Patent Publication Number: US-11391890-B1

Title: Multi-mode spiral delay device

Description:
RELATED APPLICATIONS 
     This application claims the benefit of, and priority to, U.S. Provisional Application No. 62/848,473, filed May 15, 2019, entitled “Multi-Mode Spiral Delay Device,” which is incorporated by reference herein in its entirety. 
    
    
     TECHNICAL FIELD 
     This relates generally to photonic devices and, more specifically, to optical delay devices. 
     BACKGROUND 
     Optical waveguides (or waveguides) are widely used for transmitting light. For example, optical fibers are used in various telecommunication systems. Slab or planar waveguides are used in photonic devices for manipulating light (such as directing light, coupling light, filtering light, generating light output, etc.). 
     Optical delay devices used in various optical applications, such as time-resolved spectroscopy, interferometry, and time divisional optical communications often include optical waveguides. In order to provide a sufficient delay, optical delay devices would include long optical waveguides, which increase the overall size of the optical delay devices. Accordingly, there is a need for an optical delay device having a compact size. 
     SUMMARY 
     One or more embodiments of the present disclosure provide an optical delay device that includes a first multi-mode waveguide spiraling inward toward a center region of the optical delay device, and a first coupler that is coupled to the first multi-mode waveguide and configured to receive light from the first multi-mode waveguide. The first coupler spirals further inward towards a center region of the optical delay device. The optical delay device also includes a first single-mode waveguide that is located in the center region and configured to receive light from the first coupler, and a second coupler configured to receive light from the first single-mode waveguide, the second coupler spiraling outward from the center region. The optical device further includes a second multi-mode waveguide that is coupled to the second coupler and configured to receive light from the second coupler. The second coupler spirals further outward from the center region. A first end of the first single-mode waveguide is coupled to the first coupler and a second end of the first single-mode waveguide, opposite to the first end, is coupled to the second coupler. 
     In some embodiments, the first multi-mode waveguide includes a first plurality of spiral rounds. The first plurality of spiral rounds includes a first outmost spiral portion that has a first radius of curvature and a first inmost spiral portion that has a second radius of curvature that is smaller than the first radius of curvature. Spiral portions between the first outmost spiral portion and the first inmost spiral portion have successively decreasing radii from the first radius of curvature to the second radius of curvature. The first coupler includes a second plurality of spiral rounds. The second plurality of spiral rounds includes a second outmost spiral portion that has a third radius of curvature and a second inmost spiral portion that has a fourth radius of curvature that is smaller than the third radius of curvature. Spiral portions between the second outmost spiral portion and the second inmost spiral portion have successively decreasing radii from the third radius of curvature to the fourth radius of curvature. The second coupler includes a third plurality of spiral rounds. The third plurality of spiral rounds includes a third inmost spiral portion that has a fifth radius of curvature and a third outmost spiral portion that has a sixth radius of curvature that is larger than the fifth radius of curvature. Spiral portions between the third inmost spiral portion and the third outmost spiral portion have successively increasing radii from the fifth radius of curvature to the sixth radius of curvature. The second multi-mode waveguide includes a fourth plurality of spiral rounds. The fourth plurality of spiral rounds includes a fourth inmost spiral portion that has a seventh radius of curvature and a fourth outmost spiral portion that has an eighth radius of curvature that is larger than the seventh radius of curvature. Spiral portions between the fourth inmost spiral portion and the fourth outmost spiral portion have successively increasing radii between the seventh radius of curvature and the eighth radius of curvature. 
     In some embodiments, the first single-mode waveguide includes a curved portion having a radius of curvature that is smaller than each of the fourth radius of curvature and the fifth radius of curvature. 
     In some embodiments, the first plurality of spiral rounds is interleaved with the fourth plurality of spiral rounds and the second plurality of spiral rounds is interleaved with the third plurality of spiral rounds. Any portion of the first plurality of spiral rounds is separated from any adjacent portion of the fourth plurality of spiral rounds for preventing light propagating in the first plurality of spiral rounds from being evanescently coupled into the fourth plurality of spiral rounds. Any portion of the second plurality of spiral rounds is separated from any adjacent portion of the third plurality of spiral rounds for preventing light propagating in the second plurality of spiral rounds from being evanescently coupled into the third plurality of spiral rounds. 
     In some embodiments, the first plurality of spiral rounds has a first number of spiral rounds, the second plurality of spiral rounds has a second number of spiral rounds, the third plurality of spiral rounds has a third number of spiral rounds that corresponds to the second number of spiral rounds, and the fourth plurality of spiral rounds has a fourth number of spiral rounds that corresponds to the first number of spiral rounds. 
     In some embodiments, the optical delay device includes at least 10 spiral rounds (e.g., a total number of spiral rounds in the first plurality of spiral rounds, the second plurality of spiral rounds, the third plurality of spiral rounds, and the fourth plurality of spiral rounds is at least 10). In some embodiments, the optical delay device includes at least 100 spiral rounds (e.g., the total number of spiral rounds in the first plurality of spiral rounds, the second plurality of spiral rounds, the third plurality of spiral rounds, and the fourth plurality of spiral rounds is at least 100). 
     In some embodiments, the eighth radius of curvature is substantially equal to the first radius of curvature, the seventh radius of curvature is substantially equal to the second radius of curvature, the sixth radius of curvature is substantially equal the third radius of curvature, the fifth radius of curvature is substantially equal the fourth radius of curvature, the third radius of curvature is substantially equal to the second radius of curvature, and the seventh radius of curvature is substantially equal to the sixth radius of curvature. 
     In some embodiments, the first plurality of spiral rounds, the second plurality of spiral rounds, the third plurality of spiral rounds, and the fourth plurality of spiral rounds are concentric spiral rounds. 
     In some embodiments, the optical delay device also includes an input coupler that is adiabatically coupled to the first multi-mode waveguide and an output coupler that is adiabatically coupled to the second multi-mode waveguide. The first multi-mode waveguide is configured to receive light from the input coupler and propagate the light toward to first coupler. The second multi-mode waveguide is configured to propagate light received from the second coupler toward the output coupler. 
     In some embodiments, the input coupler includes a portion having the first radius of curvature and the output coupler includes a portion having the eighth radius of curvature. 
     In some embodiments, the first multi-mode waveguide has a first width, the second multi-mode waveguide has a second width, and the first single-mode waveguide has a third width that is smaller than each of the first width and the second width. The first coupler has a width that tapers from the first width to the third width and the second coupler has a width that tapers from the second width to the third width. 
     In some embodiments, the first multi-mode waveguide has a first length, the second multi-mode waveguide has a second length, and the first single-mode waveguide has a third length; that is smaller than each of the first length and the second length. 
     In some embodiments, the first multi-mode waveguide, the second multi-mode waveguide, the first single-mode waveguide, the first coupler, and the second coupler are formed in a same layer of a material on a substrate. 
     One or more embodiments of the present disclosure provide a method of propagating light, the method includes receiving light, propagating the light in a first multi-mode waveguide toward a first coupler, and propagating the light in the first coupler toward a first single-mode waveguide such that the first multi-mode waveguide and the first coupler provide a first light path that spirals inward toward a center region. The method also includes propagating the light along the first single-mode waveguide toward a second coupler, propagating the light in the second coupler toward a second multi-mode waveguide, propagating the light in the second multi-mode waveguide, and outputting the light. The second coupler and the second multi-mode waveguide provide a second light path that spirals outward from the center region. The first single-mode waveguide provides a third light path through the center region and between the first light path and the second light path. 
     In some embodiments, the first light path includes a first plurality of spiral rounds corresponding to the first multi-mode waveguide. The first plurality of spiral rounds includes a first outmost spiral portion that has a first radius of curvature and a first inmost spiral portion that has a second radius of curvature that is smaller than the first radius of curvature. Spiral portions between the first outmost spiral portion and the first inmost spiral portion have successively decreasing radii from the first radius of curvature to the second radius of curvature. The first light path also includes a second plurality of spiral rounds corresponding to the first coupler. The second plurality of spiral rounds includes a second outmost spiral portion that has a third radius of curvature and a second inmost spiral portion that has a fourth radius of curvature that is smaller than the third radius of curvature. Spiral portions between the second outmost spiral portion and the second inmost spiral portion have successively decreasing radii from the third radius of curvature to the fourth radius of curvature. The second light path includes a third plurality of spiral rounds corresponding to the second coupler. The third plurality of spiral rounds includes a third inmost spiral portion that has a fifth radius of curvature and a third outmost spiral portion that has a sixth radius of curvature that is larger than the fifth radius of curvature. Spiral portions between the third inmost spiral portion and the third outmost spiral portion have successively increasing radii from the fifth radius of curvature to the sixth radius of curvature. The second light path further includes a fourth plurality of spiral rounds corresponding to the second multi-mode waveguide. The fourth plurality of spiral rounds includes a fourth inmost spiral portion that has a seventh radius of curvature and a fourth outmost spiral portion that has an eighth radius of curvature that is larger than the seventh radius of curvature. Spiral portions between the fourth inmost spiral portion and the fourth outmost spiral portion have successively increasing radii from the seventh radius of curvature to the eighth radius of curvature. 
     In some embodiments, propagating the light along the first single-mode waveguide includes propagating the light along a curved path having a radius of curvature that is smaller than each of the fourth radius of curvature and the fifth radius of curvature. 
     In some embodiments, the first plurality of spiral rounds has a first number of spiral rounds, the second plurality of spiral rounds has a second number of spiral rounds, the third plurality of spiral rounds has a third number of spiral rounds that corresponds to the second number of spiral rounds, and the fourth plurality of spiral rounds has a fourth number of spiral rounds that corresponds to the first number of spiral rounds. 
     In some embodiments, receiving the light includes propagating the light along an input single-mode waveguide toward an input coupler and propagating the light along the input coupler toward the first multi-mode waveguide. In some embodiments, outputting the light includes coupling the light from the second multi-mode waveguide, through an output coupler, to an output single-mode waveguide and propagating the light along the output single-mode waveguide. 
     In some embodiments, propagating the light along the input coupler includes propagating the light along a path that has the first radius of curvature. In some embodiments, coupling the light from the second multi-mode waveguide, through the output coupler, to the output single-mode waveguide includes propagating the light along a path having the eighth radius of curvature. 
     In some embodiments, propagating the light in the first multi-mode waveguide also includes propagating the light along the first multi-mode waveguide without evanescently coupling the light into the second multi-mode waveguide, propagating the light in the first coupler includes propagating the light along the first coupler without evanescently coupling the light into the second coupler, propagating the light in the second coupler also includes propagating the light along the second coupler without evanescently coupling the light into the first coupler, and propagating the light in the second multi-mode waveguide includes propagating the light along the second multi-mode waveguide without evanescently coupling the light into the first multi-mode waveguide. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the various described embodiments, reference should be made to the Detailed Description below, in conjunction with the following drawings in which like reference numerals refer to corresponding parts throughout the figures. 
         FIG. 1A  is a simplified diagram illustrating an optical delay device and an optical path of light propagating through different portions of the optical delay device in accordance with some embodiments. 
         FIGS. 1B-1D  are plan views of an optical delay device in accordance with some embodiments. 
         FIG. 1E  is a partial plan view of an optical delay device illustrating a center region of the optical device shown in  FIGS. 1A-1D  in accordance with some embodiments. 
         FIG. 1F  is a linearized view of the optical delay device shown in  FIGS. 1A-1D  in accordance with some embodiments. 
         FIG. 1G  is a cross-sectional view of the optical delay device shown in  FIGS. 1A-1D  in accordance with some embodiments. 
         FIG. 2A  is a simplified diagram illustrating an optical delay device and an optical path of light propagating through different portions of the optical delay device in accordance with some embodiments. 
         FIGS. 2B-2C  are plan views of an optical delay device in accordance with some embodiments. 
         FIG. 2D  is a partial plan view of an optical delay device illustrating an input region of the optical device shown in  FIGS. 2A-C  in accordance with some embodiments. 
         FIG. 2E  is a linearized view of the optical delay device shown in  FIGS. 2A-2C  in accordance with some embodiments. 
         FIGS. 3A-3C  are flowcharts illustrating a method of propagating light to create an optical delay in accordance with some embodiments. 
     
    
    
     Like reference numerals refer to corresponding parts throughout the several views of the drawings. The drawings may not be drawn to scale unless stated otherwise. 
     DETAILED DESCRIPTION 
     As explained above, there is a need for an optical delay device (or photonic delay line) that is compact. The disclosed optical delay devices and methods described herein meet the need by allowing transmission of light in a spiral optical path with a small footprint on a substrate. A majority of the delay path of the optical delay devices include multi-mode waveguides, resulting in reduced optical loss as light propagates along the optical delay device. 
     Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the various described embodiments. However, it will be apparent to one of ordinary skill in the art that the various described embodiments may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments. 
     It will also be understood that, although the terms first, second, etc. are, in some instances, used herein to describe various elements, these elements should not be limited by these terms. These terms are used only to distinguish one element from another. For example, a first waveguide could be termed a second waveguide, and, similarly, a second waveguide could be termed a first waveguide, without departing from the scope of the various described embodiments. The first waveguide and the second waveguide are both waveguides, but they are not the same waveguide. 
       FIG. 1A  is a simplified diagram illustrating an optical delay device  100  and an optical path of light propagating in the optical delay device in accordance with some embodiments. As shown, optical delay device  100  includes a first multi-mode waveguide  106 -in providing a first portion of the optical path that spirals inward toward a center region  102  of optical delay device  100 . First multi-mode waveguide  106 -in is coupled (e.g., physically, optically) to a first coupler  104 -in, which provides a second portion of the optical path that spirals further inward toward center region  102  of optical delay device  100 . Optical delay device  100  further includes a first single-mode waveguide  102 -A disposed (e.g., located) in center region  102  and providing a third portion of the optical path through the center region. Optical delay device  100  also includes a second coupler  104 -out providing a fourth portion of the optical path that spirals outward from center region  102 . Second coupler  104 -out is coupled (e.g., physically, optically) to a second multi-mode waveguide  106 -out, which provides a fifth portion of the optical path that spirals further outward from center region  102 . First single-mode waveguide  102 -A has a first end and a second end that is opposite to the first end. The first end of first single-mode waveguide  102 -A is coupled (e.g., physically, optically) to first coupler  104 -in and the second end of first single-mode waveguide  102 -A is coupled (e.g., physically, optically) to second coupler  104 -out. Lines with upward pointing arrows correspond to waveguides that spiral inward towards center region  102  (e.g., first multi-mode waveguide  106 -in and first coupler  104 -in) and lines with downward pointing arrows correspond to waveguides that spiral outwards from center region  102  (e.g., second multi-mode waveguide  106 -out and second coupler  104 -out). 
     First single-mode waveguide  102 -A is configured to allow propagation of light in a fundamental optical mode (e.g., TE 0 ). For example, first single-mode waveguide may have a width of 1 micrometer or less. Typically, propagation of light in higher order modes (e.g., optical modes that are not the fundamental optical mode, such as TE 1 , TE 2 , etc.) is prohibited in single-mode waveguides. In contrast, multi-mode waveguide  106 -in or  106 -out is configured to allow light to propagate, along the multi-mode waveguide, in one or more of a plurality of modes including the fundamental optical mode and higher order modes (e.g., light in a higher order mode as well as light in the fundamental optical mode can propagate through the multi-mode waveguide). For example, multi-mode waveguide  106 -in or  106 -out may have a width that is greater than 1 micrometer. In general, for propagation of light having a particular wavelength, a single-mode waveguide has a smaller width compared to a multi-mode waveguide. 
     First multi-mode waveguide  106 -in is configured to receive light, and to propagate the light along an inward spiral toward first coupler  104 -in. First coupler  104 -in is configured to receive the light from the first multi-mode waveguide, and to adiabatically couple the light to first single-mode waveguide  102 -A, which is configured to transmit the light toward second coupler  104 -out while changing the propagation direction of the light. Second coupler is configured to receive the light from first single-mode waveguide and to adiabatically couple the light to second multi-mode waveguide  106 -out, which is configured to propagate the light along an outward spiral to an output of optical delay device  100 . Arrows shown along the waveguides of optical delay device  100  indicate the optical path (e.g., propagation direction, travel direction) of light in optical delay device  100 . 
       FIGS. 1B-1D  are plan views of optical delay device  100  in accordance with some embodiments. As shown in  FIG. 1B , first multi-mode waveguide  106 -in can be coupled to an input multi-mode waveguide  190 -in at an input  191  of optical delay device  100 , and second multi-mode waveguide  106 -out can be coupled to an output multi-mode waveguide  190 -out at an output  192  of optical delay device  100 . As shown, optical delay device  100  is configured to receive light  199  at input  191  and to propagate light  199  through first multi-mode waveguide  106 -in and first coupler  104 -in in inward spirals toward center region  102 , through first single-mode waveguide  102 -A in the center region, and then through second coupler  104 -out and second multi-mode waveguide  106 -out in outward spirals toward output  192 .  FIG. 1B  also shows inset A, which is a zoomed-in view of a portion  106   b  of a second annular region  106  near input  191 . Lines with downward pointing arrows correspond to first multi-mode waveguide  106 -in and lines with upward pointing arrows correspond to second multi-mode waveguide  106 -out. 
       FIG. 1C  shows input  191  having a distance R 1  from a center  101  of optical delay device  100 , and output  192  having a distance R 2  from center  101  of optical delay device  100 . In some embodiments, R 2  is equal to R 1  (or differing by less than 1%).  FIG. 1C  also indicates a junction  193 , at which the inward spirals of optical delay device  100  transition from first multi-mode waveguide  106 -in to first coupler  104 -in, or at which first multi-mode waveguide  106 -in is coupled to first coupler  104 -in. Junction  193  has a distance R 3  from center  101 .  FIG. 1C  also indicates a junction  194 , at which the outward spirals of optical delay device  100  transition from second coupler  104 -out to second multi-mode waveguide  106 -out, or at which second multi-mode waveguide  106 -out is coupled to second coupler  104 -out. Junction  194  has a distance R 4  from center  101 . In some embodiments, R 4  is equal to R 3  (or differing by less than 1%).  FIG. 1C  also indicates a junction  195 , at which the inward spirals of optical delay device  100  transition from first coupler  104 -in to first single-mode waveguide  102 -A, or at which first coupler  104 -in is coupled to first single-mode waveguide  102 -A. Junction  195  has a distance R 5  from center  101 .  FIG. 1C  also indicates a junction  196 , at which the outward spirals of optical delay device  100  transition from first single-mode waveguide  102 -A to second coupler  104 -out, or at which second coupler  104 -out is coupled to first single-mode waveguide  102 -A. Junction  196  has a distance R 6  from center  101 . In some embodiments, R 6  is equal to R 5  (or differing by less than 1%). 
     As shown in  FIG. 1C , first multi-mode waveguide  106 -in includes a first plurality of spiral rounds located between a first outmost spiral portion  112 - 1  and a first inmost spiral portion  112 - 2  of first multi-mode waveguide  106 -in (e.g., spiral rounds located in second annular region  106  and corresponding to first multi-mode waveguide  106 -in). The first outmost spiral portion  112 - 1  has a first radius of curvature that corresponds to distance R 1 . The first inmost spiral portion  112 - 2  has a second radius of curvature that corresponds to distance R 3  and is smaller than the first radius of curvature. Spiral portions that are located between the first outmost spiral portion  112 - 1  and the first inmost spiral portion  112 - 2  have successively decreasing radii that decrease continuously and monotonously from R 1  to R 3 . 
     As shown in  FIG. 1C , first coupler  104 -in includes a second plurality of spiral rounds located between a second outmost spiral portion  112 - 3  and a second inmost spiral portion  112 - 4  of first coupler  104 -in (e.g., spiral rounds located in first annular region  104 , shown in inset B of  FIG. 1E  as spiral rounds with decreasing widths). The second outmost spiral portion  112 - 3  has a third radius of curvature that corresponds to distance R 3 . The second inmost spiral portion  112 - 4  has a fourth radius of curvature that corresponds to distance R 5  and is smaller than the third radius of curvature. Spiral portions that are located between the second outmost spiral portion  112 - 3  and the second inmost spiral portion  112 - 4  have successively decreasing radii that decrease continuously and monotonously from R 3  to R 5 . In some embodiments, the second radius of curvature and the third radius of curvature both correspond to distance R 3 . 
     As shown in  FIG. 1C , second coupler  104 -out includes a third plurality of spiral rounds located between a third inmost spiral portion  112 - 5  and a third outmost spiral portion  112 - 6 . The third inmost spiral portion  112 - 5  has a fifth radius of curvature corresponding to distance R 6 . The third outmost spiral portion  112 - 6  has a sixth radius of curvature corresponding to distance R 4  and is larger than the fifth radius of curvature. Spiral portions that are located between the third inmost spiral portion  112 - 5  and the third outmost spiral portion  112 - 6  have successively increasing radii that increase continuously and monotonously from R 6  to R 4 . In some embodiments, the third radius of curvature of the second outmost spiral portion  112 - 3  and the sixth radius of curvature of the third outmost spiral portion  112 - 6  both correspond to distance R 3 . In some embodiments, the fourth radius of curvature of the second inmost spiral portion  112 - 4  and the fifth radius of curvature of the third inmost spiral portion  112 - 5  both correspond to distance R 5 . 
     As shown in  FIG. 1C , second multi-mode waveguide  160 -out includes a fourth plurality of spiral rounds located between a fourth inmost spiral portion  112 - 7  and a fourth outmost spiral portion  112 - 8  of second multi-mode waveguide  106 -out (e.g., spiral rounds located in second annular region  106  and corresponding to second multi-mode waveguide  106 -out). The fourth inmost spiral portion  112 - 7  has a seventh radius of curvature corresponding to distance R 4 . The fourth outmost spiral portion  112 - 8  has an eighth radius of curvature corresponding to distance R 2  and is larger than the seventh radius of curvature. Spiral portions that are located between the fourth inmost spiral portion  112 - 7  and the fourth outmost spiral portion  112 - 8  have successively increasing radii that increase continuously and monotonously between R 4  and R 2 . In some embodiments, the seventh radius of curvature does not correspond to distance R 4  (e.g., the seventh radius of curvature may be greater than distance R 4 ). 
     First single-mode waveguide  102 -A, shown in  FIG. 1C , includes curved portions having a radius of curvature that is smaller than R 4  and R 5 . 
     In some embodiments, the first plurality of spiral rounds (corresponding to first multi-mode waveguide  106 -in), the second plurality of spiral rounds (corresponding to first coupler  104 -in), the third plurality of spiral rounds (corresponding to second coupler  104 -out), and the fourth plurality of spiral rounds (corresponding to second multi-mode waveguide  106 -out) are concentric spiral rounds. 
     As shown in  FIG. 1D , optical delay device  100  includes center region  102  where first single-mode waveguide  102 -A shown in  FIG. 1C  is located. Optical delay device also includes a first annular region  104  between a virtual circle with a radius corresponding to distance R 5  and a virtual circle with a radius corresponding to distance R 3  that surrounds center region  102 , and a second annular region  106  between a virtual circle with a radius corresponding to distance R 3  and a virtual circle with a radius corresponding to distance R 1  that surrounds first annular region  104  and center region  102 . First coupler  104 -in or at least a portion (e.g., a majority portion, or more than 90 percent) of first coupler  104 -in are located within the first annular region  104 . Likewise, second coupler  104 -out or at least a portion (e.g., a majority portion, or more than 90 percent) of second coupler  104 -out are located within the first annular region  104 . First multi-mode waveguide  106 -in, or at least a portion (e.g., a majority portion, or more than 90%) of first multi-mode waveguide  106 -in are located within the second annular region  106 . Likewise, second multi-mode waveguide  106 -out, or at least a portion (e.g., a majority portion, more than half) of second multi-mode waveguide  106 -out are located within the second annular region  106 . 
     In some embodiments, center region  102  has a diameter that is between 10 micrometers and 500 micrometers (i.e., 10 micrometers&lt;R 5 &lt;500 micrometers). In some embodiments, center region  102  has a diameter that is approximately 300 micrometers (i.e., R 5 ˜300 micrometers). Once R 5  is fixed, other dimensions (e.g., R 3 , R 1 ) can be determined based on required lengths for the corresponding parts (e.g., first coupler  104 -in, and first multimode waveguide  106 -in) of optical delay device  100 . For example, in certain embodiments, R 5  is approximately 100 micrometers, and R 3  is approximately 130 micrometers. In another example, R 5  is approximately 10 micrometers, and R 3  is approximately 100 micrometers. 
       FIG. 1E  provides a zoomed-in view of an area  104   c  of optical delay device  100 , corresponding to area  104   c  of optical delay device  100  shown in  FIG. 1D . Area  104   c  includes center region  102 , first annular region  104 , and portions of second annular region  106  of optical delay device  100  in accordance with some embodiments.  FIG. 1E  also provides a further zoomed view in inset B showing first coupler  104 -in in first annular region  104  having decreasing width as it spirals inward toward center region  102 , and second coupler  104 -out in first annular region  104  having increasing width as it spirals outward from center region  102 . 
       FIG. 1F  is a linearized (or stretched-out) view of optical delay device  100  shown in  FIGS. 1A-1D  and illustrates the dimensions of various portions of optical delay device  100 . As shown in  FIG. 1F , optical delay device  100  provides an optical path having an overall length of L for light  199  propagating through:
         first multi-mode waveguide  106 -in;   first coupler  104 -in;   first single-mode waveguide  102 -A;   second coupler  104 -out; and   second multi-mode waveguide  106 -out.       

     As shown in  FIG. 1F , first multi-mode waveguide  106 -in has a first length L 1 , second multi-mode waveguide  106 -out has a second length L 2 , and first single-mode waveguide  102 -A has a third length L 3  that is much smaller than each of the first length L 1  and the second length L 2  (i.e., L 3 &lt;&lt;L 1 , L 2 ). In some embodiments, the third length L 3  depends on distance R 5  or R 6 . For example, in some embodiments, third length L 3  is between two to four times distance R 5 . Since R 5  can be between 10 micrometers to 500 micrometers, third length L 3  can be between 20 micrometers and 2,000 micrometers. For example, in some embodiments, R 5  is 10 micrometers, L 3  is between 30 micrometers and 40 micrometers. In another example, when R 5  is 500 micrometers, L 3  is between 1,500 micrometers and 2000 micrometers. For example, in some embodiments, third length L 3  is approximately 400 micrometers, and first length L 1  and second length L 2  in combination can constitute a majority (e.g., more than 90%) of the overall optical path length L, which can be in the range of tens of centimeters. In some embodiments, the first length L 1  and the second length L 2  are substantially the same (e.g., differing by less than 1% or 0.001%). 
     In some embodiments, it is desirable for the first multi-mode waveguide  160 -in and the second multi-mode waveguide  160 -out to constitute the majority of the waveguide length. 
     In some embodiments, first coupler  104 -in has a fourth length L 4  and second coupler  104 -out has a fifth length L 5 . In some embodiments, fourth length L 4  is less than first length L 1 , fifth length L 5  is less than second length L 2 , and third length L 3  is smaller than each of fourth length L 4  and fifth length L 5  (i.e., L 3 &lt;L 4 , L 5 ). In some embodiments, fourth length L 4  and fifth length L 5  are substantially the same (e.g., differing by less than 1% or 0.001%). In some embodiments, fourth length L 4  and fifth length L 5  are each greater than 1 millimeter. In some embodiments, fourth length L 4  and fifth length L 5  are approximately 3 millimeters. 
     Equation 1 may be used to determine first length L 1  of first multi-mode waveguide  160 -in and second length L 2  of second multi-mode waveguide  160 -out, assuming that the two multi-mode waveguides are equal in length: 
     
       
         
           
             
               
                 
                   
                     L 
                     
                       1 
                       , 
                       2 
                     
                   
                   = 
                   
                     
                       L 
                       2 
                     
                     - 
                     
                       L 
                       
                         4 
                         , 
                         5 
                       
                     
                     - 
                     
                       
                         L 
                         3 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In Equation 1, L 1,2  is the first length L 1  or second length L 2 , L is the overall length, L 4,5  is the fourth length L 4  or fifth length L 5 , and L 3  is the third length L 3 . 
     For example, for an optical delay device that has an overall optical path length L of 40 centimeters (e.g., L=400 millimeters), a third length L 3  of 0.4 millimeters, a fourth length L 4  of 3 millimeters, and a fifth length L 5  of 3 millimeters, each of the first length L 1  and the second length L 2  would be approximately 197 millimeters (e.g., L 1 , L 2 =19.7 centimeters). In another example, for an optical delay device that has an optical path length L of 80 centimeters (e.g., L=800 millimeters) and all other lengths as described in the previous example, each of the first length L 1  and the second length L 2  would be approximately 397 millimeters (e.g., L 1 , L 2 =39.7 centimeters). In some embodiments, the combined first length L 1  of the first multi-mode waveguide  160 -in and second length L 2  of the second multi-mode waveguide  160 -out constitute at least 95% of the overall length of optical delay device (e.g., L 1 +L 2 ≥95% L). Preferably, the combined first length L 1  of the first multi-mode waveguide  160 -in and second length L 2  of the second multi-mode waveguide  160 -out constitute at least 98% of the total combined waveguide length of optical delay device (e.g., L 1 +L 2 ≥98% L). 
     As shown in  FIG. 1F , first multi-mode waveguide  106 -in has a first width w 1 , second multi-mode waveguide  106 -out has a second width w 2 , and first single-mode waveguide  102 -A has a third width w 3  that is smaller than each of the first width w 1  and the second width w 2  (i.e., w 3 &lt;w 1 , w 2 ). First coupler  104 -in has a width that tapers from the first width w 1  to the third width w 3 . Second coupler  140 -out has a width that tapers from the third width w 3  to the second width w 2 . In some embodiments, the first width w 1  and the second width w 2  are substantially the same (e.g., w 1 ˜w 2 , differing by less than 1%). In some embodiments, the first width w 1  and the second width w 2  are between 3 micrometers and 4 micrometers (e.g., 3 micrometers≤w 1 , w 2 ≤4 micrometers). In some embodiments, the first width w 1  and the second width w 2  are at least 3 micrometers (e.g., w 1 , w 2 ≥3 micrometers). In some embodiments, the first width w 1  and the second width w 2  are at least 1 micrometer (e.g., w 1 , w 2 ≥1 micrometers). In some embodiments, the third width w 3  is between 400 nanometers and 500 nanometers (e.g., 400 nanometers&lt;w 3 &lt;500 nanometers). In some embodiments, the third width w 3  is less than 1 micrometer (e.g., w 3 &lt;1 micrometers). 
     First coupler  104 -in is configured to adiabatically couple light from first multi-mode waveguide  106 -in to first single-mode waveguide  102 -A. Second coupler  104 -out is configured to adiabatically couple light from first single-mode waveguide  102 -A to second multi-mode waveguide  106 -out. For example, one or more of first coupler  104 -in and second coupler  104 -out may have a linear taper profile, a parabolic taper profile, or an exponential taper profile. For example, first coupler  104 -in or second coupler  104 -out can have a length of at least 100 micrometers, a largest tapering angle θ in first coupler  104 -in or second coupler  104 -out is less than 0.3 degrees. 
       FIG. 1G  is a cross-sectional view of optical delay device  100  shown in  FIGS. 1B-1D . Cross-sectional views of the first plurality of spiral rounds corresponding to first multi-mode waveguide  106 -in, the second plurality of spiral rounds corresponding to first coupler  104 -in, the third plurality of spiral rounds corresponding to second coupler  104 -out, the fourth plurality of spiral rounds corresponding to second multi-mode waveguide  106 -out, and first single-mode waveguide  102 -A are shown.  FIG. 1G  also includes insets illustrating top views of various portions of optical delay device  100 . In  FIG. 1G , bonded shapes with a lighter fill pattern correspond to portions of waveguides that are configured to transmit light toward first single-mode waveguide  102 -A, i.e., the first plurality of spiral rounds (e.g.,  106 -in- 1  to  106 -in-n) and the second plurality of spiral rounds (e.g.,  104 -in- 1  to  104 -in-n) corresponding to first multi-mode waveguide  106 -in and first coupler  104 -in, respectively. Likewise, bonded shapes with a darker fill pattern correspond to portions of waveguides that are configured transmit light away from first single-mode waveguide  102 -A, i.e., the third plurality of spiral rounds (e.g.,  104 -out- 1  to  104 -out-n) and the fourth plurality of spiral rounds (e.g.,  106 -out- 1  to  106 -out-n) corresponding to second coupler  104 -out second multi-mode waveguide  106 -out, respectively. Bonded shapes with no fill pattern correspond to the first single-mode waveguide  102 -A. 
     Referring to inset C, which shows a top view of a portion of second annular region  106 , the first plurality of spiral rounds (e.g.,  106 -in- 1  to  106 -in-n) is interleaved with the fourth plurality of spiral rounds (e.g.,  106 -out- 1  to  106 -out-n). Any portion of the first plurality of spiral rounds is separated from any adjacent portion of the fourth plurality of spiral rounds by a distance d 1 , which is designed to be large enough in order to prevent light propagating in the first plurality of spiral rounds from being evanescently coupled into the fourth plurality of spiral rounds. As shown in inset C, waveguide portion  106 -in- 2 , which is a portion of the first plurality of spiral rounds and has the first width w 1 , is located between waveguide portions  106 -out- 1  and  106 -out- 2 , which are portions of the fourth plurality of spiral rounds and have the second width w 2 . A respective sidewall of waveguide portion  106 -in- 2  is spaced apart from a respective sidewall of waveguide portions  106 -out- 1  and  106 -out- 2  by distance d 1 . In some embodiments, distance d 1  is greater than or equal to 1 micrometer (e.g., d 1 ≥1 micrometer). In some embodiments, distance d 1  is greater than or equal to 2 micrometers (e.g., d 1 ≥2 micrometers). In some embodiments, distance d 1  is greater than or equal to 8 micrometers. Thus, any portion of the first plurality of spiral rounds is separated from any adjacent portion of the fourth plurality of spiral rounds by distance d 1 , which is designed to be large enough in order to prevent light propagating in the first plurality of spiral rounds from being evanescently coupled into the fourth plurality of spiral rounds (or vice versa). 
     Referring to inset D, which shows a top view of a portion of first annular region  104 , the second plurality of spiral rounds (e.g.,  104 -in- 1  to  104 -in-n) is interleaved with the third plurality of spiral rounds (e.g.,  104 -out- 1  to  104 -out-n). Any portion of the second plurality of spiral rounds is separated from any adjacent portion of the third plurality of spiral rounds by distance d 2 , which is designed to be large enough in order to prevent light propagating in the second plurality of spiral rounds from being evanescently coupled into the third plurality of spiral rounds (or vice versa). As shown in inset D, waveguide portion  104 -in- 2 , which is a portion of the second plurality of spiral rounds, is located adjacent to and between waveguide portions  104 -out- 2  and  104 -out- 3 , which are portions of the third plurality of spiral rounds. Waveguide portion  104 -out- 2  has a fourth width w 4  and waveguide portion  104 -out- 3  has a fifth width w 5  that is smaller than fourth width w 4 . Fourth width w 4  is smaller than second width w 2  of second multi-mode waveguide  106 -out and fifth width w 5  is larger than third width w 3  of first single-mode waveguide  102 -A (i.e., w 2 &gt;w 4 &gt;w 5 &gt;w 3 ). Waveguide portion  104 -in- 2  has a sixth width w 6  a that is similar to fourth width w 4  and a seventh width w 7  that is substantially equal (e.g., similar) to fifth width w 5 . Sixth width w 6  is smaller than first width w 1  of first multi-mode waveguide  106 -in and seventh width w 7  is larger than third width w 3  of first single-mode waveguide  102 -A. In some embodiments, width w 6  is equal to or less than width w 4  of waveguide portion  104 -out- 2  and width w 7  is equal to or greater than width w 5  of waveguide portion  104 -out- 3 . A respective sidewall of waveguide portion  104 -in- 2  is spaced apart from a respective sidewall of waveguide portions  104 -out- 2  and  104 -out- 3  by distance d 2 . In some embodiments, distance d 2  is greater than 1 micrometer and preferably, greater than or equal to 2 micrometers. In some embodiments, adjacent spiral rounds are separated by a predetermined distance so that light is not evanescently coupled between adjacent spiral rounds. In some embodiments, the predetermined distance is greater than 1 micrometer and preferably, greater than or equal to 2 micrometers. 
     In some embodiments, the first plurality of spiral rounds (e.g.,  106 -in- 1  to  106 -in-n) has a first number of spiral rounds and the second plurality of spiral rounds (e.g.,  104 -in- 1  to  104 -in-n) has a second number of spiral rounds. In some embodiments, the third plurality of spiral rounds (e.g.,  104 -out- 1  to  104 -out-n) has a third number of spiral rounds that corresponds to (e.g., equals, is substantially the same as, differs by no more than 1 spiral round) the second number of spiral rounds. In some embodiments, the fourth plurality of spiral rounds (e.g.,  106 -out- 1  to  106 -out-n) has a fourth number of spiral rounds that corresponds to (e.g., equals, is substantially the same as, differs by no more than 1 spiral round) the first number of spiral rounds. 
     For example, for an optical delay device that has an optical path corresponding to a 5 nanosecond delay, the first number of spiral rounds or the fourth number of spiral rounds is approximately 130. In another example, for an optical delay device that has an optical path corresponding to a 10 nanosecond delay, the first number of spiral rounds or the fourth number of spiral rounds is approximately 190. 
     For example, the second number of spiral rounds or the third number of spiral rounds is approximately 7 spiral rounds. In some embodiments, the second number of spiral rounds or the third number of spiral rounds is independent of the optical path length L of optical delay device  100 . 
     In some embodiments, optical delay device  100  includes at least 10 spiral rounds (e.g., a total number of spiral rounds in the first plurality of spiral rounds, the second plurality of spiral rounds, the third plurality of spiral rounds, and the fourth plurality of spiral rounds is at least 10). In some embodiments, optical delay device  100  includes at least 100 spiral rounds (e.g., the total number of spiral rounds in the first plurality of spiral rounds, the second plurality of spiral rounds, the third plurality of spiral rounds, and the fourth plurality of spiral rounds is at least 100). For example, for an optical delay device that has an optical path corresponding to a 5 nanosecond delay, the total number of spiral rounds is approximately 140, the optical path length L is approximately 40 centimeters, and the optical delay device would have lateral dimensions of approximately 1.7 millimeters by 1.7 millimeters (e.g., a maximum diameter of approximately 0.85 millimeters). 
     In another example, for an optical delay device that has an optical path corresponding to a 10 nanosecond delay, the total number of spiral rounds is approximately 200, the optical path length is approximately 80 centimeters, and the optical delay device would have lateral dimensions of approximately 2.3 millimeters by 2.3 millimeters (e.g., a maximum diameter of approximately 1.15 millimeters). 
     In another example, for an optical delay device that has an optical path length L that is approximately 160 centimeters, the optical delay device would have lateral dimensions of approximately 3.4 millimeters by 3.4 millimeters (e.g., a maximum diameter of approximately 1.7 millimeters). 
     Referring to inset E, which shows a top view of a portion of center region  102 , first single-mode waveguide  102 -A having third width w 3  is shown located in center region  102 . A first end of first single-mode waveguide  102 -A is coupled to waveguide portion  104 -in-n, which is a portion of first coupler  104 -in, and a second end of first single-mode waveguide  102 -A is coupled to waveguide portion  104 -out-n, which is a portion of second coupler  104 -out. As shown, first single-mode waveguide  102 -A includes one or more bends. Although only two bends are shown in inset E, first single-mode waveguide  102 -A may include any number of bends. 
     In some embodiments, as shown, first multi-mode waveguide  106 -in, second multi-mode waveguide  106 -out, first single-mode waveguide  102 -A, first coupler  104 -in, and second coupler  104 -out are formed in a same layer of a material or in a same layer of two or more materials on a substrate  189 . In some embodiments, first multi-mode waveguide  106 -in, second multi-mode waveguide  106 -out, first single-mode waveguide  102 -A, first coupler  104 -in, and second coupler  104 -out have a same height h. In some embodiments, the layer of material has a largely uniform thickness and/or height. 
       FIG. 2A  illustrates an optical delay device  200  and an optical path of light propagating through optical delay device  200  in accordance with some embodiments. Optical delay device  200  includes waveguides (e.g., first multi-mode waveguide  106 -in, second multi-mode waveguide  106 -out, and first single-mode waveguide  102 -A), couplers (e.g., first coupler  104 -in and second coupler  104 -out), and regions (e.g., center region  102 , first annular region  104 , second annular region  106 ) described above with respect to optical delay device  100  in  FIGS. 1A-1C  and details regarding such features are not repeated here for brevity. 
     In addition to the waveguides and couplers described with respect to optical delay device  100 , optical delay device  200  also includes an input coupler  108 -in and an output coupler  108 -out. Input coupler  108 -in is coupled (e.g., physically, optically) to first multi-mode waveguide  106 -in at the location of input  191  and is configured to receive light from input coupler  108 -in and propagate the light toward first coupler  104 -in. Output coupler  108 -out is coupled (e.g., physically, optically) to second multi-mode waveguide  106 -out at the location of output  192  and is configured to propagate light received from second coupler  104 -out toward output coupler  108 -out. 
     In some embodiments, optical delay device may also include an input single-mode waveguide  202 -in that is coupled to input coupler  108 -in at junction  298  (shown in  FIG. 2E ). Input single-mode waveguide  202 -in is configured to receive light and transmit light toward input coupler  108 -in. In some embodiments, optical delay device may also include an output single-mode waveguide  202 -out that is coupled to output coupler  108 -out at junction  299  (shown in  FIG. 2E ). Output single-mode waveguide  202 -out is configured to receive light from output coupler  108 -out and output the light. 
     Lines with upward pointing arrows correspond to waveguides that spiral inward towards center region  102  (e.g., input single-mode waveguide  202 -in, input coupler  108 -in, first multi-mode waveguide  106 -in, and first coupler  104 -in) and lines with downward pointing arrows correspond to waveguides that spiral outwards from center region  102  (e.g., output single-mode waveguide  202 -out, output coupler  108 -out, second multi-mode waveguide  106 -out, and second coupler  104 -out). 
       FIGS. 2B and 2C  are plan views of optical delay device  200  in accordance with some embodiments. In addition to features described above with respect to optical delay device  100 , optical delay device  200  also includes a third annular region  108  that surrounds second annular region  106 , which surrounds first annular region  104 , which surrounds center region  102 . At least a portion (e.g., a majority portion, more than 90%) of each of input coupler  108 -in and output coupler  108 -out are disposed in (e.g., located in) third annular region  108 . 
     In some embodiments, when optical delay device includes input single-mode waveguide  202 -in and output single-mode waveguide  202 -out, at least a portion of each of input single-mode waveguide  202 -in and output single-mode waveguide  202 -out are disposed in (e.g., located in) third annular region  108 . 
     Optical delay device  200  is configured to receive light  199  at input  291  and to propagate light  199  through waveguide portions within third annular region  108  toward second annular region  106 , through second annular region  106  toward first annular region  104 , through first annular region  104  toward center region  102 , through center region  102  toward first annular region  104 , through first annular region toward second annular region  106 , and then through second annular region  106  toward third annular region  108 , and to output light  199  at output  292 . 
       FIG. 2D  shows zoomed-in views of an output region  202   a  of optical delay device  200  and an input region  202   b  of optical delay device  200 , respectively, as shown in  FIG. 2B , in accordance with some embodiments. As shown, input coupler  108 -in includes a portion that has a radius of curvature that is substantially the same as (e.g., same, equal to, differing by less than 5%) the first radius of curvature of first outmost spiral round  112 - 1 . Input coupler  108 -in includes a portion that has a radius of curvature that is substantially the same as (e.g., differing by less than 5%) the eighth radius of curvature of fourth outmost spiral round  112 - 8 . Input coupler  108 -in and output coupler  108 -out each include at least a portion of a spiral round. In some embodiments, input coupler  108 -in may include a fifth plurality of spiral rounds and output coupler  108 -out may include a sixth plurality of spiral rounds. 
       FIG. 2E  is a linearized (or stretched-out) view of optical delay device  200  shown in  FIG. 2B , illustrating the dimensions of various portions of optical delay device  200 . As shown in  FIG. 2E , optical delay device  200  provides an optical path having an overall length A for light  199  propagating through:
         input coupler  108 -in;   first multi-mode waveguide  106 -in;   first coupler  104 -in;   first single-mode waveguide  102 -A;   second coupler  104 -out;   second multi-mode waveguide  106 -out; and   output coupler  108 -out.       

     In some embodiments, when optical delay device  200  includes input single-mode waveguide  202 -in and output single-mode waveguide  202 -out, the optical path of light  199  also includes:
         input single-mode waveguide  202 -in; and   output single-mode waveguide  202 -out.       

     As shown in  FIG. 2E , input coupler  108 -in has a sixth length L 6  and output coupler  108 -out has a seventh length L 7 . In some embodiments, sixth length L 6  and seventh length L 7  are each larger than third length L 3  of first single-mode waveguide  102 -A (i.e., L 3 &lt;&lt;L 6 , L 7 ). In some embodiments, sixth length L 6  and seventh length L 7  are substantially the same (e.g., differing by less than 1% or 0.1%). In some embodiments, sixth length L 6  and seventh length L 7  are each greater than 1 millimeter (e.g., L 6 , L 7 &gt;1 millimeter). In some embodiments, sixth length L 6  and seventh length L 7  are approximately 3 millimeters (e.g., L 6 , L 7 ˜3 millimeters). In some embodiments, when input single-mode waveguide  102 -in and output single-mode waveguide  102 -out are included in optical delay device  200 , the length of input single-mode waveguide  202 -in between input  291  and the input coupler  108 -in is about equal to the length of output single-mode waveguide  202 -out between output  292  and the output coupler  108 -out. In some embodiments, each of the length of input single-mode waveguide  202 -in and the length of output single-mode waveguide  202 -out is less than the length of an outmost spiral round (e.g., each length is less than three quarters of an outmost spiral round). Alternatively, in some embodiments, input single-mode waveguide  102 -in and output single-mode waveguide  102 -out are not included in optical delay device  200 . 
     In some embodiments, input coupler  108 -in includes at least a portion of a spiral turn. In some embodiments, output coupler  108 -out includes at least a portion of a spiral turn. 
     In some embodiments, when optical delay device  200  includes input single-mode waveguide  202 -in and output single-mode waveguide  202 -out, input single-mode waveguide  202 -in has an eighth width w 8  and output single-mode waveguide  202 -out has a ninth width w 9 . Each of eighth width w 8  and a ninth width w 9  is smaller than each of the first width w 1  of first multi-mode waveguide  106 -in and the second width w 2  of second multi-mode waveguide  106 -out (i.e., w 8 , w 9 &lt;w 1 , w 2 ). In some embodiments, eighth width w 8  and a ninth width w 9  are the substantially the same (e.g., differing by less than 5%). In some embodiments, one or more of eighth width w 8  and a ninth width w 9  is equal to third width w 3  of first single-mode waveguide  102 -A (e.g., w 8 , w 9 ˜w 1 ). In some embodiments, eighth width w 8  and a ninth width w 9  are between 400 nanometers and 500 nanometers (e.g., 400 nanometers≤w 8 , w 9 ≤500 nanometers). In some embodiments, eighth width w 8  and a ninth width w 9  are less than 1 micrometer (e.g., w 8 , w 9 ≤1 micrometer). 
     Input coupler  108 -in has a width that tapers from first width w 1  to eighth width w 8 . Output coupler  108 -out has a width that tapers from second width w 2  to ninth width w 9 . 
     Input coupler  108 -in is configured to adiabatically couple light from input single-mode waveguide  202 -in to first multi-mode waveguide  106 -in. Output coupler  108 -out is configured to adiabatically couple light from second multi-mode waveguide  106 -out to fourth single-mode waveguide  202 -out. For example, one or more of input coupler  108 -in and output coupler  108 -out may have a linear taper profile, a parabolic taper profile, or an exponential taper profile. In some cases, a largest tapering angle θ of input coupler  108 -in and output coupler  108 -out is less than 0.3 degrees. 
       FIGS. 3A-3C  are flowcharts illustrating a method of propagating light to create an optical delay in accordance with some embodiments. 
     The method  300  includes ( 310 ) receiving light and ( 312 ) propagating the light (e.g., light  199 ) along an input single-mode waveguide  202 -in toward an input coupler  108 -in and propagating the light along the input coupler toward a first multi-mode waveguide  106 -in. In some embodiments, the method  300  also includes ( 312 - 1 ) propagating the light along a path having a first radius of curvature. 
     The method  300  also includes ( 320 ) propagating the light in the first multi-mode waveguide  106 -in toward a first coupler  104 -in and propagating the light in the first coupler  104 -in toward a first single-mode waveguide  102 -A. The first multi-mode waveguide  106 -in and the first coupler  104 -in provide a first light path that spirals inward toward a center region  102 . The first single-mode waveguide  102 -A is disposed in the center region  102 . 
     In some embodiments, ( 322  shown in  FIG. 3B ) the first light path includes a first plurality of spiral rounds (e.g., spiral rounds  106 -in- 1  to  106 -in-n) corresponding to the first multi-mode waveguide  106 -in and a second plurality of spiral rounds (e.g., spiral rounds  104 -in- 1  to  104 -in-n) corresponding to the first coupler  104 -in. The first plurality of spiral rounds includes a first outmost spiral portion  112 - 1  that has a first radius of curvature and a first inmost spiral portion  112 - 2  that has a second radius of curvature that is smaller than the first radius of curvature. Spiral portions between the first outmost spiral portion and the first inmost spiral portion have successively decreasing radii that decreases continuously and monotonously between the first radius of curvature and the second radius of curvature. The second plurality of spiral rounds includes a second outmost spiral portion  112 - 3  that has a third radius of curvature that is smaller than the second radius of curvature. The second plurality of spiral rounds also includes a second inmost spiral portion  112 - 4  that has a fourth radius of curvature that is smaller than the third radius of curvature. Spiral portions between the second outmost spiral portion and the second inmost spiral portion have successively decreasing radii that decreases continuously and monotonously between the third radius of curvature and the fourth radius of curvature. 
     In some embodiments, ( 322 - 1 ) the first plurality of spiral rounds has a first number of spiral rounds and the second plurality of spiral rounds has a second number of spiral rounds. In some embodiments, the first number of spiral rounds is substantially the same as (e.g., not differing by more than one spiral round) the second number of spiral rounds. In some embodiments, one or more of the first number of spiral rounds and the second number of spiral rounds is more than 100. 
     In some embodiments, ( 322 - 2 ) the third radius of curvature is substantially equal to (e.g., differing by less than 5%) the second radius of curvature. 
     In some embodiments, ( 324 ) propagating the light along the first light path includes propagating the light along the first multi-mode waveguide  106 -in without evanescently coupling the light into the second multi-mode waveguide  106 -out and propagating the light along the first coupler  104 -in without evanescently coupling the light into the second coupler  104 -out. 
     The method  300  also includes ( 330  shown  FIG. 3A ) propagating light along the first single-mode waveguide  102 -A toward a second coupler  104 -out. In some embodiments, the method  300  also includes ( 332 ) propagating the light along a curved path having a radius of curvature that is smaller than each of a fourth radius of curvature and a fifth radius of curvature. 
     The method  300  also includes ( 340 ) propagating the light in the second coupler  104 -out toward a second multi-mode waveguide  106 -out and propagating the light in the second multi-mode waveguide  106 -out. The second coupler  104 -out and the second multi-mode waveguide  106 -out provide a second light path that spirals outward from the center region  102 . 
     In some embodiments, ( 342 ) the second light path includes a third plurality of spiral rounds (e.g.,  104 -out- 1  to  104 -out-n) corresponding to the second coupler  104 -out and a fourth plurality of spiral rounds (e.g.,  106 -out- 1  to  106 -out-n) corresponding to the second multi-mode waveguide  106 -out. The third plurality of spiral rounds includes a third inmost spiral portion  112 - 5  that has a fifth radius of curvature and a third outmost spiral portion  112 - 6  that has a sixth radius of curvature that is larger than the fifth radius of curvature. Spiral portions between the third inmost spiral portion and the third outmost spiral portion have successively increasing radii that increases continuously and monotonously between the fifth radius of curvature and the sixth radius of curvature. The fourth plurality of spiral rounds includes a fourth inmost spiral portion  112 - 7  that has a seventh radius of curvature that is smaller than the sixth radius of curvature. The fourth plurality of spiral rounds also includes a fourth outmost spiral portion  112 - 8  that has an eighth radius of curvature that is larger than the seventh radius of curvature. Spiral portions between the fourth inmost spiral portion and the fourth outmost spiral portion have successively increasing radii that increases continuously and monotonously between the seventh radius of curvature and the eighth radius of curvature. In some embodiments, ( 342 - 1 ) the third plurality of spiral rounds has a third number of spiral rounds that corresponds to (e.g., equals to, differs by less than 2 spiral rounds) the second number of spiral rounds and the fourth plurality of spiral rounds has a fourth number of spiral rounds that corresponds (e.g., equals to, differs by less than 2 spiral rounds) to the first number of spiral rounds. In some embodiments, ( 342 - 2 ) the eighth radius of curvature is substantially equal to (e.g., differing by less than 5%) the first radius of curvature, the seventh radius of curvature is substantially equal to (e.g., differing less than 5%) the second radius of curvature, the sixth radius of curvature is substantially equal to (e.g., differing by less than 5%) the third radius of curvature, and the fifth radius of curvature is substantially equal to (e.g., differing by less than 5%) the fourth radius of curvature. In some embodiments, ( 344 ) propagating light along the second light path includes propagating the light along the second coupler  104 -out without evanescently coupling the light into the first coupler  104 -in and propagating the light along the second multi-mode waveguide  106 -out without evanescently coupling the light into the first multi-mode waveguide  106 -in. 
     The method  300  also includes ( 350 ) outputting the light. In some embodiments, the method also includes ( 352 ) coupling the light from the second multi-mode waveguide  106 -out, through an output coupler  108 -out, to an output single-mode waveguide  202 -out and propagating the light along the output single-mode waveguide  202 -out. In some embodiments, the method  300  also include ( 352 - 1 ) propagating the light along a path having an eighth radius of curvature. 
     The terminology used in the description of the various described embodiments herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used in the description of the various described embodiments and the appended claims, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and/or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will be further understood that the terms “includes,” “including,” “comprises,” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     As used herein, the term “if” is, optionally, construed to mean “when” or “upon” or “in response to determining” or “in response to detecting” or “in accordance with a determination that,” depending on the context. 
     The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the scope of the claims to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. For example, although  FIGS. 1A-1G  illustrate an optical delay device that includes a first multi-mode waveguide, a second multi-mode waveguide, a first single-mode waveguide, a first coupler, and a second coupler, additional waveguides can be added to increase the number spiral rounds, such as described above with respect to  FIGS. 2A-2E . In some embodiments, fewer components may be used. For example, in accordance with some embodiments, an optical device includes a first multi-mode waveguide; a first optical coupler coupled to the first multi-mode waveguide, the first coupler being tapered and curved; and a first single-mode waveguide having a first end coupled to the first optical coupler. Such device may be used in an optical delay device or other optical devices. The embodiments were chosen in order to best explain the principles underlying the claims and their practical applications, to thereby enable others skilled in the art to best use the embodiments with various modifications as are suited to the particular uses contemplated.