.

[0055] By virtue of this ordered arrangement, at each of filters 202, the reflected signal 120 containing the backward propagating mode, {right arrow over (E)}.sub.?.sub.BrWg., it produces is within the filter bandwidth FBW of its respective preceding filter in the series. As a result, the filter bandwidth of each filter functions as a stop band that suppresses the backward propagating mode caused by the next filter in the series. For example, the backward propagating mode, {right arrow over (E)}.sub.?.sub.BrWg., of reflection signal 120-2, which is launched into bus waveguide 102 by filter 202-2, is within the stop band of filter 202-1, the backward propagating mode, {right arrow over (E)}.sub.?.sub.BrWg., of reflection signal 120-3, which is launched into bus waveguide 102 by filter 202-3, is within the stop band of filter 202-2, and so on.

[0056] Since the first contra-DC filter in the series, filter 202-1, has no preceding contra-DC filter, system 200 includes additional optional filter 204, which is configured to suppress the backward propagating mode, {right arrow over (E)}.sub.?.sub.BrWg., launched into bus waveguide by filter 202-1. It should be noted that filter 204 can be any suitable filter having the appropriate stop band.

[0057] An inherent benefit of the architecture of system 200 is that reflections in the circuit at ?.sub.BrWg for each filter in the series are strongly inhibited/eliminated, owing to the lack of optical power present at that wavelength. This is due to the fact that an arbitrary filter 202-i, where i=1 through N, in the series filters out most of the light at the wavelengths around ?.sub.BrWg associated with filter 202-(i+1). As will be apparent to one skilled in the art, after reading this specification, for systems having filters arranged in a longest-wavelength to shortest-wavelength order, filter 202-i in the series filters out most of the light at the wavelengths around ?.sub.BrWg associated with filter 202-(i?1).

[0058] As a result, not only does an arrangement of filters in accordance with the present disclosure ensure that no backwards propagating modes travel upstream (or downstream, in some embodiments) in the PIC, it also greatly reduces the magnitude of the reflections in the bus waveguide in the first place. This alleviates the potential need to modify the bus waveguide to suppress reflections via destructive interference. A benefit of this is that the overall system design is simplified.

[0059] It should be noted that, although the invention is proposed as an alternative solution to prior-art back-reflection suppression approaches, the teachings provided herein are can also be used in conjunction with prior art. If other methods are utilized to suppress/eliminate reflections on the input port, architectural approaches in accordance with the present disclosure further reduce the magnitude of any residual backwards propagating modes that may persist due to imperfect destructive interference along the anti-reflection grating.

[0060] Furthermore, the teachings of the present disclosure are intended to support techniques aiming to eliminate the secondary reflections of contra-DC filters, so as to architecturally protect the integrated circuit from backward travelling modes. Effort should still be made through careful, well-optimized design to ensure that reflections are only weakly induced. Since the invention aims to have the contra-directional filters do double-duty, the optimization of the filter lineshape becomes even more pronounced.

[0061] Embodiments in accordance with the present disclosure can provide a significantly wider bandwidth over which reflection suppression can be accommodated. When implementing an anti-reflection grating, the bandwidth is primarily dictated by the strength of the grating. Physically, this corresponds to the achievable contrast between high-, and low-index regions of the element. As a result, reflection suppression over a broad bandwidth can require gratings with physical features that are difficult to fabricate, or are too difficult to implement from a design perspective.

[0062] Additional advantages afforded by embodiments in accordance with the present disclosure include: [0063] i. suppression of reflections commonly encountered with contra-directional coupler-based filtering approaches using a trivially scalable architecture; or [0064] ii. suppression of reflections which would jeopardize sensitive upstream active components without necessitating complicated device designs; or [0065] iii. exploitation of the working principle of contra-directional filters to simultaneously suppress N back-reflections in an N-channel system with at most one additional filtering element; or [0066] iv. additional capability of suppressing reflections over a much wider bandwidth than it is possible with alternative methods; or [0067] v. any combination of i, ii, iii, and iv.

[0068] It should be noted that a variety of approaches can be used to address the backward propagating modes in the grating elements of filters 202, which arise due to reflections at ?.sub.BrGr. The selection of the manner for addressing these modes is typically based upon such factors as the signal spectrum, the spectral range under consideration (which dictates the geometry of grating element 104), and the like.

[0069] FIG. 3 depicts the spectral response of a first exemplary approach for addressing backward propagating modes in the grating elements of a system architecture in accordance with the present disclosure. Spectrum 300 shows the spectral response of an N-filter system architecture in which all its filters 202 are configured such that reflection signals 122-1 through 122-N (i.e., the reflections at ?.sub.BrGr from all filters) are located outside of composite bandwidth CBW, which is the spectral range defined by all of filter bandwidths FBW1 through FBWN. As will be apparent to one skilled in the art, after reading this Specification, composite bandwidth CBW represents the total operating wavelength range of a system in accordance with the present disclosure (i.e., the spectral range in which any signal components might be present).

[0070] In the depicted example, N=4; therefore, CBW includes FBW1 through FBW4. As noted above, however, N can be any practical number without departing from the scope of the present disclosure.

[0071] It should be noted that, since all of reflection signals 122 manifest at wavelengths located outside composite bandwidth CBW, the inclusion of beam dumps 214 is not necessary for systems having spectra analogous to spectrum 300.

[0072] Furthermore, for clarity, only the spectral responses of filters L1 and L2 are shown in FIG. 3; however, one skilled in the art will recognize that the responses of filters L3 and L4 are analogous to those of filters L1 and L2.

[0073] FIG. 4 depicts the spectral response of a second exemplary approach for addressing backward propagating modes in the grating elements of a system architecture in accordance with the present disclosure. Spectrum 400 shows the spectral response of an N-filter system architecture in which the reflection signal 122 from each filter is positioned at the center of the inter-channel gap defined by its filter bandwidth FBW and the filter bandwidth of the next filter in the series of filters (?.sub.drop<?.sub.BrGr).

[0074] In the depicted example, N=4; however, as noted above, N can be any practical number without departing from the scope of the present disclosure.

[0075] It should be noted that, in contrast to systems characterized by spectrum 300, in some systems characterized by spectrum 400, it is preferable to include a beam dump to suppress reflected signal 122-N.

[0076] For clarity, only the spectral responses of filters L1 and L2 are shown in FIG. 4; however, one skilled in the art will recognize that the responses of filters L3 and L4 are analogous to those of filters L1 and L2.

[0077] FIG. 5 depicts the spectral response of a third exemplary approach for addressing backward propagating modes in the grating elements of a system architecture in accordance with the present disclosure. Spectrum 500 shows the spectral response of an N-filter system architecture in which the reflection signal 122 (i.e., the reflected signal containing ?.sub.BrGr) from each filter is positioned inside a pad region included in the filter bandwidth FBW of the next filter in the chain (?.sub.drop<?.sub.BrGr).

[0078] It should be noted that the filter bandwidth, FBW, of each filter 202 must be made sufficiently large to accommodate both its respective wavelength channel, L, and the reflected signal 122 from the filter that precedes it in the series of filters. The spectral region added to each filter bandwidth for accommodating reflected signal 122 is denoted as pad region 502.

[0079] In the depicted example, N=4; however, as noted above, N can be any practical number without departing from the scope of the present disclosure.

[0080] It should be noted that all of the architecture examples discussed thus far comprise contra-DC filters that are arranged in shortest-wavelength to longest-wavelength order, in which each filter is characterized by ?.sub.BrWg<?.sub.Drop<?.sub.BrGr. However, as noted above, the teachings herein are also suitable for use in architectures comprising contra-DC filters arranged in a longest-wavelength to shortest-wavelength order, in which each filter is characterized by ?.sub.BrGr<?.sub.Drop<?.sub.BrWg.

[0081] FIG. 6 depicts the spectral response of an exemplary approach for addressing backward propagating modes in the grating elements of a system architecture comprising contra-DC filters arranged in a longest-wavelength to shortest-wavelength order in accordance with the present disclosure. Spectrum 600 shows the spectral response of an N-filter system architecture in which the filter responses of filters 200 are reversed (i.e., ?.sub.BrGr<?.sub.Drop<?.sub.BrWg). In such architectures, the location of pad 502 shifts to the red side of the filtering spectrum of each filter. In the depicted example, N=4; however, as noted above, N can be any practical number without departing from the scope of the present disclosure.

[0082] It is to be understood that the disclosure teaches just some examples of the illustrative embodiment and that many variations of the invention can easily be devised by those skilled in the art after reading this disclosure and that the scope of the present invention is to be determined by the following claims.