Abstract:
A guiding element suitable for integrated optics and transmission in the visible wavelength region includes a plurality of sub-wavelength sized regions in two parallel periodic arrangements embedded within a waveguide layer located on a planar substrate. The dielectric constant of each regions may be the same but different from that of the substrate, the waveguide layer, and the cladding. The periodicity, dimensions and shape of the regions of the periodic arrangement are selected to achieve the desired transmission and guiding of the incident radiation spectrum (e.g., parallel to the two periodic arrangements). A transparent layer with a dielectric constant between the dielectric constant of the periodic arrangement and the dielectric constant of the substrate/cladding provides confinement normal to the substrate.

Description:
BACKGROUND 
     The present invention relates to optical elements, and, more specifically, to an optical waveguide having a plurality of periodic sub-wavelength sized regions or gratings in which the light propagates substantially parallel to the regions or gratings. 
     Guiding elements for electromagnetic radiation on planar substrates have typically been provided by one of two methods. One is by confining the light within a material having a relatively high dielectric constant (“core”), which is surrounded by a material having a lower dielectric constant (“cladding”). Another is by photonic crystals in which a two-dimensional periodic arrangement of materials with high and low dielectric constants creates a photonic bandgap that surrounds a defect line (“waveguide”). Confinement normal to the substrate is either provided by a transparent layer with a dielectric constant between the dielectric constant of the photonic crystal and the dielectric constant of the substrate/cladding or guiding (equals the total internal reflection) in the material of the photonic crystal itself. 
     A problem with the light confining approach is that the core material must have a relatively low absorption in the wavelength range to be transmitted. Furthermore, a relatively high contrast of the dielectric constants between the core and the cladding is required for achieving a relatively high areal integration density of the waveguides. Hence, crystalline semiconductors such as Si, GaAs or InP are typical materials for the core. However, they are not suitable for the visible wavelength range because of their absorption characteristics. 
     A problem with the photonic crystals approach is that the light penetrates into the photonic crystal structure (e.g., a two-dimensional periodic hexagonal array of holes) and decays exponentially. Hence, the material for the photonic crystal must have relatively low absorption in the wavelength range to be transmitted. Because of the required relatively high contrast of the dielectric constants between the materials in the photonic crystal (i.e., holes vs. bulk), crystalline semiconductors such as Si, GaAs or InP are typically used. However, these semiconductor materials are in general not suitable for the visible wavelength range because of their absorption characteristics. Further, the photonic crystal structure extends considerably transverse to the guiding direction (4-5 lattice periods or more), which prevents the realization of relatively dense areal integration. 
     BRIEF SUMMARY 
     According to various embodiments of the invention, a guiding element suitable for integrated optics and transmission in the visible wavelength region includes a plurality of sub-wavelength sized regions in two parallel periodic arrangements embedded within a waveguide located on a planar substrate. The periodicity, dimensions and shape of the regions of the periodic arrangement are selected to achieve the desired transmission and guiding of the incident radiation spectrum (e.g., parallel to the two periodic arrangements). A transparent layer with a dielectric constant between the dielectric constant of the periodic arrangement and the dielectric constant of the substrate/cladding provides confinement normal to the substrate. 
     Additional features and advantages are realized through the techniques of the present invention. Other embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed invention. For a better understanding of the invention with the advantages and the features, refer to the description and to the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features and advantages of the invention are apparent from the following detailed description in conjunction with the accompanying drawings in which: 
         FIG. 1  is a perspective view of a waveguide in accordance with an embodiment of the invention; 
         FIG. 2 , including  FIGS. 2A and 2B , are cross section and top views, respectively, of the waveguide of  FIG. 1 ; 
         FIG. 3 , including  FIGS. 3A and 3B , are cross section and top views, respectively, of a waveguide in accordance with another embodiment of the invention; 
         FIG. 4  is a perspective view of a waveguide in accordance with another embodiment of the invention; 
         FIG. 5  is a top view of the waveguide of  FIG. 4 ; and 
         FIG. 6  is a top view of an alternative embodiment of the waveguide of  FIG. 4 . 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , there illustrated is a perspective view of a waveguide  100  in accordance with an embodiment of the invention. The waveguide  100  includes a substrate  102 , a waveguide layer  104 , and a cladding  106  ( FIGS. 2A and 2B ), which is not shown in  FIG. 1  for clarity. Embedded within the waveguide layer  104  are two parallel periodic linear arrangements  108 ,  110  of sub-wavelength sized regions with a dielectric constant that is the same for each regions but different from that of the surrounding waveguide layer  104 . The periodicity, dimensions and shape of the regions of the periodic linear arrangements  108 ,  110  are selected such that an electromagnetic wave incident on the waveguide structure  100  experiences relatively little transverse loss through the periodic linear arrangements  108 ,  110 . Components of the electromagnetic wave which propagate under an angle with respect to the waveguide layer  104  experience a phase shift of 180 degrees when passing through the regions  108 ,  110  with a selected relatively high dielectric constant compared to space between the regions  108 ,  110  which is filled by the waveguide layer material  104  with a selected relatively low dielectric constant while the amount of optical flux through both the regions  108 ,  110  and the space between the regions  108 ,  110  is approximately the same. Because of destructive interference behind the periodic linear arrangements  108 ,  110 , most of the incident wave is reflected back into the waveguide structure  100 . The guiding in the direction normal to the substrate  102  is achieved by total internal reflection. Hence, the dielectric constant of both the substrate  102  and the cladding  106  have to be lower than the dielectric constant of the material that fills the waveguide layer  104 , for example, with polymers or transparent oxides (e.g., SiO2, Ta2O5, Al2O3) for the waveguide filling. 
     The appropriate shape of the regions  108 ,  110  is strongly dependent on the desired wavelength of operation, the dielectric constants of the involved materials and the geometry of the waveguide  100 . With simulations of Maxwell&#39;s equations, e.g., using a Finite-Difference Time-Domain method, the suitable periodicity, dimensions and shape of the regions  108 ,  110  are tailored for the intended bandwidth and transmission. The width of the waveguide  100  is chosen such that the loss perpendicular to the substrate  102  and the transversal loss through the periodic arrangements  108 ,  110  are both relatively small. A relatively high contrast in the dielectric constant is important, hence, semiconductors such as Si, GaAs or InP are suitable for the regions  108 ,  110  with high dielectric constant and dielectric materials such as SiO2, polymers or air are suitable for the regions  108 ,  110  with low dielectric constant. After an initial value for all parameters (dimensions and shape of the single elements in the periodic arrangements, their periodicity and the waveguide width), the parameters are iteratively altered to achieve the highest transmission through the waveguide  100 , which is calculated with e.g. finite-difference time-domain methods. Alternatively, this optimization can be done using one or a combination of several algorithms, e.g. Monte-Carlo, genetic algorithms and likewise. 
     Referring also to  FIGS. 2 and 3 , the waveguide  100  having periodic sub-wavelength sized regions  108 ,  110  according to the embodiment of  FIG. 1  comprises a layered stack that includes the substrate  102  with a dielectric constant of epsilon1, the waveguide layer  104  with a dielectric constant of epsilon2, the cladding  106  with a dielectric constant of epsilon3, and the two periodic linear arrangements  108 ,  110  of cylindrical elements or regions with a dielectric constant of epsilon4. The dielectric constants fulfill the condition: epsilon4&gt;epsilon2&gt;epsilon1, epsilon3. Thus, the dielectric constant of the regions  108 ,  110  may be the same but different from that of the substrate  102 , waveguide layer  104  and the cladding  106 . In addition to suitable dielectric transparent material (oxides, polymers, etc.), the cladding  106  may be made of air (epsilon3=1) or the same material as that of the substrate  102  (epsilon3=epsilon1).  FIG. 2B  illustrates an arrowhead that depicts the travel of the electromagnetic radiation within the waveguide  104  in a direction parallel to the periodic linear arrangements  108 ,  110 . 
     In an exemplary embodiment, the relevant parameters may be epsilon1=epsilon3=2.16 (corresponding to SiO2), epsilon2=2.9 (corresponding to a polymer), and epsilon4=17.6 (corresponding to Si at a wavelength of lambda=500 nm). The height of the waveguide layer  104  and the periodic structure is 1.3*a, the periodicity is 1.0*a, and the radius of the individual cylindrical elements  108 ,  110  is 0.25*a. The variable “a” may be chosen to scale the structure and the resonant frequency f, for example, to use the calculated resonance at f=0.56*c/a (c=speed of light) to realize a waveguide for a vacuum wavelength of lambda=500 nm, “a” is set to a=0.56*lambda=280 nm. 
     Referring to  FIGS. 3A and 3B , a waveguide  300  having periodic sub-wavelength sized regions according to another embodiment comprises a layered stack made up of a substrate  302  with a dielectric constant of epsilon1, a waveguide layer  304  with a dielectric constant of epsilon2, a cladding  306  with a dielectric constant of epsilon3, and two periodic linear arrangements (structure)  308 ,  310  of cuboid elements with dielectric constant epsilon4 and adjacent planes with dielectric constant epsilon3. The dielectric constants of this embodiment fulfill the condition: epsilon4&gt;epsilon2&gt;epsilon1, epsilon3. The material for the waveguide layer  304  and the regions  308 ,  310  may comprise the same material (epsilon2=epsilon4). In addition to suitable dielectric transparent material (oxides, polymers, etc.), the cladding  306  may comprise air (epsilon3=1) or the same material as that of the substrate  302  (epsilon3=epsilon1).  FIG. 3B  illustrates an arrowhead that depicts the travel of the electromagnetic radiation within the waveguide layer  304  in a direction parallel to the periodic linear arrangements  308 ,  310 . 
     Referring to  FIGS. 4 and 5 , there illustrated is another embodiment of a waveguide  400  in accordance with the invention that changes the propagation direction of the electromagnetic wave using two parallel periodic sub-wavelength sized curved arrangements  406 ,  408  of elements. Similar to the previously described embodiments, the waveguide  400  comprises a layered stack that includes a substrate  402  with a dielectric constant of epsilon1, a waveguide layer  404  with a dielectric constant of epsilon2, a cladding (not shown for clarity) with a dielectric constant of epsilon3, and the two arrangements  406 ,  408  of elements with a dielectric constant of epsilon4. The periodicity, shape (e.g., cylindrical, cuboid, trapezoidal), and size of the elements in the arrangements  406 ,  408  embedded in the waveguide layer  404  may be selected to have the highest transmission at the desired wavelength. The dielectric constants fulfill the condition: epsilon4&gt;epsilon2&gt;epsilon1, epsilon3. In addition to suitable dielectric transparent material (oxides, polymers, etc.), the cladding may comprise air (epsilon3=1) or the same material as the substrate  402  (epsilon3=epsilon1). 
     Referring to the top view of  FIG. 6 , the waveguide  400  according to an alternative embodiment of that in  FIGS. 4-5  changes the propagation direction of the electromagnetic wave using two parallel periodic sub-wavelength sized arrangements  406 ,  408  of elements in a different manner from the waveguide  400  of  FIGS. 4-5 . Specifically, instead of the gradually curved arrangements  406 ,  408  of  FIGS. 4-5 , each of the arrangements  406 ,  408  of the waveguide  400  of  FIG. 6  has two straight sections—one oriented horizontally in  FIG. 6  and the other oriented vertically in  FIG. 6 . The turning of the electromagnetic wave is achieved through two angled reflective elements  410 ,  412  located in the upper right hand corner within the periodic arrangements  406 ,  408 , respectively of  FIG. 6 . As with the elements of the two straight sections, the elements of the angled sections  410 ,  412  have suitable periodicity, shape and size. The optimization of this geometry through simulations of Maxwell&#39;s equations is targeted to have the highest transmission through the waveguide bend at the desired wavelength. The dielectric constants fulfill the condition: epsilon4&gt;epsilon2&gt;epsilon1, epsilon3. In addition to suitable dielectric transparent material (oxides, polymers etc.) the cladding can be made of air (epsilon3=1) or the same material as the substrate (epsilon3=epsilon1). 
     An advantage of the various embodiments of the waveguide of the invention is that the waveguide has considerably less transmission loss than prior art waveguides when the material for the guiding structure absorbs in the wavelength range to be transmitted (e.g., the visible range). This enables the use of crystalline semiconductors such as Si, GaAs or InP also in the visible wavelength range without the need of structuring the waveguide layer which may comprise polymers or transparent oxides. This facilitates the integration of chip-based silicon photonics with the polymer waveguide technology, which is compatible with printed circuit boards. Suitable fluids may also be used as the waveguide material. 
     Another advantage is that the light is guided in the transparent waveguide layer with a lower dielectric constant compared to the guiding elements, thereby allowing the use of a wide range of materials. The transparent layer may be easily deposited (e.g., spin coating of a polymer) and does not require further structuring. Thus, it is relatively straightforward to incorporate nonlinear or gain functionalities in the waveguide. If the guiding elements consist of a doped semiconductor, the elements may also be also used as electrodes to inject charges into the waveguide material or to apply electromagnetic fields (increased gain, electro-optical modulation etc.). The waveguide layer may also comprise a suitable fluid, and the electrodes may then be used to manipulate (e.g., charge, trap, analyze, etc.) nanoparticles that may be contained in the fluid. Still another advantage is the smaller footprint compared to photonic crystal waveguides which allows denser areal integration. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “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. 
     The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated. 
     While the preferred embodiments to the invention have been described, it will be understood that those skilled in the art, both now and in the future, may make various improvements and enhancements which fall within the scope of the claims which follow. These claims should be construed to maintain the proper protection for the invention first described.