Patent Publication Number: US-9405071-B2

Title: Delay line interferometer multiplexer

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 13/463,565, filed May 3, 2012, titled DELAY LINE INTERFEROMETER MULTIPLEXER, which claims the benefit of and priority to U.S. Provisional Application No. 61/482,118 filed May 3, 2011, titled DELAY LINE INTERFEROMETER MULTIPLEXER, both of which are incorporated herein by reference in their entireties. 
    
    
     BACKGROUND 
     1. Field of the Invention 
     Embodiments disclosed herein generally relate to techniques for multiplexing optical signals. More particularly, some example embodiments relate to an optical multiplexer (MUX) including a cascaded delay line interferometer (DLI). 
     2. Related Technology 
     An optical multiplexer (MUX) merges multiple optical signals that are each at a different wavelength into mutual optical alignment as a single multiplexed signal. For example, optical signals produced at different wavelengths by a corresponding number of distinct lasers may be combined by an optical multiplexer into a multiplexed signal that can then be transmitted from a single multiplexed signal transmitting port. 
     Some MUX designs, such as arrayed waveguide gratings (AWGs) and bulk optics (e.g., Echelle grating, spatial grating MUX), suffer from various limitations. For example, the size of such MUX designs may be relatively large, making them too large to be used in certain applications where space is limited. Such MUX designs may also have a relatively high insertion loss, such as about 3 dB or more. Also, such MUX designs can be relatively expensive. 
     The subject matter claimed herein is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is only provided to illustrate one exemplary technology area where some embodiments described herein may be practiced. 
     BRIEF SUMMARY OF SOME EXAMPLE EMBODIMENTS 
     Embodiments disclosed herein generally relate to a DLI MUX. 
     In an example embodiment, a delay line interferometer (DLI) multiplexer (MUX) includes a first stage and a second stage. The first stage includes a first DLI and a second DLI. The first DLI includes a first left input, a first right input, and a first output and has a free spectral range (FSR) that is about four times a nominal channel spacing. The second DLI includes a second left input, a second right input, and a second output and has an FSR that is about four times the nominal channel spacing. Transmission peaks of the second DLI may be shifted relative to those of the first DLI by an amount about equal to the nominal channel spacing. The second stage is coupled to the first stage and includes a third DLI. The third DLI includes a third left input optically coupled to the first output of the first DLI, a third right input optically coupled to the second output of the second DLI, and a third output. An FSR of the third DLI is about two times the nominal channel spacing. 
     In another example embodiment, a DLI MUX includes a first stage and a second stage. The first stage includes a first DLI and a second DLI. The first DLI is configured to receive first and second optical signals having respective first and second wavelengths and is further configured to output a first multiplexed signal including the first and second optical signals. The second DLI is configured to receive third and fourth optical signals having respective third and fourth wavelengths and is further configured to output a second multiplexed signal including the third and fourth optical signals. An FSR of each of the first and second DLIs is about four times a nominal channel spacing of the first, second, third and fourth optical signals. Transmission peaks of the second DLI may be shifted relative to those of the first DLI by an amount about equal to the nominal channel spacing. The second stage is coupled to the first stage and includes a third DLI configured to receive the first and second multiplexed signals and further configured to output a third multiplexed signal including the first, second, third, and fourth optical signals. 
     In yet another example embodiment, a monolithic chip includes a DLI MUX and multiple optical signal sources. The DLI MUX includes a first and second stage. The first stage includes a first DLI and a second DLI. The first DLI includes a first left input, a first right input, and a first output and has an FSR that is about four times a nominal channel spacing. The second DLI includes a second left input, a second right input, and a second output and has an FSR that is about four times the nominal channel spacing. Transmission peaks of the second DLI may be shifted relative to those of the first DLI by an amount about equal to the nominal channel spacing. The second stage includes a third DLI including a third left input optically coupled to the first output of the first DLI, a third right input optically coupled to the second output of the second DLI, and a third output. An FSR of the third DLI is about two times the nominal channel spacing. The optical signal sources include at least first, second, third and fourth optical signal sources, each configured to emit an optical signal having a respective first, second, third or fourth wavelength into a respective one of the first left input, first right input, second left input or second right input. 
     Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The features and advantages of the invention may be realized and obtained by means of the instruments and combinations particularly pointed out in the appended claims. These and other features of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       To further clarify the above and other advantages and features of the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope. The invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG. 1  illustrates an example of a DLI MUX according to some embodiments described herein; 
         FIG. 2  illustrates an example of a DLI that may be included in the DLI MUX of  FIG. 1 ; 
         FIG. 3  illustrates various transmission functions that may be associated with the DLI MUX of  FIG. 1 ; 
         FIG. 4  illustrates another example of a DLI MUX according to some embodiments described herein; 
         FIG. 5  illustrates a monolithic chip including an embodiment of a DLI MUX; and 
         FIG. 6  illustrates a monolithic chip including another embodiment of a DLI MUX. 
     
    
    
     DETAILED DESCRIPTION OF SOME EXAMPLE EMBODIMENTS 
     Some example embodiments disclosed herein relate to an optical MUX including a cascaded delay line interferometer (DLI). Accordingly, the optical MUX may be referred to herein as a DLI MUX. In general, the DLI MUX may be configured to multiplex 2 n  optical signals (n&gt;1) into a single multiplexed optical signal. In some embodiments, the 2 n  optical signals have a nominal channel spacing. 
     Moreover, the DLI MUX may include multiple stages, where each stage includes one or more DLIs. In some embodiments, each DLI includes a 2×2 multi-mode interference (MMI) device, an MMI combiner, and two optical paths of different lengths coupled between the 2×2 MMI device and the MMI combiner. 
     The multiple stages included in the DLI MUX may include at least first and second stages, where the second stage is an output stage. The second or output stage may include a DLI having a free spectral range (FSR) of about two times the nominal channel spacing. The first stage may be an input stage or an intermediate stage between the second stage and at least one earlier stage. The first stage may include two DLIs, each having an FSR of about four times the nominal channel spacing. In embodiments including an earlier stage before the first stage, the earlier stage may include four DLIs, each having an FSR of about eight times the nominal channel spacing. 
     Some of the disclosed embodiments have a relatively low coupling loss of between about 0.5 to 1 dB for each 2×1 MMI combiner or 2×2 MMI device included in the DLI MUX. Alternately or additionally, the DLI MUX may have a relatively small footprint of less than about 300 micrometers (μm) by 100 μm. Alternately or additionally, the DLI MUX may be monolithically integrated with an array of optical signal sources, such as an array of directly modulated lasers (DMLs) or an array of external modulated lasers (EMLs). In some embodiments, wavelengths of the optical signal sources and DLI filter peaks may move together with temperature such that precise control of thermo-electric cooler (TEC) temperature is not necessary for proper operation. 
     Optionally, embodiments of a DLI MUX can be implemented to multiplex up to 32 optical signals or more, either alone or in combination with a polarization multiplexer or other multiplexer. 
     In some examples, the filter slope of one or more of the DLIs may be used to enhance an extinction ratio (ER) of frequency modulated (FM) and/or amplitude modulated (AM) optical signals. Alternately or additionally, the filter slope of the one or more DLIs can be used to reduce the ER of FM and/or AM modulated optical signals which may be desirable in, e.g., applications involving semiconductor optical amplifiers (SOAs) for amplitude amplification without inter-channel cross talk. 
       FIG. 1  illustrates an example of a DLI MUX  100 , arranged in accordance with at least some embodiments described herein. Various parameters associated with a specific example embodiment of the DLI MUX  100  of  FIG. 1  are provided below. It will be understood with the benefit of the present disclosure, however, that the parameters associated with the specific example embodiment are provided by way of illustration only and are not intended to be limiting. 
     Generally, the DLI MUX  100  may be configured to receive multiple optical signals  102 A,  102 B,  102 C,  102 D (collectively “optical signals  102 ”) having different wavelengths λ1, λ2, λ3 and λ4, and to output a single multiplexed signal  104  made up of the optical signals  102 . In some embodiments, the optical signals  102  are spaced apart from each other at a nominal channel spacing Δ f . The nominal channel spacing Δ f  may be about 400 or about 800 GigaHertz (GHz) in Local Area Network (LAN) Wavelength Division Multiplexing (LWDM) systems, about 20 nm in Course Wavelength Division Multiplexing (CWDM) systems (e.g., systems implementing ITU-T G.694.2), or about 25 or about 50 GHz in Dense Wavelength Division Multiplexing (DWDM) systems, or any other suitable channel spacing. In some embodiments, λ2 is offset from λ1 by 2Δ f , λ3 is offset from λ1 by Δ f , and λ4 is offset from λ1 by 3Δ f . 
     As shown, the DLI mux  100  includes a first stage  106  and a second stage  108 . The first stage  106  includes a first DLI  110  and a second DLI  112 . The second stage  108  includes a third DLI  114 . Each of the first, second and third DLI  110 ,  112 ,  114  respectively includes a left (L) input  116 A,  116 B, or  116 C, a right (R) input  118 A,  118 B, or  118 C, and an output  120 A,  120 B, or  120 C. Optionally, the L input  116 A, the R input  118 A and the output  120 A of the first DLI  110  may be respectively referred to as the first left input, the first right input, and the first output, while the L input  116 B, the R input  118 B and the output  120 B of the second DLI  112  may be respectively referred to as the second left input, the second right input, and the second output, and the L input  116 C, the R input  118 C and the output  120 C of the third DLI  114  may be respectively referred to as the third left input, the third right input, and the third output, respectively. 
     Each of the first, second and third DLI  110 ,  112 ,  114  has an FSR. The FSR of each of the first and second DLI  110 ,  112  may be about four times the nominal channel spacing Δ f , plus or minus 15% of the FSR of the corresponding DLI for a loss of about 0.5 dB in some embodiments. Alternately or additionally, the FSR of the third DLI  114  may be about two times the nominal channel spacing Δ f , plus or minus 15% of the FSR of the third DLI  114  for a loss of about 0.5 dB in some embodiments. 
     Each of the first, second and third DLI  110 ,  112 ,  114  includes a 2×2 MMI device  122 A,  122 B,  122 C, respectively, and an MMI combiner  124 A,  124 B,  124 C, respectively. Each 2×2 MMI device  122 A- 122 C includes a respective one of the first, second, or third L inputs  116 A,  116 B,  116 C of the first, second, or third DLI  110 ,  112 ,  114 , a respective one of the first, second or third R inputs  118 A,  118 B,  118 C of the first, second, or third DLI  110 ,  112 ,  114 , a left output, and a right output. Each MMI combiner  124 A- 124 C includes a left input, a right input, and a respective one of the first, second, or third outputs  120 A,  120 B,  120 C of the first, second, or third DLI  110 ,  112 ,  114 . 
     Each of the first, second and third DLI  110 ,  112 ,  114  also includes a first optical path  126 A,  126 B or  126 C coupled between the left output of the corresponding 2×2 MMI device  122 A,  122 B or  122 C and the left input of the corresponding MMI combiner  124 A,  124 B or  124 C. Each of the first, second and third DLI  110 ,  112 ,  114  further includes a second optical path  128 A,  128 B or  128 C coupled between the right output of the corresponding 2×2 MMI device  122 A,  122 B or  122 C and the right input of the corresponding MMI combiner  124 A,  124 B or  124 C. The second optical path  128 A- 128 C of each of the first, second and third DLI  110 ,  112 ,  114  has a different length than the corresponding first optical path  126 A- 126 C. 
     Various details regarding the operation of the first DLI  110  will now be described with respect to  FIG. 2 . The operation of the second and third DLI  112 ,  114  is generally analogous to the operation of the first DLI  110  and will not be described separately. 
     As shown in  FIG. 2 , the 2×2 MMI device  18 A may receive the optical signal  102 A at its L input  116 A and the optical signal  102 B at its R input  118 A and may split each into two components having substantially equal power. In particular, a first portion  202 A of the optical signal  102 A is transmitted directly through the 2×2 MMI device  122 A to its left output while a second portion  202 B having substantially equal power as the first portion  202 A crosses through the 2×2 MMI device  122 A to its right output. Similarly, a first portion  204 A of the optical signal  102 B is transmitted directly through the 2×2 MMI device  122 A to its right output while a second portion  204 B having substantially equal power as the first portion  102 B crosses through the 2×2 MMI device  122 A to its left output. 
     The second portion  202 B of the optical signal  102 A travels a longer distance than the first portion  202 A and thus experiences a phase delay. Similarly, the second portion  204 B of the optical signal  102 B travels a longer distance than the first portion  204 A and therefore also experiences a phase delay. 
     The first portion  202 A of the optical signal  102 A and the second portion  204 B of the optical signal  102 B are received into the first optical path  126 A and directed to the left input of the MMI combiner  124 A by the first optical path  126 A. Similarly, the first portion  204 A of the optical signal  102 B and the second portion  202 B of the optical signal  102 A are received into the second optical path  128 A and directed to the right input of the MMI combiner  124 A by the second optical path  128 A. Because the first optical path  126 A is longer than the second optical path  128 A, the first portion  202 A of the optical signal  102 A and the second portion  204 B of the optical signal  120 B experience a phase delay compared to the second portion  202 B of the optical signal  102 A and the first portion  204 A of the optical signal  102 B. 
     In the MMI combiner  124 A, interference patterns are created by constructive and destructive interference between the first portion  202 A and the second portion  202 B of the optical signal  102 A, and between the first portion  204 A and the second portion  204 B of the optical signal  102 B. The output of the MMI-combiner  124 A is positioned to coincide with a location of constructive interference of the first portion  202 A with the second portion  202 B, and of the first portion  204 A with second portion  204 B such that the MMI-combiner  124 A outputs a multiplexed optical signal  206  including the optical signal  102 A and the optical signal  102 B. 
     Referring to  FIG. 3 , the first DLI  110  may be configured to have a first frequency-dependent transmission function  302  resulting from interference between the first and second portions  202 A,  202 B of the optical signal  102 A initially received at the L input  116 A of the first DLI  110 , and a second frequency-dependent transmission function  304  resulting from interference between the first and second portions  204 A,  204 B of the optical signal  102 B initially received at the R input  118 A of the first DLI  110 . The first transmission function  302  may also be referred to as the left transmission function since it is applied to the optical signal received at the L input  116 A of the first DLI  110 , while the second transmission function  304  may also be referred to as the right transmission function since it is applied to the optical signal received at the R input  118 A of the first DLI  110 . 
     As shown in  FIG. 3 , the left and right transmission functions  23 ,  24  each have periodic transmission peaks  302 A,  304 A, respectively. The separation between adjacent transmission peaks  302 A in the left transmission function  302  is the FSR of the left transmission function  302 . Similarly, the separation between adjacent transmission peaks  304 A in the right transmission function  304  is the FSR of the right transmission function  304 . The FSR may be determined by, among other things, the difference in the path length of the first and second optical paths  126 A,  128 A, and the properties of the 2×2 MMI device  122 A. In some embodiments, for example, the FSR may be calculated according to 
               FSR   ≅       λ   2       n   ⁢           ⁢   Δ   ⁢           ⁢   L         ,         
where λ is a wavelength of the incident light, n is an effective refractive index of the DLI  110 , and ΔL is a difference in the path length of the two arms. ΔL becomes smaller for a wider channel spacing. For example, ΔL may be ˜25 μm for an FSR of 3200 GHz.
 
     Generally, the first DLI  110  may be configured such that the left and right transmission functions  302 ,  304  each have the same FSR of about four times the nominal channel spacing. For example, if the nominal channel spacing for wavelengths λ1-λ4 is 800 GHz, the FSR of each of the left and right transmission functions  302 ,  304  may be about 3200 GHz. Alternately or additionally, the first DLI  110  may be configured such that the right transmission function  304  is offset from the left transmission function  302  by about two times the nominal channel spacing, which may be 1600 GHz for a nominal channel spacing of 800 GHz. 
     The second DLI  112  has similar left and right transmission functions  306 ,  308  as the first DLI  110 , except that the left and right transmission functions  306 ,  308  of the second DLI  112  are respectively offset from the left and right transmission functions  302 ,  304  of the first DLI  110  by about the nominal channel spacing, which may be about 800 GHz in some embodiments. For instance, the left transmission function  306  of the second DLI  112  may be offset from the left transmission function  302  of the first DLI  110  by about the nominal channel spacing, while the right transmission function  308  of the second DLI  112  may also be offset from the right transmission function  304  of the first DLI  110  by about the nominal channel spacing. 
     The third DLI  114  also has left and right transmission functions  310 ,  312 , each including periodic transmission peaks  310 A,  312 A. However, the FSR of each of the left and right transmission functions  310 ,  312  of the third DLI  114  is about two times the nominal channel spacing in some embodiments. Additionally, the right transmission function  312  may be offset from the left transmission function  310  by about the nominal channel spacing, or about 800 GHz in some embodiments. 
     Accordingly, and with combined reference to  FIGS. 1-3 , the first DLI  110  may be configured to receive first and second optical signals  102 A and  102 B having respective first and second wavelengths λ1 and λ2 and to output a first multiplexed signal  206  ( FIG. 2 ) including the first and second optical signals  102 A and  102 B. Additionally, the second DLI  112  may be configured to receive third and fourth optical signals  102 C and  102 D having respective third and fourth wavelengths λ3 and λ4 and to output a second multiplexed signal (not shown) including the third and fourth optical signals  102 C and  102 D. The foregoing multiplexed signals may then be respectively provided to the left input  116 C and the R input  118 C of the third DLI  114  via optical fibers or other suitable optical waveguides (not labeled). The third DLI  114  may be configured to receive the foregoing multiplexed signals from the outputs  120 A,  120 B of the first and second DLI  110 ,  112  and to output the multiplexed signal  104  including the first, second, third and fourth optical signals  102 . 
     Returning to  FIG. 1 , in some embodiments, the first, second and third DLI  110 ,  112 ,  114  may be monolithically integrated together on a substrate  130  as a monolithic chip  131  (hereinafter “chip  131 ”). Alternately or additionally, the first, second and third DLI  110 ,  112 ,  114  may be monolithically integrated on the substrate  130  with one or more optical signal sources  132 . Each of the optical signal sources  132  may be configured to emit a corresponding one of the optical signals  102  at the corresponding wavelength λ1-λ4. In the illustrated embodiment of  FIG. 1 , the optical signal sources  132  are depicted as Distributed Bragg Reflector (DBR) lasers. More generally, however, each of the optical signal sources  132  may include, but is not limited to, a DML or an EML, which may include one or more of a distributed feedback (DFB) laser, a DBR laser, an electro-absorption (EA) modulator, a Mach-Zehnder (MZ) modulator, or the like or any combination thereof. In the illustrated embodiment, each of the optical signal sources  132  includes a Gain section, a Phase section and a DBR section, although other configurations may be implemented in other embodiments. 
     The dimensions of a footprint of the DLI MUX  100 , e.g., the dimensions of the substrate  130 , may be about 650 μm by about 200 μm (or about 300 μm by about 100 μm) in some embodiments in which the FSR of the third DLI  114  is about 400 GHz (or about 1600 GHz) and the nominal channel spacing is about 200 GHz (or about 800 GHz). For larger nominal channel spacing, the dimensions of the DLI MUX  100  may be smaller, while for smaller nominal channel spacing, the dimensions of the DLI MUX  10  may be larger in some embodiments. 
     Optionally, one or more TECs or other temperature-control elements may be provided to control temperatures of one or more of the first, second and third DLI  110 ,  112 ,  114 , and/or to control the temperatures of the optical signal sources  132 . In some embodiments, a temperature sensitivity of each of the first, second and third DLI  110 ,  112 ,  114  may be about 85 picometers per degree Celsius (pm/C), or more or less than 85 pm/C when a semiconductor substrate is implemented as the substrate  130 . Alternately or additionally, a temperature sensitivity of the optical signal sources  132  may be about 100 pm/C, or more or less than 100 pm/C. In these and other embodiments, because the temperature sensitivity of each of the first, second and third DLI  110 ,  112 ,  114  is relatively close to the temperature sensitivity of the optical signal sources  132 , the wavelengths of the optical signal sources  132  and transmission peaks of the first, second and third DLI  110 ,  112 ,  114  may generally move together. As such, precise control of TEC temperature may not be required in some embodiments. Alternately or additionally, local temperature increase by a heater in an arm of a given one of the DLIs  110 ,  112 ,  114  can alter a loss in the arm of the given one of the DLIs  110 ,  112 ,  114 . Ideal interference at the output of the given one of the DLIs  110 ,  112   114 , namely a high extinction ratio, can be realized by adjusting the loss of each arm to make it equal to each other. 
     The slope of the transmission functions  302 ,  304 ,  306 ,  308 ,  310 ,  312  of the first, second and/or third DLI  110 ,  112 ,  114  can optionally be used to enhance the ER of incoming optical signals  102  that have adiabatic chirp or frequency modulation. For example, each of the optical signals  102  may include a frequency modulated optical signal, or a frequency and amplitude modulated optical signal, in which 1 bits are blue-shifted relative to 0 bits, or vice versa. In other words, the 1 bits of each optical signal  102  may have a first frequency or corresponding wavelength, while the 0 bits of each optical signal  102  may have a second frequency or corresponding wavelength that is red-shifted relative to the first frequency. The frequency offset between the 1 bits and the 0 bits may be between about 20% and 80% of a bit rate of the corresponding optical signal  102 , or between about 30% and 70% of the bit rate, or about 50% of the bit rate in some embodiments. Additionally, the corresponding wavelengths (or frequencies) of the corresponding one of the optical signals  102  at the 1 bits and at the 0 bits may be centered about or may otherwise generally be equal to the corresponding wavelength λ1, λ2, λ3 and λ4 of the corresponding one of the optical signals  102 . 
     In these and other embodiments, the transmission functions  302 ,  304 ,  306 ,  308 ,  310 ,  312  of the first, second and third DLI  110 ,  112 ,  114  can be aligned with respect to the wavelengths λ1, λ2, λ3 and λ4 of the optical signals  102  so as to enhance the extinction ratio of the optical signals  102 . In particular, the transmission functions  302 ,  304 ,  306 ,  308 ,  310 ,  312  can be aligned with respect to the wavelengths λ1, λ2, λ3 and λ4 of the optical signals  102  so as to attenuate the second frequency (or wavelength) corresponding to 0 bits of each of the optical signals  102  more than the first frequency (or wavelength) corresponding to 1 bits of each of the optical signals  102 . Stated another way, positive slope portions of the transmission functions  302 ,  304 ,  306 ,  308 ,  310 ,  312  can be aligned to the wavelengths λ1, λ2, λ3 and λ4 such that blue-shifted 1 bits in each optical signal  102  are attenuated less than the corresponding red-shifted 0 bits. 
     Alternately or additionally, the slope can be used to reduce the ER of adiabatically chirped optical signals which may be desirable for amplification without inter-channel cross talk using an SOA. In particular, the transmission functions  302 ,  304 ,  306 ,  308 ,  310 ,  312  can be aligned with respect to the wavelengths λ1, λ2, λ3 and λ4 of the optical signals  102  so as to attenuate the first frequency (or wavelength) corresponding to 1 bits of each of the optical signals  102  more than the second frequency (or wavelength) corresponding to 0 bits of each of the optical signals  102 . Stated another way, negative slope portions of the transmission functions  302 ,  304 ,  306 ,  308 ,  310 ,  312  can be aligned to the wavelengths λ1, λ2, λ3 and λ4 such that blue-shifted 1 bits in each optical signal  102  are attenuated more than the corresponding red-shifted 0 bits. 
     Various details regarding the use of DLI slope to alter the ER of optical signals are provided in U.S. patent application Ser. No. 13/370,796, filed Feb. 10, 2012 and entitled OPTICAL FILTER FOR USE IN A LASER TRANSMITTER, which application is herein incorporated by reference in its entirety. 
     The DLI MUX  100  of  FIG. 1  may be modified and used alone or in combination with other components to multiplex up to 32 channels or more into a single multiplexed output signal. For example, one or more DLI MUXs  100  or modified versions thereof may be combined with a polarization multiplexer or other multiplexer to multiplex up to 32 channels or more. Alternately or additionally, a modified version of the DLI MUX  100  may be used to multiplex up to 32 channels or more. 
     The DLI MUX  100  of  FIG. 1  is configured to multiplex four optical signals  102  into a single multiplexed signal  104 .  FIG. 4  illustrates another embodiment of a DLI MUX  400  that is configured to multiplex eight optical signals  402  into a single multiplexed signal  404  including the eight optical signals  402 . The optical signals  402  may have wavelengths λ1-λ8 spaced at the nominal channel spacing Δ f . In some examples, λ2 is offset from λ1 by 4Δ f , λ3 is offset from λ1 by 2Δ f , λ4 is offset from λ1 by 6Δ f , λ5 is offset from λ1 by Δ f , λ6 is offset from λ1 by 5Δ f , λ7 is offset from λ1 by 3Δ f , and λ8 is offset from λ1 by 7Δ f . 
     The DLI MUX  400  of  FIG. 4  includes the same first and second stage  106  and  108  as the DLI MUX  100  of  FIG. 1 . The first stage  106  of  FIG. 4  is generally configured similar to the first stage  106  of  FIG. 1  in which each of the first DLI  110  and the second DLI  112  has an FSR of about four times the nominal channel spacing, where the right transmission function of each is offset from the left transmission function of each by about two times the channel spacing, and the left and right transmission functions of the second DLI  112  are offset from the left and right transmission functions of the first DLI  110  by about the nominal channel spacing. The second stage  108  of  FIG. 4  is configured similar to the second stage  108  of  FIG. 1  in which the third DLI  114  has an FSR of about two times the nominal channel spacing and the right transmission function of the third DLI  114  is offset from the left transmission function of the third DLI  114  by about the nominal channel spacing. 
     In addition, the DLI MUX  400  of  FIG. 4  includes a third stage  406  coupled to the first stage  106 . The third stage  402  includes fourth, fifth, sixth and seventh DLIs  408 A- 408 D (collectively “DLIs  408 ”). Similar to the first, second and third DLI  110 ,  112 ,  114 , each of the DLIs  408  includes a left or L input, a right or R input, an output (not labeled), a 2×2 MMI device (not labeled), an MMI combiner (not labeled), and first and second optical paths (not labeled) of different lengths coupled between the corresponding 2×2 MMI device and MMI combiner. Additionally, the output of the fourth DLI  408 A is coupled to the left input  116 A of the first DLI  110 . The output of the fifth DLI  408 B is coupled to the right input  118 A of the first DLI  110 . The output of the sixth DLI  408 C is coupled to the left input  116 B of the second DLI  112 . The output of the seventh DLI  408 D is coupled to the right input  118 B of the second DLI. 
     In these and other embodiments, an FSR of each of the fourth, fifth, sixth and seventh DLI  408  may be about eight times the nominal channel spacing, with the right transmission function of each being offset from the respective left transmission function of each by about four times the nominal channel spacing. 
     Returning to  FIG. 1 , and as indicated previously, the DLI MUX  100  of  FIG. 1  may be integrated on the substrate  130  with four optical signal sources  132  in some embodiments. To avoid radio frequency (RF) cross-talk at RF inputs to the optical signal sources  132 , adjacent RF inputs of the optical signal sources  132  may be separated by a minimum pitch. In some embodiments, for example, the minimum pitch may be about 800 μm, in which case the substrate  130  may be at least 2,400 μm wide. However, other configurations may be implemented to reduce the width of a monolithic chip, such as the chip  131 , including the substrate  130 , optical signal sources  132  and respective RF inputs, and the DLI MUX  100 . 
     For example,  FIG. 5  illustrates a monolithic chip  500  (hereinafter “chip  500 ”) including another embodiment of a DLI MUX  502  including a first, second, and third DLI  504 ,  506 ,  508 , each generally configured similar to the respective first, second and third DLI  110 ,  112 ,  114  of  FIG. 1 . For instance, the first and second DLI  504 ,  506  may make up a first stage of the DLI MUX  502 , similar to the first stage  106  of  FIG. 1 , while the third DLI  508  may make up a second stage of the DLI MUX  502 , similar to the second stage  108  of  FIG. 1 . 
     The chip  500  may additionally include a substrate  510  and four optical signal sources  512 ,  514 ,  516 ,  518  formed thereon. The optical signal sources  512 ,  514 ,  516 ,  518  may generally be spaced equally around a perimeter of the substrate  510 , such as generally in each of the four corners of the substrate  510 . 
     The chip  500  may further include multiple waveguides  520 ,  522 ,  524 ,  526  coupled between the optical signal sources  512 ,  514 ,  516 ,  518  and corresponding inputs of the first and second DLI  504 ,  506 , each of the waveguides  520 ,  522 ,  524 ,  526  providing a 180 degree turn. In more detail, the waveguide  520  is coupled between the optical signal source  512  and the left input of the first DLI  504 . The waveguide  522  is coupled between the optical signal source  514  and the right input of the first DLI  504 . The waveguide  524  is coupled between the optical signal source  518  and the left input of the second DLI  506 . The waveguide  526  is coupled between the optical signal source  516  and the right input of the second DLI  506 . 
     Using the configuration of  FIG. 5 , RF inputs  512 A,  514 A,  516 A,  518 A of the optical signal sources  512 ,  514 ,  516 ,  518  may be separated by a corresponding minimum pitch while the overall dimensions of the chip  500  may be relatively compact. For example, for a minimum pitch of 800 μm, the overall dimensions of the chip  500  may be about 800 μm by 800 μm, or a little more than 800 μm by 800 μm to accommodate bonding pads or the like. In contrast, configurations in which optical signal sources are aligned in parallel, such as the configuration of  FIG. 1 , may have a width of at least about 2400 μm for four optical signal sources as already discussed above. 
       FIG. 6  illustrates a monolithic chip  600  (hereinafter “chip  600 ”) including another embodiment of a DLI MUX  602  including a first, second, and third DLI  604 ,  606 ,  608 , the first and second DLI  604  making up a first stage  610  of the DLI MUX  602  and the third DLI  608  making up a second stage  612  of the DLI MUX  602 . 
     The second stage  612  and the third DLI  608  of  FIG. 6  may generally correspond in form and function to the second stage  108  and the third DLI  114  of  FIG. 1 . As such, an additional description of the second stage  612  and the third DLI  608  will not be provided herein and reference may be made to the discussion of the second stage  108  and the third DLI  114  of  FIG. 1 . 
     The first stage  610  and the first and second DLI  604 ,  606  may generally correspond to the first stage  106  and the first and second DLI  110 ,  112  of  FIG. 1 , with some differences as explained below. Each of the first and second DLI  604 ,  606  may respectively include a left (L) input  612 A or  612 B, a right (R) input  614 A or  614 B, and an output  616 A or  616 B, similar to the first and second DLI  110 ,  112  of  FIG. 1 . 
     Each of the L input  612 A of the first DLI  604 , the R input  614 A of the first DLI  604 , the L input  612 B of the second DLI  606  and the R input  614 B of the second DLI  606  may be respectively coupled to a corresponding optical signal source  618 ,  620 ,  622 ,  624  configured to emit optical signals having respective wavelengths λ1, λ2, λ3 and λ4. The optical signal sources  618 ,  620 ,  622 ,  624  may be provided on the same chip  600  as the DLI MUX  602  as illustrated, or external to the chip  600 . The wavelengths λ1, λ2, λ3 and λ4 of the optical signals emitted by the optical signal sources  618 ,  620 ,  622 ,  624  may be spaced apart from each other at the nominal spacing Δ f . In some embodiments, λ2 is offset from λ1 by 2Δ f , λ3 is offset from λ1 by Δ f , and λ4 is offset from λ1 by 3Δ f , as described above. 
     Each of the first and second DLI  604 ,  606  may additionally include a 2×2 MMI device  626 A,  626 B, respectively, and an MMI combiner  628 A,  628 B, respectively. Two optical paths  630 A,  630 B of different lengths are provided between the 2×2 MMI device  626 A and the MMI combiner  628 A. Similarly, two optical paths  632 A,  632 B of different lengths are provided between the 2×2 MMI device  626 B and the MMI combiner  628 B. 
     Aspects of the first DLI  604  will now be explained which may be similarly applicable to the second DLI  606 . The long optical path  630 A in the first DLI  604  has four 90 degree turns in the illustrated embodiment. A radius of each of the 90 degree turns may be about 150 μm, or more or less than 150 μm. In some embodiments, a length of the long optical path  630 A may be about 2.5 millimeters (mm) longer than a length of the short optical path  630 B to achieve an FSR of about 30 GHz for the first DLI  604 . An FSR of about 30 GHz may be suitable for optical signals having data rates of about 10 gigabits per second (G), for example. 
     Loss in the long optical path  630 A may be higher than the loss in the short optical path  630 B, such as about 1.5 decibels (dB) higher in some embodiments. To compensate for the relatively higher loss in the long optical path  630 A as compared to the loss in the short optical paths  630 B, the 2×2 MMI device  626 A may be configured to split each of the optical signals received on the L and R inputs  612 A,  614 A unequally. For instance, the 2×2 MMI device  626 A may apply a 60:40 splitting ratio, or some other unequal splitting ratio. Accordingly, the optical signal received on the L input  612 A may be split such that about 60 percent is transmitted onto the long optical path  630 A and 40 percent is transmitted onto the short optical path  630 B. Similarly, the optical signal received on the R input  614 A may be split such that about 60 percent is transmitted onto the long optical path  630 A and 40 percent is transmitted onto the short optical path  630 B. An estimated total loss of the first DLI  604  may be reduced by applying a 60:40 splitting ratio (or some other unequal splitting ratio) by about 1.7 dB rather than applying an equal 50:50 splitting ratio at the 2×2 MMI device  626 A. In these and other embodiments, the 2×2 MMI device  626 A and/or the 2×2 MMI device  626 B may include a butterfly MMI device or other suitable 2×2 MMI device configured to split two incoming optical signals unequally. 
     Alternately or additionally, the optical signal sources  618  and  620  and the optical signal sources  622  and  624  may be monolithically formed in the chip  600 , e.g., on a substrate  634 , within a loop formed by a respective one of the long optical path  630 A or  632 A to simultaneously minimize bending loss and the size of the chip  600 . In an example embodiment, the chip  600  may be about 800 μm by about 700 μm when each of the first and second DLI  604 ,  606  has an FSR of about 30 GHz for 10 G applications. Alternately or additionally, the chip  600  may be smaller than about 800 μm by about 700 μm when each of the first and second DL  604 ,  606  has an FSR of about 100 GHz for 25 G applications, or larger than about 800 μm by about 700 μm. 
     The chip  600  may be used in any of a variety of applications. For example, the chip  600  may be used in 80 kilometer (km) uncooled 10 G applications, 40-60 km high-power 10 G passive optical network (PON) applications, or the like. Alternately or additionally, the chip  600  may be used in 40 km 1310 nm 25 G applications as a replacement for four externally modulated lasers (EMLs) with relatively low power output, while allowing elimination of a semiconductor optical amplifier (SOA) typically used in front of a positive-intrinsic-negative (PIN) photodiode on the receive side in such applications. The foregoing are only some example applications in which the chip  600  and other embodiments described herein may be implemented. 
     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.