Patent Publication Number: US-2023135027-A1

Title: Geometry for a semiconductor optical amplifier

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This patent application claims priority to U.S. Provisional Patent Application No. 63/263,405, filed on Nov. 2, 2021, and entitled “MAXIMUM EFFICIENCY GEOMETRY FOR SEMICONDUCTOR OPTICAL AMPLIFIERS.” The disclosure of the prior application is considered part of and is incorporated by reference into this patent application. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates generally to optical amplifiers and to a geometry for a semiconductor optical amplifier. 
     BACKGROUND 
     An optical amplifier is a device that is to receive signal light and generate amplified signal light (i.e., signal light with comparatively higher optical power). Typically, the optical amplifier provides optical amplification using a so-called gain medium, which is “pumped” (i.e., provided with energy) by a source, such as a pump laser or an electrical current source. In some cases, the optical amplifier may utilize a semiconductor as a gain medium (such a device may be referred to as a semiconductor optical amplifier). 
     SUMMARY 
     In some implementations, a method includes generating, by a device, a data set including at least modal gain values and modal loss values for a semiconductor optical amplifier (SOA) slice; determining, by the device and based on the data set, respective widths for a plurality of slices of an SOA using an autoregressive model, where a width, of the respective widths, for a slice, of the plurality of slices, is associated with a maximum conversion efficiency achievable for the slice at a given current density; and generating, by the device, information indicating a geometry for the SOA based on the respective widths for the plurality of slices. 
     In some implementations, an SOA device includes an SOA having a plurality of slices of respective widths, where a first slice, of the plurality of slices, precedes a second slice, of the plurality of slices, in a light propagation direction, where a first width of the first slice is associated with a maximum conversion efficiency achievable for the first slice at an input optical power to the first slice and at a given current density, the first width defining an output optical power from the first slice to the second slice, and where a second width of the second slice is associated with a maximum conversion efficiency achievable for the second slice at the output optical power from the first slice to the second slice and at the given current density. 
     In some implementations, an SOA device includes an SOA having an input end and an output end in a light propagation direction, where a section of the SOA, between the input end and the output end, has a taper that gradually increases in width in the light propagation direction, and where a slope of the taper decreases in the light propagation direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram of a top view of an example semiconductor optical amplifier (SOA) that is tapered. 
         FIGS.  2 A- 2 B  are diagrams of an example associated with optimizing a geometry for an SOA. 
         FIG.  3    is a diagram of an example illustrating a relationship between conversion efficiency, width, and length for an SOA. 
         FIGS.  4 - 7    are diagrams of top views of example SOAs of SOA devices. 
         FIG.  8    is a diagram of an example environment in which systems and/or methods described herein may be implemented. 
         FIG.  9    is a diagram of example components of one or more devices of  FIG.  8   . 
         FIG.  10    is a flowchart of an example process associated with optimizing a geometry for an SOA. 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description of example implementations refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements. 
     High-power, high-efficiency semiconductor optical amplifiers (SOAs) may be used in light detection and ranging (LIDAR) and telecommunication applications. An SOA may provide an output optical power of about 150 milliwatts (mW) for an input optical power of about 20-30 mW. However, LIDAR applications may need an output optical power greater than 300 mW. Furthermore, as output optical power is increased, an efficiency of an SOA may decrease. In some examples, an SOA may be tapered (e.g., increasing in width from an input end to an output end) to improve the SOA&#39;s efficiency. Moreover, different types (e.g., geometries) of tapers, such as exponential tapers, may be employed in various SOAs. However, a taper for an SOA has not been designed to provide a highest possible efficiency, thereby degrading a performance of LIDAR or telecommunications using the SOA. 
     Some implementations described herein provide an SOA with an improved geometry that maximizes efficiency. In some implementations, a section of an SOA may have a taper having a slope that decreases, and a width that gradually increases, in a light propagation direction of the SOA. In some implementations, a technique for determining an optimized geometry for an SOA may utilize an autoregressive model based on a traveling wave technique. For example, the SOA may be conceptualized as a plurality of slices through which light propagates, and for each slice, a width may be determined that maximizes a conversion efficiency for the slice with respect to an input optical power to the slice. Pursuant to the autoregressive model, the input optical power to the slice may be an output optical power of a preceding slice (e.g., based on a width, and associated conversion efficiency, determined for the preceding slice). 
       FIG.  1    is a diagram of a top view of an example SOA  100  that is tapered. An output optical power P out  of the SOA  100  may be based on an input optical power P in  to the SOA  100  and a current I applied to the SOA  100 . The current I is related to a current density J of the SOA  100 , and the current density J may be assumed to be uniform across a cross-section of the SOA  100 . The conversion efficiency (i.e., power added efficiency) η of a slice  105  of the SOA, having a length L and a width w, may be determined according to Equation 1: 
     
       
         
           
             
               
                 
                   η 
                   = 
                   
                     
                       
                         
                           P 
                           out 
                         
                         - 
                         
                           P 
                           in 
                         
                       
                       IV 
                     
                     = 
                     
                       
                         
                           
                             
                               P 
                               in 
                             
                             ⁢ 
                             
                               exp 
                               [ 
                               
                                 
                                   ( 
                                   
                                     G 
                                     - 
                                     α 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 L 
                               
                               ] 
                             
                           
                           - 
                           
                             P 
                             in 
                           
                         
                         
                           
                             ( 
                             JwL 
                             ) 
                           
                           ⁢ 
                           V 
                         
                       
                       = 
                       
                         
                           
                             P 
                             in 
                           
                           ⁢ 
                           
                             { 
                             
                               
                                 exp 
                                 [ 
                                 
                                   
                                     ( 
                                     
                                       G 
                                       - 
                                       α 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   L 
                                 
                                 ] 
                               
                               - 
                               1 
                             
                             } 
                           
                         
                         
                           
                             ( 
                             JwL 
                             ) 
                           
                           ⁢ 
                           V 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   1 
                 
               
             
           
         
       
     
     where V is a voltage applied to the SOA  100 , G is a modal gain value, and a is a modal loss value. Moreover, a local conversion efficiency η local  of the SOA  100  (e.g., for a slice of the SOA  100  of infinitesimally small length) may be determined according to Equation 2: 
     
       
         
           
             
               
                 
                   
                     η 
                     local 
                   
                   = 
                   
                     
                       
                         lim 
                         
                           L 
                           → 
                           0 
                         
                       
                          
                       η 
                     
                     = 
                     
                       1 
                       
                         J 
                         ⁢ 
                         V 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   2 
                 
               
             
           
         
       
     
     where P is a local optical power. As described herein, at a given current density J and optical power P, there may be a width of the slice  105  of the SOA  100  associated with a maximum local conversion efficiency. 
     As indicated above,  FIG.  1    is provided as an example. Other examples may differ from what is described with regard to  FIG.  1   . 
       FIGS.  2 A- 2 B  are diagrams of an example  200  associated with optimizing a geometry for an SOA. As shown in  FIGS.  2 A- 2 B , example  200  includes an optimization system and a fabrication system. These devices are described in more detail in connection with  FIGS.  8  and  9   . 
     As shown in  FIG.  2 A , and by reference number  210 , the optimization system may generate a data set for an SOA device (e.g., for one or more slices of the SOA device). The SOA device may include an SOA (e.g., a waveguide, such as a ridge waveguide). Moreover, the SOA device may include a particular epitaxial structure (e.g., a particular semiconductor layer stack), as described below. The data set may include at least modal gain values (G values) and modal loss values (a values) for the SOA device (e.g., for a region of the SOA device). In some implementations, the data set may include temperature values for the SOA device. At a given current density J, the modal gain values, modal loss values, and/or temperature values may be associated with a plurality of SOA widths w and/or a plurality of input optical powers P (e.g., an i th  G value may be represented as G i (w i , J, P i ) and an i th  α value may be represented as α i (w i , J, P i )). The optimization system may generate the data set using a laser simulation model (e.g., a laser solver) configured to output a quantitative characterization for an epitaxial structure (e.g., an SOA device epitaxial structure). The optimization system may generate the data set prior to determining a width for the SOA, or the optimization system may generate the data set in an ongoing manner in connection with determining the width for the SOA. 
     As shown by reference number  220 , the optimization system may determine, based on the data set, respective widths for a plurality of slices of the SOA of the SOA device using an autoregressive model. A “slice” of the SOA may refer to a segment of the SOA having a length in a light propagation direction of the SOA, along the z-axis shown, and a width in a direction transverse to the light propagation direction (e.g., a ridge width of the SOA), along the x-axis shown. Each slice of the SOA may have the same length and height, while different slices of the SOA may have different widths, as described herein. In some implementations, the length used for slices of the SOA may be configured to any value greater than zero. As the length used for the slices approaches zero (e.g., the length is infinitesimally small), the respective widths determined using the autoregressive model define an increasingly smooth curve for the geometry of the SOA. 
     Using the autoregressive model, the optimization system may determine a width for a subsequent slice of the SOA based on an optical power associated with a width determined for a previous slice of the SOA. In an example with a first slice of the SOA that immediately precedes a second slice of the SOA in the light propagation direction, the autoregressive model may use an output optical power associated with a first width determined for the first slice as an input optical power for determining a second width for the second slice. In other words, the autoregressive model may use a traveling wave technique to determine the respective widths for the plurality of slices (e.g., as light propagates through the SOA, the width for each slice is determined slice by slice). 
     Reference number  222  shows an example of the traveling-wave technique of the autoregressive model. Here, the optimization system may initialize the autoregressive model with a starting input optical power P in . A value of P in  may be configured, arbitrary, based on specifications of the SOA device, or the like. The optimization system, using the autoregressive model and based on the input optical power P in  and the data set, may determine a width for a first slice (shown as slice 1) of the SOA that maximizes a conversion efficiency (e.g., a local conversion efficiency) for the first slice. For example, as illustrated by plot  224 , for a given current density J, the optimization system may determine (e.g., using Equation 2 above) conversion efficiencies for the first slice at various widths based on the starting input optical power P in  and using local modal gain value(s) and local modal loss value(s) from the data set. Continuing with the example, the optimization system may determine the width for the first slice that is associated with a maximum conversion efficiency of the conversion efficiencies determined for the first slice. Moreover, the optimization system may determine (e.g., using Equation 1 above) an output optical power P out,1  of the first slice based on the width determined for the first slice. 
     For a second slice (shown as slice 2) of the SOA, the optimization system, using the autoregressive model and based on the output optical power P out,1  of the first slice (in other words, an input optical power to the second slice) and the data set, may determine a width for the second slice that maximizes a conversion efficiency (e.g., a local conversion efficiency) for the second slice, in a similar manner as described above. For example, for the given current density J, the optimization system may determine (e.g., using Equation 2 above) conversion efficiencies for the second slice at various widths based on the output optical power P out,1  of the first slice and using local modal gain value(s) and local modal loss value(s) from the data set. Continuing with the example, the optimization system may determine the width for the second slice that is associated with a maximum conversion efficiency of the conversion efficiencies determined for the second slice. Moreover, the optimization system may determine (e.g., using Equation 1 above) an output optical power P out,2  of the second slice based on the width determined for the second slice. 
     The optimization system may use the output optical power P out,2  to determine a width for a third slice of the SOA, and so forth for each slice of the SOA. In other words, from the first slice to a last slice in the light propagation direction, a width and an optical power for each slice is determined autoregressively using the autoregressive model. In particular, the optimization system determines an optimal width (e.g., associated with a maximum conversion efficiency) for each slice based on an input optical power to the slice (i.e., an output optical power of a preceding slice) and determines an output optical power from the slice based on the optimal width. 
     Thus, using the autoregressive model, a width that is determined for a slice of the SOA may be associated with a maximum conversion efficiency for the slice at a given input optical power and at a given current density. For example, each slice of the SOA may have a width associated with a maximum conversion efficiency achievable for the slice at a local optical power for the slice and at a given current density. However, in some implementations, widths of the slices may be constrained by a minimum width and/or a maximum width (e.g., to avoid an unstable far field), such that a width for a slice may be the minimum width or the maximum width rather than a width associated with a maximum conversion efficiency. Accordingly, the optimization system may increase a width that is determined for a slice to a minimum width (e.g., a minimum width configured for the optimization system) and/or the optimization system may decrease a width that is determined for a slice to the maximum width (e.g., a maximum width configured for the optimization system). 
     The geometry for the SOA may be based on the respective widths determined for the plurality of slices of the SOA. That is, the respective widths define a curve that indicates the geometry for the SOA. Moreover, the geometry for the SOA, determined using the autoregressive model, may be associated with a maximum conversion efficiency that is achievable for the SOA or the SOA device (e.g., rather than merely a high conversion efficiency). Relative to an exponential taper, the geometry described herein provides higher device conversion efficiency and less aggressive width expansion at the same target output power. 
     As shown in  FIG.  2 B , and by reference number  230 , the optimization system may generate information indicating a geometry for the SOA. The information may be in the form of a data set, a plot, or the like. In some implementations, the information may indicate a width for the SOA with respect to a length of the SOA, as shown by plot  232  (in which the slices of the SOA are constrained by a minimum width and a maximum width). In some implementations, the information may indicate an output optical power of the SOA with respect to a length of the SOA, as shown by plot  234 . 
     In some implementations, the optimization system, using the autoregressive model in the manner described above, may determine respective widths for the plurality of slices of the SOA at multiple current density values, as shown by plot  232 . Here, the optimization system may select a current density and corresponding geometry for the SOA that is associated with a maximum output optical power, a target output optical power, or the like, in accordance with plot  234 . For example, the optimization system may determine a particular current density and/or a particular SOA length that is to be used for the SOA based on a target output optical power for the SOA. 
     In some implementations, the SOA device may be fabricated based on the information indicating the geometry for the SOA. For example, as shown by reference number  240 , the optimization system may transmit the information to another device, such as a fabrication system (e.g., an epitaxy system and/or a semiconductor lithography system), for fabrication of the SOA device. Fabrication of the SOA device may include defining the geometry for the SOA in lithography mask sets and/or processing semiconductor using lithography, etching, and/or epitaxial growth steps, among other examples. 
     In this way, the optimization system may determine a geometry for the SOA that has a highest possible conversion efficiency as optical power changes from an input optical power P in  to the SOA device to an output optical power P out  of the SOA device. The local power for the SOA device may be expressed using Equation 3: 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       IV 
                       , 
                       local 
                     
                   
                   = 
                   
                     dP 
                     
                       η 
                       local 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   3 
                 
               
             
           
         
       
     
     where P IV,local  is the local electrical power consumption (current x voltage) for an SOA slice and dP is a change in power. A total power of the SOA device is an integral over the local power, as shown by Equation 4: 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       IV 
                       , 
                       device 
                     
                   
                   = 
                   
                     
                       
                         ∫ 
                         
                           P 
                           in 
                         
                         
                           P 
                           out 
                         
                       
                       
                         dP 
                         
                           η 
                           local 
                         
                       
                     
                     = 
                     
                       
                         
                           P 
                           out 
                         
                         = 
                         
                           P 
                           in 
                         
                       
                       
                         η 
                         device 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   4 
                 
               
             
           
         
       
     
     Thus, using the autoregressive model, the optimization system determines a minimum local electrical power (P IV,local ) in the entire range from P in  to P out . Accordingly, an optimal SOA device may have a smallest total power consumption integrated area (P IV,device ), or stated differently, may have a maximum device conversion efficiency (η device ) among possible geometries. 
     In some implementations, an SOA device (e.g., that is fabricated in accordance with a geometry determined using the autoregressive model) may include an SOA having a plurality of slices of respective widths. Here, the plurality of slices of the SOA are conceptual slices (e.g., segments of the SOA), and in practice the SOA is continuous. The plurality of slices of the SOA may include a first slice and a second slice, and the first slice may precede the second slice in the light propagation direction. 
     The first slice may have a first width associated with a maximum conversion efficiency (e.g., according to Equation 2 above) achievable for the first slice (e.g., based on the particular epitaxial structure of the SOA device, which defines modal gain values and modal loss values, as described above) at a given current density and at an input optical power to the first slice (e.g., an input optical power to the SOA if there is no slice preceding the first slice or an output optical power from a slice immediately preceding the first slice). The first width for the first slice may define an output optical power from the first slice to the second slice (e.g., an output optical power from the first slice may be determined based on an input optical power to the first slice and the first width for the first slice). The second slice may have a second width associated with a maximum conversion efficiency achievable for the second slice (e.g., based on the particular epitaxial structure of the SOA device) at the given current density and at the output optical power from the first slice to the second slice (i.e., an input optical power to the second slice). 
     The plurality of slices of the SOA may include additional slices in a similar manner as described above. For example, the plurality of slices may include a third slice that immediately follows the second slice in the light propagation direction. The third slice may have a third width associated with a maximum conversion efficiency achievable for the third slice at the given current density and at an output optical power from the second slice to the third slice (i.e., an input optical power to the third slice). Thus, each slice of the SOA may have a width associated with a maximum conversion efficiency at a local optical power for the slice. In other words, for every slice of the SOA, a conversion efficiency is at a maximum with respect to waveguide width and local optical power. 
     As indicated above,  FIGS.  2 A- 2 B  are provided as an example. Other examples may differ from what is described with regard to  FIGS.  2 A- 2 B . 
       FIG.  3    is a diagram of an example  300  illustrating a relationship between conversion efficiency, width, and length for an SOA. Plot  305  shows contours of the local conversion efficiency as a function of optical power and SOA width (η local (P,w)) at a given current density. The optimal SOA width follows the maximum conversion efficiency as shown by line  310 . A relationship between optical power and SOA longitudinal position (e.g., position in the light propagation direction) is defined by Equation 5: 
       Δ P=Δz·G ( z )· P ( z )   Equation 5
 
     where z represents a longitudinal position of the SOA. Using Equation 5, the optimal SOA width indicated by plot  305  may be converted to longitudinal position of the SOA, as shown by plot  315 . 
     In some implementations, the optimization system may employ the technique described in connection with  FIG.  3    in addition to, or as an alternative to, the technique described in connection with  FIGS.  2 A- 2 B  (e.g., the technique described in connection with  FIG.  3    is an alternative expression of the technique described in connection with  FIGS.  2 A- 2 B , and therefore will produce the same outcome). For example, the optimization system may generate a contour plot (e.g., plot  305 ) for the local conversion efficiency of an SOA of an SOA device at a given current density. Based on the contour plot, the optimization system may determine width and optical power data points corresponding to a maximum conversion efficiency (e.g., line  310 ). Based on the width and optical power data points, the optimization system may determine (e.g., using Equation 5) widths for the SOA at a plurality of longitudinal positions of the SOA. Moreover, the optimization system may generate information indicating a geometry for the SOA based on the widths at the plurality of longitudinal positions. For example, the optimization system may generate a plot of width versus longitudinal position of the SOA (e.g., plot  315 ). In some implementations, an SOA device may be fabricated based on the information indicating the geometry for the SOA, in a similar manner as described in connection with  FIGS.  2 A- 2 B . 
     As indicated above,  FIG.  3    is provided as an example. Other examples may differ from what is described with regard to  FIG.  3   . 
       FIG.  4    is a diagram of a top view of an example SOA  400  of an SOA device. The SOA  400  has an input end  402  and an output end  404  in a light propagation direction. The SOA  400  may include a section  406  between the input end  402  and the output end  404 . The section  406  may extend from the input end  402  to the output end  404  of the SOA  400 , as shown in  FIG.  4   . 
     The section  406  of the SOA  400  may have a taper that gradually increases in width in the light propagation direction. For example, the taper may nonlinearly increase in width in the light propagation direction. Moreover, a slope of the taper may decrease (e.g., linearly or nonlinearly) in the light propagation direction. For example, the taper may include a convex curve (e.g., relative to an axis of the SOA defined by the light propagation direction). The taper may define a geometry for the SOA that is associated with a maximum conversion efficiency that is achievable for the SOA device, as described herein. 
     As indicated above,  FIG.  4    is provided as an example. Other examples may differ from what is described with regard to  FIG.  4   . 
       FIG.  5    is a diagram of a top view of an example SOA  500  of an SOA device. The SOA  500  has an input end  502  and an output end  504  in a light propagation direction. The SOA  500  may include a section  506  between the input end  502  and the output end  504 . The section  506  may extend from a position proximally distanced from the input end  502  to the output end  504  of the SOA  500 , as shown in  FIG.  5   . The section  506  of the SOA  500  may have a taper as described in connection with  FIG.  4    (e.g., the taper may gradually increase in width and decrease in slope in the light propagation direction). 
     The SOA  500  may include an input section  508 . The input section  508  may extend from the input end  502  to the section  506  of the SOA  500 . In some implementations, the input section  508  may have a constant width in the light propagation direction. That is, the input width of the SOA  500  may be capped (i.e., constrained by a minimum width). 
     As indicated above,  FIG.  5    is provided as an example. Other examples may differ from what is described with regard to  FIG.  5   . 
       FIG.  6    is a diagram of a top view of an example SOA  600  of an SOA device. The SOA  600  has an input end  602  and an output end  604  in a light propagation direction. The SOA  600  may include a section  606  between the input end  602  and the output end  604 . The section  606  may extend from the input end  602  to a position proximally distanced from the output end  604  of the SOA  600 , as shown in  FIG.  6   . The section  606  of the SOA  600  may have a taper as described in connection with  FIG.  4    (e.g., the taper may gradually increase in width and decrease in slope in the light propagation direction). 
     The SOA  600  may include an output section  608 . The output section  608  may extend from the section  606  to the output end  604  of the SOA  600 . In some implementations, the output section  608  may have a constant width in the light propagation direction. That is, the output width of the SOA  600  may be capped (i.e., constrained by a maximum width). 
     As indicated above,  FIG.  6    is provided as an example. Other examples may differ from what is described with regard to  FIG.  6   . 
       FIG.  7    is a diagram of a top view of an example SOA  700  of an SOA device. The SOA  700  has an input end  702  and an output end  704  in a light propagation direction. The SOA  700  may include a section  706  between the input end  702  and the output end  704 . The section  706  may extend from a position proximally distanced from the input end  702  to a position proximally distanced from the output end  704  of the SOA  700 , as shown in  FIG.  7   . The section  706  of the SOA  700  may have a taper as described in connection with  FIG.  4    (e.g., the taper may gradually increase in width and decrease in slope in the light propagation direction). 
     The SOA  700  may include an input section  708  as described in connection with  FIG.  5    (e.g., the input section  708  may have a constant width in the light propagation direction). The SOA  700  may also include an output section  710  as described in connection with  FIG.  6    (e.g., the output section  710  may have a constant width in the light propagation direction). 
     As indicated above,  FIG.  7    is provided as an example. Other examples may differ from what is described with regard to  FIG.  7   . 
     An SOA device described herein (e.g., in connection with  FIGS.  2 A- 2 B,  3 ,  4 ,  5 ,  6   , and/or  7 ) may be an edge emitting device or a vertically emitting device. The SOA device may include an epitaxial structure (e.g., including a substrate and one or more active regions) that includes an SOA (e.g., a ridge waveguide) described herein. The SOA device may also include one or more electrodes, metal contacts, or the like. The SOA device may additionally include an antireflection coating at end faces of the epitaxial structure. 
       FIG.  8    is a diagram of an example environment  800  in which systems and/or methods described herein may be implemented. As shown in  FIG.  8   , environment  800  may include an optimization system  810 , a fabrication system  820 , and a network  830 . Devices of environment  800  may interconnect via wired connections, wireless connections, or a combination of wired and wireless connections. 
     The optimization system  810  includes one or more devices capable of receiving, generating, storing, processing, providing, and/or routing information associated with a geometry for an SOA, as described elsewhere herein. For example, the optimization system  810  may implement the autoregressive model, as described elsewhere herein. The optimization system  810  may include a communication device and/or a computing device. For example, the optimization system  810  may include a server, such as an application server, a client server, a web server, a database server, a host server, a virtual server (e.g., executing on computing hardware), or a server in a cloud computing system. In some implementations, the optimization system  810  includes computing hardware used in a cloud computing environment. 
     The fabrication system  820  includes one or more devices capable of receiving, generating, storing, processing, providing, and/or routing information associated with fabrication of an SOA in accordance with a particular geometry, as described elsewhere herein. The fabrication system  820  may be an epitaxy system and/or a semiconductor lithography system. The fabrication system  820  may include a communication device and/or a computing device. For example, the fabrication system  820  may include a server, such as an application server, a client server, a web server, a database server, a host server, a virtual server (e.g., executing on computing hardware), or a server in a cloud computing system. In some implementations, the fabrication system  820  includes computing hardware used in a cloud computing environment. 
     The network  830  includes one or more wired and/or wireless networks. For example, the network  830  may include a wireless wide area network (e.g., a cellular network or a public land mobile network), a local area network (e.g., a wired local area network or a wireless local area network (WLAN), such as a Wi-Fi network), a personal area network (e.g., a Bluetooth network), a near-field communication network, a telephone network, a private network, the Internet, and/or a combination of these or other types of networks. The network  830  enables communication among the devices of environment  800 . 
     The number and arrangement of devices and networks shown in  FIG.  8    are provided as an example. In practice, there may be additional devices and/or networks, fewer devices and/or networks, different devices and/or networks, or differently arranged devices and/or networks than those shown in  FIG.  8   . Furthermore, two or more devices shown in  FIG.  8    may be implemented within a single device, or a single device shown in  FIG.  8    may be implemented as multiple, distributed devices. Additionally, or alternatively, a set of devices (e.g., one or more devices) of environment  800  may perform one or more functions described as being performed by another set of devices of environment  800 . 
       FIG.  9    is a diagram of example components of a device  900 , which may correspond to optimization system  810  and/or fabrication system  820 . In some implementations, optimization system  810  and/or fabrication system  820  includes one or more devices  900  and/or one or more components of device  900 . As shown in  FIG.  9   , device  900  may include a bus  910 , a processor  920 , a memory  930 , an input component  940 , an output component  950 , and a communication component  960 . 
     Bus  910  includes one or more components that enable wired and/or wireless communication among the components of device  900 . Bus  910  may couple together two or more components of  FIG.  9   , such as via operative coupling, communicative coupling, electronic coupling, and/or electric coupling. Processor  920  includes a central processing unit, a graphics processing unit, a microprocessor, a controller, a microcontroller, a digital signal processor, a field-programmable gate array, an application-specific integrated circuit, and/or another type of processing component. Processor  920  is implemented in hardware, firmware, or a combination of hardware and software. In some implementations, processor  920  includes one or more processors capable of being programmed to perform one or more operations or processes described elsewhere herein. 
     Memory  930  includes volatile and/or nonvolatile memory. For example, memory  930  may include random access memory (RAM), read only memory (ROM), a hard disk drive, and/or another type of memory (e.g., a flash memory, a magnetic memory, and/or an optical memory). Memory  930  may include internal memory (e.g., RAM, ROM, or a hard disk drive) and/or removable memory (e.g., removable via a universal serial bus connection). Memory  930  may be a non-transitory computer-readable medium. Memory  930  stores information, instructions, and/or software (e.g., one or more software applications) related to the operation of device  900 . In some implementations, memory  930  includes one or more memories that are coupled to one or more processors (e.g., processor  920 ), such as via bus  910 . 
     Input component  940  enables device  900  to receive input, such as user input and/or sensed input. For example, input component  940  may include a touch screen, a keyboard, a keypad, a mouse, a button, a microphone, a switch, a sensor, a global positioning system sensor, an accelerometer, a gyroscope, and/or an actuator. Output component  950  enables device  900  to provide output, such as via a display, a speaker, and/or a light-emitting diode. Communication component  960  enables device  900  to communicate with other devices via a wired connection and/or a wireless connection. For example, communication component  960  may include a receiver, a transmitter, a transceiver, a modem, a network interface card, and/or an antenna. 
     Device  900  may perform one or more operations or processes described herein. For example, a non-transitory computer-readable medium (e.g., memory  930 ) may store a set of instructions (e.g., one or more instructions or code) for execution by processor  920 . Processor  920  may execute the set of instructions to perform one or more operations or processes described herein. In some implementations, execution of the set of instructions, by one or more processors  920 , causes the one or more processors  920  and/or the device  900  to perform one or more operations or processes described herein. In some implementations, hardwired circuitry is used instead of or in combination with the instructions to perform one or more operations or processes described herein. Additionally, or alternatively, processor  920  may be configured to perform one or more operations or processes described herein. Thus, implementations described herein are not limited to any specific combination of hardware circuitry and software. 
     The number and arrangement of components shown in  FIG.  9    are provided as an example. Device  900  may include additional components, fewer components, different components, or differently arranged components than those shown in  FIG.  9   . Additionally, or alternatively, a set of components (e.g., one or more components) of device  900  may perform one or more functions described as being performed by another set of components of device  900 . 
       FIG.  10    is a flowchart of an example process  1000  associated with optimizing a geometry for an SOA. In some implementations, one or more process blocks of  FIG.  10    are performed by a device (e.g., optimization system  810 ). In some implementations, one or more process blocks of  FIG.  10    are performed by another device or a group of devices separate from or including the device, such as a fabrication system (e.g., fabrication system  820 ). Additionally, or alternatively, one or more process blocks of  FIG.  10    may be performed by one or more components of device  900 , such as processor  920 , memory  930 , input component  940 , output component  950 , and/or communication component  960 . 
     As shown in  FIG.  10   , process  1000  may include generating a data set including at least modal gain values and modal loss values for an SOA slice (block  1010 ). For example, the device may generate a data set including at least modal gain values and modal loss values for an SOA slice, as described above. 
     As further shown in  FIG.  10   , process  1000  may include determining, based on the data set, respective widths for a plurality of slices of an SOA using an autoregressive model (block  1020 ). For example, the device may determine, based on the data set, respective widths for a plurality of slices of an SOA using an autoregressive model. In some implementations, a width, of the respective widths, for a slice, of the plurality of slices, is associated with a maximum conversion efficiency achievable for the slice at a given current density. 
     As further shown in  FIG.  10   , process  1000  may include generating information indicating a geometry for the SOA based on the respective widths for the plurality of slices (block  1030 ). For example, the device may generate information indicating a geometry for the SOA based on the respective widths for the plurality of slices, as described above. 
     Process  1000  may include additional implementations, such as any single implementation or any combination of implementations described below and/or in connection with one or more other processes described elsewhere herein. 
     In a first implementation, the autoregressive model uses a traveling wave technique. 
     In a second implementation, alone or in combination with the first implementation, the autoregressive model uses an output optical power associated with a first width, of the respective widths, determined for a first slice, of the plurality of slices, as an input optical power for determining a second width, of the respective widths, for a second slice of the plurality of longitudinal slices. 
     In a third implementation, alone or in combination with one or more of the first and second implementations, the respective widths for the plurality of slices are associated with respective maximum conversion efficiencies achievable for the plurality of slices at the given current density. 
     In a fourth implementation, alone or in combination with one or more of the first through third implementations, an SOA device is fabricated based on the information indicating the geometry for the SOA. 
     In a fifth implementation, alone or in combination with one or more of the first through fourth implementations, process  1000  includes transmitting the information indicating the geometry for the SOA to another device for fabrication of an SOA device. 
     In a sixth implementation, alone or in combination with one or more of the first through fifth implementations, the slice has a length in a light propagation direction of the SOA and a width in a direction transverse to the light propagation direction. 
     In a seventh implementation, alone or in combination with one or more of the first through sixth implementations, the geometry for the SOA is associated with a maximum conversion efficiency achievable for the SOA. 
     Although  FIG.  10    shows example blocks of process  1000 , in some implementations, process  1000  includes additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in  FIG.  10   . Additionally, or alternatively, two or more of the blocks of process  1000  may be performed in parallel. 
     The foregoing disclosure provides illustration and description, but is not intended to be exhaustive or to limit the implementations to the precise forms disclosed. Modifications and variations may be made in light of the above disclosure or may be acquired from practice of the implementations. Furthermore, any of the implementations described herein may be combined unless the foregoing disclosure expressly provides a reason that one or more implementations may not be combined. 
     As used herein, the term “component” is intended to be broadly construed as hardware, firmware, and/or a combination of hardware and software. It will be apparent that systems and/or methods described herein may be implemented in different forms of hardware, firmware, or a combination of hardware and software. The actual specialized control hardware or software code used to implement these systems and/or methods is not limiting of the implementations. Thus, the operation and behavior of the systems and/or methods are described herein without reference to specific software code—it being understood that software and hardware can be designed to implement the systems and/or methods based on the description herein. 
     Even though particular combinations of features are recited in the claims and/or disclosed in the specification, these combinations are not intended to limit the disclosure of various implementations. In fact, many of these features may be combined in ways not specifically recited in the claims and/or disclosed in the specification. Although each dependent claim listed below may directly depend on only one claim, the disclosure of various implementations includes each dependent claim in combination with every other claim in the claim set. As used herein, a phrase referring to “at least one of” a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover a, b, c, a-b, a-c, b-c, and a-b-c, as well as any combination with multiple of the same item. 
     No element, act, or instruction used herein should be construed as critical or essential unless explicitly described as such. Also, as used herein, the articles “a” and “an” are intended to include one or more items, and may be used interchangeably with “one or more.” Further, as used herein, the article “the” is intended to include one or more items referenced in connection with the article “the” and may be used interchangeably with “the one or more.” Furthermore, as used herein, the term “set” is intended to include one or more items (e.g., related items, unrelated items, or a combination of related and unrelated items), and may be used interchangeably with “one or more.” Where only one item is intended, the phrase “only one” or similar language is used. Also, as used herein, the terms “has,” “have,” “having,” or the like are intended to be open-ended terms. Further, the phrase “based on” is intended to mean “based, at least in part, on” unless explicitly stated otherwise. Also, as used herein, the term “or” is intended to be inclusive when used in a series and may be used interchangeably with “and/or,” unless explicitly stated otherwise (e.g., if used in combination with “either” or “only one of”).