Patent Publication Number: US-2022221645-A1

Title: 3d printed waveguides and method based on photonic crystal fibers

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Patent Application No. 63/137,427, filed on Jan. 14, 2021, entitled “3D PRINTED WAVEGUIDES BASED ON PHOTONIC CRYSTAL FIBER DESIGNS FOR COMPLEX FIBER-END PHOTONIC DEVICES,” the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Technical Field 
     Embodiments of the subject matter disclosed herein generally relate to optical waveguide segments based on geometrically unbound photonic crystal fibers, and more particularly, to 3D printing optical waveguide segments, or a combination of such segments, to obtain miniaturized complex devices that implement advanced photonic operations. 
     Discussion of the Background 
     Photonic crystal fibers (PCFs), also known as micro-structured optical fibers or holey fibers, are single-material optical fibers in which an array of microscopic longitudinal hollow channels are made to enable light guidance. The design of the geometry of the longitudinal hollow channels in PCFs is a powerful tool for controlling and tuning the fiber waveguide parameters, such as optical mode size and shape, modal dispersion, birefringence, and nonlinearity. With the development of PCFs, unprecedented fine control of the fiber waveguide parameters across a wider range has become achievable, opening up unique possibilities like supercontinuum generation, fiber chromatic dispersion engineering, and ultrahigh birefringence. Furthermore, PCFs are unique in allowing the creation of hollow-core fibers, which have important applications such as fiber propagation with ultralow nonlinearity or novel gas and optofluidic sensors. 
     Optical waveguides based on PCF designs could be exploited on the small scale as building blocks to create on-fiber complex miniaturized devices that implement advanced photonic operations including, but not limited to, mode conversion, Y-splitting, and polarization splitting. For such devices, the accurate and geometrically unbound manufacture of the designed PCF transverse hole patterns is of paramount importance. Additionally, precise control of the longitudinal variation of the PCF geometry allows the creation of elements such as ultrashort adiabatic tapers or periodic structures, which will pave the way for the development of novel miniaturized photonic devices. 
     As an example of a PCF segment, element  100  is shown in  FIG. 1  having a core  102  through which the light is guided. The core  102  is surrounded by a cladding  104 . Different from the traditional optical fiber where the cladding is just a selected material, different from the core material, the cladding  104  includes, in addition to the selected material, plural holes/channels  106  that extend along the core  102 , but at a distance from the core. These plural holes  106  form a lattice and due to their diameter d, and the distance between them A, also called the lattice spacing, confine the propagating light inside the core  102 . The PCF  100  may also have an air cladding  108 , distributed around the plural holes  106 . The air cladding  108  is a set of tubes that are filled with air. This air cladding is used to create a guiding region in the cladding  104 , to obtain the so-called double clad PCF. Finally, the PCF is covered with a protective coating  110 . 
     However, current PCF fabrication methods have important limitations in manufacturing PCF segments  100  with the desired characteristics. In addition, optically connecting the various PCF segments  100  to each other to create complex miniaturized photonic systems is problematic with the existing methods. This is so because the PCF segments are primarily fabricated by drawing a cylindrical “preform” of cm-scale diameter. Essentially this method takes the preform, i.e., a segment that has a large scale so that the desired channels can be made, and stretch the preform to reduce its diameter to the desired diameter of the PCF segments, which might be in the mm scale. In other words, the preform has a cross-sectional geometry that corresponds to a scaled-up version of the desired final sub-mm-scale geometry of the PCF segment. 
     The current method for creating the preform, however, offer only limited freedom in the design of the preform. Additionally, during the drawing process, the preform geometry is generally not preserved due to material viscosity, gravity, and surface tension effects. Therefore, obtaining the desired PCF cross-sectional structure is not a straightforward process, and can be especially difficult. Specific hole geometries are even impossible to realize [1]. The 3D printing of cm-scale PCF preforms has been recently proposed as a means to increase the freedom of design, but the perturbing effects of drawing still present a major limiting factor that prevents the accurate realization of arbitrary PCF designs [2-4]. Lastly, μm-scale control of the length of the PCF segments and of their longitudinal tapering, which is needed to create miniaturized photonic systems, is very difficult with the existing preform-based methods. 
     Thus, there is a need for a new method and corresponding PCF segments that can be manufactured at a small scale with intricate empty channels to achieve the desired optical properties, without being mechanically limited by the used process. 
     BRIEF SUMMARY OF THE INVENTION 
     According to an embodiment, there is an optical waveguide configured to guide an optical beam. The optical waveguide includes a down-taper element configured to reduce a diameter of an incoming light beam having a random polarization, a dual-core directional coupler element configured to separate the incoming light beam into a horizontally-polarized beam and a vertically-polarized beam, each beam being confined in first and second cores, respectively, and a core fan-out element configured to increase a distance between the horizontally-polarized beam and the vertically-polarized beam upon exit from the core fan-out element. Each of the down-taper element, the dual-core directional coupler element, and the core fan-out element are 3-dimensional, 3D, printed using a single material. 
     According to another embodiment, there is an optical waveguide that includes a body extending along a longitudinal axis X, a core located inside the body and extending along the longitudinal axis X, and plural channels formed in the body, around the core, and configured to confine a light beam into the core. An internal surface of the plural channels has a surface roughness larger than 10 nm as the plural channels are 3D printed. 
     According to yet another embodiment, there is a method for making an optical waveguide configured to guide an optical beam, the method including printing a down-taper element directly on a face of an optical fiber, wherein the down-taper element is configured to reduce a diameter of an incoming light beam having a random polarization, printing a dual-core directional coupler element directly on the down-taper element, wherein the dual-core directional coupler element is configured to separate the incoming light beam into a horizontally-polarized beam and a vertically-polarized beam, each beam being confined in first and second cores, respectively, and printing a core fan-out element directly onto the dual-core directional coupler element, the core fan-out element being configured to increase a distance between the horizontally-polarized beam and the vertically-polarized beam upon exit from the core fan-out element. Each of the down-taper element, the dual-core directional coupler element, and the core fan-out element are 3-dimensional, 3D, printed using a single material. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a schematic diagram of photonic crystal fibers configured to confine light inside a core; 
         FIG. 2  is a flow chart of a method for forming an optical waveguide based on photonic crystal fibers; 
         FIG. 3  illustrates a printed optical waveguide having a solid core surrounded by plural parallel channels; 
         FIG. 4  illustrates a printed optical waveguide having an empty core surrounded by twisted plural channels; 
         FIG. 5  illustrates a printed optical waveguide having an empty core surrounded by plural parallel channels that uses a photonic bandgap hollow-core; 
         FIG. 6  illustrates a printed optical waveguide having an empty core surrounded by semi-elliptical channels; 
         FIG. 7  illustrates a printed optical waveguide having an empty core surrounded by fractal plural channels; 
         FIG. 8  illustrates a printed polarization beam splitter; 
         FIGS. 9A to 9D  show various views of the printed polarization beam splitter of  FIG. 8  and  FIG. 9E  shows the surface roughness of the various channels of the splitter due to the printing process; 
         FIG. 10  illustrates how the various parameters of the printed polarization beam splitter of  FIG. 8  are iteratively modified to achieve a desired geometry; 
         FIG. 11A  shows four different iterations for determining the size of the various channels and cores of the printed polarization beam splitter and  FIG. 11B  shows the final structure of this device; 
         FIG. 12  illustrates the extinction ratios on the two cores of the printed polarization beam splitter, which simultaneously exceed 10 dB on a 100 nm bandwidth centered at around 1550 nm; and 
         FIG. 13  is a flow chart of a method for printing the polarization beam splitter of  FIG. 8 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following description of the embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. The following embodiments are discussed, for simplicity, with regard to a polarization beam splitter PCF segment. However, the embodiments to be discussed next are not limited to such a PCF segment, but may be used to any PCF segment. 
     Reference throughout the specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments. 
     According to an embodiment, a PCF segment is 3D printed, for example, directly on the face of a traditional optical fiber. No drawing step is involved in this process, which makes the manufactured device to have exact dimensions and shapes. Also, the 3D printing method allows the manufacturing of any type, shape, and size of PCF segments. This process allows for in situ single-step fabrication of stacked ultrashort PCF-like segments with different geometries to create all-fiber integrated devices that perform complex optical operations in sub-mm lengths. This approach entirely avoids the drawing process that introduces so many limitations and drawbacks, and offers unprecedented design flexibility and precision in the control of the transverse and longitudinal PCF geometry. 
     The high-resolution 3D printing process can precisely replicate the hole array geometry for virtually any class of manufactured PCF designs known in the art. The method is now discussed with regard to  FIG. 2 . Note that the same method can be applied to any PCF segment. In this embodiment, a 3D printing through two-photon lithography offers sub-μm resolution [5], 3D design freedom, and has been recently exploited in several fields, including micro-optics. In two-photon lithography, a focused near-infrared femtosecond laser beam induces the highly localized polymerization of a photopolymer. The photopolymer used in this embodiment is the IP-Dip photopolymer (Nanoscribe GmbH). This photopolymer provides the highest fabrication resolution among those available from this manufacturer. This photoresist is mainly composed of pentaerythritol triacrylate. The method uses this resist with a 63×1.4 NA microscope objective in a dip-in lithography configuration, in which the microscope objective is directly dipped into the photoresist. 
     For the selected printing configuration, a polymerized voxel has an ellipsoidal shape, with a typical size of about 0.3 μm×1 μm. The writing laser may be a near-infrared femtosecond fiber laser with a pulse duration of about 100 fs, a 780 nm wavelength, and a 80 MHz repetition rate. The system may use galvanometric mirrors for beam steering in the system, which allows a high linear writing speed up to 100 mm/s. The 3D printing process starts in step  200 , by providing an optical fiber. Then, the printing is executed in step  202  layer by layer, directly on a face of the optical fiber, with the transverse (x−y) scanning performed by the galvo system while the axial (z) movement is carried out by a piezo actuator. The distance between the different exposed lines is usually referred to as “hatching” in the case of the x−y plane and as “slicing” for the z axis. In one application, the method uses a 0.3 μm slicing distance, a 0.2 μm hatching distance, a scan speed of 10 mm/s, and a laser power of 13.5 mW. Under these settings, the total fabrication time of the complete structure, which was about 210 μm long, printed on the face of a traditional fiber is around 25 min. 
     Following the completion of the 3D printing in step  202 , the structures are developed in step  204  in the mr-Dev 600 developer. To ensure the complete development of the very high aspect ratio hollow channels of the PCF-like waveguides, e.g., 140 μm long and 0.7 μm in diameter in the case of a dual-core DC PCF segment, a multi-step strategy may be implemented. For example, the process applies in step  204  a 5 min development step to remove the bulk of the unpolymerized photoresist. Then, still in step  204 , two 20 min development steps are applied to remove any remaining unpolymerized photoresist from the hollow channels. Next, in step  206 , the printed segment is immersed in isopropanol for 25 min to remove any remaining developer, and the sample is then allowed to air-dry. After the fabrication, fluorescence confocal laser scanning microscopy was used to assess if the hollow channels were completely developed. The structures can be fabricated either on glass slides using a standard substrate holder, or directly on the end-face of single-mode optical fibers. In one application, to guarantee optical fiber alignment and stability during the 3D printing, the inventors inserted the fiber in a ferrule, and then terminated and connectorized the fiber. Using this approach, the fiber is more stable compared to using a v-groove-based fiber holder. 
     Based on this method, various segments were fabricated as now discussed with regard to  FIGS. 3 to 7 . Scanning electron microscope (SEM) images and the optical guidance of 3D printed PCF-like segments with various solid or hollow-core geometries were obtained to determine the accuracy and flexibility of the proposed method. To prove the potency of this method, an assortment of known PCF designs were manufactured, where these designs are based on radically different guiding mechanisms, core shapes, and sizes. In this regard,  FIG. 3  shows a 3D printed segment  300  having a highly nonlinear (HNL) structure [6], with a core  302  diameter D 1  of 2 μm, an air-filling fraction, which is defined as the ratio of the air hole diameter d to the lattice spacing Δ, equal to 0.75, and a mode field diameter (MFD) of 1.8 μm. Note that the core  302  is a solid material while plural holes  304  are made in the body  301  of the segment, around the solid core  302 , and the plural holes  304  act as the cladding. The cladding also has a portion  306  of a solid material, which is the same material as the core  302 . Thus, the PCF segment  300  is made of a single material, in which plural holes/channels  304  are made by 3D printing. For the HNL PCF segment  300 , the entire core  302 ′ and the channels  304 ′ corresponding to the holes  304  (as shown in the bottom of the figure) extend along straight lines parallel to each other. Only one full channel  304 ′ is shown in the figure for simplicity, but one skilled in the art would understand that all the channels extend along straight lines and are parallel to the core  302 ′. Note that a cross-section of each channel  304 ′ is hexagonal (only one shown for simplicity) in this embodiment. This type of HNL PCF is characterized by a small core (few μm in diameter), with hexagonal holes  302  and a high air-filling fraction. The light guiding mechanism in the core  302  in the HNL PCF  300  is based on the modified total internal reflection (MTIR), which is analogous to that of a standard single-mode fiber, whereby the pattern of holes  304  surrounding the central core  302  acts as an effective cladding  308  with a reduced refractive index. For this embodiment, the HNL PCF segment  300  was directly printed on the end-face of a single-mode fiber  310  with a 6 μm MFD. The large modal mismatch between the optical fiber  310  and the 3D printed segment  300  was compensated for by including a 70-μm-long PCF-like adiabatic taper (not shown) in the 3D printed structure, similar to that described in [7], which resulted in a 1.7 dB insertion loss. 
       FIG. 4  shows a 3D printed, helically twisted, core-less PCF segment  400  with the same geometrical pattern proposed by [8]. More specifically, a central hole  402  is present instead of the solid core in  FIG. 3  and this hole continues with a channel  402 ′. The channel  402 ′ extends through the body  401  of the PCF segment  400  along a straight line, parallel to the longitudinal axis X of the body. The surrounding holes  404 , which act as the cladding, i.e., they confine the light moving along the channel  402 ′ due to their geometry, are symmetrically distributed around the central hole  402 , in a pattern or lattice similar to the segment  300  above. However, different from the segment  300 , the corresponding channels  404 ′ are not extending along straight lines, but rather they twist (rotate) around the channel  402 ′, having a helical path. The twist of the channels  404 ′ around the central channel  402 ′ induces confinement of the light, within the central hole  402 , which is not twisted.  FIG. 4  indicates a region  406  made of the material that forms the body  401 , in which the light is confined. Note that the light is guided within and around the central channel  402 ′, within a cylinder defined by the first set  410  of twisted channels  404 ′. Increasing the twist rate for the channels  404 ′ makes the guided mode more confined and less sensitive to perturbations. Due to the high resolution offered by the 3D printing method, it is possible to achieve a very high twist rate of 10π [rad/mm], corresponding to a twist period of 200 μm, which is higher than any twist rate previously reported in the literature. As expected for this type of PCF design, a well-defined hollow mode confined to the first ring  410  around the central non-twisted hole  402  was obtained, with an MFD of 6.57 μm. The body  401  also includes a solid cladding portion  408 , i.e., a portion of the material that has no holes or channels. The solid cladding portion  408  is formed around the holes  404  and has a circular circumference. Note that while  FIG. 4  shows the entire body  401  being made of a single material, it is possible in another embodiment to use materials with different indices of refraction. 
     Next, the 3D printing method illustrated in  FIG. 2  was used to fabricate a hollow-core PCF-like segment  500 , as shown in  FIG. 5 . The segment  500  is based on a photonic bandgap (PBG) hollow-core fibers while the next embodiment to be discussed is based on hollow-core anti-resonant fibers (HC-ARFs) [9]. In PBG hollow-core fibers, the optical confinement is provided by the PBG mechanism, in which the periodic array of holes in the cladding acts as a photonic crystal that prohibits the propagation of light, which is then trapped in the hollow core. The PBG PCF-like segment  500  is shown in  FIG. 5  having a central hole  502 , which corresponds to a central channel  502 ′, and an array of holes  504 , which correspond to plural channels  504 ′. The light propagates through the empty central channel  502 ′ and is confined by the plural channels  504 ′. In this embodiment, the body  501  is formed of a single material and the plural channels  504 ′ extend parallel to the longitudinal axis X, similar to the central channel  502 ′. The segment  500  in this embodiment has a geometry similar to a commercially available fiber (HC-1060-02, NTK Photonics), and the final structure was found to show the expected light guidance in the central hole, with an MFD of 8.2 μm. 
     In HC-ARFs, the light is confined through a combination of inhibited coupling between the core and the cladding modes and anti-resonant reflection at the air—fiber—material interfaces. The hollow-core region is defined by anti-resonant elements with a negative curvature. The 3D printed HC-ARF element  600 , which is illustrated in  FIG. 6 , replicates a more recent design [10], where the anti-resonant elements  602  are semi-elliptical. Semi-elliptical elements are typically problematic to manufacture using traditional preform drawing-based methods. However, in this embodiment, the semi-elliptical structures  602  can be easily and accurately reproduced by 3D printing.  FIG. 6  shows the semi-elliptical wings  602  extending from a cylindrical body  601 , and defining the coreless region  604 , in which the light is confined. Note that each of the semi-elliptical wings  602  has an empty region/channel  603 . The light guidance in the central hollow core  604  was found to have an MFD of 12.1 μm. Note that hollow-core PBG and HC-ARF segments rely on guiding mechanisms that are very sensitive to the geometric precision of these structures. The optical guidance achieved by the segments  500  and  600  discussed above intrinsically demonstrates that the 3D printed PCF structures are geometrically accurate. 
     Another PCF segment is shown in  FIG. 7 , and this segment  700  shows a solid ring-core  702 , surrounded by a fractal-like pattern of holes, which supports a well-defined annular mode through an MTIR guidance mechanism. The solid core  702  is bordered by a central hole  704  having a diameter d, and a first ring  706  of plural holes  708 . The first ring  706  is surrounded by a second ring  710  of holes. Further rings may be present. The core  702  has an annulus shape and is formed of the same material as the body  701 . A diameter d 1  of the holes of the first ring  706  is mathematically related to a diameter d 2  of the holes of the second ring, and the diameter of the holes of the second ring is mathematically related to a diameter of the holes of the third ring, and so on. In one application the mathematical relation is an arithmetic relation. In another application, the mathematical relation is a geometric relation. For example, the diameter d 1  of the holes of the first ring is half of the diameter d 2  of the holes of the second ring, which encircles the first ring. The channels  704 ′,  708 ′ extend along straight lines, parallel to the longitudinal axis X. These types of structures are attractive because they have been recently shown to support modes that carry an orbital angular momentum. 
     The traditional PCFs manufacturing methods that use a drawing step require a final fiber cleavage step, which can eventually distort the final fiber structure or create non-flat output surfaces. Contrary to this, the 3D printing of PCF-like waveguides  300  to  700  is not affected by this issue because the 3D printing process allows direct production of flat perpendicular or angled output surfaces. 
     The propagation losses through the 3D printed PCF-like waveguides  300  to  700  have been measured for segments of different lengths, up to 350 μm. For a solid-core PCF design with a core size of 12 μm and 
     
       
         
           
             
               
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     the inventors found an attenuation of 0.44 dB/mm at 1070 nm and of 0.79 dB/mm at 1550 nm. For comparison, a pure silica fiber with the same PCF geometry (e.g., ESM 12B, Thorlabs) has an attenuation of about 8 dB/km. The propagation losses of the 3D printed PCF segment closely match the extinction coefficient for the bulk polymerized photoresists that are 0.43 dB/mm at 1070 nm and 0.78 dB/mm at 1550 nm, which is thus the dominant loss contribution. For the 3D printed waveguide with a PBG hollow-core PCF design illustrated in  FIG. 5 , the inventors found an attenuation of 0.3 dB/mm at 1070 nm. This attenuation, while being lower than the intrinsic photopolymerized material losses, is not as low as expected for propagation in a hollow core. This could be explained with the fact that a dominant factor in hollow-core PCF losses is the surface roughness of the core wall. While pure silica hollow-core PCFs have typically a sub-nanometer root mean square (RMS) roughness value, in this case the 3D printing layer-by-layer fabrication introduced a larger RMS roughness of about 30 nm (estimated from SEM images and discussed later with reference to  FIG. 9E ). This roughness value is consistent to what was measured by other groups using the same 3D printing technology and material. 
     Based on the 3D printing method discussed above, an all-fiber integrated PCF polarization beam splitter (PBS) is now discussed with regard to  FIGS. 8 to 9E . With an appropriate configuration [11], the PCFs can have high birefringence, and this has been used in the past to create fiber polarizers based on single-core highly birefringent PCFs. In this embodiment, an on-fiber ultrashort PBS based on a dual-core PCF configuration is introduced, which demonstrates the multiple strengths of the 3D printing approach. Several sub-mm dual-core PCF PBS designs have been proposed over recent years; however, the limitations of current PCF fabrication methods have prevented their successful manufacture. Indeed, the dual-core geometries that have been proposed in the literature to date have all been generally asymmetric, with the inclusion of holes of different sizes and shapes, all factors that add significant complexity to the design of the preform. Moreover, these PCF PBS designs have a sub-mm length that requires a precise control to a sub-μm level to create the desired output polarization split. These combined factors make it difficult to handle and cut segments to the required length from a long fiber that has been drawn. Furthermore, on-fiber integration of the PCF PBS requires rigid coupling to a standard fiber, e.g., by fusion splicing. This coupling also requires a small but critical lateral offset of a few micrometers in order to directly couple just one of the two cores of the dual-core structure. This integration step is also significantly challenging with the traditional PCFs manufactured by fiber drawing. 
       FIG. 8  shows the configuration for a dual-core PCF PBS structure  800  (also called an optical waveguide), the principle of which was theoretically suggested by [12]. The PCF PBS structure  800  is implemented here using the 3D printing technique discussed above. This configuration features a very large bandwidth that includes the telecommunication C-band and an ultrashort length. Note that the ultrashort length is achieved due to the ultrahigh birefringence enabled by the PCF design. The PCF PBS structure  800  is shown in  FIG. 8  being formed on a single-mode optical fiber  310  and includes a down-taper element  810 , a dual-core directional coupler  820 , and a core fan-out element  830 . The dual-core PCF element  820  acts as a directional coupler (DC), and is characterized by a coupling length (CL) for each polarization, which is defined as the waveguide length for which there is a complete transfer of power from one core to the other. In particular, the CLs are given by: 
     
       
         
           
             
               
                 
                   
                     
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     where λ is the wavelength of the light beam, n i   e , and n i   o  are the effective indices for the even and odd mode of the dual-core waveguide, respectively, and i=x, y is either of the two orthogonal polarizations of the light beam. Because of the birefringence introduced by this PCF configuration, the two CLs are different, which allows the structure  800  to act as a PBS for a proper tuning of its design parameters and at specific lengths. It is noted that the length of the dual-core DC PCF element  820  must be simultaneously (1) an odd integer multiple of the CL for one polarization and (2) an even integer multiple of the CL for the other polarization (wherein one of the polarizations is horizontal and the other one is vertical). The shortest possible polarization splitting dual-core DC is obtained when the length of the structure is equal to the CL for one polarization and twice the CL for the other polarization, thus giving a CL ratio (CLR) of 2. 
     Efficient integration of the dual-core DC PCF element  820  on a standard single-mode optical fiber  310  requires the addition of the additional elements  810  and  830  discussed above. By leveraging one of the strengths of the 3D printing approach, the inventors have embedded the dual-core DC PCF element  820  into a more complex photonic structure  800  composed of three sequential waveguiding segments (see  FIG. 8 ): the PCF-like tapered coupler (down-taper)  810 , the dual-core DC birefringent PCF element  820 , and the fan-out segment  830 , which increases the spatial separation of the two cores. The down-taper element  810  allows for efficient and alignment-free coupling of a 6 μm MFD single-mode fiber  310  to one of the two cores  822  and  824  of the birefringent dual-core DC PCF segment  820 . Note that the two cores  822  and  824  are made of solid material in this case. In this regard,  FIGS. 8 and 9A  show how an incoming light beam  802 , that is randomly polarized, is tapered to have a smaller diameter prior to entering one core  822  of the two cores  822  and  824  of the dual-core DC PCF segment  820 .  FIG. 9A  shows that plural channels  812  are formed around a central core  803 , to guide the light beam  802  and reduce its diameter. The plural channels  812  are shown in  FIG. 9A  being not only tilted relative to a longitudinal axis X, but also having a varying diameter, that changes from a first initial large value to a second final narrower value as the light advances along the longitudinal axis X. The plural channels  812  may be arranged in concentric circles in a body  811 , around the core  803 , as shown in the cross-section illustrated in  FIG. 9B . Note that the core  803  is a solid material, which is made of the same material as the body  811 . Also note that an external diameter of the element  810  is larger than an external diameter of the element  820 . Further note that a chamber  814  is formed between the segments  810  and  820 , as shown in  FIG. 9A . 
     In one embodiment, the two cores  822  and  824  of the dual-core DC PCF segment  820  are non-circular, relatively small (1 μm along the minor axis), and positioned close to each other (e.g., 2.4 μm apart) to maximize the core inter-coupling and obtain the shortest possible CLs. A cross-section thorough the dual-core DC PCF segment  820  is illustrated in  FIG. 9C , which shows the two cores being non-circular. This figure also shows the two cores (solid cores) being separated by a central channel  829 . Note that although only one optical beam  802  enters the dual-core DC PCF segment  820 , more precisely, through the core  822 , the arrangement of plural channels  826  around the cores  822  and  824  makes the light to split into two beams  827  and  828  (see  FIG. 9A ), where the two beams have different polarizations, e.g., horizontal and vertical polarizations, respectively. The plural channels  826  are formed in the body  821  of the dual-core DC PCF segment  820 , around the two cores  822  and  824 , so that the randomly polarized optical beam  802  is separated into the horizontal and vertical polarized light beams and these two beams are confined in the first and second cores, respectively. In one embodiment, the channels  826  have a specific arrangement, as shown in  FIG. 9C  (note that channels  842  and  844 , which are adjacent to the cores  822  and  844 , have a smaller diameter than the cores). In this embodiment, the channels  826  extend along the X axis from the chamber  814  up to the element  830 , and they fluidly communicate with the chamber  814 . Note that the same material is used in this embodiment for the body  821  of the dual-core DC PCF segment  820 , the body  811  of the down-taper element  810 , and the body  831  of the fan-out segment  830 , and all the chambers and holes and channels are filled with ambient air. The element  820  may be printed directly on top of the element  810 . 
     The fan-out segment  830 , which is formed directly on top pf the element  820 , spatially increases a distance between the two cores  822  and  824 , using corresponding cores  832  and  834 , up to a 10 μm distance, to facilitate optical measurements of the PBS outputs. The cores  832  and  834  are inclined relative to the longitudinal axis X with a non-zero angle. The cores  832  and  834  are solid for this segment. Each of the cores  832  and  834  is surrounded by a corresponding pattern of channels  833  and  835 , respectively. In one example, each pattern is a hexagon with the solid core located in the center of the hexagon. In this embodiment, the two hexagon patterns  833  and  835  share one or more common channels  836 , as illustrated in  FIG. 9D .  FIG. 9A  shows that a chamber  838  is formed to surround the channels  833  and  835 , and the chamber has one or more open slots  838 A,  838 B, at the top of the chamber. This segment also provides a solution for coupling to other optical fibers (not shown) or for integration into optical chip components by allowing a modal reshape of the two orthogonally polarized output beams  827  and  828 . In the embodiment shown in the figures, an adiabatic transformation from an asymmetric 1×2 μm mode to a 3-μm-diameter round mode is achieved. The working spectral range for the PBS structure  800  was selected to be centered at 1550 nm, thus covering the optical communications C-band. 
     The channels of the various segments  810  to  830  share a same characteristic, i.e., their surface roughness is larger than the surface roughness of an equivalent segment made by drawing. In other words, if two PBS having an identical configuration are compared, one made by drawing and one made by 3D printing as described herein, the surface roughness of the channels for the 3D printed PBS structure is at least one order of magnitude, if not two, larger than the surface roughness of traditional PBS. The same is true for the elements  300  to  700 . For example, the surface roughness for the traditional PBS is 1 nm or less, while the surface roughness for the PBS structure  800  is 10 nm or higher, even 30 nm. The surface roughness is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. The surface roughness of the PBS structure  800  is illustrated in  FIG. 9E  (figure is not at scale) and the surfaces of the various channels are exaggerated for a better visualization. Note that the same structure is true for the devices  300 ,  400 ,  500 ,  600  and  700 .  FIG. 9E  also shows channels  842  and  844 , which are adjacent to the cores  822  and  824 , respectively. 
     A design of an optimal (CLR=2) dual-core DC PCF structure  800 , based uniquely on the calculation of the modal effective indices, and the use of equation (1), cannot account for several aspects of the entire real-world design-to-fabrication process, such as the discretized geometry in the 3D printing system and possible anisotropic shrinkage of the structures during post-exposure development. These effects could make the fabricated PCF-like structure to slightly geometrically deviate from the desired PCF design. Additionally, it is difficult to simulate the role of the transition from the dual-core DC PCF segment  820  to the down-taper segment  810  and the fan-out segment  830 . For this reason, the inventors defined the final design of the complete PCF PBS structure  800  using an iterative approach that involves modal analysis, fabrication, and optical measurements; this iterative approach was enabled by the fast turnover time achievable by the 3D printing. 
     The modal analysis was used to provide reliable guidelines on how the CLs change with size variations of different parts of the structure&#39;s geometry. In each step of this iterative optimization process, a different geometrical parameter of the dual-core PCF segment was selected to be varied, based on its effect on the CLs for the two orthogonal polarizations, and hence on the CLR, as indicated by the numerical calculations with modal analysis. Then, an array of different PBS structures was fabricated on a glass coverslip, where each structure had a different value for the selected geometrical parameter. The initial guess for the dual-core PCF geometry was generated from modal analysis of a geometry very similar to the one presented in [12], while accounting for the refractive index of the used photopolymer (e.g., 1.532 at 1550 nm). The structures in each array were individually coupled with a focused free-space beam, and their output sections were imaged onto an InGaAs infrared camera to extract, for each polarization, the ratio between the powers carried by the two cores. 
       FIG. 10  shows an example of an optimization iteration method. Here, the inventors exploited the dependence of the CLR on the ellipticity of the central hole  829  in the dual-core DC PCF segment  800 . Note that this figure shows the central hole  829  being surrounded by the plural channels  826 . The plural channels  826  are distributed so that there is at least one row  1010  of holes above the central hole  829 , and at least one row  1012  of holes below the central hole  829 . Further, the core  822  is located at one side and the core  824  is located at the opposite side of the central hole  829 , so that the rows  1010 ,  1012 , and the cores  822  and  824  box-in the central hole  829 , and directly influence the light propagation thorough the cores. In one application, the first and second cores  822  and  824  are approximately rectangular and the central hole  829  is elliptical, with the large axes of the cores being parallel to each other and the large axis of the central hole being perpendicular to the large axes of the first and second cores, as shown in  FIG. 10 .  FIG. 10  further shows, consistent with  FIG. 9C , that two elliptical holes  846  and  848  are boxing the two cores  822  and  824 , and the two elliptical holes  846  and  848  have their large axes perpendicular to the large axis of the central hole  829 . 
     To determine the CL for each configuration, the inventors printed an array of structures  800  with four different ellipticities (for the central hole  829 ), and for each ellipticity, three more structures were printed with different longitudinal lengths, increasing from left to right in  FIG. 10 , for a total of 16 structures in the array. By fitting the variation in the ratio of powers carried by the two cores at different lengths, it was possible to extrapolate the two CLs, hence giving the CLR for each different ellipticity. The structure with the geometry that gave a CLR closest to 2 was used as a starting point for the next round of the iteration process, where a different geometrical parameter was changed. In one application, the parameters adjusted during these iterations where: (1) the positions of the three holes (belonging to the row  1010 ) directly above the central hole  829 , (2) the positions of the three holes (belonging to the row  1012 ) directly below the central hole  829 , (3) the ellipticity of the central hole  829 , that separates the two cores  822  and  824 , and (4) the diameters of the 10 holes closest to the cores. 
     From the new fabricated array, a new geometry of the PBS  800  is found, which achieves a CLR even closer to 2. The complete optimization process involved four steps in this embodiment (more or less steps may be used, depending on the number of parameters that are calculated) and the variation of three geometrical parameters, as illustrated in  FIG. 11A , concluding with the optimized design shown in  FIG. 11B , which gave a satisfactory CLR of 1.97. The optimized design has a 140-μm-long dual-core DC PCF segment  820  and the entire PBS has a length of 210 μm. Each step in  FIG. 11A  optimizes a different parameter. 
     The finalized PCF PBS structure  800  was directly printed on the end-face of a single-mode fiber  310 . This PCF PBS structure  800 , which is 3D printed on the fiber  310 , was found to have an extinction ratio of more than 10 dB over a bandwidth of 100 nm and centered around 1550 nm, as shown in  FIG. 12 . Both cores had an extinction ratio above 12.6 dB in the fiber optics communication C-band (1530-1565 nm). At 1550 nm, the PBS structure  800  achieved a minimum extinction ratio of 14.37 dB. The insertion loss at 1550 nm was 1.18 dB for the horizontal polarization and 1.35 dB for the vertical polarization. These insertion losses could be further improved by using a longer down-taper section, to make it adiabatic according to the length-scale criterion. The bandwidth of the PCF PBS structure  800  was very broad (i.e., 150 nm at 10 dB extinction ratio). 
     The above embodiments demonstrate the successful direct 3D printing and optical guidance of a selection of optical waveguides with PCF-like designs that rely on different guiding mechanisms. By successfully fabricating these PCF designs, the 3D printing method has been proven to achieve the fabrication precision and optical quality required for obtaining the final desired cross-sectional PCF geometry considerably faster than current PCF fabrication methods. It was also demonstrated that this method is capable of fabricating PCF-like waveguides with geometries that were previously impossible to manufacture because of their complexity. Specifically, this method succeeded in fabricating the first-ever PCF PBS structure  800 . This PCF PBS is the first example of miniaturized complex structure made of stacked segments with PCF designs, presenting fast longitudinal tapers and precisely controlled lateral offsets. Through the realization of the PCF PBS structure  800 , it was showed how direct 3D printing of PCF-like waveguides allows for a comprehensive optimization process that is significantly faster than current PCF fabrication methods based on the drawing of a preform. 
     Besides demonstrating the strengths of this novel approach, fabricating the PCF PBS structure  800  is significant in itself, as miniaturization and fiber integration of polarization splitting devices are highly desirable features, especially in optical communication systems. Polarizing beam splitters 3D printed on optical fibers have been already reported in the literature [13,14]; however, they are based on diffraction mechanisms, and a further integration of such systems in a fiber optical system could be complicated by their intrinsic free-space output. 
     Based on current high-resolution 3D printing technology, the maximum length that can be achieved for a PCF-like waveguide may be limited. However, it is expected that advances in multi-photon lithography fabrication performance will soon allow for the fabrication of longer segments and at faster speeds. 3D printing fabrication also opens up the possibility to fabricate the bulk parts of the structures that are not used in light propagation (e.g., the outer part of the waveguide cladding) as a wireframe mesh. With this approach, lighter and faster fabrication of robust structures is achievable, potentially leading to the design of unique opto-mechanical properties. Such wireframe structuring is not currently achievable with traditional drawing-based methods. The current propagation losses for 3D printed solid-core PCF-like waveguides are relatively high, and are contributed mainly by the extinction coefficient of the polymerized photoresist, which is significantly higher than that of standard fiber optic materials such as fused silica. It is expected that future improvements in multiphoton polymerizable materials will lead to more favorable propagation losses. 
     Additionally, an approach described recently for high-resolution 3D printing of glass-ceramics could allow the use of less lossy materials, which could also provide better mechanical and thermal properties to the printed PCF segments than what is offered by polymers. The propagation losses of 3D printed hollow-core PCF designs are also relatively high, in this case mainly because of the intrinsic roughness of longitudinal surfaces, which is 2 orders of magnitude higher than typical values for drawn glass PCFs. This roughness is determined by the chosen slicing step-size that, while allowing for a reasonable fabrication time, was nevertheless not optimal for reducing propagation losses. As fabrication speeds and methods improve in the future, smaller slicing steps will become more viable, leading to smoother surfaces and lower propagation losses. Nevertheless, even if the current propagation losses of the 3D printed waveguides based on PCF designs are a little too high for long propagation distances, they are still suitably low enough to achieve unique and well-performing miniaturized photonic devices. It is expected that this novel approach will open up new possibilities to enhance optical fiber end-faces with miniaturized hybrid complex photonic systems based on segments having PCF designs, as well as their easy combination with other 3D-printable refractive, reflective, diffractive, and metamaterial-based elements. These structures may find application in orbital angular momentum, optical tweezers, and quantum technologies. New, more sophisticated fiber-end probes for biomedical applications may also emerge. The inventors also foresee the development of novel fiber end-face sensors that use 3D printed hollow-core PCF designs for bioanalytics and optofluidics. These applications could benefit from new photoresists with low autofluorescence that are being developed. The inclusion of metals and liquids in high-resolution 3D printed structures has already been demonstrated; this technology could be combined with the novel method discussed herein to create multi-material hybrid PCF-like structures. It is also expected that optical and fiber-optic engineers could benefit from the unprecedented possibilities offered by the freedom of design of PCF geometries in several ways: (a) the easier fabrication of previously difficult-to-produce PCF geometries could unlock new designs, including not-yet-proposed designs that were hitherto considered impossible to fabricate; (b) several properties (e.g., mode shape, mode size) of special PCF designs could be experimentally tested without concern for long turnaround times to achieve the desired fiber geometries fabricated, etc. 
     It is also expected that this novel technology could be applied in the development of twisted optical fibers. In addition to the very high twist rates achievable, a finely controlled transverse and/or axial modulation of the twist rate, as is easily achieved by 3D printing, could lead to new optical effects. The 3D printing approach discussed herein that create optical waveguides that exploit the unique properties of PCF designs could integrate/complement other recently proposed methods that share the same printing technology, for creating and coupling optical waveguides and photonic chips. 
     The PBS structure  800  discussed above may be manufactured based on a method as now discussed. The method may include a step  1300  of printing a down-taper element directly on a face of an optical fiber, wherein the down-taper element is configured to reduce a diameter of an incoming light beam having a random polarization, a step  1302  of printing a dual-core directional coupler element directly on the down-taper element, wherein the dual-core directional coupler element is configured to separate the incoming light beam into a horizontally-polarized beam and a vertically-polarized beam, each beam being confined in first and second cores, respectively, and a step  1304  of printing a core fan-out element directly onto the dual-core directional coupler element, the core fan-out element being configured to increase a distance between the horizontally-polarized beam and the vertically-polarized beam upon exit from the core fan-out element. Each of the down-taper element, the dual-core directional coupler element, and the core fan-out element are 3-dimensional, 3D, printed using a single material. 
     A surface roughness of interior channels is larger than 10 nm due to the printing. The method may further include a step of printing a body of the dual-core directional coupler element to extend along a longitudinal axis, a step of forming first and second cores in the body, the first and second cores extending along the longitudinal axis, a step of forming a central passage in the body, between the first and second cores, the central passage extending along the longitudinal axis, and a step of forming plural passages in the body, around the first and second cores, the plural passages extending along the longitudinal axis. In one application, the first and second cores are approximately rectangular. The first core hosts the horizontally-polarized beam and the second core hosts the vertically-polarized beam. 
     The disclosed embodiments provide an optical waveguide that is manufactured by 3D printing, to have plural channels extending through a body of the optical waveguide. It should be understood that this description is not intended to limit the invention. On the contrary, the embodiments are intended to cover alternatives, modifications and equivalents, which are included in the spirit and scope of the invention as defined by the appended claims. Further, in the detailed description of the embodiments, numerous specific details are set forth in order to provide a comprehensive understanding of the claimed invention. However, one skilled in the art would understand that various embodiments may be practiced without such specific details. 
     Although the features and elements of the present embodiments are described in the embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the embodiments or in various combinations with or without other features and elements disclosed herein. 
     This written description uses examples of the subject matter disclosed to enable any person skilled in the art to practice the same, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims. 
     REFERENCES 
     The entire content of all the publications listed herein is incorporated by reference in this patent application.
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