Statement Regarding Federally Sponsored Research

[oooi] This invention was made with Government support under Contract No. DE- AR0000849 awarded by the Advanced Research Projects Agency-Energy (ARPA-E) and Contract No. 1827633 awarded by the National Science Foundation. The Government has certain rights in the invention.

Cross Reference to Related Applications

[0002] This application claims the benefit of U.S. Provisional Application Serial Number 62/749,536, filed October 23, 2018, entitled "Wavelength-Division Multiplexer Based on Cascaded Beam Splitters" (Attorney Docket: 332-008PR1), which is incorporated herein by reference. If there are any contradictions or inconsistencies in language between this application and one or more of the cases that have been incorporated by reference that might affect the interpretation of the claims in this case, the claims in this case should be interpreted to be consistent with the language in this case.

Background

[0003] Wavelength multiplexers are key components in broadband communications systems, such as optical telecommunications networks and optical data communications networks. Historically, such multiplexers have typically been based on one of only a few component choices, including the arrayed waveguide grating (AWG), echelle grating, micro- ring resonator, Mach-Zehnder interferometer, or star coupler.

[0004] The AWG is perhaps the most ubiquitous wavelength multiplexer and is based on a planar-lightwave circuit (PLC) comprising surface waveguides configured to define a pair of optically coupled planar NxN star couplers. AWGs have been implemented on various surface-waveguide platforms that include materials such as compound

semiconductors (e.g., InGaAsP/InP, etc.), silicon, low-loss silicon nitride, silicon oxynitride, doped and undoped glass, and the like. Unfortunately, variations in the widths of the surface waveguides, as well as evanescent coupling between the waveguides in the delay arm region often introduce phase errors, resulting in defocusing that gives rise to high insertion loss and high channel crosstalk. In addition, AWGs typically require very large footprints, making them undesirable in space-constrained applications. Furthermore, an AWG must be designed for a specific set of wavelengths; therefore, wavelength changes or drift can significantly increase optical loss.

[0005] An echelle grating has substantially the same working principle as that of an AWG; however, an echelle grating can have a much smaller footprint and also tends to be less sensitive to phase errors because the phase delays between different channels are introduced in a slab region. Unfortunately, echelle gratings require reflectors with very high verticality (< 0.2°) uniform phase response to achieve low insertion loss and low channel crosstalk. Furthermore, like the AWG, an Echelle grating multiplexers must be designed for a specific set of wavelengths and the wavelengths provided to its different input ports are not interchangeable.

[0006] A micro-ring resonator has a high cavity quality factor (Q), which makes it a versatile device for providing narrow-band filtering functions in a wavelength division multiplexing (WDM) application. Unfortunately, geometry variations (e.g., the width of its coupling gap between the ring and its bus waveguide) due to fabrication tolerances, as well as changes in the ambient temperature, can significantly degrade the performance of a micro-ring resonator.

[0007] Cascaded or multi-stage wavelength filters based on Mach-Zehnder interferometers offer advantages such as low insertion loss, flat-band response, and high degree of freedom for designing the free spectral range. Although loss is predominantly determined by the waveguide propagation loss, careful control over the phase difference between different stages is required for aligning the channel wavelength and achieving flat pass bands.

[0008] Although typically used in pairs to form an array waveguide grating, star couplers can be used on their own to achieve NxN wavelength multiplexing. Each of the N inputs is situated and angled such that light in each port diffracts through an empty slab region and evenly illuminates the N output ports. While such star couplers can be designed to produce a reasonably uniform intensity between the N outputs, this comes at the expense of an extreme decrease in coupling efficiency, thereby limiting their usefulness as a wavelength multiplexer. Summary

[0009] An advance is made in the art according to aspects of the present disclosure directed to low-loss wavelength-division multiplexers that combine a plurality of input wavelength signals received at a plurality of input ports into a multi-wavelength output signal at each of a plurality of output ports, where the multi-wavelength output signals contain substantially equal portions of each of the input wavelength signals. Multiplexers in accordance with the present disclosure have input ports that are wavelength agnostic for all input wavelength signals within a wide spectral range. As a result, the input ports are interchangeable such that any of the plurality of input wavelength signals can be provided to any of the input ports without significantly affecting the output signals. Furthermore, multiplexers in accordance with the present disclosure can be lower loss and more tolerant of refractive-index variations and temperature changes than prior-art multiplexers.

[ooio] Multiplexers in accordance with the present disclosure include a multiplexer block comprising a plurality of low-loss optical couplers (/.e., couplers) that are arranged in multiple stages connected via low-loss optical links, thereby defining a cascaded network of couplers. Each coupler has multiple inputs and multiple outputs and is configured so that optical energy received at each of its inputs is substantially uniformly distributed to all of its outputs.

[ooii] An illustrative embodiment of a multiplexer in accordance with the present disclosure is a photonic-lightwave circuit disposed on a single substrate, where the photonic-lightwave circuit includes a multiplexer block comprising N stages of low-loss mxm couplers that are optically coupled between m ^N input ports and m ^N output ports. The stages of couplers are connected via low-loss optical links such that each input port is optically coupled with every output port via a different low-loss optical path through a cascade of 50: 50 splitters. As a result, the multiplexer block can combine m ^N input wavelength signals received at its input ports into m ^N output signals, where each output signal contains approximately l/m ^N of the optical energy of every input wavelength signal.

[0012] In some embodiments, at least one of the plurality of couplers includes a multimode interference coupler, an adiabatic directional coupler, or a free-space beam splitter.

[0013] In some embodiments, the optical links include one or more multimode interference waveguide crossings. In some embodiments, the optical links include a waveguide crossing other than a multimode interference crossing. In some embodiments, the optical links include surface waveguides formed in different planes above the substrate on which the PLC is disposed and no waveguide crossings are required.

[ooi4] In some embodiments, at least one element included in a PLC-based multiplexer or multiplexer block is designed using inverse-design techniques.

[0015] In some embodiments, the multiplexer is a free-space optical system comprising bulk-optics elements and free-space optical paths through the multiplexer.

[0016] In some embodiments, at least one of the couplers has an input/output ratio other than 1 : 1.

[0017] An embodiment in accordance with the present disclosure is a wavelength- division multiplexer comprising a multiplexer block (100) including : a plurality of input ports (106), each configured to receive at least one wavelength signal (110) of a plurality thereof, the plurality of wavelength signals being within a first spectral range; a plurality of first optical couplers (102) that is optically coupled with the plurality of input ports, each first optical coupler of the plurality thereof being configured to distribute optical energy received at each of m first inputs (204) substantially equally to n first outputs (206), where m>l and n> l, wherein the plurality of first optical couplers is arranged in a series of stages having N stages (S(l) to S(N)), where N>1, and each stage of the series thereof includes at least two optical couplers of the first plurality thereof; and a plurality of output ports (108) that is optically coupled with the plurality of first optical couplers; wherein the multiplexer block is configured such that each light signal of the plurality thereof received at the plurality of input ports is distributed substantially equally to the plurality of output ports.

[0018] Another embodiment in accordance with the present disclosure is a method for multiplexing a plurality of optical signals (110), the method comprising : providing a multiplexer block (100) having a plurality of input ports (106), a plurality of output ports (108), and a plurality of first optical couplers (102), each first optical coupler having m inputs (204) and n outputs (206), where m>l and n>l, and being configured such that optical energy received at each of its inputs is distributed substantially equally to all of its outputs, wherein the plurality of first optical couplers is arranged in a series of stages having N stages (S(l) to S(N)), where N>1, and each stage of the series thereof includes at least two first optical couplers of the plurality thereof; uniquely receiving at least one wavelength signal (110) of a plurality thereof at each input port of the plurality thereof, wherein the plurality of wavelength signals is within a first spectral range; and distributing the at least one wavelength signal of the plurality thereof received at each input port of the plurality thereof substantially equally to the plurality of output ports.

Brief Description of the Drawings

[0019] FIG. 1 depicts a schematic drawing of an illustrative embodiment of a generic multiplexer block in accordance with the present disclosure.

[0020] FIG. 2 depicts operations of a method for multiplexing a plurality of wavelength signals via a multiplexer block in accordance with the present disclosure.

[0021] FIG. 3 depicts a schematic drawing of an exemplary multiplexer block in accordance with the present disclosure.

[0022] FIG. 4 depicts a schematic drawing of an exemplary MMI coupler in accordance with the present disclosure.

[0023] FIG. 5 depicts a simulation of the normalized transmission of light through coupler 302 as a function of wavelength.

[0024] FIG. 6A depicts an MMI crossing in accordance with the present disclosure.

[0025] FIG. 6B depicts a simulation of the transmission of light through MMI crossing 314 as a function of wavelength.

[0026] FIG. 7 depicts an alternative arrangement for an integrated-optics-based multiplexer block in accordance with the present disclosure.

[0027] FIG. 8 depicts another alternative arrangement for an integrated-optics- based multiplexer block in accordance with the present disclosure.

[0028] FIG. 9 depicts a schematic drawing of a three-stage eight-wavelength multiplexer block in accordance with the present disclosure.

[0029] FIG. 10 depicts plots of the lowest-loss optical path and highest-loss optical path, respectively, through multiplexer block 900.

[0030] FIG. 11 depicts a schematic drawing of an alternative embodiment of a wavelength multiplexer in accordance with the present disclosure. Detailed Description

[0031] FIG. 1 depicts a schematic drawing of an illustrative embodiment of a generic multiplexer block in accordance with the present disclosure. Multiplexer block 100 includes optical couplers 102(1,1) through 102(M,N), optical links 104, input ports 106( 1) through 106(P), and output ports 108( 1) through 108(P).

[0032] Each of optical couplers 102( 1,1) through 102(M,N) (referred to, collectively, as couplers 102) is an mxm optical coupler having m inputs and m outputs. Each of couplers 102 is configured such that optical energy received at any one or more of its inputs is substantially equally distributed among all of its outputs and such that each output receives an equal portion of the optical energy received at every input. In other words, for each coupler, each input functions as a lxm splitter that splits its respective input signal into m substantially equal output signals that are provided to the m outputs, while each output functions as an mx l combiner that combines a portion of every input signal into a composite signal. In some embodiments, at least one of couplers 102 has m inputs and n outputs, where m¹n.

[0033] Optical couplers 102 are arranged in a series of N stages (/.e., stages S(l) through S(N)), each containing M optical couplers, where M = m ^(N_1) . Adjacent stages in the series are optically coupled such that the outputs of the first stage are optically coupled with the inputs of the second stage. As a result, each input port is optically coupled with each output port by a different cascade of lxm splitters that defines a different low-loss optical path through the multiplexer block. The stages and optical links are configured such that optical energy received at any of input ports 106(1) through 106(P) (referred to, collectively, as input ports 106) is distributed, substantially uniformly, to all of output ports 108( 1) through 108(P) (referred to, collectively, as output ports 108).

[0034] Typically, each of signals 110( 1) through 110(P), (referred to, collectively, as signals 110) is a unique wavelength signal that contains light characterized by a different wavelength within a spectral range. In some embodiments, however, one or more of wavelength signals 110 includes multiple wavelength signals.

Operating Principle

[0035] Embodiments in accordance with the present disclosure are based on the basic concept of a multi-input, multi-output optical coupler that is configured to function as a beam splitter, such that a different light signal received at each input of each optical coupler is split into a plurality of substantially equal parts that are received at the outputs of the optical coupler. As a result, at each output of the optical coupler, an equal portion of the light signal received at every input is combined into a composite light signal. When each input receives a different, unique wavelength signal, for example, a substantially identical multi-wavelength signal will result at every output.

[0036] In order to demonstrate the fundamental principles of the present disclosure, operation of a simple implementation of an integrated-optics-based, four-wavelength multiplexer block comprising two stages of 2x2 optical couplers is described below.

[0037] FIG. 2 depicts operations of a method for multiplexing a plurality of wavelength signals via a multiplexer block in accordance with the present disclosure.

Method 200 is described with reference to FIGS. 3 through 6B and begins with operation 201, wherein multiplexer block 300 is provided.

[0038] FIG. 3 depicts a schematic drawing of an exemplary multiplexer block in accordance with the present disclosure. Multiplexer block 300 includes optical couplers 302( 1,1) through 302(2,2), optical links 304( 1) through 304(4), input ports 306( 1) through 306(4), and output ports 308( 1) through 308(4), which collectively define planar-lightwave circuit (PLC) 310.

[0039] PLC 310 is a network of surface waveguides formed in conventional fashion on substrate 312. In the depicted example, the surface waveguides of PLC 310 are silicon- photonics ridge waveguides having ridge portions that are approximately 220 nm thick and slab portions that are approximately 110 nm thick, and substrate 312 is a silicon substrate; however, any suitable waveguide technology and/or substrate can be used without departing from the scope of the present disclosure.

[0040] Each of optical couplers 302( 1,1) through 302(2,2) (referred to collectively, as couplers 302) is a 2x2 multimode interference (MMI) coupler configured to function as a 50: 50 beam splitter for each of its two inputs. As a result (neglecting loss within the coupler), optical energy received at each input is equally split such that half of the optical energy it receives is directed to each of its outputs. When each input receives a different wavelength signal, therefore, the coupler provides two substantially identical output signals, each containing half of the power of both wavelength signals. In some embodiments, couplers 302 are different integrated-optics-based beam-splitting elements, such as directional couplers, adiabatic couplers, and the like. Furthermore, in some embodiments, multiplexer block 300 is a free-space system comprising free-space optical couplers, such as bulk-optic beam splitters, pellicle beam splitters, etc.

[0041] FIG. 4 depicts a schematic drawing of an exemplary MMI coupler in accordance with the present disclosure. Coupler 302 is representative of each of couplers 302( 1,1) through 302(2,2) and includes multimode waveguide 402 and waveguides

404( 1) through 404(4).

[0042] Multimode waveguide 402 is a multimode-waveguide region having length LI and width wl.

[0043] Waveguides 404(1) through 404(4) are single-mode waveguides having width w2. Waveguides 404(1) and 404(2) are symmetrically arranged along the x- direction at the input side of multimode waveguide 402 to define inputs 406(A) and

406(B) with separation si. Waveguides 404(3) and 404(4) are symmetrically arranged along the x-direction at the output side of multimode waveguide 402 to define outputs

408(A) and 408(B) also having separation si.

[0044] In the depicted example, length LI is chosen such that the fundamental mode of the light received from either of inputs IA and IB primarily excites the first three TE modes 410 (having wavenumbers ko, ki, and ki), which copropagate along the z- direction and interfere to give rise to an interference pattern that substantially evenly splits at each of outputs 408(A) and 408(B).

[0045] For couplers 302 that are configured for operation with any wavelength signal within the "O band" (/.e., approximately 1260 nm to approximately 1360 nm), for example, suitable design values include, without limitation, LI of approximately 15.8 microns, wl of approximately 1.75 micron, w2 of approximately 500 nm, and separation si of

approximately 500 nm.

[0046] When input 406(A) receives wavelength signal A and input 406(B) receives wavelength signal lB, each of outputs 408(A) and 408(B) provide substantially identical light signals that include half the power of each of wavelength signals lA and lB (/.e.,

0.5lA+0.5lB).

[0047] FIG. 5 depicts a simulation of the normalized transmission of light through coupler 302 as a function of wavelength. Plot 500 shows the fraction of light at each of outputs 408(A) and 408(B), respectively, normalized to the ideal 50% transmission. [0048] As seen from plot 500, excess loss (/.e., loss with respect to 50% transmission) is substantially equal for both outputs at shorter wavelengths, while some slight deviation occurs as the wavelength increases beyond the center point of the design window. One skilled in the art will recognize that these transmission characteristics are a function of coupler design and myriad design variations are within the scope of the present disclosure.

[0049] Returning now to method 200, at operation 202, wavelength signals lΐ through l4 are received at input ports 306(1) through 306(4). In the depicted example, each input port of multiplexer block 300 receives a single, unique wavelength signal;

however, in some embodiments, at least one input port receives optical energy of more than one wavelength signal.

[0050] At operation 203, at stage S(l) of multiplexer 302, each of couplers

302(1,1) and 302(2,1) distributes the optical energy received at each of its input ports IA and IB substantially equally among its output ports OA and OB.

[0051] Specifically, coupler 302(1,1) couples approximately half the energy of each of wavelength signals lΐ and l2 into each of optical links 304(1) and 304(2) as light signals 316(1) and 316(2), respectively, while coupler 302(2,1) couples approximately half the energy of each of wavelength signals l3 and l4 into each of optical links 304(3) and 304(4) as light signals 316(3) and 316(4), respectively. As a result, each of light signals 316(1) and 316(2) includes half the power of each of wavelength signals lΐ and l2 and each of light signals 316(3) and 316(4) includes half the power of each of wavelength signals l3 and l4.

[0052] At operation 204, optical link 304(1) conveys light signal 316(1) to input IA of coupler 302(1,2) and optical link 304(2) conveys light signal 316(2) to input IA of coupler 302(2,2).

[0053] At operation 205, optical link 304(3) conveys light signal 316(3) to input IB of coupler 302(1,2) and optical link 304(4) conveys light signal 316(4) to input IB of coupler 302(2,2).

[0054] At operation 206, at stage S(2) of multiplexer 302, each of couplers

302(1,2) and 302(2,2) distributes the optical energy received at each of its input ports IA and IB substantially equally among its output ports OA and OB. [0055] Specifically, coupler 302(1,2) couples approximately half the energy of each of light signals 316( 1) and 316(3) to each of output ports 308(1) and 308(2) as output signals 318( 1) and 318(2), respectively. As a result, each of output signals 318(1) and 318(2) contains one-quarter of the original optical power of each of wavelength signals lΐ, l2, l3, and l4.

[0056] In similar fashion, coupler 302(2,2) couples approximately half the energy of each of light signals 316(2) and 316(4) to each of output ports 308(3) and 308(4) as output signals 318(3) and 318(4), respectively. As a result, each of output signals 318(3) and 318(4) also contains one-quarter of the original optical power of each of wavelength signals lΐ, l2, l3, and l4.

[0057] It should be noted that, in the depicted example, optical links 304(2) and 304(3) cross at MMI crossing 314, which is configured to realize a low-loss waveguide crossing.

[0058] FIG. 6A depicts an MMI crossing in accordance with the present disclosure. MMI crossing 314 comprises multimode waveguides 602A and 602B, which reside within crossing region 604.

[0059] Multimode waveguide 602A is optically coupled between waveguide portions 304(2)A and 304(2)B of waveguide 304(2) via substantially adiabatic taper regions. In similar fashion, multimode waveguide 602B is optically coupled between waveguide portions 304(3)A and 304(3)B of waveguide 304(3) via substantially adiabatic taper regions.

[0060] Each of multimode waveguides 602A and 602B is a silicon-photonics-based ridge waveguide having length L2 and width w3. The multimode waveguides are preferably arranged such that they are perpendicular within crossing region 604. In the depicted example, L2 is approximately 15 microns and w2 is approximately 1.7 microns.

[0061] The values of length L2 and width w3 are selected to enable the fundamental mode of a light signal entering it to primarily excite the first two even modes of the wider multimode waveguide regions. As the light propagates along length L2, these modes copropagate and interfere to form a focusing intensity pattern near the center of the multimode waveguide. In other words, in MMI crossing 314, more of the optical energy of light propagating through crossing region 604 is concentrated toward the center of a multimode waveguide, which leaves less of its optical energy near the edges where structural discontinuities can give rise to scattering, etc.

[0062] As a result, light propagating through multimode waveguide 602A is substantially unaffected by the presence of multimode waveguide 602B as the light passes through crossing region 604, while light propagating through multimode waveguide 602B is similarly unaffected by the presence of multimode waveguide 602A as the light passes through the crossing region.

[0063] FIG. 6B depicts a simulation of the transmission of light through MMI crossing 314 as a function of wavelength. Plot 606 shows that MMI crossing is

substantially loss-free at the center wavelength of its desired operative spectral range (/.e., the O band), with only minimal loss (~0.25 dB) at its minimum and maximum wavelengths.

[0064] Although the depicted example employs MMI crossings to reduce optical loss, in some embodiments, waveguide crossings other than MMI crossings are used. Waveguide crossings suitable for use in accordance with the present disclosure include, without limitation, conventional, high-angle waveguide crossings, elliptical waveguide crossings, mode-expanded waveguide crossings, photonic-crystal-based waveguide crossings, etc. In some embodiments, optical links between stages include surface waveguides that are formed in waveguide layers formed in different planes above a substrate such that waveguide crossings are eliminated.

[0065] It should be noted that inverse-design techniques can be used to design couplers and/or waveguide crossings included in an integrated-optics-based multiplexer or multiplexer block of any embodiment in accordance with the present disclosure.

[0066] FIG. 7 depicts an alternative arrangement for an integrated-optics-based multiplexer block in accordance with the present disclosure. Multiplexer block 700 includes couplers 302(1,1) through 302(2,2) and optical links 704( 1) through 704(4).

Multiplexer block 700 is analogous to multiplexer block 300; however, multiplexer block 700 is defined by PLC 702, which includes integrated-optics elements formed in waveguide layers located in different planes above substrate 312, as well as vertical couplers for providing optically coupling between these waveguide layers.

[0067] Optical links 704(1) through 704(4) are analogous to optical links 304(1) through 304(4) described above; however, each of optical links 704(2) and 704(3) includes a waveguide portion formed in each of the two different waveguide layers, as well a vertical coupler for optically coupling the waveguide portions.

[0068] In the depicted example, PLC 702 includes two substantially parallel layers of single-crystal silicon disposed on substrate 312, each having a thickness of approximately 220 nm. These upper and lower silicon layers are separated by a silicon dioxide cladding layer having thickness sufficient to mitigate undesired optical interaction (e.g., cross-talk, parasitic loss, etc.) between components on different levels.

[0069] Specifically, coupler 302(1,1), coupler 302(1,2), optical link 704(1), waveguide portion 704(2)A of optical link 704(2), and waveguide portion 704(3)B of optical link 704(3) are formed in the upper silicon layer (denoted by solid lines), while coupler 302(2,1), coupler 302(2,2), optical link 704(4), waveguide portion 704(3)A of optical link 704(3), and waveguide portion 704(2)B of optical link 704(2) are formed in the lower silicon layer (denoted by dashed lines).

[0070] Optical link 704(2) includes conventional vertical coupler 706( 1), which optically couples waveguide portions 704(2)A and 704(2)B.

[0071] Optical link 704(3) includes conventional vertical coupler 706(2), which optically couples waveguide portions 704(3)A and 704(3)B.

[0072] By forming PLC 702 with two optically isolated, vertically-stacked layers, waveguide portions can pass over or under one another without intersecting. For example, waveguide portion 704(2)A passes over waveguide portion 704(3)A without resulting in optical interaction between the wavelength signals propagating through these optical links. As will be apparent to one skilled in the art, it is possible to fabricate vertical couplers that have lower loss, greater spectral bandwidth, and less sensitivity to fabrication variations than waveguide crossings - even most MMI crossings. In addition, such an architecture reduces the total number of components that light must propagate through along the highest-loss paths through a multiplexer block.

[0073] FIG. 8 depicts another alternative arrangement for an integrated-optics- based multiplexer block in accordance with the present disclosure. Multiplexer block 800 includes couplers 804( 1,1) through 804(2,2) and integrated reflectors 806(1) through 806(4), which collectively define PLC 802. [0074] In contrast to multiplexer block 300, multiplexer block 800 employs waveguiding that is limited to one dimension - namely, the vertical dimension. By employing high-index slab waveguides, in-plane diffraction is enabled, which results in quasi-free-space operation of the system that allows wavelength signals to cross without interfering.

[0075] Each of couplers 804( 1,1) through 804(2,2) is configured as a 2x2 splitter that accepts a wavelength signal as a diffracting beam at each of its inputs IA and IB. The couplers then provide an output beam at each of its outputs OA and OB, where the output beams diffract within the high-index slab and propagate to two couplers of the next stage.

[0076] Integrated photonic reflectors 806( 1) and 806(4) are included in optical link 808(2) to facilitate bending the direction of the beam projected by output OB of coupler 804( 1,1) toward input IA of coupler 804(2,2). In similar fashion, integrated photonic reflectors 806(3) and 806(2) are included in optical link 808(3) to facilitate bending the direction of the beam projected by output OB of coupler 804(2,1) toward input IB of coupler 804( 1,2).

[0077] FIG. 9 depicts a schematic drawing of a three-stage eight-wavelength multiplexer block in accordance with the present disclosure. Multiplexer block 900 includes PLC 902, which includes a pair of multiplexer blocks 300 that collectively define its first and second stages, as well as an additional plurality of couplers 302 that defines its third stage. PLC 902 is disposed on substrate 312 and is analogous to PLC 310 described above.

[0078] Multiplexer blocks 300(A) and 300(B) collectively include 8 couplers 302 arranged as described above and with respect to FIG. 3. Multiplexer blocks 300(A) and 300(B) are arranged to function in parallel such that multiplexer block 300(A) receives individual wavelength signals lΐ through l4 at its input ports and provides output signals 318( 1)A through 318(4)A at its output ports, where each of the output signals includes one-fourth of the power of each of wavelength signals lΐ through l4. In similar fashion, while multiplexer block 300(B) receives individual wavelength signals l5 through l8 at its input ports and provides output signals 318( 1)B through 318(4)B at its output ports, where each of the output signals includes one-fourth of the power of each of wavelength signals l5 through l8.

[0079] Stage S(3) includes four couplers 302 (/.e., couplers 302(9) through 302( 12)) that are optically coupled with the outputs of multiplexer blocks 300( 1) and 300(2) via optical links 304 such that each coupler receives one output signal 318 from multiplexer block 300(A) and one output signal 318 from multiplexer block 300(B) and equally distributes the optical power of the wavelength signals in each among its outputs.

As a result, stage S(3) provides eight output signals, each containing one-eighth of the optical power of each of wavelength signals lΐ through l8.

[0080] FIG. 10 depicts plots of the lowest-loss optical path and highest-loss optical path, respectively, through multiplexer block 900.

[0081] As seen in plot 1000, the lowest-loss optical path through multiplexer block 900 incurs only about 0.2 dB loss at the center wavelength of its desired operative spectral range (/.e., the O band), while the losses at the minimum and maximum wavelengths of the band are approximately 2.4 and 0.9 dB, respectively.

[0082] As seen in plot 1002, the highest-loss optical path through multiplexer block 900 incurs slightly more loss at the center wavelength (~ 0.3 dB), while the losses at the minimum and maximum wavelengths of the band are approximately 3.4 and 2.5 dB, respectively.

[0083] FIG. 11 depicts a schematic drawing of an alternative embodiment of a wavelength multiplexer in accordance with the present disclosure. Multiplexer 1100 includes multiplexer block 100, beam combiner 1102, and beam splitter 1104. Multiplexer block 100, wavelength combiner 1102, and beam splitter 1104 collectively define PLC

1006 disposed on substrate 312. PLC 1006 is analogous to PLC 310 described above.

[0084] Wavelength combiner 1102 is analogous to coupler 302 described above; however, wavelength combiner 1102 includes a plurality of inputs and a single output. As a result, wavelength combiner 1102 can combine a plurality of wavelength signals (/.e., wavelength signals Xj through Xk) into a multi-wavelength light signal that is provided to input port 106( 1) as signal 110(1). The inclusion of one or more wavelength combiners 1102 in multiplexer 1100 enables a multiplexer that can provide a multi-wavelength output signal comprising more wavelength signals than the number of its output ports.

[0085] Beam splitter 1104 is analogous to coupler 302 described above; however, beam splitter 1104 includes a single input and a plurality of outputs. As a result, beam splitter 1104 can distribute the optical energy of a light signal received at its input into a plurality of equal-intensity output signals. The inclusion of one or more beam splitters

1104 in multiplexer 1100 enables a multiplexer having more output ports than input ports. [0086] It is to be understood that the disclosure teaches just one example 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.