Patent Publication Number: US-7218809-B2

Title: Integrated planar composite coupling structures for bi-directional light beam transformation between a small mode size waveguide and a large mode size waveguide

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 10/083,674, filed Oct. 19, 2001 now abandoned, and this application also claims the benefit of U.S. Provisional Application 60/242,213, filed Oct. 20, 2000, entitled, MULTIPORT INTEGRATED COUPLER FOR BI-DIRECTIONAL LIGHT BEAM TRANSFORMATION BETWEEN A SMALL SIZE WAVEGUIDE AND A LARGE SIZE WAVEGUIDE, the entire contents of which applications are hereby incorporated by reference in their entirety as if set forth in full in this document. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates, in general, to optical structures that enable optical beam transformation between a large-mode-size waveguide and a small-mode-size waveguide, and methods of making the same. In particular, the present invention relates to methods for transforming the optical mode between a photonic device and one or more optical fibers. The present invention also relates, in particular, to the integrated fabrication of such structures on a module platform or the photonic device, their connections with one or more input/output optical fibers. 
     2. Description of the Related Art 
     The current strong demand for bandwidth over the Internet has resulted in great demand for photonic device components in optical communications and data or information processing. These device components include fiber optics, non-linear crystal optics, and integrated optics in such material systems as dielectrics, polymers, optical crystals, and semiconductors (also called electro-optic or optoelectronic systems). 
     Optical-crystal and dielectric-material-based discrete optical components such as LiNbO 3 -based-modulators, glass ion-exchange-based optical power splitters and flame-hydrolysis-deposited silica-on-silicon multiplexers/demultiplexers, can play certain roles, but their sizes are generally large and their functions are limited. Hence, in the long run, it is very unlikely that they can compete with waveguide based photonic devices such as Photonic Integrated Circuits (PICs), which can be made very small and also multifunctional with high packing density similar to today&#39;s large scale integration of microelectronic circuits. 
     Waveguides are used for inputting and out putting light energy for such photonic devices to optical fibers. The input/output waveguides in a photonic device are typically made up of dielectric or semiconductor materials. A photonic device may contain one or more such input/output waveguides. Unless otherwise specified, such input/output optical waveguides will be referred to as device waveguides below. 
     In spite of the promise of waveguide based photonic devices, in general, and photonic integrated circuits, in particular, however, several challenges remain. One challenge is at the optical interface. Light must be efficiently coupled, with high precision and stability, between drastically dissimilar components and materials, in a cost effective, manufacturable way. There are several issues that need to be addressed with respect to this challenge, including the following:
         (1) The drastically different spot or mode profile in terms of size and symmetry between a fiber and a photonic device waveguide.   (2) The difficulty in the alignment of a fiber and a photonic device waveguide, as well as of any other intermediate component such as a ball lens.   (3) The difficulty of coupling multiple fibers to a photonic device with multiple device waveguides efficiently in a cost effective way.       

     Prior-art efforts addressing each of these challenges are summarized below. 
     (1) Prior Art in Dealing with the Mode-Size Conversion Issue 
     With regard to mode-size conversion, in order to ensure single-mode operation (as required for high-speed, large-capacity optical signal manipulation), the dimension of a device waveguide is typically one order of magnitude less than that of a silica fiber waveguide. The result is a substantial mode-field mismatch between these two waveguides. As shown in  FIGS. 1(   a ) and ( b ), for optimal performance, the mode profile of a single-mode optical fiber  110  is circular, and its size is generally about 5 to 10 μm in diameter, whereas the mode profile of a photonic device waveguide  120  is elliptical and its dimension is typically less than 1 to 3 μm—as small as 0.2 μm for high-density photonic integrated circuits. 
     Various methods are currently used for transforming the optical modes between an optical fiber and a device waveguide. These methods are broadly summarized below. 
     Method 1—Butt-Coupling Method 
     The simplest coupling arrangement is a direct butt-joining between a fiber and a semiconductor laser (or other semiconductor waveguide) as shown in  FIG. 2 . Since light is only required to couple in one direction—i.e., from the laser  210  to the fiber  220 —one can adjust the gap distance  230  to allow the divergent cone of light  240  to expand and roughly match the size of a fiber core  250 . One problem with this approach is the relatively low coupling efficiency caused by the large divergence angle and the fact that a fiber can only capture and guide a narrower cone of light within a small capturing angle. As a result, the typical coupling efficiency for a direct butt-joining is less than 5–30% depending on the size of the device waveguide. In spite of the low coupling efficiency, this technique is being explored by NEC of Japan (among others) for low-cost mass packaging of transceivers because this technique requires the fewest of components, which minimizes component cost. (Kenji Yamauchi et al., “Automated mass production line for optical module using passive alignment technique,” 50th Electronic Components and Technology Conference, May 21–24, 2000, Las Vegas, Nev., USA). 
     Method 2—Lensed Fiber or Microlens Method 
     A method improved over the direct butt-joining technique is to make the fiber end into a lens  310  (lensed fiber) as shown in  FIG. 3  so that more light can be captured by the fiber. (Kazuhiko Kurata, “Mass production techniques for optical modules,” 48th Electronic Components and Technology Conference, May 27–28, 1998, Seattle, Wash., USA). Another improved method uses a separate lens  410  placed in the gap  420  as shown in  FIG. 4 . Various lenses have been used, including glass ball lenses and GRIN (graded refractive index) rod lenses, as well as aspheric injection molded plastic lenses. (Keith Anderson, “Design and manufacturability issues of a co-packaged DFB/MZ module,” 49th Electronic Components and Technology Conference, Jun. 2–4, 1999, San Diego, Calif., USA). With these lenses, the coupling efficiency is increased to 50% to 70% for device waveguide mode about 2 μm in size. 
     Method 3—Cylindrical Lenses Method 
     Besides geometric discontinuities between a device waveguide and an optical fiber, the imperfect coupling efficiency results also in part from the elliptical shape of the light cone emerging from a typical device waveguide such as that from a Fabry-Perot cavity semiconductor laser, which causes a non-perfect match with the circular mode pattern of the fiber. A method to correct for such elliptical or astigmatic beam shape is shown in  FIG. 5 , which illustrates the use of a combination of two perpendicular cylindrical lenses  510  and  520  of different focusing powers along the vertical lens ( 510 ) and lateral lens ( 520 ) directions, which can circularize the elliptical beam and theoretically increase the coupling efficiency to about 85% for a typical semiconductor laser with a mode size of about 1 μm (vertical) by 3 μm (horizontal). (Sun-Yuan Huang et al., “High coupling optical design for laser diodes with large aspect ratio,” 49th Electronic Components and Technology Conference, Jun. 2–4, 1999, San Diego, Calif., USA). 
     Method 4—Cylindrical Lensed Fiber Method 
     A cylindrical lensed fiber (CLF) has also been used. (Soon Jang “Automation manufacturing systems technology for opto-electronic device packaging” 50th Electronic Components and Technology Conference, May 21–24, 2000, Las Vegas, Nev., USA). Although the coupling efficiency with the use of a CLF can be high (.about. 90%), the cost is also high because a CLF is not easy to make, and achieving high coupling efficiency also requires difficult labour-intensive alignment, as a practical matter. 
     Method 5—Laterally Tapered Rectangular Waveguide on Top of a Large Rectangular Waveguide Method 
     Another approach to mode-size conversion is to place a laterally tapered rectangular waveguide on a large mode size rectangular waveguide, where light coupling between the top and the bottom waveguide occurs as a result of the top lateral taper. This method can serve the function of mode-size conversion in both the vertical and horizontal directions, but it is not well accepted in practice due to the difficulty in integrating such a structure with a device waveguide and also the cost of manufacturing such a structure.  FIG. 6  shows such a polymer based waveguide structure  610  inserted between a semiconductor laser  620  and a fiber  630 . (D. J. Goodwill et al., “Polymer tapered waveguides and flip-chip solder bonding as compatible technologies for efficient OEIC coupling,” 47th Electronic Components and Technology Conference (ECTC), May 18–21, 1997, San Jose, Calif., USA). One difficulty in this approach is the integration of such a tapered waveguide  610  made of polymer with a laser  620  made of semiconductor material due to the large difference in their coefficients of thermal expansion and mechanical stabilities. In the case where such a structure is made of the same semiconductor material as that of the semiconductor laser, it would require the epitaxial growth of a large bottom waveguide layer and the cost will be high. 
     Method 6—Vertically Tapered Down Rectangular Waveguide Method 
     To enable easy integration, vertically tapered down semiconductor waveguide spot-size converters that squeeze the guided optical mode into the cladding have been integrated with semiconductor lasers. (Aaron E. Bond et al., “High speed packaged electroabsorption modulators for optical communications” 50th Electronic Components and Technology Conference, May 21–24, 2000, Las Vegas, Nev., USA; Y. Inaba et al., “Multiquantum-well lasers with tapered active stripe for direct coupling to single mode fiber” IEEE Photonics Technology Letters, Vol. 6, pp. 722, 1997; M. Kitamura, “Method of making a tapered thickness waveguide integrated semiconductor laser,” U.S. Pat. No. 5,792,674, issued Aug. 11, 1998; Jeon et al., “Laser diode device having a substantially circular light output beam and a method of forming a tapered section in a semiconductor device to provide for a reproducible mode profile of the output beam,” U.S. Pat. No. 6,052,397, issued Apr. 18, 2000). Although this method can enlarge the optical mode in the vertical direction, Problems associated with such structures include the required length of the tapered down structure that will lead to additional light propagation loss and the additional expense of III–V semiconductor materials. 
     2) Costs of Photonic Device Module Connection with Optical Fibers [Problem #2] 
     While the above-mentioned methods may be employed to transfer optical energy somewhat efficiently between an optical fiber and a device waveguide of about 2 μm in size, the approaches of these methods are costly. Typically, an enclosure is used to house the device, the discrete mode-transferring element (e.g. a ball lens), and the optical fiber, thereby forming a packaged module. To align the device waveguide to the fiber and the mode transferring module, most photonic device manufacturers are still performing manual alignment under a microscope because of the very disparate nature of the components, their high price and low product volumes. Such a process is not well suited to high-volume, low-cost production. 
     Existing techniques for fixing a fiber (and lens) in position with respect to a rectangular semiconductor waveguide include epoxy curing, soldering, mechanical fixture, and laser welding. In order to reduce the need for manual placement/alignment and fixing in the packaging process, efforts have been focused on automating the fixing process. For example, Newport, JDS-Uniphase and NEC are developing automatic parts-handling and assembling procedures using machine vision combined with micro-stages or micro-robots to achieve sub-micron precision (Soon Jang, “Automation manufacturing systems technology for opto-electronic device packaging,” 50th Electronic Components and Technology Conference, May 21–24, 2000, Las Vegas, Nev., USA; Peter Mueller and Bernd Valk, “Automated fiber attachment for 980 nm pump module,” 50th Electronic Components and Technology Conference, May 21–24, 2000, Las Vegas, Nev., USA; Kazuhiko Kurata, “Mass production techniques for optical modules,” 48th Electronic Components and Technology Conference, May 27–28, 1998, Seattle, Wash., USA). 
     At the same time, the concept of a silicon optical bench (SiOB) on which V-grooves are wet-etched to guide the mounting or placement of photonic components including fibers, lenses, and even semiconductor chips has been well accepted; SiOBs are disclosed in several U.S. patents (e.g., Murphy, “Fiber-waveguide self alignment coupler,” U.S. Pat. No. 4,639,074, issued Jan. 27, 1987; Albares et al,. “Optical fiber-to-channel waveguide coupler,” U.S. Pat. No. 4,930,854, issued Jun. 5, 1990; Benzoni et al., “Single in-line optical package,” U.S. Pat. No. 5,337,398, issued Aug. 9, 1994; Francis et al., “Waveguide coupler,” U.S. Pat. No. 5,552,092, issued Sep. 3, 1996; Harpin et al., “Assembly of an optical component and an optical waveguide,” U.S. Pat. No. 5,881,190, issued Mar. 9, 1999; Roff, “Package for an optoelectronic device,” U.S. Pat. No. 5,937,124, issued Aug. 10, 1999). It is very likely that high precision automation will be combined with silicon V-groove technology to produce fiber-pigtailed or fiber-connectable photonic devices. The V-groove technology, however, still needs some alignment procedure. 
     In spite of the above-mentioned approaches, the current packaging cost is still very high. For example, about 70 to 80% of the total cost of any fiber-pigtailed III–V optoelectronic module such as an optical transceiver is due to its packaging. Moreover, most of the prior art has been aimed at solving the semiconductor-laser-to-fiber coupling problem, which is one-directional. For future dense wavelength division multiplexing (DWDM) optical communication systems, bidirectional multi-port devices like M×N switches will be in large demand, and the prior art is not able to provide an adequate solution. 
     (3) Difficulty of Current Methods for Multiple Fiber Connections [Problem #3] 
     The current methods are somewhat adequate for large photonic device with one input/output waveguide, they generally become difficult when more than one input/output and fibers are involved. This is because the yield for the alignment procedures referred to above rapidly decreases as the number of input and output fibers increases. This yield reduction can seriously limit the application of such coupling and packaging techniques to high-density photonic integrated circuits, for which tens to hundreds of input and output fibers are expected to be connected to a single photonic chip. 
     The main criteria needed for optical mode transferring methods and devices to achieve a cost-effective and efficient optical energy transfer between a device waveguide and one or more optical fibers can be more specifically described as follows:
         (i) The methods and devices should be able to achieve mode size transformation from about 10 μm down to about 2 μm (for λ=1.55 μm) or in the reverse direction for typical waveguide devices.   (ii) The methods and devices should be able to achieve mode size transfer from about 10 μm to below 1 μm (for λ=1.55 μm) or in the reverse direction for more challenging waveguide devices such as high-density semiconductor photonic integrated circuit.   (iii) The methods and devices should be capable of achieving self-alignment between the photonic device and the optical fibers or other intermediate beam transferring elements. Self-alignment lends itself to low-cost manufacturing. It also allows cost-effective coupling between a photonic device and more than one optical fibers.   (iv) The methods and devices should have low optical reflection and absorption losses between the photonic device and the optical fibers.   (v) The methods and devices should have the flexibility of transferring the vertical and lateral mode size separately. This allows it to correct for beam astigmatism in the device waveguide mode.   (vi) The methods and devices should have high yield and low fabrication costs.       

     The current mode transformation methods can not adequately achieve the majority of criteria (i)–(vi). For example, the ball lens method can achieve (i) and (iv) but not (ii), (iii), (v) and (vi) 
     What is still needed in the field, therefore, are devices and methods for transferring the mode size between photonic device and one or more optical fibers that satisfy some or a majority of criteria (i) to (vi) above. 
     The present invention described herein overcomes the various difficulties encountered by the previous methods by the use of new optical structures referred to as integrated composite coupling structures (ICCS). The mode transformation device or mode transformer is referred to as an Integrated Composite Mode Transformer (ICMT). With the use of the new optical structures according to the present invention, disadvantages associated with prior methods are addressed. 
     BRIEF SUMMARY OF THE INVENTION 
     The integrated composite coupling structures of the present invention provide an integrated approach to optical mode transformation. The integrated approach allows fabrication of a large number of couplers using established processes used frequently in electronics industries and photonic integrated circuit industries, thereby resulting in lower fabrication cost. The composite optical structures allow the beam to be transformed differently in the vertical and lateral directions. 
     An embodiment of the present invention provides a planar optical structure that can transform the vertical mode size between a photonic device and an optical fiber. The size of the optical structure is small relative to the optical fiber diameter, which reduces alignment sensitivity. In one aspect of the present invention, the vertical mode transformation is achieved via the use of a micro vertical graded refractive index (μ-VGRIN) structure that is capable of beam size transformation down to below λ/1.5 (or 1 μm for λ=1.5 μm). Moreover, the μ-VGRIN structure can be fabricated according to the present invention using established process technology such as Jon-Assisted-Deposition with low cost and low optical loss. 
     In another aspect of the present invention, a composite structure is formed by combining a μ-VGRIN structure with a horizontal taper structure to achieve separate transformation of the horizontal and vertical beam mode sizes, thereby allowing 2-D beam transformation capable of astigmatic beam size correction. The composite structure can include a cascaded or concurrent geometry. 
     In yet another aspect of the present invention, an integrated composite coupling structure or its composite variants is further integrated to an alignment V-groove structure for fiber on one side and a alignment platform for photonic chip on the other side to achieve self-alignment between the photonic device, the optical fiber and the coupling structure (or its composite variants). 
     In yet another aspect of the present invention, μ-VGRIN structure is combined with a micro-lateral graded refractive index (μ-LGRIN) structure to achieve separate transformation of the vertical and lateral beam sizes. The μ-LGRIN structure can be fabricated with low cost and large quantity using UV-imprinting process used in the photonic industry. The composite μ-VGRIN and μ-LGRIN structure can include a cascaded or concurrent geometry. 
     In yet another aspect of the present invention, a high-refractive-index-contrast vertical sharp taper (HRC-VST) and dielectric structure is used for which the relative refractive index of the vertical taper material is substantially higher than that of the dielectric material. The high index contrast allows beam transformation down to about λ/15 (or 0.1 μm for λ=1.5 μm) when the taper is made up of silicon and the dielectric is made up of glass. The HRC-VST can be fabricated according to the present invention using established processes in the electronics and photonics industries with low costs. 
     In yet another aspect of the present invention, a composite structure is formed by combining an HRC-VST structure with either a high-refractive-index-contrast laterally gradual taper (HRC-LGT) or a μ-LGRIN structure to achieve separate transformation of the vertical and lateral beam sizes thereby allowing 2-D transformations capable of astigmatic beam size correction. The composite structure can include a cascaded or concurrent geometry. 
     In yet another aspect of the present invention, a HRC-VST structure or a composite variant is further integrated to a V-groove structure for fiber on one side and an alignment platform for photonic chip on the other side to achieve self-alignment between the photonic device, the optical fiber and the HRC-VST structure (or its composite variants). 
     In yet another aspect of the present invention, the sharp taper is in the lateral/horizontal direction, resulting in a high-refractive-index-contrast lateral sharp taper (HRC-LST) which provide beam transformation in the lateral/horizontal direction. 
     In yet another aspect of the present invention, a plurality of μ-GRIN structures, sharp taper structures, gradual taper structures and their composite variants are further integrated to a V-groove structure for fiber on one side and an alignment platform for photonic chip on the other side to achieve self-aligned beam transformation between a photonic chip device and more than one. optical fibers. 
     In yet another aspect of the present invention, a μ-GRIN structure or a sharp taper structure, or one of their composite variants is fabricated directly on a photonic device chip. 
     A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  illustrates the mode profile of a typical single-mode fiber. 
         FIG. 1B  illustrates the mode profile of a typical single mode III–V compound semiconductor channel waveguide. 
         FIG. 2  shows a prior-art system in which light is transmitted directly from a semiconductor laser to a single mode optical fiber. 
         FIG. 3  shows a prior-art system in which light is transmitted from a semiconductor laser into a lensed optical fiber. 
         FIG. 4  shows a prior-art system in which light is transmitted via a lens from a semiconductor laser into an optical fiber. 
         FIG. 5  shows side and top views of a prior-art system in which light is transmitted via two perpendicular cylindrical lenses of different focusing powers from a semiconductor laser into an optical fiber. 
         FIG. 6  shows a prior-art system in which light is transmitted via a tapered polymer waveguide from a semiconductor laser into an optical fiber. 
         FIG. 7  shows an optical interface between two media, illustrating the principles of reflection, refraction, the critical angle, and total internal reflection. 
         FIG. 8  illustrates a principle of light guiding in a step-index optical fiber or waveguide. 
         FIG. 9  illustrates a principle of light guiding in a GRIN optical fiber or waveguide. 
         FIG. 10  illustrates a principle of approximating a continuous graded refractive index change by using a series of small refractive index steps. 
         FIG. 11A  illustrates a planar silicon waveguide film. 
         FIGS. 11B–G  show a profile of the propagating mode of a silicon waveguide film with a thickness of 0.4 micron, 0.3 micron, 0.2 micron, 0.1 micron, 0.05 micron, and 0.01 micron, respectively. 
         FIG. 12  shows the mode size of the propagating mode of a silicon waveguide as a function of the waveguide core thickness. 
         FIG. 13  is a side view of a vertically down-tapered basic mode transformation module according to the present invention. 
         FIG. 14  is a result of a computer simulation of light propagation in the module of  FIG. 13 . 
         FIGS. 15A–C  illustrates exemplary fabrication steps for the module of  FIG. 13 . 
         FIG. 16  is a top view of a horizontally/laterally down-tapered basic mode transformation module according to the present invention. 
         FIG. 17  is a result of a computer simulation of light propagation in the module of  FIG. 16 . 
         FIGS. 18A–D  illustrates exemplary fabrication steps for the module of  FIG. 16 . 
         FIG. 19  is a top view of a horizontally/laterally up-tapered basic mode transformation module according to the present invention. 
         FIG. 20  is a result of a computer simulation of light propagation in the module of  FIG. 19 . 
         FIGS. 21A–E  illustrates exemplary fabrication steps for the module of  FIG. 19 . 
         FIGS. 22A–B  are, respectively, a top and a side view of a vertically down-tapered, horizontally/laterally up-tapered basic mode transformation module according to the present invention. 
         FIG. 23  is a result of a computer simulation of light propagation in the module of  FIG. 22 . 
         FIGS. 24A–F  illustrates exemplary fabrication steps for the module of  FIG. 22 . 
         FIG. 25  is a perspective view of a glass/polymer waveguide module with a step refractive index in the vertical and horizontal/lateral direction according to the present invention. 
         FIG. 26  is a result of a computer simulation of light propagation in the module of  FIG. 25 . 
         FIGS. 27A–E  illustrates exemplary fabrication steps for the module of  FIG. 25 . 
         FIG. 28  is a perspective view of a glass/polymer waveguide module with a step refractive index in the horizontal/lateral direction and a graded refractive index in the vertical direction according to the present invention. 
         FIG. 29  is a result of a computer simulation of light propagation in the module of  FIG. 28 . 
         FIGS. 30A–D  illustrates exemplary fabrication steps for the module of  FIG. 28 . 
         FIG. 31  is a perspective view of a glass/polymer waveguide module with a graded refractive index in both the horizontal/lateral direction and the vertical direction according to the present invention. 
         FIG. 32  is a result of a computer simulation of light propagation in the module of  FIG. 31 . 
         FIGS. 33A–B  illustrates exemplary fabrication steps for the module of  FIG. 31 . 
         FIGS. 34A–B  are, respectively, a side view and a top view of a super mode transformation coupler with a vertically down-tapered, horizontally/laterally up-tapered high-index waveguide core embedded in a glass/polymer waveguide with a graded refractive index in the vertical direction and a step refractive index in the horizontal/lateral direction according to the present invention. 
         FIG. 35  is a result of a computer simulation of light propagation in the super mode transformation coupler of  FIG. 34 . 
         FIGS. 36A–N  illustrate exemplary fabrication steps for the super mode transformation coupler of  FIG. 34 . 
         FIGS. 37A–B  are, respectively, a side view and a top view of a super mode transformation coupler with a vertically down-tapered, horizontally/laterally down-tapered high-index waveguide core embedded in a glass/polymer waveguide with a graded refractive index in both the horizontal/lateral and the vertical direction according to the present invention. 
         FIG. 38  is a result of a computer simulation of light propagation in the super mode transformation coupler of  FIG. 37 . 
         FIGS. 39A–N  illustrate exemplary fabrication steps for the super mode transformation coupler of  FIG. 37 . 
         FIG. 40A  is a side view of a super mode transformation coupler with a vertically down-tapered high-index waveguide core embedded in a glass/polymer waveguide with a non-symmetric graded refractive index in the vertical direction and a step refractive index in the horizontal/lateral direction according to the present invention. 
         FIG. 40B  is a top view of the super mode transformation coupler of  FIG. 40A , in which the high-index waveguide core is horizontally up-tapered. 
         FIG. 40C  is an alternative top view of the super mode transformation coupler of  FIG. 40A , in which the high-index waveguide core is horizontally down-tapered. 
         FIG. 41  is a result of a computer simulation of light propagation in the super mode transformation coupler of  FIG. 40A . 
         FIGS. 42A–N  illustrate exemplary fabrication steps for the super mode transformation couplers of  FIG. 40 . 
         FIG. 43  is a result of a computer simulation of light propagation in a variation of the super mode transformation coupler of  FIG. 40A . 
         FIGS. 44A–C  illustrate exemplary fabrication steps for a variation of the super mode transformation coupler of  FIG. 40A . 
         FIGS. 45A–C  illustrate exemplary fabrication steps for mounting an optical fiber and a semiconductor optical device coupled by a super mode transformation coupler according to the present invention. 
         FIG. 46  illustrates a device in which a number of semiconductor optical devices are coupled to a number of optical fibers using super mode transformation couplers according to the present invention. 
         FIG. 47  is a schematic illustration of a photonic breadboard on which various integrated photonic chips are mounted and interconnected via coupler modules according to the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Contents of Detailed Description 
     I. General Background and Terminology 
     II. General Introduction 
     III. Exemplary devices and embodiments 
     (1) Exemplary device  1 : a high-refractive-index-contrast vertical sharp-down-taper (HRC-VSDT) ICMT device 
     (2) Exemplary device  2 : a high-refractive-index-contrast lateral sharp-down-taper (HRC-LSDT) ICMT device 
     (3) Exemplary device  3 : a high-refractive-index-contrast-lateral gradual-up-taper (HRC-LGUT) ICMT device 
     (4) Exemplary device  4 : a vertical sharp-down-taper and lateral gradual-up-taper (VSDT×LGUT) ICMT device 
     (5) Exemplary device  5 : a lateral-step-refractive-index and vertical-step-refractive-index (LSRIN×VSRIN) ICMT device 
     (6) Exemplary device  6 : 
     (A) a composite-lateral-step-refractive-index and vertical-graded-refractive index (LSRIN×VGRIN) ICMT device 
     (B) a composite-lateral-graded-refractive-index and vertical-graded-refractive index (LGRIN×VGRIN) ICMT device 
     (7) Exemplary device  7 : a vertical-sharp-down-taper-and-lateral-gradual-up- taper-cascaded-with-a-vertical-graded-refractive-index-and-lateral--step-refractive-index (VSDT×LGUT+VGRIN×LSRIN) ICMT device 
     (8) Exemplary device  8 : a vertical-sharp-down-taper-and-lateral-sharp-down- taper-embedded-in-a-symmetric-vertical-graded-refractive-index-and--lateral-graded-refractive-index (VSDT×LSDT+VGRIN×LGRIN) ICMT device 
     (9) Exemplary device  9 : a vertical-sharp-down-taper-cascaded-with-a--nonsymmetric-vertical-graded-refractive-index-(VSDT+NSVGRIN) ICMT device 
     (10) Variations of exemplary devices and integration of ICMT with v-grooves for fiber alignments platform for photonic chips 
     IV. Applications 
     Description of the Specific Exemplary Embodiments 
     I. General Background and Terminology 
     Described herein are various exemplary processes and embodiments of the integrated composite mode transformer (ICMT) structures of the present invention. The structures can, for example, be used to provide efficient beam transformation between a photonic waveguide device and one or more optical fibers, wherein the transformation can correct for astigmatic beam sizes in the waveguides of the photonic devices. The ICMT structures can further be placed on a platform for self-alignment with the photonic device and one or more optical fibers. 
     To be consistent throughout the present specification and for clear understanding of the present invention, the following background and terminological definitions are hereby provided for terms used therein: 
     a) Refractive Index, Optical Wavelength, Law of Reflection, Snell&#39;s Law of Refraction, Critical Angle 
     As is well known, light is an electromagnetic wave oscillating at very high frequency. When light travels in an electrically nonconductive medium such as glass, its speed will be reduced as compared to traveling in a vacuum and the ratio of the phase velocity of light in a vacuum (c) to that in a medium (v) is the refractive index n of the medium, 
     
       
         
           
             n 
             = 
             
               c 
               v 
             
           
         
       
     
     Due to the fact that the frequency of the wave will not change as light travels from vacuum into a medium, the optical wavelength in a medium, λ, is thus reduced to λ=λ 0 /n, where λ 0  is the wavelength in a vacuum. 
     Light can be regarded as a ray traveling in a straight line within a medium of the same refractive index if the size of the medium (such as a lens) is much greater than the wavelength. At an optical interface  710  of two different refractive indices n i  and n t , a light ray will be reflected back into the first medium  720  (n i ) and also refracted/transmitted into the second medium  730  (n t ) as shown in  FIG. 7 . Law of reflection tells us that the angle of incidence (θ i ) equals the angle of reflection (θ r ) and Snell&#39;s law of refraction says that the retraction angle (θ t ) is related to the incidence angle (θ i ) through the equation
 
n i  sin θ i =n t  sin θ t .
 
     However, if n i &gt;n t , as θ i  increases to a particular value called the critical angle, θ c  will reach 90°, and afterwards, the incident light ray will be totally reflected  740 . Thus, as shown in  FIG. 8 , light guiding in a step refractive index optical waveguide or fiber can be explained by successive total internal reflections  810 . 
     (b) Optical Waveguide, Planar Waveguide, Channel Waveguide 
     From the above, we see that an optical waveguide is made up of a material with a high refractive index, surrounded by materials with a lower refractive index. The optical energy that is guided lies primarily within the layer with high refractive index. The layer with high refractive index is called the waveguide core while the surrounding layers with low refractive indices are called the waveguide cladding. If the waveguide is in the form of a two-dimensional layered structure, it is known to those skilled in the art as a planar waveguide for which optical energy will be confined to guide along a plane. If the waveguide core is in the form of a cylindrical or rectangular or other bar type shape, it is known to those skilled in the art as a channel waveguide. While the present application is primarily directed towards channel waveguides, planar waveguides are often used to demonstrate the basic idea of the principles involved because of their simplicity. 
     (c) Graded Refractive Index and Related Waveguide Structures, Parabolic Distribution Periodic Focusing 
     As shown in  FIG. 9 , in a graded refractive index (GRIN) optical waveguide or fiber  910 , the waveguiding material has a refractive index that decreases continuously from the central axis. In this case, light rays travel through the waveguide or fiber in a fashion as shown in  FIG. 9 . Such a GRIN waveguide relies on refraction and not reflection, except possibly at the cladding layer. 
     A parabolic refractive index distribution will cause the light rays to bend towards the axis and to get refocused periodically. As shown in  FIG. 10 , the behavior can be simply explained by modeling the continuous change as a series of small step changes  1010 . Note that at each step or interface, the bending of the ray follows the law of refraction. As the ray travels from the axis  1020  to the low refractive index region, at each step or interface, it will bend further towards the horizontal direction until the incident angle exceeds the critical angle in which case, the ray will be totally internally reflected  1030 . Now the ray is traveling from low to high refractive index medium and hence, the law of refraction tells us that at each boundary or interface, the ray will bend towards the axis until it crosses the axis. Afterward, it will repeat the cycle. Note that, in addition to guiding light, the GRIN waveguide also functions as a lens to focus or expand/collimate a beam of light if the waveguide is cut into the right length. 
     (d) Wave Behavior and Critical Wave-Behavior Dimension (CWBD) for Waveguide Taper 
     When the size of the guiding region is no longer much larger than the wavelength but rather smaller than the wavelength, the ray concept can no longer give an accurate picture of how light propagates, and one must resort to wave theory to better describe light propagation. As an example, consider a semiconductor taper embedded in a glass medium. There exists a critical wave-behavior dimension (CWBD) for the waveguide taper of CWBD=λ 0 /(4√{square root over ((n c   2 −n cl   2 )}) (where λ 0  is the wavelength in vacuum, n c  is the refractive index of the tapering waveguide core and n cl  is the refractive index of the waveguide cladding), below which light will penetrate substantially into the cladding medium while being guided.  FIGS. 11   b  to  11   f  show the electric field profile of the propagating mode for a silicon waveguide  1119  ( FIG. 11   a ) with a thickness equal to 0.4 μm, 0.3 μm, 0.2 μm, 0.1 μm, 0.05 μm, and 0.01 μm, respectively. In  FIG. 11 , the x-axis indicates space position across the waveguide in μm, the y-axis indicates normalized electric field of the lowest transverse electric (“TE”) mode. The wavelength of light is 1.5 μm, the refractive index of the cladding  1120  is assumed to be 1.5 and the refractive index of the silicon waveguide core  1110  is assumed to be 3.5.  FIG. 12  plots the mode size (given by the full-width at half maximum of the mode intensity) as a function of the waveguide core thickness t. From  FIG. 12 , as the Si waveguide thickness decreases, the mode size first decreases and then starts to become larger at approximately
 
 t= 1.5/(4√{square root over ((3.5 2 −1.5 2 ))}≈0.1 μm.
 
     (c) Propagating Refractive Index of Waveguide, Waveguide End Facet Reflectance, Sharp-Tip Tapered Waveguide, Sharp Taper and Gradual Taper 
     In an optical waveguide, it is useful to define the propagating refractive index of the waveguide as n g =n c  sin(θ i ). This propagating refractive index takes a value between the refractive index of the core n c  and the refractive index of the cladding n cl . As the waveguide gets thinner, θ i  approaches the critical angle, and n g  approaches the refractive index of the cladding n cl . In fact, most of the optical energy will reside in the cladding when t is very small. If this waveguide (thinner than the critical wave-behavior dimension CWBD) is abruptly terminated at an end facet, beyond which is filled by the cladding material, the reflectance (percentage of reflected optical power with respective to the incident optical power) for a guided wave hitting the end facet is given approximately by the end facet reflectance of 
     
       
         
           
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                         n 
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                         n 
                         g 
                       
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                         n 
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     Hence, such end-facet reflectance can be reduced to zero provided n g  approaches n cl , which will be the case if the waveguide is very thin (i.e. all is transmitted). 
     A waveguide with a gradually decreasing or increasing thickness along the direction of propagation is called a taper waveguide. A taper waveguide can in some way be seen as composed of many waveguide sections with decreasing or increasing thickness. From the above discussion, we see that a waveguide taper that tapers down to a near-zero thickness will first reduces the mode size and when the mode hits a region with a thickness smaller than the critical thickness, the mode size will starts to be enlarged. Furthermore, since the thickness of the waveguide approaches zero at the taper end, we can expect the optical power reflection at the taper end is to be negligible. Thus, a waveguide taper that tapers down to near zero thickness (a sharp-tip tapered waveguide) can be used to enlarge the mode size of a guided wave and also reduce the end facet reflection to a negligible value at the same time. Such a sharp-tip tapered waveguide will be referred to as “sharp taper” as opposed to “gradual taper”; a gradual taper will not taper down to reach the CWBD or reach a sharp tip. A gradual taper, for example, will slowly reduce the mode size and is typically used as a mode reducer. Furthermore, a gradual down taper will have reflection at the end face and will typically use anti-reflection techniques to reduce the end facet reflection. 
     The foregoing description serves as a general background providing a context within which embodiments of the present invention will be described below and are not meant to restrict any of the embodiment of the present invention. 
     II. General Introduction 
     When a submicron semiconductor channel waveguide is to be connected to a single mode optical fiber with a typical dimension of about 10 μm, one critical need is the expansion or enlargement of the mode size from the semiconductor channel waveguide to match that of the optical fiber, or the reverse process. 
     According to the embodiments of present invention, several different mode transformation and coupling structures can be cost effectively fabricated in either a single structure format or a composite structure format forming various mode transformation modules. 
     As discussed above, the integrated composite mode transformer (ICMT) structures include at least three types of basic mode transformation structures, namely: 
     (I). The sharp-taper structure (ST) includes a sharp tapering in either the vertical direction (VST) or the lateral direction (LST). These structures may be referred to below simply as ST, VST, and LST, respectively, with the high-refractive-index-contrast assumed. The sharp taper can further be distinguished as down or up depending on the direction of assumed mode propagation. For the purpose of nomenclature convenience only, the mode propagating direction below is taken to be from the photonic chip to the optical fiber. Those skilled in the art will readily be able to generalize it to other mode propagating configurations. 
     (II). The gradual-taper structure (GT), includes gradual tapering in either the vertical direction (VGT) or the lateral direction (LGT). These structures may be referred to below simply as GT, VGT, and LGT respectively. The gradual taper can further be distinguished as down or up and the propagating direction issue is as described in (I). 
     (III). The micro graded refractive index structure (μ-GRIN) includes a graded refractive index distribution in either the vertical (μ-VGRIN) or lateral (μ-LGRIN) directions. These structures may be referred to below simply as GRIN, VGRIN, or LGRIN. The GRIN structure can further be distinguished as symmetric or non-symmetric depending on whether the graded index has a profile symmetric or asymmetric with respect to the optical axis of propagation for the input wave. 
     Further, the sharp taper (ST) and the gradual taper (GT) may be in the form of high refractive index contrast structures and will be referred to as HRC-ST and HRC-GT, respectively. The high refractive index contrast enables much shorter tapering lengths to be used while maintaining large transformation of mode sizes. 
     A brief description of some of these basic module types are provided below. 
     (I). HRC-ST (High-Refractive-Index-Contrast, Sharp Taper Structure) 
     In this structure type, a high-refractive-index waveguide layer with vertical or lateral tapering to a sharp tip provides the mode size transformation. For the case of vertical tapering, the high-index waveguide layer is fabricated on top of a lower cladding layer. The upper and side cladding material may be either identical to or different from the lower cladding; hence the cladding index can be either symmetric or asymmetric. One novel feature of embodiments of this structure is the high contrast of the refractive index of the down taper waveguide core relative to the refractive index of the cladding, which confines propagating light to a very small mode size. For example, for the case where the material of the waveguide core is Si; the refractive index can be as high as about 3.5. The cladding material can be glass of various compositions that can have a range of refractive index values from about 1.45 to about 2.5. The sharp point of the taper must reach a dimension smaller than the critical wave-behavior dimension of CWBD=θ 0 /(4√{square root over ((n c   2 −n cl   2 ))} introduced above. In that case, transformation of the mode size from as small as λ/15, (submicron for λ=1.5 μm) to a few λ (a few microns for λ=1.5 μm) can be typically achieved. 
     (II). HRC-GT (High-Refractive-Index-Contrast, Gradual Taper Structure) 
     In this structure type, a gradual taper provides the mode size transformation in either the lateral or the vertical direction. The mode size transformation is due to the fact that gradual mode size will follow the waveguide size if the waveguide changes size gradually. One aspect of the embodiments of this structure is the high contrast of the refractive index of the taper waveguide core relative to the refractive index of the cladding, which allows it to achieve large changes in the mode size within a short propagation distance. 
     (III). μ-GRIN (Micro-Graded-Refractive-Index Structure) 
     In this structure type, a graded refractive index layer with either a vertical or lateral refractive index gradient provides the mode size transformation. For the case of a vertical graded refractive index structure, a stepwise refractive index distribution (e.g., the core has a first constant index, and the cladding has a second constant index, lower than the first) or a graded refractive index distribution (index varies throughout the waveguide, in one of the embodiments, being highest near the center) is present in the vertical direction. One feature of the embodiments of this structure is the smallness of the structure, for which the GRIN structure is less than about 50 μm. This thickness is small relative to the diameter of the optical fiber. 
     The above three basic beam-transforming structure types together with other waveguide structures, are combined in various composite ways in the vertical and lateral directions, to form different basic beam-transforming modules. The composite structures allows a basic module to transform the beam size in either the vertical or lateral direction, or both the vertical and lateral directions. 
     Furthermore, two or more basic modules can be cascaded spatially to form a combined module. The combined module can be used to either increase the degree of mode transformation over that of a basic module, or to have one basic module perform the vertical mode size transformation and another basic module perform the lateral mode size transformation. 
     Described below are specific embodiments of various mode transforming devices based on the integrated composite mode transformer (ICMT) structures of the present invention. The various basic modules as well as the combined modules will be described. In the sequence of presentation below, this includes: 
     (1) A downward VST or vertical sharp down taper (VSDT) to enlarge the vertical mode size of an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 13–15 ). 
     (2) A downward LST or lateral sharp down taper (LSDT) to enlarge the lateral mode size of an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 16–18 ). 
     (3) An upward LGT or lateral gradual up taper (LGUT) to enlarge the lateral mode size of an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 19–21 ). 
     (4) A composite VSDT and LGUT structure forming a (VSDT×LGUT) module to enlarge the mode size vertically and laterally for an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 22–24 ). 
     (5) A step-refractive-index (SRIN) waveguide module that provides simple wave propagation without mode size transformation. This SRIN module is used as a basic module to combine with other modules (e.g.,  FIGS. 25–27 ). In the case illustrated in  FIGS. 25–27 , a vertical step index waveguide (VSRIN) and a lateral step index waveguide (LSRIN) structures are combined to provide simple mode waveguiding in both the vertical and the lateral directions. 
     (6) A composite vertical graded refractive index (VGRIN) and LSRIN structure forming a (VGRIN×LSRIN) module to enlarge the vertical mode size for an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 28–30 ). 
     (7) A composite vertical graded refractive index (VGRIN) and lateral graded refractive index (LGRIN) structure forming a (VGRIN×LGRIN) module to enlarge the mode size vertically and laterally for an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 31–33 ). 
     (8) A combined module including a cascaded (VSDT×LGUT) module and (VGRIN×LSRIN) module, namely a (VSDT×LGUT)+(VGRIN×LSRIN) combined module, to increase the enlargement of the mode size vertically and laterally for an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 34–36 ). 
     (9) A combined module made up of a cascade of (VSDT×LSDT) module and (VGRIN×LGRIN) module, namely a (VSDT×LSDT)+(VGRIN×LGRIN) combined module, to increase the enlargement of the mode size vertically and laterally for an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 37–39 ). 
     (10) A combined module made up of either a cascade of (VSDT×LGUT) module and (VGRIN×LSRIN) module with asymmetric GRIN structure, namely a (VSDT×LGUT)+(VGRIN×LSRIN) combined asymmetric GRIN module, or a cascade of (VSDT×LSDT) module and a (VGRIN×LGRFN) module with asymmetric GRIN structure, namely a (VSDT×LSDT)+(VGRIN×LGRIN) combined asymmetric GRIN module, to increase the enlargement of the mode size vertically and laterally for an optical beam from a photonic chip to an optical fiber (e.g.,  FIGS. 40–43 ). 
     (11) A waveguide bonding process useful for the fabrication of the vertical sharp taper structures (e.g.,  FIG. 44 ) 
     (12) The integration of the ICMT structures with a V-groove structure for fiber on one side and an alignment platform for photonic chip on the other side. Such an integrated structure allows self-alignment of the ICMT with a photonic chip and an optical fiber (e.g.,  FIGS. 45–46 ). 
     While the exemplary devices ( 1 )–( 12 ) typically refer to transformation of an optical beam between a photonic chip and optical fibers, it is not meant to limit the applications, embodiments, or scopes of the exemplary devices. It should be clear to those skilled in the art that these exemplary devices can be more generally used to transform optical beams from any type of small core waveguide to any type of large core waveguide or vice versa. 
     III. Exemplary Devices and Embodiments 
     Beam transforming devices based on ICMT according to embodiments of the present invention are described in detail below. 
     The devices will be described with respect to transmission of a single light beam with wavelength λ. It should be understood that the terms light beam, optical beam, laser beam, etc., are used interchangeably. Moreover, while descriptions of the devices refer to a single light beam, there may be more than one light beam propagating in the device, the light beams may be made up of light with many wavelengths, the light beam may be continuous-wave light or pulsed light, and the light beam may have various beam sizes. Thus the nature of the light beam is used only for illustrative purposes and is not meant to limit the scope of the invention. 
     Unless otherwise stated, the exemplary dimensions below will be specified with respect to an exemplary optical wavelength of 1.5 μm. Those skilled in the art will know that the exemplary dimensions will scale proportionally to the wavelength used which can range from ultra-violet (e.g., on the order of 0.1 μm) to far infrared (e.g., on the order of 10 μm). 
     The various device embodiments described herein are useful for transforming the mode size of an input beam having a dimension on the order of from about 0.2 μm or even less to a beam dimension on the order of about 10 μm to 50 μm or more, and vice versa, with appropriate changes to the various device parameters disclosed. Thus one skilled in the art should understand that the various device embodiment parameters (e.g., length and width dimensions) disclosed herein are exemplary and may be varied according to the desired application. 
     (1) Exemplary Device  1 : A High-Refractive-Index-Contrast Vertical Sharp-Down-Taper (HRC-VSDT) ICMT Device 
       FIG. 13  illustrates a first general embodiment of an ICMT device  1300  employing a vertical down-tapering beam enlarger with high refractive-index contrast between the enlarger core region and its surrounding cladding region. The device performs as a one dimensional beam-size enlarging element in the vertical direction for a propagating optical beam and can, for example, enlarge an optical beam from a semiconductor waveguide with a beam size as small as λ/7.5 (or 0.2 μm for λ=1.5 μm) to a large optical beam such as one with a beam size more than five times larger. The device is not limited to use as a beam enlarger but can also function as a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used in conjunction with another ICMT module such as a graded refractive index waveguide module (described below) to further enlarge and collimate the beam for direct coupling into an optical fiber and vice versa. It should be understood that these exemplary applications of device  1300  are intended to illustrate the uses for device  1300  and are not intended to limit the applications of other embodiments of device  1300 . The device can be referred to as a “high-refractive-index-contrast-vertical-sharp-down-taper (HRC-VSDT) ICMT”. 
     HRC-VSDT ICMT  1300  preferably includes a tapering-down waveguiding core region occupied by Waveguide Core WC  1345 . Waveguide Core WC  1345  is surrounded by Upper Waveguide Cladding UWCL  1350  above and Lower Waveguide Cladding LWCL  1310  below. The Waveguide Core WC  1345  preferably includes a small-beam input/output port SB-PT  1346 , a straight waveguiding core region SWC  1347 , a tapering-down waveguiding core region TDWC  1348 , a straight radiation core region SRC  1351 , and a large-beam output/input port LB-PT  1349 . The straight waveguiding core region SWC  1347  has a length l SWC  and a thickness t SWC . The tapering down waveguiding core region TDWC  1348  has a length l TDWC , a thickness t TDWCSB  at the small-beam input/output side and a thickness t TDWCLB  at the large-beam input/output side. The straight radiation core region SRC  1351  has a length l SRC  and a thickness t SRC . The total length of the waveguide core is given by l WC =l SWC +l TDWC +l SRC . The thickness of the lower waveguide cladding LWCL  1310  is t LWCL . The thickness of the upper waveguide cladding UWCL  1350  at the small-beam input/output side is t UWCLSB  and at the large-beam input-output side is t UWCLLB . The length of the upper cladding l UWCL  and the length of the lower cladding l LWCL  are about equal to the total length of the waveguide core l WC . The refractive index of the Waveguide Core WC  1345  is n WC . The refractive index of the Upper Waveguide Cladding LWCL  1350  is n UWCL . The refractive index of the Lower Waveguide Cladding LWCL  1310  is n LWCL . Lower waveguide cladding LWCL  1310  is formed on a substrate  1315  as will be described in more detail below. The length of the straight waveguide core l SWC  and the straight radiation core l SRC  are typically not very critical to the operation of the device and can be zero in some applications (i.e., with these sections absent). 
     For choice of refractive index, there are three options for operation for the ICMT device  1300 , namely the small-refractive-index-contrast option, the medium-refractive-index-contrast option and the large-refractive-index-contrast option. For the small-refractive-index contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1345  and that of the Waveguide Cladding  1350  or  1310 , i.e. n WC /n UWCL  or n WC /n LWCL , is assumed to be larger than 1.0 but smaller than about 1.3. That is 1.3≧n WC /n UWCL &gt;1.0 or 1.3≧n WC /n LWCL &gt;1.0. For the medium-refractive-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1345  and that of the Waveguide Cladding  1350  or  1310 , i.e. n WC /n UWCL  or n WC /n LWCL , is assumed to be larger than about 1.3 but smaller than about 1.5. That is 1.5≧n WC /nU WCL ≧1.3 or 1.5≧n WC /n LWCL ≧1.3. For the large-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1345  and that of the Waveguide Cladding  1350  or  1310 , i.e. n WC /n UWCL  or n WC /n LWCL , is assumed to be larger than about 1.5. That is n WC /n UWCL ≧1.5 or n WC /n LWCL ≧1.5. A short tapering length can be achieved if the relative refractive index contrast is high—in the region of either the medium-refractive-index contrast or the large-refractive-index contrast. The medium and large refractive index contrast will be referred to as the high-refractive index case. 
     In an exemplary device, the input/output port SB-PT  1346  is configured to receive/transmit a light beam  1341  typically having wavelength λ with a beam diameter d SB , and the output/input port LB-PT  1349  is configured to transmit/receive a light beam  1342  typically having wavelength λ with a beam diameter d LB . 
     (i) An Exemplary Device for High-Refractive-Index-Contrast Case 
     In an exemplary embodiment of device  1300  with high refractive-index contrast, the Waveguide Core WC  1345  is made up of silicon (Si) with a refractive index of n WC =3.5, the Upper Waveguide Cladding  1350  is made up of silica-titania (SiO 2 —TiO 2 ) material mixture with a mixture composition to achieve a refractive index of n UWCL =1.7 or alternatively Si 3 N 4  with a refractive index of about 1.7 can be used. The Lower Waveguide Cladding  1310  is made up of silicon dioxide (SiO 2 ) with a refractive index of n LWCL =1.5. The thicknesses of the waveguide core are t SWC =0.3 μm, t TDWCSB =0.3 μm, and t TDWCLB =t SRC =0, by “0” it is meant that t TDWCLB =t SRC &lt;&lt;λ. The thicknesses of the waveguide claddings are t UWCLSB =5.0 μm, t UWCLLB =5.3 μm, and t LWCL =0.6 μm. The lengths of the waveguide core are l SWC =10 μm, l TDWC =30 μm, l SRC =10 μm, and l WC =50 μm. The lengths of the waveguide claddings are l UWCL =l LWCL =l WC =50 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. It should also be appreciated by one skilled in the art that other materials for the core and cladding of the various exemplary embodiments may be used. 
     (ii) General Operation of the Device. 
       FIG. 14  shows the results of a computer simulation of the spatial distribution of the electric field strength for light input at λ=1.5 μm after propagating into waveguide  1347 , using the above exemplary parameters. The mode size at the input end was approximately 0.3 μm. After propagating for about 35 μm, it begins to expand at the point where the waveguide thickness (at 5 μm distance from the tip) is tapered down to about 0.05 microns, which is near the tip of the tapering down region. The mode then radiates at an angle from that point to a larger mode size. The mode size reaches a size of about 5 μm at 10 μm away from the tip of the taper. The compact mode transfer device thus expands the mode from about 0.3 to about 5 μm over a distance of about 50 μm. This is a much smaller distance compared with mode expansion distances provided by other prior art devices. Thus such ICMT devices according to the present invention provide a clear advantage for coupling fibers to a photonic chip relative to prior art devices. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating a HRC-VSDT-ICMT such as device  1300  will now be described with reference to  FIGS. 15A–C . This procedure is given for the purpose of illustration and not limitation as other similar procedures can be used to achieve the same fabrication results, and other materials systems or device structures can be utilized to fabricate devices with the same functional capabilities. 
     The HRC-VSDT-ICMT type structure is fabricated according to an embodiment by starting with a Silicon-On-Insulator (SOI) wafer. For a SOI wafer, a high refractive index silicon (Si) layer  1305  having a thickness of t SWC  is already made or bonded on top of a low refractive index layer of SiO 2    1310  with a thickness of t LWCL . The SiO 2  layer  1310  is typically either deposited on a Si substrate  1315  or thermally oxidized on the Si substrate or thermally oxidized in the Si substrate after an oxygen ion implantation process. A fabrication procedure according to one embodiment is now described below. 
     A photoresist layer  1320  s deposited (e.g. spin-coated) on the silicon layer  1305 , as shown in  FIG. 15A . A gray-scale mask  1325  is used as a mask to expose the photoresist  1320  under UV light  1330 . The gray-scale mask pattern is designed so that it provides a graduated exposure level with an exposure dosage that varies from a small value to a large value that will somewhat result in a linear photoresist taper after exposure and development across a length of approximately 30 μm. The photoresist is then developed. The shape of the photoresist after exposure and development has a vertical down tapered shape that corresponds to the variation in the exposure dosage, as shown by photoresist pattern  1335  in  FIG. 15B . 
     A dry plasma etching procedure  1340  with selectivity of 1:0.3:˜0 between photoresist and Si and SiO 2  is used to etch down the Si layer vertically. Such a process is accomplished using a reactive ion etching system, or an inductively coupled plasma system, or another equivalent dry plasma system. The exemplary processing gases are SF 6 /O 2 /Cl 2 , as F-reactants and/or their neutrals etch Si, whereas O 2  etch photoresist and S—Cl reactants and/or their neutrals inhibit the etching of SiO 2 . Exemplary process parameters using a reactive ion etching system are: a mixture of 30 sccm:20 sccm:20 sccm of SF 6 :O 2 :Cl 2 , with an RF power of 350 W, and a process pressure of 25 mTorr. This etching process transfers the down tapered pattern of the photoresist to the high-refractive-index Si layer and forms the vertically tapered down Si section  1345 . It should be noted that the ease of this transfer process is dependent on the thickness tswc of the top waveguiding Si layer. Typically the starting thickness for a tapered down Si waveguide is in the range of 0.2 to 0.5 μm. Considering that the photoresist layer has a typical thickness of about 1.0 μm and that the etching process typically etches Si at a rate that is not drastically different from that for the photoresist, such a direct pattern transfer can be achieved. As the etching process can be made to etch SiO 2  at a lower rate, the interface between the top Si layer  1305  and the lower cladding SiO 2    1310  can be used as a natural stop during the dry etching process. It should be understood that the above process parameters are presented for purposes of illustrating a useful embodiment of the fabrication method and are not intended as a limitation on the device. For example, a variety of dry etching parameters can be used depending on the photoresist type and the quality of the SOI wafer. As is known to those skilled in the art, the end result of a dry etched structure can be achieved via various combinations of the etching parameters. 
     To make the glass upper cladding layer  1350 , flame hydrolysis deposition, chemical vapor deposition, sputtering, Ion-Assisted-Deposition or sol-gel spin coating of dielectric material, can generally be employed to deposit the upper cladding layer  1350 , shown in  FIG. 15C . The TiO 2 —SiO 2  material required can, in particular, be achieved using a sol-gel mixture of TiO 2  and SiO 2  precursors as is well known to those skilled in the art. The surrounding cladding, including the bottom, top and side cladding medium, can all have various refractive indices and also a spatial variation or distribution of the refractive index value (as will be discussed below), and the actual value that can be selected for this purpose can cover a wide range, for instance 1.4 to 2.5. 
     It should be understood that these dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  1300  and are not intended to limit other embodiments of any exemplary device, or the device  1300 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the various embodiments of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces. 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the devices. 
     It should be understood to those skilled in the art that the device  1300  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (2) Exemplary Device  2 : A High-Refractive-Index-Contrast-Lateral Sharp-Down-Taper (HRC-LSDT) ICMT Device 
       FIG. 16  illustrates a second general embodiment of an ICMT device  1400  employing a lateral down-tapering beam enlarger with high refractive-index contrast between the enlarger core region and its surrounding cladding region. The device performs as a one dimensional beam-size enlarging element in the lateral direction for a propagating optical beam and can, for example, enlarge an optical beam from a semiconductor waveguide with a beam size as small as λ/7.5 (or 0.2 μm for λ=1.5 μm) to a large optical beam such as one with a beam size close to that of an optical fiber. The device is not limited to use as a beam enlarger but can also function as a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used in conjunction with another ICMT module such as a graded-refractive-index waveguide module to further enlarge and collimate the beam for direct coupling into an optical fiber. It should be understood that these exemplary applications of device  1400  are intended to illustrate the uses for device  1400  and are not intended to limit the application of other embodiments of device  1400  to these examples. The device can be referred to as a “high-refractive-index-contrast-lateral-sharp-down-taper (HRC-LSDT) ICMT”. 
     The present HRC-LSDT ICMT preferably includes a tapering-down waveguiding core region occupied by Waveguide Core WC  1450 , Waveguide Core WC  1450  is surrounded on both sides by Waveguide Cladding WCL  1460 . Waveguide Core  1450  preferably includes a small-beam input/output port SB-PT  1451 , a straight waveguiding core region SWC  1452 , a tapering-down waveguiding core region TDWC  1453 , a straight radiation core region SRC  1454 , and a large-beam input/output port LB-PT  1455 . The straight waveguiding core region SWC  1452  has a length l SWC  and a width of w SWC . The tapering down waveguiding core region TDWC  1453  has a length of l TDWC , a width of w TDWCSB  at the small-beam input/output side, and a width w TDWCLB  at the large-beam input/output side. The straight radiation core region SRC  1454  has a length of l SRC  and a width of w SRC . The total length of the waveguide core is given by l WC =l SWC +l TDWC +l SRC . The width of the waveguide cladding WCL  1460  on both sides of the waveguide core WC  1450  is w WCLSB  at the small beam input/output side, and is w WCLLB  at the large beam side. The length of the waveguide cladding WCL  1460  l WCL  is about equal to the total length of the waveguide core l WC . The refractive index of the Waveguide Core WC  1450  is n WC . The refractive index of the Waveguide Cladding WCL  1460  is w WCL . The length of the straight waveguide core l SWC  and the straight radiation core l SRC  are typically not very critical to the operation of the device and can be zero in some applications (i.e. with these sections absent). 
     For choice of refractive index, there are three options for the operation of the ICMT device  1400 , namely the small-refractive-index-contrast option, the medium-refractive-index-contrast option and the large-refractive-index-contrast option. For the small-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1450  and that of the Waveguide Cladding  1460  i.e. n WC /n WCL , is assumed to be larger than 1.0 but smaller than 1.3. That is, 1.3≧n WC /n WCL ≧1.0. For the medium-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1450  and that of the Waveguide Cladding  1460  i.e. n WC /n WCL , is assumed to be larger than 1.3 but smaller than 1.5. That is, 1.5≧n WC /n WCL ≧1.3. For the large-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1450  and that of the Waveguide Cladding  1460  i.e. n WC /n WC , is assumed to be larger than 1.5. That is, n WC /n WCL ≧1.5. A short tapering length can be achieved if the relative refractive index contrast is HIGH—in the region of either the medium-refractive-index contrast or the large-refractive-index contrast. The medium and large refractive index contrast will be referred to as the high-refractive index case. 
     In an exemplary device, the input/output port SB-PT  1451  is configured to receive/transmit a light beam  1461  typically having wavelength λ with a beam width W SB , and the input/output port LB-PT  1455  is configured to receive/transmit a light beam  1465  typically having wavelength λ with a beam width w LB . 
     (i) An Exemplary Device for High-Refractive-lndex-Contrast Case 
     In an exemplary embodiment of device  1400  in the high-refractive-index-contrast operation region, the Waveguide Core WC  1450  is made up of silicon (Si) with a refractive index of n WC =3.5, the Waveguide Cladding WCL  1460  is made up of silica-titania (SiO 2 —TiO 2 ) material mixture with a mixture composition to achieve a refractive index of n UWCL =1.7 or alternatively Si 3 N 4  with a refractive index of about 1.7 can be used. The widths of the waveguide core are w SWC =0.3 μm, w TDWCSB =0.3 μm, and w TDWCLB =w SRC =0 μm. The widths of the waveguide claddings are w WCLSB =4.85 μm and w WCLLB =5.0 μm. The lengths of the waveguide core regions are l SWC =0 μm, l TDWC =30 μm, l SRC =26 μm, and l WC =56 μm. The length of the waveguide cladding is l WCL =56 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 17  shows the results of a computer simulation of the spatial distribution of the electric field strength for the light input at λ=1.5 μm after propagating into waveguide  1452 . The mode size at the input end was 0.3 μm. After propagating for 25 μm, it begins to expand at the point where the waveguide thickness (at 5 μm from the tip) is tapered down to 0.05 microns, which is near the tip of the tapering down region. The mode then radiates at an angle from that point to a larger mode size. The mode size reaches a size of about 10 μm at 10 μm away from the tip of the taper. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating HRC-LSDT-ICMT device  1400  will now be described with reference to  FIGS. 18A–D . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     The HRC-LSDT ICMT can be fabricated by starting with a Silicon-On-Insulator (SOI) wafer. For a SOI wafer, a high refractive index silicon (Si) layer  1410  having a thickness of t 1  is already made or bonded on top of a low refractive index layer of SiO 2    1415  with a thickness of t 2 . The SiO 2  layer  1415  is typically either deposited on a Si substrate  1420  or thermally oxidized on the Si substrate or thermally oxidized in the Si substrate after an oxygen ion implantation process. A fabrication procedure according to one embodiment is described below: 
     A UV or e-beam resist layer  1405  is first spin-coated on the Si layer  1410 , as shown in  FIG. 18B . A mask  1425  with a laterally tapered down/narrow mask pattern  1430  as shown in  FIG. 18A  is used as a mask to expose the photoresist  1405  under UV light or e-beam  1435 . The photoresist is then developed. The shape of the photoresist after exposure and development has a lateral down-tapered shape as shown by photoresist pattern  1440  in  FIG. 18B  and  FIG. 18C . 
     A dry plasma etching procedure  1445  that selectively etches Si but not the photoresist  1440  or the SiO 2    1415  is used. Such a process can be accomplished using a reactive ion etching system, or an inductively coupled plasma system, or any dry plasma system. The exemplary processing gases are SF 6 /Cl 2 , as F-reactants and/or their neutrals etch Si, and S—Cl reactants and/or their neutrals inhibit the etching of SiO 2 . Exemplary process parameters using a reactive ion etching system are: a mixture of approximately 30 sccm:20 sccm of SF 6 :Cl 2 , with an RF power of 200 W, and a process pressure of about 25 mTorr. This etching process transfers the laterally down tapered pattern of the photoresist  1440  to the high-refractive-index Si layer and forms the laterally tapered down Si section  1450 . It should be noted that this transfer process is performed with the starting thickness for the Si waveguide layer in the range of 0.2 to 0.5 μm, and the photoresist layer has a typical thickness of about 1.0 μm. As the etching process can be made to etch SiO 2  at a lower rate, the interface between the top Si layer  1410  and the lower cladding SiO 2    1415  can be used as a natural stop during the dry etching process. A top view of the result of the process is shown in  FIG. 18D . It should be understood that the above process parameters are presented for purposes of illustrating a useful embodiment of the fabrication method and are not intended to limit other embodiments of the method. For example, a variety of dry etching parameters can be used depending on the photoresist type and the quality of the SOI wafer. As is known to those skilled in the art, the end result of a dry etched structure can be achieved via various combinations of the etching parameters. It should, also be noted that due to the limitation in the smallest feature size of UV based photolithography, e-beam lithography might be necessary or at least it might be required to form the tip part of the taper. 
     To make the glass cladding  1460 , flame hydrolysis deposition, chemical vapor deposition, sputtering, Ion-Assisted-Deposition, or sol-gel spin coating of dielectric material, is employed to deposit the cladding regions  1460  shown in  FIG. 16 . The TiO 2 —SiO 2  material required can, in particular, be achieved using a sol-gel mixture of TiO 2  and SiO 2  precursors as is well known to those skilled in the art. Note that the surrounding cladding, including the bottom, top and side cladding medium, can all have various fixed or spatially varying or distributed refractive indices and also a spatial variation or distribution of the refractive index value (as described below), and the actual value that can be selected for this purpose can cover a wide range of 1.4 to 2.5. 
     It should be understood that these dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  1400  and are not intended to limit other embodiments of any exemplary device, or the device  1400 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the devices. 
     It should be understood to those skilled in the art that the device  1400  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (3) Exemplary Device  3 : A High-Refractive-Index-Contrast-Lateral Gradual-Up-Taper (HRC-LGUT) ICMT Device 
       FIG. 19  illustrates a third general embodiment of an ICMT device  1500  employing lateral tapering up beam enlarger with high refractive index contrast between the enlarger core region and its surrounding cladding region. The device performs as a one dimensional beam-size enlarging element in the lateral direction for a propagating optical beam and can for example enlarge an optical beam from a semiconductor waveguide with a beam size as small as λ/7.5 (or 0.2 μm for λ=1.5 μm) to a large optical beam such as one with a beam size close to that of an optical fiber. The device is not limited to use as a beam enlarger but can also function as a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used in conjunction with another ICMT module such as a step-index waveguide module as will be described below to further collimate the beam for direct coupling into an optical fiber. It should be understood that these exemplary applications of device  1500  are intended to illustrate the uses for device  1500  and are not intended to limit the application of other embodiments of device  1500 . The device can be referred to as a “high-refractive-index-contrast-lateral-gradual-up-taper (HRC-LGUT) ICMT”, and the tapering up is in the lateral direction. 
     The present HRC-LGUT ICMT preferably includes a tapering-up waveguiding core region occupied by Waveguide Core WC  1550 . Waveguide Core WC  1550  is surrounded on both sides by Waveguide Cladding WCL  1560 . Waveguide Core  1550  preferably includes a small-beam input/output port SB-PT  1551 , a straight waveguiding core region SWC  1552 , a tapering-up waveguiding core region TUWC  1553 , a straight radiation core region SRC  1554 , and a large-beam input/output port LB-PT  1555 . The straight waveguiding core region SWC  1552  has a length l SWC  and a width of w SWC . The tapering up waveguiding core region TUWC  1553  has a length of l TUWC , a width of w TUWCSB  at the small-beam input/output side, and a width w TUWCLB  at the large-beam input/output side. The straight radiation core region SRC  1554  has a length of l SRC  and a width of w SRC . The total length of the waveguide core is given by l WC =l SWC +l TUWC +l SRC . The width of the waveguide cladding WCL  1560  on both sides of the waveguide core WC  1550  is w WCLSB  at the small beam input/output side, and is w WCLLB  at the large beam side. The length of the waveguide cladding WCL  1560  l WCL  is about equal to the total length of the waveguide core l WC . The refractive index of the Waveguide Core WC  1550  is n WC . The refractive index of the Waveguide Cladding WCL  1560  is n WCL . The length of the straight waveguide core l SWC  and the straight radiation core l SRC  are typically not very critical to the operation of the device and can be zero in some applications (i.e. with these sections absent). 
     There are three options for the refractive index contrast of the ICMT device  1500 , namely the small-refractive-index-contrast option, the medium-refractive-index-contrast option and the large-refractive-index-contrast option. For the small-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1550  and that of the Waveguide Cladding  1560  i.e. n WC /n WCL , is assumed to be larger than 1.0 but smaller than about 1.3. That is 1.3≧n WC /n WCL ≧1.0. For the medium-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1550  and that of the Waveguide Cladding  1560  i.e. n WC /n WCL , is assumed to be larger than about 1.3 but smaller than about 1.5. That is 1.5≧n WC /n WCL ≧1.3. For the large-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1550  and that of the Waveguide Cladding  1560  i.e. n WC /n WCL , is assumed to be larger than about 1.5. That is n WC /n WCL ≧1.5. A short tapering length can be achieved if the relative refractive index contrast is HIGH—in the region of either the medium-refractive-index contrast or the large-refractive-index contrast. In an exemplary device, the input/output port SB-PT  1551  is configured to receive/transmit a light beam  1561  typically having wavelength λ with a beam width w SB , and the input/output port LB-PT  1555  is configured to receive/transmit a light beam  1565  typically having wavelength λ with a beam width w LB . The medium and large refractive index contrast will be referred to as the high-refractive index case. 
     (i) An Exemplary Device for High-Refractive-Index-Contrast Case 
     In an exemplary embodiment of device  1500  with high-refractive-index-contrast, the Waveguide Core WC  1550  is made up of silicon (Si) with a refractive index of n WC =3.5, the Waveguide Cladding WCL  1560  is made up of silica-titania (SiO 2 —TiO 2 ) material mixture with a mixture composition to achieve a refractive index of n UWCL =1.7 or alternatively Si 3 N 4  with a refractive index of about 1.7 can be used. T with a refractive index of n WCL =1.7. The widths of the waveguide core are w SWC =0.3 μm, w TUWCSB =0.3 μm, and w TUWCLB =w SRC =10 μm. The widths of the waveguide claddings are w WCLSB =6.85 μm and w WCLLB =2 μm. The lengths of the waveguide core regions are l SWC =10 μm, l TUWC =100 μm, l SRC =10 μm, and l WC =120 μm. The length of the waveguide cladding is l WCL =120 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 20  shows the results of a computer simulation of the spatial distribution of the electric field strength for the light input at λ=1.5 μm after propagating into waveguide  1552 . The mode size at the input end was 0.3 μm. After propagating for 10 μm, it begins to expand at the point where the waveguide core tapers up. The mode then enlarges following the up-tapering waveguide core section to a larger mode size. The mode size reaches a size of about 10 μm at the end of the up-taper. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating an LGUT-ICMT device  1500  will now be described with reference to  FIGS. 21A–E . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     It should be noted that the fabrication steps here are very similar to those described for the laterally tapered down case. In fact, the present structure is even easier to fabricate because e-beam lithography is not required and hence the cost is even lower. The HRC-LGUT ICMT type structure can be fabricated by starting with a Silicon-On-Insulator (SOI) wafer that can be fabricated via a commercial process known to those skilled in the art. For a SOI wafer, a high refractive index silicon (Si) layer  1510  having a thickness of t 1  is already made or bonded on top of a low refractive index layer of SiO 2    1515  with a thickness of t 2 , as shown in  FIG. 21A . The SiO 2  layer  1515  is typically either deposited on a Si substrate  1520  or thermally oxidized on the Si substrate or thermally oxidized in the Si substrate after an oxygen ion implantation process. The fabrication procedure according to one embodiment is now described below. 
     A photoresist layer  1505  is first spin-coated on the Si layer  1510 , as shown in  FIG. 21A . A mask  1525  with a laterally tapered up mask pattern  1530 , shown in  FIG. 21B , is used as a mask to expose the photoresist  1505  under UV light  1535 . The photoresist is then developed. The shape of the photoresist after exposure and development has a lateral up tapered shape as shown by photoresist pattern  1540  in  FIG. 21D . 
     A dry plasma etching procedure  1545  that selectively etches Si but not the photoresist  1540  or the SiO 2    1515  can be used, as shown in  FIG. 21C . Such an etch process is accomplished using a reactive ion etching system, or an inductively coupled plasma system, or any dry plasma system. The exemplary processing gases are SF6/Cl 2 , as F-reactants and/or their neutrals etch Si, and S—Cl reactants and/or their neutrals inhibit the etching of SiO 2 . Exemplary process parameters using a reactive ion etching system are: a mixture of 30 sccm:20 sccm of SF 6 :Cl 2 , with an RF power of 200 W, and a process pressure of 25 mTorr. This etching process transfers the laterally up tapered pattern of the photoresist  1540  to the high-refractive-index Si layer and forms the laterally up-tapered Si section  1550 . It should be noted that this transfer process is possible because the starting thickness of the Si waveguide layer is in the range of 0.2 to 0.5 μm, and the photoresist layer has a typical thickness of about 1.0 μm. As the etching process can be made to etch SiO 2  at a lower rate, the interface between the top Si layer  1510  and the lower cladding SiO 2    1515  can be used as a natural stop during the dry etching process. It should be understood that the above process parameters are presented for purposes of illustrating a useful embodiment of the fabrication method and are not intended to limit other embodiments of the method. For example, a variety of dry etching parameters can be used depending on the photoresist type and the quality of the SOI wafer. As is known to those skilled in the art, the end result of a dry etched structure can be achieved via various combinations of the etching parameters. 
     To make the glass cladding  1560 , flame hydrolysis deposition, chemical vapor deposition, sputtering, Ion-Assisted-Deposition, or sol-gel spin coating of dielectric material, can generally be employed to deposit the cladding regions  1560  shown in  FIG. 19 . The TiO 2 —SiO 2  material required can, in particular, be achieved using a sol-gel mixture of TiO 2  and SiO 2  precursors as is well known to those skilled in the art. Note that the surrounding cladding, including the bottom, top and side cladding medium, can all have various refractive indices and also a spatial variation or distribution of the refractive index value (as described below), and the actual value that can be selected for this purpose can cover a wide range, for instance 1.4 to 2.5. 
     It should be understood that these dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  1500  and are not intended to limit other embodiments of any exemplary device, or the device  1500 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces. 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the devices. 
     It should be understood to those skilled in the art that the device  1500  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (4) Exemplary Device  4 : A Vertical Sharp-Down-Taper and Lateral Gradual-Up-Taper (HRC-VSDT×LGUT) ICMT Device 
       FIGS. 22A–B  illustrates a fourth general embodiment of an ICMT device  1600  including a lateral gradual up-tapered and vertical sharp down-tapered beam transformer with high refractive index contrast between the enlarger core region and its surrounding cladding region. The device can perform as a two dimensional beam-size enlarging element in both the lateral and the vertical directions for a propagating optical beam and can, for example, enlarge an optical beam from a semiconductor waveguide with a beam size as small as λ/7.5 (or 0.2 μm for λ=1.5 μm) to a large optical beam such as one with a beam size more than five times larger. The device is not limited to use as a beam enlarger but can also function as a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used other ICMT modules such as a lateral step-index waveguide module and a vertical graded index waveguide module as will be discussed below to further collimate the beam for direct coupling into an optical fiber. It should be understood that these exemplary applications of device  1600  are intended to illustrate the uses for device  1600  and are not intended to limit the applications of other embodiments of device  1600 . The device can be referred to as a “high-refractive-index-contrast-vertical sharp-down-taper and lateral gradual-up-taper ICMT” (HRC-VSDT×LGUT ICMT). 
     The present HRC-VSDT×LGUT ICMT preferably includes a laterally up-tapered and vertically down-tapered waveguiding core region occupied by Waveguide Core WC  1650 . When viewed from the top, Waveguide Core WC  1650  is surrounded on both sides by Side Waveguide Cladding SWCL  1670 . Waveguide Core  1650  preferably includes a lateral small-beam input/output port LSB-PT  1671 , a laterally straight waveguiding core region LSWC  1672 , a laterally tapering-up waveguiding core region LTUWC  1673 , a laterally straight radiation core region LSRC  1674 , and a lateral large-beam input/output port LLB-PT  1675 . The laterally straight waveguiding core region LSWC  1672  has a length l LSWC  and a width of w LSWC . The laterally tapering up waveguiding core region LTUWC  1673  has a length of l LTUWC , a lateral width of w LTUWCSB  at the small-beam input/output side, and a width w LTUWCLB  at the large-beam input/output side. The laterally straight radiation core region LSRC  1674  has a length of l LSRC  and a width of w LSRC . The total length of the waveguide core when viewed from the top is given by l WC =l LSWC +l LTUWC + LSRC . The width of the side waveguide cladding SWCL  1670  on both sides of the waveguide core WC  1650  is w SWCLSB  at the small beam input/output side, and is w SWCLLB  at the large beam side. The length of the side waveguide cladding SWCL  1670  l SWCL  is about equal to the total length of the waveguide core l WC . The length of the straight waveguide core l SWC  and the straight radiation core l LSRC  are typically not very critical to the operation of the device and can be zero in some applications (i.e., with these sections absent). 
     When viewed from the side, Waveguide Core WC  1650  is surrounded at the bottom by Lower Waveguide Cladding LWCL  1615 , and at the top by Upper Waveguide Cladding UWCL  1690 . Waveguide Core  1650  preferably includes a vertical small-beam input/output port VSB-PT  1691 , a vertically straight waveguiding core region VSWC  1692 , a vertically tapering-down waveguiding core region VTDWC  1693 , a vertically straight radiation core region VSRC  1694 , and a vertical large-beam input/output port VLB-PT  1695 . The vertically straight waveguiding core region VSWC  1692  has a length l VSWC  and a thickness of t VSWC . The vertically tapering down waveguiding core region VTDWC  1693  has a length of l VTDWC , a vertical thickness of t VTDWCSB  at the small-beam input/output side, and a vertical thickness of t VTDWCLB  at the large-beam input/output side. The vertically straight radiation core region VSRC  1694  has a length of l VSRC  and a thickness of t VSRC . The total length of the waveguide core when viewed from the side is given by l WC =l VSWC +l VTDWC +l VSRC . The thickness of the lower waveguide cladding LWCL  1615  is t LWCL . The thickness of the upper waveguide cladding UWCL  1690  at the small-beam input/output side is t UWCLSB  and at the large-beam input-output side is t UWCLLB . The length of the upper cladding l UWCL  and the length of the lower cladding l LWCL  are about equal to the total length of the waveguide core l WC . The length of the straight waveguide core l LSWC  and the straight radiation core l LSRC  are typically not very critical to the operation of the device and can be zero in some applications (i.e., with these sections absent). 
     The refractive index of the Waveguide Core WC  1650  is n WC . The refractive index of the Side Waveguide Cladding SWCL  1670  is n SWCL . The refractive index of the Lower Waveguide Cladding LWCL  1615  is n LWCL . The refractive index of the Upper Waveguide Cladding UWCL  1690  is n UWCL . 
     There are three options for the refractive index of the ICMT device  1600 , namely the small-refractive-index-contrast option, the medium-refractive-index-contrast option and the large-refractive-index-contrast option. For the small-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1650  and that of the Waveguide Claddings  1615 / 1690 / 1670  i.e. n WC /n LWCL , n WC /n UWCL , n WC /n SWCL , is assumed to be larger than 1.0 but smaller than about 1.3. That is 1.3≧n WC /n LWCL , n WC /n UWCL , n WC /n SWCL , ≧1.0. For the medium-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1650  and that of the Claddings  1615 / 1690 / 1670  i.e. n WC /n LWCL , n WC /n UWCL , n WC /n SWCL , is assumed to be larger than 1.3 but smaller than about 1.5. That is 1.5≧n WC /n LWCL , n WC /n UWCL , n WC /n SWCL , ≧.1.3. For the large-refractive-index-contrast option, the refractive index ratio between the refractive index of the Waveguide Core  1650  and that of the Claddings  1615 / 1690 / 1670  i.e. n WC /n LWCL , n WC /n UWCL , n WC /n SWCL , is assumed to be larger than about 1.5. That is n WC /n LWCL , n WC /n UWCL , n WC /n SWCL , ≧1.5. A short tapering length can be achieved if the relative refractive index contrast is high—in the region of either the medium-refractive-index contrast or the large-refractive-index contrast. The medium and large refractive index contrast will be referred to as the high-refractive index case. 
     In an exemplary device, the input/output port LSB-PT/VSB-PT  1671 / 1691  is configured to receive/transmit a light beam  1678 / 1698  typically having wavelength λ with a lateral beam width w LSB , and a vertical beam width w VSB . The input/output port LLB-PTJVLB-PT  1675 / 1695  is configured to receive/transmit a light beam  1679 / 1699  typically having wavelength λ with a lateral beam width of w LLB , and a vertical beam width of w VLB . 
     (i) An Exemplary Device 
     In an exemplary embodiment of device  1600 , the Waveguide Core WC  1650  is made up of silicon (Si) with a refractive index of n WC =3.5, the Lower Waveguide Cladding LWCL  1615  is made up of silica (SiO 2 ) with a refractive index of n LWCL =1.5, and the Upper and Side Waveguide Claddings UWCL/SWCL are made of silica-titania (SiO 2 —TiO 2 ) material mixture with a mixture composition to achieve a refractive index of n UWCL =1.7 or alternatively Si 3 N 4  with a refractive index of about 1.7 can be used. 
     When viewed from the top, the lateral widths of the waveguide core are w LSWC =0.3 μm, w LTUWCSB =0.3 μm, and w LTUWCLB =w LSRC =10 μm. The widths of the side waveguide claddings are w SWCLSB =4.85 μm and w SWCLLB =0 μm. The lengths of the waveguide core regions are l LSWC =10 μm, l LTUWC =100 μm, l LSRC =10 μm, and l WC =120 μm. The length of the side waveguide cladding is l SWCL =120 μm. 
     When viewed from the side, the vertical thicknesses of the waveguide core are t VSWC =0.3 μm, t VTDWCSB =0.3 μm, and t VTDWCLB =t VSRC =0. The thicknesses of the upper and lower waveguide claddings are t UWCLSB =9.7 μm, t UWCLLB =10 μm, and t LWCL =0.6 μm. The lengths of the waveguide core regions are l VSWC =80 μm, l VTDWC =30 μm, l VSRC =0 μm, and l WC =110 μm. The lengths of the upper and lower waveguide claddings are l UWCL =l LWCL =l WC =120 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 23  shows the result of a computer simulation of the spatial distribution of the electric field strength in the vertical and lateral directions for the light input at λ=1.5 μm after propagating into waveguide  1672 / 1692 . The mode size at the input end was 0.3 μm in both the vertical and lateral directions. 
     When viewed from the side, the light beam begins to expand at the point where the waveguide thickness (at 5 μm distance from the tip) is tapered down to 0.05 microns, which is near the tip of the tapering down region. The mode then radiate at an angle from that point to a larger mode size. The mode size reaches a size of about 5 μm at 10 μm away from the tip of the taper. 
     When viewed from the top, the light beam begins to expand at the point where the waveguide core tapers up laterally. The mode then enlarges following the lateral up-tapering waveguide core section  1673  to a larger mode size. The mode size reaches a size of about 10 μm at the end of the up-taper. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating the HRC-VSDT×LGUT ICMT device  1600  will now be described with reference to  FIGS. 24A–F . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     The HRC-VSDT×LGUT ICMT is fabricated by starting with a Silicon-On-Insulator (SOI) wafer. For a SOI wafer, a high refractive index silicon (Si) layer  1610  having a thickness of t 1  is already made or bonded on top of a low refractive index layer of SiO 2    1615  with a thickness of t 2 , as illustrated in  FIG. 24A . The SiO 2  layer  1615  is typically either deposited on a Si substrate  1620  before wafer bonding or thermally oxidized on the Si substrate before wafer bonding or thermally oxidized in the Si substrate after an oxygen ion implantation process. The fabrication procedure according to one embodiment is now described below: 
     A photoresist layer  1605  is first spin-coated on the Si layer  1610 , as shown in  FIG. 24A . A mask  1625  with a pattern  1630  as shown in  FIG. 24B  is used to expose the photoresist  1605  under UV light  1635 . The mask pattern  1630  is gray scaled in the longitudinal direction and laterally tapered up in the lateral direction. The gray-scale mask pattern is designed so that it gives a graduated exposure level with exposure dosage that varies from a small value to a large value across a length of 30 μm. The photoresist is then developed. The shape of the photoresist after exposure and development is a vertical down tapered shape that corresponds to the variation in the exposure dosage and a laterally tapered up shape as shown by photoresist pattern  1640  in  FIG. 24C  and  FIG. 24D . 
     A dry plasma etching procedure  1645  with selectivity of 1:0.3:˜0 between photoresist and Si and SiO 2  is used to etch down the Si layer vertically. Such a process is accomplished using a reactive ion etching system, or an inductively coupled plasma system, or any dry plasma system. The exemplary processing gases are SF 6 /O 2 /Cl 2 , as F-reactants and/or their neutrals etch Si, whereas O 2  etches photoresist and S—Cl reactants and/or their neutrals inhibit the etching of SiO 2 . Exemplary process parameters using a reactive ion etching system are: a mixture of 30 sccm:20 sccm:20 sccm of SF 6 :O 2 :Cl 2 , with an RF power of 350 W, and a process pressure of 25 mTorr. This etching process transfers the laterally up tapered and vertically down tapered pattern of the photoresist  1640  to the high-refractive-index Si layer and forms the laterally tapered up and vertically tapered down Si section  1650 . The resulting structure is shown in  FIGS. 24E and 24F . It should be noted that the easiness of this transfer process is dependent on the thickness t 1  of the top waveguiding Si layer. Typically the starting thickness for such a Si waveguide should be in the range of 0.2 to 0.5 μm. Considering that the photoresist layer has a typical thickness of about 1.0 μm and that the etching process typically etches Si at a rate that is not drastically different from that for the photoresist, such a direct pattern transfer can be achieved. As the etching process can be made to etch SiO 2  at a much slower rate, the interface between the top Si layer  1610  and the lower cladding SiO 2    1615  can be used as a natural stop during the dry etching process. It should be understood that the above process parameters are presented for purposes of illustrating a useful embodiment of the fabrication method and are not intended to limit other embodiments of the method. For example, a variety of dry etching parameters can be used depending on the photoresist type and the quality of the SOI wafer. As is known to those skilled in the art, the end result of a dry etched structure can be achieved via various combinations of the etching parameters. 
     To make the glass cladding, flame hydrolysis deposition, chemical vapor deposition, sputtering, Ion-Assisted-Deposition, or sol-gel spin coating of dielectric material, can generally be employed to deposit the top and side cladding regions  1690 / 1670  shown in  FIGS. 22A–B . The TiO 2 —SiO 2  material required can, in particular, be achieved using a sol-gel mixture of TiO 2  and SiO 2  precursors as is well known to those skilled in the art. Note that the surrounding cladding, including the bottom, top and side cladding medium, can all have various refractive indices and also a spatial variation or distribution of the refractive index value (described below), and the actual value that can be selected for this purpose can cover a wide range, e.g., 1.4 to 2.5. 
     It should be understood that these dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  1600  and are not intended to limit other embodiments of any exemplary device, or the device  1600 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces. 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the devices. 
     It should be understood to those skilled in the art that the device  1600  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (5) Exemplary Device  5 : A Lateral-Step-Refractive-Index and Vertical-Step-Refractive-Index (LSRIN×VSRIN) ICMT Device 
       FIG. 25  illustrates a fifth general embodiment of an ICMT device  1700  including a vertical and lateral step refractive index distribution to form a step index channel waveguide with refractive index difference between the core region and its surrounding cladding region. The device can perform as a two dimensional beam-size collimating element in both the lateral and the vertical directions for a propagating optical beam and can, for example, confine an optical beam that has already been expanded or enlarged from a small semiconductor waveguide using devices such as any of exemplary devices  1 – 4 . The device is not limited to use as a beam collimator but can also function as a waveguide to direct a light beam to a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used for direct light beam coupling into an optical fiber. It should be understood that these exemplary applications of device  1700  are intended to illustrate the uses for device  1700  and are not intended to limit the applications of other embodiments of device  1700 . The device can be referred to as a “low-refractive-index-contrast-vertical-step-refractive-index and lateral-step-refractive-index (LRC-LSRIN×VSRIN) ICMT”. 
     The present LRC-LSRIN×VSRIN ICMT preferably includes a waveguiding core region occupied by Waveguide Core WC  1730 . Waveguide Core WC  1730  is surrounded at the bottom by Lower Waveguide Cladding LWCL  1710 , on the top by Upper Waveguide Cladding UWCL  1745  and on both sides by Side Waveguide Cladding SWCL  1720 . Waveguide Core  1730  preferably includes a front beam input/output port FB-PT  1731 , a straight waveguiding core region SWC  1730 , and a back beam input/output port BB-PT  1732 . The straight waveguiding core region SWC  1730  has a length l SWC , a width of w SWC  and a thickness of t SWC . Lower Waveguide Cladding LWCL  1710  has a length of l LWCL , a width of w LWCL  and a thickness of t LWCL . Upper Waveguide Cladding UWCL  1745  has a length of l UWCL , a width of w UWCL  and a thickness of t UWCL . The two side waveguide claddings SWCL  1720  have a length of l SWCL , a width of w SWCL  and a thickness of t SWCL . The lengths of the waveguide claddings LWCL/UWCL/SWCL  1710 / 1745 / 1720 , l LWCL , l UWCL , and l SWCL  are about equal to the length of the waveguide core l WC . The refractive index of the Waveguide Core WC  1730  is n WC . The refractive index of the Lower Waveguide Cladding LWCL  1710  is n LWCL . The refractive index of the Upper Waveguide Cladding UWCL  1710  is n UWCL . The refractive index of the Side Waveguide Cladding SWCL  1710  is n SWCL . 
     In an exemplary device, the front beam input/output port FB-PT  1731  is configured to receive/transmit a light beam typically having wavelength λ with a beam size that roughly equals the size of an optical fiber, and the back beam input/output port LB-PT  1732  is also configured to receive/transmit a light beam typically having wavelength λ with a beam size that roughly equals the size of an optical fiber. 
     (i) An Exemplary Device 
     In an exemplary embodiment, the Waveguide Core WC  1730  is made up of lead-titania-silica with a refractive index of n WC =1.71, or Si 3 N 4  with a refractive index of about 1.7. The Lower Waveguide Cladding LWCL  1710  is made up of silica with a refractive index of n LWCL =1.5. The Upper Waveguide Cladding UWCL is made up of silica-titania with a refractive index of n UWCL =1.7, or Si 3 N 4  with a refractive index of about 1.7. The Side Waveguide Cladding SWCL is made up of lead silica-titania with a refractive index of n SWCL =1.7, or Si 3 N 4  with a refractive index of about 1.7. The size of the waveguide core is l WC =50 μm, w WC =10 μm and t WC =10 μm. The size of the lower waveguide cladding is l LWCL =50 μm, w LWCL =20 μm and t LWCL =1 μm. The size of the upper waveguide cladding is l UWCL =50 μm, w UWCL =20 μm and t UWCL =1 μm. The size of the two side waveguide claddings is l SWCL =50 μm, w SWCL =5 μm and t SWCL =10 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 26  shows the result of a computer simulation of the spatial distribution of the electric field strength for the light input at λ=1.5 μm after propagating into waveguide  1730 . The mode size at the input end is 10 μm. The waveguide confines the mode and guides its propagation to the other port. The mode size remains at about 10 μm at the other end of the waveguide. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating the LRC-LSRIN×VSRIN ICMT device  1700  will be described with reference to  FIGS. 27A–E . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     The LRC-LSRIN×VSRIN ICMT can be fabricated by starting with a Silica-On-Silicon (SOS) wafer that can be fabricated via a commercial process known to those skilled in the art, as shown in  FIG. 27A . For a SOS wafer, a low refractive index layer of SiO 2    1710  with a thickness of t LWCL  is already made on the Si substrate (not shown). The SiO 2  layer  1710  is typically either deposited on a Si substrate or thermally oxidized on the Si substrate. There are at least two possible ways to fabricate the LRC-LSRIN×VSRIN ICMT. 
     Method 1: As shown in  FIG. 27A , a dielectric or glass waveguiding film  1705  is deposited on the SiO 2  layer  1710 , which acts as a lower waveguide cladding. Depending on the dielectric material, an appropriate film deposition method can be used including evaporation, sputtering, Ion-Assisted-Deposition, chemical vapor deposition, flame hydrolysis, and spin or dip coating. As is well known to those skilled in the art, a common way to make a lateral step refractive index distribution is to dry etch a stripe  1706  in the deposited film. This can be easily achieved by photolithography. A photoresist layer  1702  can be deposited and UV-exposed through a conventional stripe mask. After photoresist development, a photoresist stripe pattern  1703  is generated, as shown in  FIG. 27B . Dry etching can then be used to transfer the photoresist stripe pattern to the dielectric or glass waveguide film  1705  to form a stripe pattern  1706 , shown in  FIG. 27C . While air can be used as the top and side cladding, generally speaking, a surrounding cladding material is preferred and such a cladding  1715 , which acts both as the upper waveguide cladding and the side waveguide cladding, can always be deposited, as shown in  FIG. 27C . 
     Method 2: Another approach to make a step refractive index distribution in the lateral direction is to first deposit a photosensitive waveguide film  1720  on the SiO 2    1710 , as shown in  FIG. 27D . In the case of silica-based glass, typically, Ge or Pb can be incorporated to make the glass film photosensitive. The incorporation of Ge or Pb for making a glass film photosensitive are described in a copending U.S. patent application Ser. No. 09/884,691 having the same inventors herein, entitled: “Method for Forming a Refractive-Index-Patterned Film for Use in Optical Device Manufacturing,” the disclosure of which is hereby incorporated by reference herein in its entirety. After the deposition of such a film  1720 , UV photo-imprinting  1725  through a conventional photomask  1735  can be used to define a refractive index increased stripe  1730 . If an upper cladding is preferred, a film  1745  with a refractive index lower than that of the photoimprinted stripe can then be deposited, as shown in  FIG. 27E . Alternatively, such a film can even be deposited before the UV photoimprinting as long as this upper cladding film does not substantially absorb the UV light. An obvious advantage of the photoimprinting approach is that the fabrication of a buried channel waveguide is significantly simplified as it does not involve etching, and hence the fabrication cost is also significantly lowered. 
     Either of the two methods produces a buried channel waveguide that has a step refractive index distribution in both the vertical and the horizontal/lateral direction. 
     It should be understood that these dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  1700  and are not intended to limit other embodiments of any exemplary device, or the device  1700 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces. 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the devices. 
     It should be understood to those skilled in the art that the device  1700  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (6) Exemplary Device  6  (A) A Composite-Lateral-Step-Refractive-Index and Vertical-Graded-Refractive Index (LSRIN×VGRIN) ICMT Device 
       FIG. 28  illustrates a sixth general embodiment of an ICMT device  1800  including a vertically graded and laterally step refractive index distribution to form a channel waveguide. The device  1800  can perform as a two dimensional beam-size collimating element in both the lateral and the vertical directions for a propagating optical beam and can, for example, confine and collimate an optical beam that has already been expanded or enlarged from a small semiconductor waveguide using a device such as any of exemplary devices  1 – 4 . The device is not limited to use as a beam collimator but can also function as a waveguide to direct a light beam to a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used for direct light beam coupling into an optical fiber. It should be understood that these exemplary applications of device  1800  are intended to illustrate the uses for device  1800  and are not intended to limit the applications of other embodiments of device  1800 . The device can be referred to as a “composite-lateral-step-refractive-index and vertical-graded-refractive index (LSRIN×VGRIN) ICMT”. 
     LSRIN×VGRIN ICMT  1800  preferably includes a waveguiding core region occupied by Waveguide Core WC  1835 . Waveguide Core WC  1835  is surrounded at the bottom by Lower Waveguide Cladding LWCL  1810 , on the top by Upper Waveguide Cladding UWCL  1840  and on both sides by Side Waveguide Cladding SWCL  1825 . Waveguide Core  1835  preferably includes a front beam input/output port FB-PT  1831 , a straight waveguiding core region SWC  1835 , and a back beam input/output port BB-PT  1832 . The straight waveguiding core region SWC  1835  has a length l SWC , a width of w SWC  and a thickness of t SWC . The Lower Waveguide Cladding LWCL  1810  has a length of l LWCL , a width of w LWCL  and a thickness of t LWCL . The Upper Waveguide Cladding UWCL  1840  has a length of l UWCL , a width of w UWCL  and a thickness of t UWCL . The two side waveguide claddings SWCL  1825  have a length of l SWCL , a width of w SWCL  and a thickness of t SWCL . The lengths of the waveguide claddings LWCL/UWCL/SWCL  1810 / 1840 / 1825 , l LWCL , l UWCL , and l SWCL  are about equal to the length of the waveguide core l WC . The refractive index of the Waveguide Core WC  1835  is not a constant. It is graded in the vertical direction and varies from the center of the core to the outer border of the core; the variation is represented by n WC (y) with y being the vertical coordinate. In the horizontal or lateral direction, the refractive index has a step profile. In other words, for a particular vertical coordinate y 0 , the refractive index is a constant n WC (y 0 ) within the core region and drops to the refractive index value of the side cladding n SWCL (y 0 ) at the two side borders. The refractive index of the Lower Waveguide Cladding LWCL  1810  is n LWCL . The refractive index of the Upper Waveguide Cladding UWCL  1840  is n UWCL . The refractive index of the Side Waveguide Cladding SWCL  1825  is n SWCL (y), which means it is y-coordinate dependent. 
     In an exemplary device, the front beam input/output port FB-PT  1831  is configured to receive/transmit a light beam typically having wavelength λ with a beam size that is already fully enlarged in the lateral direction and partially enlarged to an intermediate size in the vertical direction by a high-refractive-contrast tapered waveguide, and the back beam input/output port LB-PT  1832  is configured to receive/transmit a light beam typically having wavelength λ with a beam size that roughly equals the size of an optical fiber. 
     (i) An Exemplary Device 
     In an exemplary embodiment, the Waveguide Core WC  1835  is made up of lead-titania-silica with a refractive index distribution that approximates a parabolic distribution as given in Table I below. 
     
       
         
           
               
             
               
                 TABLE I 
               
             
            
               
                   
               
               
                 Refractive Index distribution 
               
            
           
           
               
               
               
            
               
                 y coordinate (μm) 
                 Refractive index of WC 
                 Refractive index of SWCL 
               
               
                   
               
            
           
           
               
               
               
            
               
                 −5.0 to −4.6 
                 1.610 
                 1.600 
               
               
                 −4.6 to −4.2 
                 1.624 
                 1.614 
               
               
                 −4.2 to −3.8 
                 1.636 
                 1.626 
               
               
                 −3.8 to −3.4 
                 1.648 
                 1.638 
               
               
                 −3.4 to −3.0 
                 1.658 
                 1.648 
               
               
                 −3.0 to −2.6 
                 1.668 
                 1.658 
               
               
                 −2.6 to −2.2 
                 1.676 
                 1.666 
               
               
                 −2.2 to −1.8 
                 1.683 
                 1.673 
               
               
                 −1.8 to −1.4 
                 1.688 
                 1.678 
               
               
                 −1.4 to −1.0 
                 1.693 
                 1.683 
               
               
                 −1.0 to −0.6 
                 1.696 
                 1.686 
               
               
                 −0.6 to −0.2 
                 1.699 
                 1.689 
               
               
                 −0.2 to 0.2   
                 1.700 
                 1.690 
               
               
                 0.2 to 0.6 
                 1.699 
                 1.689 
               
               
                 0.6 to 1.0 
                 1.696 
                 1.686 
               
               
                 1.0 to 1.4 
                 1.693 
                 1.683 
               
               
                 1.4 to 1.8 
                 1.688 
                 1.678 
               
               
                 1.8 to 2.2 
                 1.683 
                 1.673 
               
               
                 2.2 to 2.6 
                 1.676 
                 1.666 
               
               
                 2.6 to 3.0 
                 1.668 
                 1.658 
               
               
                 3.0 to 3.4 
                 1.658 
                 1.648 
               
               
                 3.4 to 3.8 
                 1.648 
                 1.638 
               
               
                 3.8 to 4.2 
                 1.636 
                 1.626 
               
               
                 4.2 to 4.6 
                 1.624 
                 1.614 
               
               
                 4.6 to 5.0 
                 1.610 
                 1.600 
               
               
                   
               
            
           
         
       
     
     The Lower Waveguide Cladding LWCL  1810  is made up of silica with a refractive index of n LWCL =1.5. The Upper Waveguide Cladding UWCL is made up of silica-titania with a refractive index of n UWCL =1.6. The Side Waveguide Cladding SWCL is made up of lead silica-titania with a refractive index of distribution given by Table I. The size of the waveguide core is l WC =50 μm, w WC =10 μm and t WC =10 μm. The size of the lower waveguide cladding is l LWCL =50 μm, w LWCL =30 μm and t LWCL =10 μm. The size of the upper waveguide cladding is l UWCL =50 μm, w UWCL =30 μm and t UWCL =10 μm. The size of the two side waveguide claddings is l SWCL =50 μm, w SWCL =10 μm and t SWCL =10 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 29  shows the results of a computer simulation of the spatial distribution of the electric field strength for the light input at λ=1.5 μm after propagating into waveguide  1835 . The mode size at the input end is 10 μm in both the lateral and vertical directions. In the lateral direction, the waveguide confines the mode and guides its propagation to the other port. In the vertical direction, in addition to the guiding of the light beam, the waveguide also functions as a lens in the sense that the beam size is changed periodically. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating LSRIN×VGRIN ICMT device  1800  will now be described with reference to  FIGS. 30A–D . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     The LSRIN×VGRIN ICMT can be fabricated by starting with a Silica-On-Silicon (SOS) wafer that can be fabricated via a commercial process known to those skilled in the art. For a SOS wafer, as shown in  FIG. 30A , a low refractive index layer of SiO 2    1810  with a thickness of t LWCL  is already made on the Si substrate (not shown). There are at least two ways to fabricate the LSRIN×VGRIN ICMT structure and these are now described by fabrication methods 1–2 below: 
     Method 1: As shown in  FIG. 30A , a graded index distribution in the vertical direction can be achieved by depositing multiple sufficiently thin layers of different material compositions  1805  on a lower cladding layer  1810 . In such a case, a continuous distribution of the refractive index can be approximated by a series of small effective refractive index steps with each thin layer having a different refractive index value. Depending on the property of the dielectric material, an appropriate film deposition method can be used. These methods include evaporation, flame hydrolysis, sputtering, Ion-Assisted-Deposition, chemical vapor deposition, and others. An exemplary method is sol-gel spin or dip coating which offers a possibility to vary the material composition of each thin layer easily. As a natural extension, a channel waveguide with a graded refractive index distribution in the vertical direction and a step refractive index distribution in the horizontal/lateral direction can be fabricated by etching a stripe  1815  in the film  1805 ; the result of etching is shown in  FIG. 30B . If a surrounding cladding is preferred, a subsequent deposition of a cladding material  1820  can always be performed. 
     Method 2: Another approach to make a step refractive index distribution in the lateral direction is to first deposit a photosensitive vertically graded refractive index film  1825  on the SiO 2    1810 , as shown in  FIG. 30C . In the case of silica-based glass, typically, Ge or Pb can be incorporated to make the glass film photosensitive. After the deposition of such a film  1825 , UV photo-imprinting through a conventional channel photomask  1830  can be used to induce a nearly step refractive index distribution in the lateral direction to form the channel waveguide  1835 . 
     If an upper cladding is preferred, a film  1840  with a refractive index lower than that of the photoimprinted stripe can then be deposited as shown in  FIG. 30D . Alternatively, such a film can even be deposited before the UV photoimprinting as long as this upper cladding film does not substantially absorb the UV light. An obvious advantage of the photoimprinting approach is that the fabrication of a buried channel waveguide is significantly simplified as it does not involve etching and hence the fabrication cost is also significantly lowered. 
     Either method produces a buried channel waveguide that has a step refractive index distribution in the horizontal/lateral direction and a graded refractive index distribution in the vertical direction. 
     It should be understood that these dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  1800  and are not intended to limit other embodiments of any exemplary device, or the device  1800 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces of the present invention 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bidirectional nature of the said devices. 
     It should be understood to those skilled in the art that the device  1800  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (B) A Composite-Lateral-Graded-Refractive-Index and Vertical-Graded-Refractive Index (LGRIN×VGRIN) ICMT Device 
       FIG. 31  illustrates an alternative embodiment of an ICMT device  1850  including a vertical as well as a lateral graded refractive index distribution to form a channel waveguide. The device  1850  can perform as a two dimensional beam-size collimating element in both the lateral and the vertical directions for a propagating optical beam and can, for example, confine and collimate an optical beam that has already been partially expanded or enlarged from a small semiconductor waveguide via a tapered structure such as any of exemplary devices  1 – 4 . The device is not limited to use as a beam collimator but can also function as a waveguide to direct a light beam to a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used for direct light beam coupling into an optical fiber. It should be understood that these exemplary applications of device  1850  are intended to illustrate the uses for device  1850  and are not intended to limit the applications of other embodiments of device  1850 . The device can be referred to as a “(composite-lateral-graded-refractive-index and vertical-graded-refractive index” (LGRIN×VGRIN) ICMT. 
     LGRIN×VGRIN ICMT  1850  preferably includes a waveguiding core region occupied by Waveguide Core WC  1885 . Waveguide Core WC  1885  is surrounded at the bottom by Lower Waveguide Cladding LWCL  1860 , on the top by Upper Waveguide Cladding UWCL  1890  and on both sides by Side Waveguide Cladding SWCL  1875 . Waveguide Core  1885  preferably includes a front beam input/output port FB-PT  1881 , a straight waveguiding core region SWC  1885 , and a back beam input/output port BB-PT  1882 . The straight waveguiding core region SWC  1885  has a length l SWC , a width of w SWC  and a thickness of t SWC . The Lower Waveguide Cladding LWCL  1860  has a length of l LWCL , a width of w LWCL  and a thickness of t LWCL . The Upper Waveguide Cladding UWCL  1890  has a length of l UWCL , a width of w UWCL  and a thickness of t UWCL . The two side waveguide claddings SWCL  1875  have a length of l SWCL , a width of w SWCL  and a thickness of t SWCL . The lengths of the waveguide claddings LWCL/UWCL/SWCL  1860 / 1890 / 1875 , l LWCL , l UWCL , and l SWCL  are about equal to the length of the waveguide core l WC . The refractive index of the Waveguide Core WC  1885  is not a constant. In both the vertical and the lateral directions, it is graded and varies from the center of the core to the outer borders of the core. The variation can be represented in the vertical direction by n WC (y) with y being the vertical coordinate and in the lateral direction by n WC (x) with x being the lateral coordinate. The refractive index of the Lower Waveguide Cladding LWCL  1860  is n LWCL . The refractive index of the Upper Waveguide Cladding UWCL  1890  is n UWCL . The refractive index of the Side Waveguide Cladding SWCL  1875  is n SWCL (y), which means it can be y coordinate dependent. 
     In an exemplary device, the front beam input/output port FB-PT  1881  is configured to receive/transmit a light beam typically having wavelength λ with a beam size that is already enlarged to an intermediate size by a high-refractive-contrast tapered waveguide, and the back beam input/output port LB-PT  1882  is configured to receive/transmit a light beam typically having wavelength λ with a beam size that roughly equals the size of an optical fiber. 
     (i) An Exemplary Device 
     In an exemplary embodiment, the Waveguide Core WC  1885  is made up of lead-titania-silica with a refractive index distribution that approximates a parabolic distribution in both the vertical and the lateral directions as given by the equation 
     
       
         
           
             
               
                 n 
                 WC 
               
               ⁡ 
               
                 ( 
                 
                   x 
                   , 
                   y 
                 
                 ) 
               
             
             = 
             
               1.61 
               + 
               
                 
                   0.09 
                   ⁡ 
                   
                     [ 
                     
                       1 
                       - 
                       
                         ( 
                         
                           
                             
                               x 
                               2 
                             
                             + 
                             
                               y 
                               2 
                             
                           
                           
                             
                               
                                 5 
                                 ⁢ 
                                 μ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 m 
                               
                               ) 
                             
                             2 
                           
                         
                         ) 
                       
                     
                     ] 
                   
                 
                 . 
               
             
           
         
       
     
     The Lower Waveguide Cladding LWCL  1860  is made up of silica with a refractive index of n LWCL =1.5. The Upper Waveguide Cladding UWCL is made up of silica-titania with a refractive index of n UWCL =1.6. The Side Waveguide Cladding SWCL is made up of lead silica-titania with a refractive index distribution given by Table I (above). The size of the waveguide core is l WC =50 μm, w WC =10 μm and t WC =10 μm. The size of the lower waveguide cladding is l LWCL =50 μm, w LWCL =30 μm and t LWCL =10 μm. The size of the upper waveguide cladding is l UWCL =50 μm, w UWCL =30 μm and t UWCL =10 μm. The size of the two side waveguide claddings is l SWCL =50 μm, w SWCL =10 μm and t SWCL =10 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 32  shows the results of a computer simulation of the spatial distribution of the electric field strength for the light input at λ=1.5 μm after propagating into waveguide  1885 . The mode size at the input end is 10 μm in both the lateral and vertical directions. In both the vertical and the lateral directions, in addition to the guiding of the light beam, the waveguide also functions as a lens in the sense that the beam size get focused and collimated periodically. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating LGRIN×VGRIN ICMT device  1850  will now be described with reference to  FIGS. 33A–B . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     The LGRIN×VGRIN ICMT can be fabricated by starting with a Silica-On-Silicon (SOS) wafer that can be fabricated via a commercial process known to those skilled in the art. For a SOS wafer, as illustrated in  FIG. 33A , a low refractive index layer of SiO 2    1860  with a thickness of t LWCL  is already made on the Si substrate (not shown). The fabrication of the LGRIN×VGRIN ICMT according to one embodiment below. 
     As shown in  FIG. 33A , a graded refractive index distribution in the vertical direction can be achieved by depositing a multiple sufficiently thin layers of photosensitive materials with different compositions  1855  on a lower cladding layer  1860 . In such a case, a continuous distribution of the refractive index can be approximated by a series of small effective refractive index steps with each thin layer having a different refractive index value. Depending on the property of the dielectric material, an appropriate film deposition method can be used. These methods include evaporation, flame hydrolysis, sputtering, Ion-Assisted-Deposition, chemical vapor deposition, and others. An exemplary method is sol-gel spin or dip coating which offers a possibility to vary the material composition of each thin layer easily. In the case of silica-based glass, the photosensitivity of the glass material can be enabled by incorporating Ge or Pb into the glass film as set forth above. 
     As for the graded refractive index distribution in the lateral direction, it can be created by using a gray scale mask  1880  to optically imprint a graded refractive index change in the film because the refractive index change can be made to depend on the dosage of the photoimprinting which can be controlled by the gray scale of the gray mask. If an upper cladding  1890  is preferred, such a film can then be deposited on top of the photosensitive film, as shown in  FIG. 33B . Alternatively, such an upper cladding film  1890  can be deposited before the UV photoimprinting as long as it does not substantially absorb the photoimprinting light. The approaches described here are obviously advantageous because of their simplicity in terms of fabrication as set forth above. Alternatively, a vertical refractive index variation can be achieved by varying the amount of photosensitive materials such as the Ge or Pb content in the vertical direction. In this case, the UV photoimprinting described above will result in vertical refractive index variation in addition to the lateral refractive index variation. 
     The resulting device is a buried channel waveguide that has a graded index distribution in the both the vertical and the lateral directions. 
     It should be understood that these dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  1850  and are not intended to limit other embodiments of any exemplary device, or the device  1850 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces of the present invention 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the said devices. 
     It should be understood to those skilled in the art that the device  1850  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (7) Exemplary Device  7 : A Vertical-Sharp-Down-Taper-and-Lateral-Gradual-Up- Taper-Cascaded-with-a-Vertical-Graded-Refractive-Index-and-Lateral-Step-Refractive-Index (VSDT×LGUT+VGRIN×LSRIN) ICMT Device 
       FIGS. 34A–B  illustrates a seventh general embodiment of a combined module ICMT device  1900  including a vertical-sharp-down-taper and lateral-gradual-up-taper waveguide core embedded in and connected to a large channel waveguide with a nearly symmetric vertical graded refractive index and lateral step refractive index distribution. It is in fact one possible combination of a taper waveguide integrated with a lower refractive-index-contrast large-size channel waveguide. The device  1900  performs as a two dimensional beam-size enlargement and collimating element in both the lateral and the vertical directions for a propagating optical beam, and can, for example, enlarge and collimate an optical beam from a small semiconductor waveguide to a large beam size such as one with a beam size close to that of an optical fiber. The device is not limited to use as a beam enlarger/collimator but can also function as a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device is used for direct light beam coupling into an optical fiber. It should be understood that these exemplary applications of device  1900  are intended to illustrate the uses for device  1900  and are not intended to limit the applications of other embodiments of device  1900  to these examples. The device can be referred to as a “vertical-sharp-down-taper-and-lateral-gradual-up-taper-cascaded-with-a-vertical-graded-refractive-index-and-lateral-step-refractive-index (VSDT×LGUT+VGRIN×LSRIN) ICMT. 
     The present VSDT×LGUT+VGRIN×LSRIN ICMT  1900  preferably includes a Waveguiding Core region occupied by Waveguide Core WC  1945 . This Waveguide Core WC  1945  is embedded in an optical medium  1915 / 1950  that acts as the cladding for the Waveguide Core WC  1945  wherever the Waveguide Core WC  1945  exists, but at the same time the same optical medium  1915 / 1950  acts as a Lower Refractive index Contrast Waveguiding Core region. This Lower Refractive index Contrast Waveguiding Core region  1915 / 1950  is occupied by Waveguide Core LRCWC  1915 / 1950 , and is further surrounded by an even lower refractive index cladding region  1905 / 1955 / 1976 . 
     Waveguide Core WC  1945  is surrounded at the bottom by Lower Graded Waveguide Cladding LGWCL  1915 , on the top by Upper Graded Waveguide Cladding UGWCL  1950  and on both sides by Side Stratified Waveguide Cladding SSWCL  1970 , which is basically a combination of the Lower Graded Waveguide Cladding LGWCL  1915  and the Upper Graded Waveguide Cladding UGWCL  1950 . 
     When viewed from the side, the Waveguide Core WC  1945  preferably includes a small beam input/output port SB-PT  1971   a , a straight waveguiding core region SWC  1972   a , a vertically tapered down region VTD  1973   a , and an intermediate beam output/input port region  1974   a . The straight waveguiding core region SWCa  1972   a  has a length l HRCSWCa , and a thickness of t HRCSWCa . The vertically tapered down waveguiding core region VTDWC  1973   a  has a length of l HRCVTDWCa , a vertical thickness of t HRCVTDWCaSB  at the small-beam input/output side, and a vertical thickness of t HRCVTDCaLB  at the large-beam input/output side. 
     When viewed from the top, Waveguide Core  1945  preferably includes a small beam input/output port SB-PT  1971   b , a straight waveguiding core region SWC  1972   b , a laterally tapered up region LTU  1973   b , a wider straight waveguiding core region WSWC  1975  and a large beam output/input port region  1974   b . The straight high refractive index contrast waveguiding core region SWCb  1972   b  has a length l HRCSWCb , and a width of w HRCSWCb . The laterally tapered up waveguiding core region LTUWC  1973   b  has a length of l HRCLTUWCb , a width of w HRCLTUWCbSB  at the small-beam input/output side, and a width of w HRCLTUCbLB  at the large-beam input/output side. The wider straight waveguide core region WSWC  1975  has a length of l HRCWSWCb  and a width of w HRCWSWCb =w HRCLTUCbLB . 
     It should be understood that the straight waveguiding core regions  1972   a  and  1972   b  (based on whether the structure is viewed from the side or from the top), may have the same or a different length. Similarly, the vertically tapered down region  1973   a  (when viewed from the top) and the laterally tapered up region  1973   b  (when viewed from the side) may have the same or a different length. In other words, the vertical and lateral beam size transformation may be achieved independently or at the same time or with one slightly earlier than the other. Furthermore, the taper regions do not need to be symmetric with respect to the central axis and also the tapering up or down slope do not need to be straight and may be of any curve shape. 
     Lower-Refractive-index-Contrast-Waveguide Core LRCWC  1915 / 1950  preferably surrounds and embeds the Waveguide Core WC  1945 . When viewed from the side, the Lower Refractive index Contrast Waveguide Core LRCWC  1915 / 1950  is sandwiched at the bottom by a Lower Waveguide Cladding LWCL  1905 , and on the top by an Upper Waveguide Cladding UWCL  1955 . As the Lower-Refractive-index-Contrast-Waveguide Core LRCWC  1915 / 1950  has a graded refractive index distribution along the vertical direction, it can take the intermediate size beam launched at the tip region  1974   a  from the Waveguide Core WC  1945  and further expand the beam; after the beam has traveled a certain distance equivalent to the focal length of the graded refractive index lens structure, the beam will be collimated and reach the back large beam output/input port LB-PT  1977 , from where another single mode waveguide such as a single mode optical fiber will continue to guide the light beam. When viewed from the top, the LRCWC  1970  (i.e.  1915 / 1950 ) is surrounded on both sides by Side Waveguide Cladding SWCL  1976 , (with lower refractive index when compared to the Waveguide Core LRCWC  1970 ). The Lower Refractive index Contrast Waveguide Core LRCWC  1970  has a length of l LRCWC , a width of w LRCWC  and a thickness of t LRCWC . The Lower Waveguide Cladding LWCL  1905  has a length of l LWCL , a width of w LWCL  and a thickness of t LWCL . The Upper Waveguide Cladding UWCL  1955  has a length of l UWCL , a width of w UWCL  and a thickness of t UWCL . The two side waveguide claddings SWCL  1976  have a length of l SWCL , a width of w SWCL  and a thickness of t SWCL . The lengths of the waveguide claddings LWCL/UWCL/SWCL  1905 / 1955 / 1976 , l LWCL , l UWCL , and l SWCL  are about equal to the length of the lower refractive index contrast waveguide core l LRCWC . 
     The refractive index of the Waveguide Core WC  1945  is n HRCWC . The refractive index of the Lower Refractive index Contrast Waveguide Core LRCWC  1915 / 1950  is n LRCWC (y), which means it is y coordinate dependent, with y being the vertical coordinate. The refractive index of the Lower Waveguide Cladding LWCL  1905  is n LWCL . The refractive index of the Upper Waveguide Cladding UWCL  1955  is n UWCL . The refractive index of the Side Waveguide Cladding SWCL  1976  is n SWCL (y), which means it can also be y coordinate dependent. It should be understood that the Side Waveguide Cladding SWCL  1976  can have either a uniform or non-uniform refractive index distribution. In other words, the refractive index of the Side Waveguide Cladding may or may not be a constant. In the latter case, it can be graded in the vertical direction. In device  1900 , as in exemplary device  6 , the refractive index of the Waveguide Core LRCWC  1915 / 1950  is not a constant. It is graded in the vertical direction and varies from the center plane of the core to the top and bottom border of the core. The variation can be represented by n LRCWC (y) with y being the vertical coordinate. In the horizontal or lateral direction, the refractive index may have a step profile. In other words, for a given vertical coordinate y 0 , the refractive index is a constant, n LRCWC (y 0 ), within the core region and drops at the two side borders to the refractive index value of the side cladding, n SWCL (y 0 ). 
     In an exemplary device, the front beam input/output port FB-PT  1971   a / 1971   b  is configured to receive/transmit a light beam typically having wavelength λ with a very small beam size. The mode size of the straight section of the Waveguide Core WC  1945  can be designed to match the mode size of a preceding very small size waveguide. The laterally tapering up section of the WC  1945  will enlarge the beam fully in the lateral direction and the vertical tapering down section will partially enlarge the beam in the vertical direction to an intermediate size. The vertically graded Lower Refractive index Contrast Waveguide Core LRCWC is configured to take the vertically intermediate size beam launched at region  1974   a  and further expand and collimate it. The back beam input/output port LB-PT  1977  is configured to receive/transmit a light beam typically having wavelength λ with a beam size that roughly equals the size of an optical fiber. 
     (i) An Exemplary Device 
     In an exemplary embodiment, the High Refractive index Contrast Waveguide Core WC  1945  is made up of silicon with a refractive index of n HRCWC 3.5, the Low Refractive index Contrast Waveguide Core LRCWC  1915 / 1950  is made up of lead-titania-silica material mixture with a mixture composition to achieve a refractive index of a refractive index distribution that approximates a parabolic distribution as given in Table II below. 
     
       
         
           
               
             
               
                 TABLE II 
               
             
            
               
                   
               
               
                 Refractive Index distribution 
               
            
           
           
               
               
               
            
               
                   
                 Refractive index of 
                   
               
               
                 y coordinate (μm) 
                 LRCWC 
                 Refractive index of SWCL 
               
               
                   
               
            
           
           
               
               
               
            
               
                 −5.0 to −4.6 
                 1.610 
                 1.600 
               
               
                 −4.6 to −4.2 
                 1.624 
                 1.614 
               
               
                 −4.2 to −3.8 
                 1.636 
                 1.626 
               
               
                 −3.8 to −3.4 
                 1.648 
                 1.638 
               
               
                 −3.4 to −3.0 
                 1.658 
                 1.648 
               
               
                 −3.0 to −2.6 
                 1.668 
                 1.658 
               
               
                 −2.6 to −2.2 
                 1.676 
                 1.666 
               
               
                 −2.2 to −1.8 
                 1.683 
                 1.673 
               
               
                 −1.8 to −1.4 
                 1.688 
                 1.678 
               
               
                 −1.4 to −1.0 
                 1.693 
                 1.683 
               
               
                 −1.0 to −0.6 
                 1.696 
                 1.686 
               
               
                 −0.6 to −0.2 
                 1.699 
                 1.689 
               
               
                 −0.2 to 0.2   
                 1.700 
                 1.690 
               
               
                 0.2 to 0.6 
                 1.699 
                 1.689 
               
               
                 0.6 to 1.0 
                 1.696 
                 1.686 
               
               
                 1.0 to 1.4 
                 1.693 
                 1.683 
               
               
                 1.4 to 1.8 
                 1.688 
                 1.678 
               
               
                 1.8 to 2.2 
                 1.683 
                 1.673 
               
               
                 2.2 to 2.6 
                 1.676 
                 1.666 
               
               
                 2.6 to 3.0 
                 1.668 
                 1.658 
               
               
                 3.0 to 3.4 
                 1.658 
                 1.648 
               
               
                 3.4 to 3.8 
                 1.648 
                 1.638 
               
               
                 3.8 to 4.2 
                 1.636 
                 1.626 
               
               
                 4.2 to 4.6 
                 1.624 
                 1.614 
               
               
                 4.6 to 5.0 
                 1.610 
                 1.600 
               
               
                   
               
            
           
         
       
     
     The Lower Waveguide Cladding LWCL  1905  is made up of silica-titania with a refractive index of n LWCL =1.5. The Upper Waveguide Cladding UWCL is made up of silica-titania with a refractive index of n UWCL =1.5. The Side Waveguide Cladding SWCL is made up of lead silica-titania with a refractive index distribution also given in Table II. 
     The dimensions of the Waveguide Core WC  1945  are as follows: l HRCSWCa =110 μm, t HRCSWCa =0.3 μm, l HRCVTDWCa =30 μm, t HRCVTDWCaSB =0.3 μm, t HRCVTDCaLB =0 μm, l HRCSWCb =10 μm, w HRCSWCb. =0.3 μm, l HRCLTUWCb =100 μm, w HRCLTUWCbSB =0.3 μm, w HRCLTUCbLB =10 μm, l HRCWSWCb =30 μm and w HRCWSWCb =10 μm. The dimensions of the Lower Refractive index Contrast Waveguide Core LRCWC  1915 / 1950  are as follows: l LRCWC =170 μm, w LRCWC =10 μm, t LRCWC =10 μm. The Lower Waveguide Cladding LWCL  1905  has a length of l LWCL =170 μm, a width of w LWCL =30 μm and a thickness of t LWCL =2 μm. The Upper Waveguide Cladding UWCL  1955  has a length of l UWCL =170 μm, a width of w UWCL =30 μm and a thickness of t UWCL =2 μm. The two side waveguide claddings SWCL  1976  have a length of l SWCL =170 μm, a width of w SWCL =10 μm and a thickness of t SWCL =10 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 35  shows the results of a computer simulation of the spatial distribution of the electric field strength for the light input at λ=1.5 μm after being launched from the left into the small light beam input/output port  1971   a / 1971   b . The mode size at the input end is 0.3 μm in both the lateral and vertical directions. In the vertical direction, as the tapering down section only lies towards the right for the last 30 μm and the cascading beam expansion action occurs on both the left and the right part of the WC taper tip, the computer simulation is thus zoomed into the last 60 μm of the coupler structure. In the lateral direction, the beam expansion is entirely enabled by the tapering up section  1973   b , which has a length of 100 μm, hence the computer simulation is zoomed mainly in this section. As can be seen from  FIG. 35 , the combined module coupler structure can transform a very small beam of about 0.3 μm in size to a large size beam of about 10 μm in both the vertical and the horizontal directions. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating a HRC-VSDT×LGUT+VGRIN×LSRIN ICMT device  1900  will now be described with reference to  FIGS. 36A–N . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     The HRC-VSDT×LGUT+VGRIN×LSRIN ICMT  1900  may be fabricated by starting with a Silica-On-Silicon (SOS) wafer shown in  FIG. 36A , which may be fabricated via a commercial process known to those skilled in the art. For a SOS wafer, a low refractive index layer of SiO 2    1905  with a thickness of t LWCL  is already made on a Si substrate  1910 . The fabrication of the HRC-VSDT×LGUT+VGRIN×LS-RIN ICMT structure according to one embodiment now described below. 
     As shown in  FIGS. 36B–C , a graded index distribution in the vertical direction can be achieved by depositing multiple sufficiently thin layers of photosensitive materials with different compositions  1915  on a lower cladding layer  1905 . In such a case, a continuous distribution of the refractive index can be approximated by a series of small refractive index steps with each thin layer having a different refractive index value. Depending on the property of the dielectric material, an appropriate film deposition method can be used. These methods include evaporation, flame hydrolysis, sputtering, Ion-Assisted-Deposition, chemical vapor deposition, and others. An exemplary method is sol-gel spin or dip coating which offers a possibility to vary the material composition of each thin layer easily. In the case of silica-based glass, the photosensitivity of the glass material can be enabled by incorporating Ge or Pb into the glass film. It should be understood that any optically transparent dielectric material in the spectrum region of interest to optical communication can be used for the deposition; examples include lead silica, germania-silica, titania-silica, silicon oxynitride, silicon nitride, polysilicon, silicon-rich-silica, silicon carbide, polymer and a combination of different materials. The parameter details of one exemplary embodiment of the design for the GRIN layers has already been shown in Table II. Note that the refractive index distribution does not have to follow the parabolic profile and may be of any profile. It should also be understood that other film deposition techniques such as flame hydrolysis, sputtering, Ion-Assisted-Deposition and chemical vapor deposition may also be used to deposit the bottom half of the GRIN dielectric waveguide. 
     As shown in  FIG. 36D , a thin silicon layer  1920 , which is to be made into the high refractive index contrast waveguide core WC  1945 , may be defined in another piece of bare Si wafer using, for example, ion implantation. A thin silicon layer  1920  is formed on an ion implanted layer  1925  that is sitting on top of a Si substrate  1930 . This ion-implanted wafer may then be flipped over and wafer-bonded to the GRIN dielectric-coated SiO 2 —Si wafer, as shown in  FIG. 36E . The top thick Si part  1930  and the ion-implanted layer  1925  may then be removed using a lift-off technique such as rapid thermal annealing and/or wafer thinning. The result after removing the ion-implanted layer is shown in  FIG. 36F . This technique may be modified if, for instance, a non-symmetric vertical-GRIN waveguide is desired, as will be described below. 
     To form a vertically down-tapered and horizontally/laterally up-tapered high-index core, the fabrication steps described with regard to Exemplary device  4  may be used. In short, a photoresist layer is first spin-coated on the Si waveguide layer  1920 . A mask pattern  1935  with a gray-scaled transparency along the longitudinal direction, and a horizontal/lateral up taper, shown in  FIG. 36G , can be used together with UV exposure and photoresist development to make a vertically tapered down and horizontally/laterally tapered up photoresist pattern  1940 , shown in  FIG. 36H . The lateral and vertical tapers may be made independent from each other, although in  FIG. 36H , they have been put together to save space and also to illustrate the principle. Followed by dry etching, as indicated in  FIG. 36I , the vertically down tapered and horizontally/laterally up tapered photoresist pattern  1940  is transferred to the high refractive index Si layer to form the vertically down-tapered and horizontally/laterally up-tapered Si section  1945 , as shown in  FIGS. 36J–K . As was previously noted, the interface between the top Si layer and the SiO 2  based layer may be used as a natural stop during the dry etching process. It should also be noted that a shadow mask based dry etching process or a diffusion-limited wet etching process could also be used to form the Si taper as well. 
     To form the top half of the vertically GRIN dielectric waveguide part, an effective refractive-index-decreasing dielectric region  1950  is deposited, as shown in  FIG. 36L . Preferably photosensitive sol-gel silica is spin-coated in almost the same way as for the bottom half of the dielectric waveguide except that the order of the layers is now reversed. It should again be understood that the parabolic refractive index distribution cited here is only one example and, as is well known to those skilled in the art, various other refractive index distributions may be used. On the very top, a relatively thick (say 2 μm) silica layer  1955  can be deposited to act as an upper cladding. 
     Note that the sol-gel technique has an advantage in that the spin-coated film will change shape from conformal coating to planarized coating. The initial layer thickness may not be so even and uniform. However, due to the fact that the Si taper  1945  is generally only about 0.2˜0.5 μm high, after a few spin-on layers, the following layers should be flat and uniform as suggested in  FIG. 36L . With a top cladding  1955 , a buried GRIN planar waveguide  1915 / 1950  is thus formed with the Si taper  1945  in the center of the GRIN waveguide core. 
     To form a dielectric channel waveguide with a step refractive index distribution in the lateral direction to confine light propagation, dry etching can be used. However, UV imprinting is preferred since the deposited GRIN dielectric film can be made photosensitive. A step channel mask  1960 , as shown in  FIG. 36M , can be used to form a single mode step refractive index channel waveguide  1965  to confine light in the horizontal/lateral direction. When viewed from the top, as shown in  FIG. 36N , the result is a tapered up Si taper  1945  integrated with a step index channel waveguide  1965 . 
     It should be understood that these dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  1900  and are not intended to limit other embodiments of any exemplary device, or the device  1900 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the various embodiments of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces, of the present invention 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the said devices. 
     It should be understood to those skilled in the art that the device  1900  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (8) Exemplary Device  8 : A Vertical-Sharp-Down-Taper-and-Lateral-Sharp-Down-Taper-Cascaded-with-a-Symmetric-Vertical-Graded-Refractive-Index-and-Lateral-Graded-Refractive Index (VSDT×LSDT+VGRIN×LGRIN) ICMT Device 
       FIGS. 37A–B  illustrates an eighth general embodiment of a combined module ICMT device  2000  including a vertically and laterally down-tapered waveguide core embedded in and connected to a large channel waveguide with a nearly symmetric vertically and laterally graded refractive index distribution. It is in fact a second possible combination of a taper integrated with a lower-refractive-index-contrast large-size channel waveguide. The device  2000  can perform as a two dimensional beam-size enlargement and collimating element in both the lateral and the vertical directions for a propagating optical beam, and can in particular enlarge and collimate an optical beam from a small semiconductor waveguide to enable the beam to match with a single mode optical fiber. The device is not limited to use as a beam enlarger/collimator but can also function as a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used for direct light beam coupling into an optical fiber. It should be understood that these exemplary applications of device  2000  are intended to illustrate the uses for device  2000  and are not intended to limit the applications of other embodiments of device  2000 . The device can be referred to as a “vertical-sharp-down-taper and lateral-sharp-down-taper-cascaded-with-asymmetric-vertical-graded-refractive-index-and-lateral-graded-refractive-index (VSDT×LSDT+VGRIN×LGRIN) ICMT”. 
     VSDT×LSDT+VGRIN×LGRIN ICMT  2000  preferably includes a Waveguiding Core region occupied by Waveguide Core WC  2045 . This Waveguide Core WC  2045  is embedded in an optical medium  2015 / 2050  that acts as the cladding for the Waveguide Core WC  2045  wherever the Waveguide Core WC  2045  exists, but at the same time, the same optical medium  2015 / 2050  acts as a Lower Refractive index Contrast Waveguiding Core region. This Lower Refractive index Contrast Waveguiding Core region is occupied by Waveguide Core LRCWC  2015 / 2050 , and is further surrounded by an even lower refractive index cladding region 
     Waveguide Core WC  2045  is surrounded at the bottom by Lower Graded Waveguide Cladding LGWCL  2015 , on the top by Upper Graded Waveguide Cladding UGWCL  2050  and on both sides by Side Stratified Waveguide Cladding SSWCL  2070 , which is basically a combination of the Lower Graded Waveguide Cladding LGWCL  2015  and the Upper Graded Waveguide Cladding UGWCL  2050 . 
     When viewed from the side, the Waveguide Core WC  2045  preferably includes a small beam input/output port SB-PT  2071   a , a high refractive index contrast straight waveguiding core region SWC  2072   a , a high refractive index contrast vertically tapered down region VTD  2073   a , and an intermediate beam output/input port region  2074   a . The straight high refractive index contrast waveguiding core region SWCa  2072   a  has a length l HRCSWCa , and a thickness of t HRCSWCa . The high refractive index contrast vertically tapered down waveguiding core region VTDWC  2073   a  has a length of l HRCVTDWCa , a vertical thickness of t HRCVTDWCaSB  at the small-beam input/output side, and a vertical thickness of t HRCVTDCaLB  at the large-beam input/output side. 
     When viewed from the top, the Waveguide Core  2045  preferably includes a small beam input/output port SB-PT  2071   b , a straight waveguiding core region SWC  2072   b , a laterally tapered down region LTD  2073   b , and an intermediate beam output/input port region  2074   b . The straight waveguiding core region SWCb  1972   b  has a length l HRCSWCb , and a width of w HRCSWCb . The laterally tapered down waveguiding core region LTDWC  1973   b  has a length of l HRCLTDWCb , a width of w HRCLTDWCbSB  at the small-beam input/output side, and a width of w HRCLTDCbLB  at the large-beam input/output side. 
     It should be understood that the straight waveguiding core regions  2072   a  and  2072   b  (based on whether the structure is viewed from the side or from the top), may have the same or a different length. Similarly, the vertically tapered down region  2073   a  (when viewed from the side) and the laterally tapered down region  2073   b  (when viewed from the side) may have the same or a different length, provided that the tip for both tapering down geometries ends at the same point in space. Furthermore, the taper regions do not need to be symmetric with respect to the central axis and also the tapering down slopes do not need to be straight and may be of any curve shape. 
     Lower-Refractive-index-Contrast-Waveguide Core LRCWC  2015 / 2050  preferably surrounds and embeds the Waveguide Core WC  2045 . When viewed from the side, the Lower Refractive index Contrast Waveguide Core LRCWC  2015 / 2050  is sandwiched at the bottom by a Lower Waveguide Cladding LWCL  2005 , and on the top by an Upper Waveguide Cladding UWCL  2055 . As the Lower-Refractive-index-Contrast-Waveguide Core LRCWC  2015 / 2050  has a graded refractive index distribution along both the vertical and lateral directions, it can take the intermediate size beam launched at the tip region  2074   a / 2074   b  from the Waveguide Core WC  2045  and further expand the beam. After the beam has traveled a certain distance equivalent to the focal length of the graded refractive index lens structure, the beam will be collimated and reach the back large beam output/input port LB-PT  2077 , from where another single-mode waveguide such as a single-mode optical fiber will continue to guide the light beam. The Lower Refractive index Contrast Waveguide Core LRCWC  2070  has a length of l LRCWC , a width of w LRCWC  and a thickness of t LRCWC . The Lower Waveguide Cladding LWCL  2005  has a length of l LWCL , a width of w LWCL  and a thickness of t LWCL . The Upper Waveguide Cladding UWCL  2055  has a length of l UWCL , a width of w UWCL  and a thickness of t UWCL . The two side waveguide claddings SWCL  2076  have a length of l SWCL , a width of w SWCL  and a thickness of t SWCL . The lengths of the waveguide claddings LWCL/UWCL/SWCL  2005 / 2055 / 2076 , l LWCL , l UWCL , and l SWCL  are about equal to the length of the low refractive index contrast waveguide core l LRCWC . 
     The refractive index of the Waveguide Core WC  2045  is n HRCWC . The refractive index of the Lower Refractive index Contrast Waveguide Core LRCWC  2015 / 2050  is n LRCWC (x, y), which means it is x and y coordinate dependent, with x being the lateral coordinate and y being the vertical coordinate. The refractive index of the Lower Waveguide Cladding LWCL  2005  is n LWCL . The refractive index of the Upper Waveguide Cladding UWCL  2055  is n UWCL . The refractive index of the Side Waveguide Cladding SWCL  2076  is n SWCL (y), which means it may also be y-coordinate dependent. It should be understood that the Side Waveguide Cladding SWCL  2076  may have either a uniform or non-uniform refractive index distribution. In other words, the refractive index of the Side Waveguide Cladding may or may not be a constant. In the latter case, it may be graded in the vertical direction. In a preferred embodiment, the refractive index of the Waveguide Core LRCWC  2015 / 2050  is not a constant. It is graded in the vertical direction and varies from the center plane of the core to the top and bottom border of the core. The variation can be represented by n LRCWC (y) with y being the vertical coordinate. In the lateral direction, the refractive index of the Lower Refractive index Contrast Waveguide Core LRCWC  2070  also have a graded profile. However, for a given vertical coordinate y 0 , the refractive index n LRCWC (x, y 0 ) is graded within the core region and drops to n SWCL (y 0 ), the refractive index value of the side cladding at the two side borders. 
     In an exemplary device, the front beam input/output port FB-PT  2071   a / 2071   b  is configured to receive/transmit a light beam typically having wavelength λ with a very small beam size. The mode size of the straight section of the Waveguide Core WC  2045  can be designed to match the mode size of a preceding very-small-size waveguide. The laterally and vertically tapering down section  2073   a / 2073   b  will partially enlarge the beam in both the vertical and the lateral directions to an intermediate size. The laterally and vertically graded Lower Refractive index Contrast Waveguide Core LRCWC is configured to take the intermediate size beam launched at region  2074   a / 2074   b  and further expand and collimate it. The back beam input/output port LB-PT  2077  is configured to receive/transmit a light beam typically having wavelength λ with a beam size that roughly equals the size of an optical fiber. 
     (i) An Exemplary Device 
     In an exemplary embodiment, the Waveguide Core WC  2045  is made up of silicon with a refractive index of n HRCWC =3.5, the Lower Refractive index Contrast Waveguide Core LRCWC  2015 / 2050  is made up of lead-titania-silica material mixture with mixture composite designed to give a refractive index distribution that approximates a parabolic distribution in both the vertical and the lateral directions as given by the equation: 
     
       
         
           
             
               
                 n 
                 LRCWC 
               
               ⁡ 
               
                 ( 
                 
                   x 
                   , 
                   y 
                 
                 ) 
               
             
             = 
             
               1.61 
               + 
               
                 
                   0.09 
                   ⁡ 
                   
                     [ 
                     
                       1 
                       - 
                       
                         ( 
                         
                           
                             
                               x 
                               2 
                             
                             + 
                             
                               y 
                               2 
                             
                           
                           
                             
                               
                                 5 
                                 ⁢ 
                                 μ 
                                 ⁢ 
                                 
                                     
                                 
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                                 m 
                               
                               ) 
                             
                             2 
                           
                         
                         ) 
                       
                     
                     ] 
                   
                 
                 . 
               
             
           
         
       
     
     The Lower Waveguide Cladding LWCL  2005  is made up of silica-titania with a refractive index of n LWCL =1.5. The Upper Waveguide Cladding UWCL is made up of silica-titania with a refractive index of n UWCL =1.5. The Side Waveguide Cladding SWCL is made up of lead silica-titania with a refractive index distribution given in Table II. 
     The dimensions of the Waveguide Core WC  2045  are as follows: lHRCSWCa=10 μm, t HRCSWCa =0.3 μm, l HRCVTDWCa =30 μm, t HRCVTDDWCaSB =0.3 μm, t HRCVTDCaLB =0 μm, l HRCSWCb =10 μm, w HRCSWCb =0.3 μm, l HRCLTDWCb =30 μm, w HRCLTDWCbSB =0.3 μm, w HRCLTDCbLB =0 μm. The dimensions of the Lower Refractive index Contrast Waveguide Core LRCWC  2015 / 2050  are as follows: l LRCWC =70 μm, w LRCWC =10 μm, t LRCWC =10 μm. The Lower Waveguide Cladding LWCL  2005  has a length of l LWCL =70 μm, a width of w LWCL =30 μm and a thickness of t LWCL =2 μm. The Upper Waveguide Cladding UWCL  2055  has a length of l LWCL =70 μm, a width of w UWCL =30 μm and a thickness of t UWCL =2 μm. The two side waveguide claddings SWCL  2076  have a length of l SWCL =70 μm, a width of w SWCL =10 μm and a thickness of t SWCL =10 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 38  shows the results of a computer simulation of the spatial distribution of the electric field strength for the light input at λ-1.5 μm after being launched from the left into the small light beam input/output port  2071   a / 2071   b . The mode size at the input end is 0.3 μm in both the lateral and vertical directions. As the tapering down section only lies towards the right for the last 30 μm in both the vertical and the lateral directions and the cascading beam expansion action occurs on both the left and the right part of the WC taper tip, the computer simulation is thus zoomed into the last 60 μm of the coupler structure. Although the computer simulation is only 2 dimensional, it can be applied to both the vertical and the lateral directions because the structures are very similar in this case. As can be seen from  FIG. 38 , the whole combined module coupler structure can transform a very small beam of 0.3 μm in size to a large size beam of 10 μm in both the vertical and the horizontal directions. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating a VSDT×LSDT+VGRIN.time-s.LGRIN ICMT device  2000  will now be described with reference to  FIGS. 39A–N . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     The VSDT×LSDT+VGRIN×LGRIN ICMT may be fabricated by starting with a Silica-On-Silicon (SOS) wafer, shown in  FIG. 39A , which may be fabricated via a commercial process known to those skilled in the art. For an SOS wafer, a low refractive index layer of SiO 2    2005  with a thickness of t LWC  is already made on a Si substrate  2010 . The fabrication of the VSDT×LSDT+VGRIN×LGRIN ICMT structure according to one embodiment is now described below. 
     As shown in  FIGS. 39B–C , a graded refractive index distribution in the vertical direction may be achieved by depositing multiple sufficiently thin layers of photosensitive materials with different compositions  2015  on a lower cladding layer  2005 . In such a case, a continuous distribution of the refractive index can be approximated by a series of small effective refractive index steps with each thin layer having a different refractive index value. Depending on the property of the dielectric material, an appropriate film deposition method can be used. These methods include evaporation, flame hydrolysis, sputtering, Ion-Assisted-Deposition, chemical vapor deposition, and others. An exemplary method is sol-gel spin or dip coating which offers the ability to vary the material composition of each thin layer easily. In the case of silica-based glass, the photosensitivity of the glass material may be enabled by incorporating Ge or Pb into the glass film. It should be understood that any optically transparent dielectric material in the spectrum region of interest to optical communication may be used for the deposition; examples include lead silica, germania-silica, titania-silica, silicon oxynitride, silicon nitride, polysilicon, silicon-rich-silica, silicon carbide, polymer and a combination of different materials. The parameter details of one preferred embodiment of the design for the GRIN layers has already been shown in Table II. Note that the refractive index distribution does not have to follow the parabolic profile and may be of any profile. It should also be understood that other film deposition techniques such as flame hydrolysis, sputtering, Ion-Assisted-Deposition and chemical vapor deposition may also be used to deposit the bottom half of the GRIN dielectric waveguide. 
     As shown in  FIG. 39D , a thin silicon layer  2020 , which is to be made into the high index contrast waveguide core, may be defined in another piece of bare Si wafer using, for example, ion implantation. This will form a thin silicon layer  2020  on an ion implanted layer  2025  that is sitting on top of a Si substrate  2030 . This ion-implanted wafer may be flipped over and wafer-bonded to the GRIN dielectric-coated SiO 2 —Si wafer, as shown in  FIG. 39E . The top thick Si part  2030  and the ion-implanted layer  2025  may then be removed using a lift-off technique such as rapid thermal annealing and/or wafer thinning. The result is shown in  FIG. 39F . This technique may be modified if, for instance, a non-symmetric vertical-GRIN waveguide is desired, as will be described below. 
     To form a vertically as well as horizontally/laterally tapered down section, the fabrication steps are similar to those described above for exemplary device  4 . A photoresist layer is first spin-coated on the Si waveguide layer  2020 . A mask pattern  2035 , shown in  FIG. 39G , with a gray scaled transparency along the longitudinal direction and meanwhile a horizontal/lateral down/narrow taper can be used together with UV exposure and photoresist development to make a vertically as well as horizontally/laterally down tapered photoresist pattern  2040 , as shown in  FIG. 39H . Followed by dry etching, as shown in  FIG. 39I , the vertically as well as horizontally/laterally down tapered photoresist pattern  2040  can be transferred to the high refractive index Si layer and form the vertically and horizontally/laterally tapered down/narrow Si section  2045 , as shown in  FIGS. 39J–K . It should again be noted that the interface between the top Si layer and the glass-based cladding material can be used as a natural stop during the dry etching process. 
     To form the top half of the vertically GRIN glass/polymer waveguide, a refractive-index-decreasing dielectric region  2050  is deposited as shown in  FIG. 39L . Preferably photosensitive sol-gel silica is spin-coated in almost the same way as for the bottom half of the glass/polymer waveguide except that the order of the layers is now reversed. It should again be understood that the parabolic refractive index distribution cited here is only one example and, as is well known to those skilled in the art, other refractive index distributions may be used. On the very top, a relatively thick (say 3 μm) silica layer  2055  may be deposited to act as an upper cladding. 
     It should be noted that the sol-gel technique has an advantage in that the spin-coated film will change shape from conformal coating to planarized coating. The initial layer thickness may not be so even and uniform. However, due to the fact that the Si taper  2045  is generally only about 0.2.about.0.5 μm high, after a few spin-on layers, the following layers should be flat and uniform. With a top cladding  2055 , a buried GRIN planar waveguide  2015 / 2050  can thus be formed with the Si taper  2045  in the center of the GRIN waveguide core. 
     As has been described before, to form a dielectric channel waveguide with a GRIN distribution in the horizontal/lateral direction to confine light propagation, UV imprinting may be used since the deposited GRIN glass/polymer film may be made photosensitive. A GRIN channel mask  2060 , as shown in  FIG. 39M  can be used to form a single mode GRIN channel waveguide  2065  to confine light in the horizontal/lateral direction, resulting in the structure shown in  FIG. 39N . 
     It should be understood that the above dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  2000  and are not intended to limit other embodiments of any exemplary device, or the device  2000 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the various embodiments of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces. 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the devices. 
     It should be understood to those skilled in the art that the device  2000  can be fabricated on a different substrate other than silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (9) Exemplary Device  9 : A Vertical-Sharp-Down-Taper-Cascaded-with-a-Nonsymmetric-Vertical-Graded-Refractive-Index-(VSDT+NSVGRIN) Device 
       FIGS. 40A–C  illustrates a ninth general embodiment of a combined module ICMT device  2100  involving a vertically down-tapered waveguide core cascaded with and connected to a large channel waveguide with a non-symmetric vertically graded refractive index distribution. In the lateral direction, the high refractive index contrast taper can be either gradually tapered up, as shown in  FIG. 40B , or sharply tapered down, as shown in  FIG. 40C . In the former case, the large channel waveguide has a step index profile in the lateral direction. In the latter case, the large channel waveguide has a graded index profile. Device  2100  differs from exemplary device  7  or  8  in that the vertical GRIN waveguide in device  2100  is non-symmetric. 
     The device  2100  can perform as a two-dimensional beam-size enlargement and collimating element in both the lateral and the vertical directions for a propagating optical beam, and can in particular enlarge and collimate an optical beam from a small semiconductor waveguide to enable the beam to match with a single mode optical fiber. The device is not limited to use as a beam enlarger/collimator but can also function as a beam reducer when the optical beam propagates in the reverse direction. Furthermore, the device can be used for direct light beam coupling into an optical fiber. It should be understood that these exemplary applications of device  2100  are intended to illustrate the uses for device  2100  and are not intended to limit the applications of other exemplary embodiments of device  2100  to these examples. The device can be referred to as a “vertical-sharp-down-taper-cascaded-with-a-nonsymmetric-vertical-graded-refractive-index (VSDT+NSVGRIN) ICMT”. 
     The present VSDT+NSVGRIN ICMT preferably includes a Waveguiding Core region occupied by Waveguide Core WC  2145 / 2150 . This Waveguide Core WC  21415 / 2150  is sandwiched at the bottom by a Lower Waveguide Cladding LWC  2110  and on the top as well as at both sides by a vertically graded refractive medium  2155  that acts as the top and side cladding for the Waveguide Core WC  2145 / 2150  wherever the Waveguide Core WC  2145 / 2150  exists. The same graded refractive index medium  2155  acts as a Lower Refractive Index Contrast Waveguiding Core region. This Lower Refractive index Contrast Waveguiding Core region is occupied by Waveguide Core LRCWC  2155 , and is further surrounded at the top by an even lower refractive index Upper Waveguide Cladding  2160 . 
     When viewed from the side, the Waveguide Core WC  2145 / 2150  preferably includes a small beam input/output port SB-PT  2171   a , a high refractive index contrast straight waveguiding core region SWC  2172   a , a high refractive index contrast vertically down-tapered region VTD  2173   a , and an intermediate beam output/input port region  2174   a . The straight high refractive index contrast waveguiding core region SWCa  2172   a  has a length l HRCSWCa , and a thickness of t HRCSWCa . The high refractive index contrast vertically tapered down waveguiding core region VTDWC  2173   a  has a length of l HRCVTDWCa , a vertical thickness of t HRCVTDWCaSB  at the small-beam input/output side, and a vertical thickness of t HRCVTDCaLB  at the large-beam input/output side. 
     In the laterally up-tapering case, when viewed from the top, the Waveguide Core  2145  preferably includes a small beam input/output port SB-PT  2171   b , a straight waveguiding core region SWC  2172   b , a laterally up-tapered region LTU  2173   b , a wider straight waveguiding core region WSWC  2175  and a large beam output/input port region  2174   b . The straight waveguiding core region SWCb  2172   b  has a length l HRCSWCb , and a width of w HRCSWCb . The laterally up-tapered waveguiding core region LTUWC  2173   b  has a length of l HRCLTUWCb , a width of w HRCLTUWCbSB  at the small-beam input/output side, and a width of w HRCLTUCbLB  at the large-beam input/output side. The wider straight waveguide core region WSWC  2175  has a length of l HRCWSWCb  and a width of w HRCWSWCb =w HRCLTUCbLB . 
     In the laterally down-tapering case, when viewed from the top, the Waveguide Core  2150  preferably includes a small beam input/output port SB-PT  2171   c , a straight waveguiding core region SWC  2172   c , a laterally down-tapered region LTD  2173   c , and an intermediate beam output/input port region  2174   c . The straight waveguiding core region SWCc  2172   c  has a length l HRCSWCc , and a width of w HRCSWCc . The laterally tapered down waveguiding core region LTDWC  2173   c  has a length of l HRCLTDWCc , a width of w HRCLTDWCcSB  at the small-beam input/output side, and a width of w HRCLTDCcLB  at the large-beam input/output side. 
     It should be understood that the straight waveguiding core regions  2171   a  and  2171   b/c  (based on whether the structure is viewed from the side or from the top), may have the same or a different length. Similarly, the vertically down-tapered region  2172   a  (when viewed from the side) and the laterally up/down-tapered region  2172   b/c  (when viewed from the side) may have the same or a different length, provided that in the case where the waveguide core is both laterally and vertically down-tapered, the tip for both down-tapering geometries ends at the same point in space. Furthermore, the taper regions do not need to be symmetric with respect to the central axis and also the down-tapering slope (or slopes) do(es) not need to be straight and may be of any curve shape. 
     Lower-Refractive-index-Contrast-Waveguide Core LRCWC  2155  surrounds and embeds the Waveguide Core WC  2145 / 2150  either partially or entirely. When viewed from the side, the Lower Refractive index Contrast Waveguide Core LRCWC  2155  is sandwiched at the bottom by a Lower Waveguide Cladding LWCL  2110 , and on the top by an Upper Waveguide Cladding UWCL  2160 . As the Lower-Refractive-index-Contrast-Waveguide Core LRCWC  2155  has a graded refractive index distribution in the vertical direction, it can take a vertically intermediate size beam launched at the tip region  2174   a  from the Waveguide Core WC  2145 / 2150  and further expand the beam. After the beam has traveled a certain distance equivalent to the focal length of the graded refractive index structure, the beam will be collimated and reach the back large beam output/input port LB-PT  2177 , from where another single mode waveguide such as a single mode optical fiber will continue to guide the light beam. The Lower Refractive index Contrast Waveguide Core LRCWC  2155  has a length of l LRCWC , a width of W LRCWC  and a thickness of t LRCWC . The Lower Waveguide Cladding LWCL  2110  has a length of l LWCL , a width of w LWCL  and a thickness of t LWCL . The Upper Waveguide Cladding UWCL  2160  has a length of l UWCL , a width of w UWCL  and a thickness of t UWCL . The side waveguide claddings SWCL  2176   b/c  have a length of l SWCL , a width of w SWCL  and a thickness of t SWCL . The lengths of the waveguide claddings LWCL/UWCL/SWCL  2005 / 2055 / 2076 , l LWCL , l UWCL , and l SWCL  are about equal to the length of the low refractive index contrast waveguide core l LRCWC . 
     The refractive index of the Waveguide Core WC  2145 / 2150  is n HRCWC . The refractive index of the Lower Refractive index Contrast Waveguide Core LRCWC  2155  is n LRCWC (x, y), which means that it may be x- and y-coordinate dependent, with x being the lateral coordinate and y being the vertical coordinate. The refractive index of the Lower Waveguide Cladding LWCL  2110  is n LWCL . The refractive index of the Upper Waveguide Cladding UWCL  2160  is n UWCL . The refractive index of the Side Waveguide Cladding SWCL  2176   b/c  is n SWCL (y), which means it may also be y coordinate dependent. It should be understood that the Side Waveguide Cladding SWCL  2176   b/c  may have either a uniform or non-uniform refractive index distribution. In other words, the refractive index of the Side Waveguide Cladding may or may not be a constant. In the latter case, it may be graded in the vertical direction. Similar to exemplary device  6 , the refractive index of the Lower Refractive index Contrast Waveguide Core LRCWC  2155  is preferably not a constant. It is graded in the vertical direction and varies from the bottom to the top. The variation can be represented by n LRCWC (y), with y being the vertical coordinate. In the lateral direction, the refractive index of the Lower Refractive index Contrast Waveguide Core LRCWC  2155  may have either a step or a graded profile. In the step profile case, for a fixed y value, the refractive index n LRCWC (x, y) has a fixed higher value within the core region and a lower value outside the core region. For the graded profile case, for a given y coordinate y 0 , the refractive index n LRCWC (x, y 0 ) is graded within the core region and drops to n SWCL (y 0 ), the refractive index value of the side cladding, at the two side borders. 
     In an exemplary device, the front beam input/output port FB-PT  2171   a/b/c  is configured to receive/transmit a light beam typically having wavelength λ with a very small beam size. The mode size of the straight section  2172   a/b/c  of the Waveguide Core WC  2145 / 2150  is preferably designed to match the mode size of a preceding very small size waveguide. The vertically down-tapering section  2173   a  will partially enlarge the beam in the vertical direction to an intermediate size. The vertically graded Lower Refractive index Contrast Waveguide Core LRCWC  2155  is configured to take the intermediate size beam launched at region  2174   a  and further expand and collimate it. Note that in device  2100 , only the top half of a symmetric GRIN waveguide is fabricated on top of the Waveguide Core taper. The consequence is that the refractive index distribution is no longer symmetric in the vertical direction (Note that in the lateral direction across a channel waveguide, the refractive index distribution can still be made symmetric using, e.g., UV imprinting as has been explained). The coupler is functional because the situation is equivalent to using half of a lens with the Si taper located on the central axis of the lens. The lateral beam enlargement for both the laterally up tapering and down tapering cases is substantially the same as has been described for exemplary devices  7  and  8  and will thus not be repeated. The back beam input/output port LB-PT  2177  is configured to receive/transmit a light beam typically having wavelength λ with a beam size that roughly equals the size of an optical fiber. 
     (i) An Exemplary Device 
     In an exemplary embodiment, the Waveguide Core WC  2145 / 2150  is made up of silicon with a refractive index of n HRCWC =3.5. The Lower Refractive index Contrast Waveguide Core LRCWC  2155  is made up of lead-titania-silica material mixture with mixture composite designed to give a refractive index distribution that approximates half of a parabolic distribution in the vertical direction as governed by the following equation and detailed in Table III. 
     
       
         
           
               
             
               
                 TABLE III 
               
             
            
               
                   
               
               
                 
                   
                     
                       
                         
                           
                             
                               n 
                               LRCWC 
                             
                             ⁡ 
                             
                               ( 
                               y 
                               ) 
                             
                           
                           = 
                           
                             1.65 
                             + 
                             
                               0.03 
                               ⁡ 
                               
                                 [ 
                                 
                                   1 
                                   - 
                                   
                                     ( 
                                     
                                       
                                         y 
                                         2 
                                       
                                       
                                         
                                           
                                             10 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             μm 
                                           
                                           ) 
                                         
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                           
                         
                         , 
                         
                           y 
                           ≥ 
                           0. 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 The refractive index profile of a high focusing power 
               
               
                 10 μm height half GRIN waveguide 
               
            
           
           
               
               
               
            
               
                 coordinate y (μm) 
                 LRCWC refractive index n 
                 SWCL refractive index n 
               
               
                   
               
               
                 0.0–0.4 
                 1.950 
                 1.940 
               
               
                 0.4–0.8 
                 1.948 
                 1.938 
               
               
                 0.8–1.2 
                 1.946 
                 1.936 
               
               
                 1.2–1.6 
                 1.942 
                 1.932 
               
               
                 1.6–2.0 
                 1.938 
                 1.928 
               
               
                 2.0–2.4 
                 1.933 
                 1.923 
               
               
                 2.4–2.8 
                 1.926 
                 1.916 
               
               
                 2.8–3.2 
                 1.919 
                 1.909 
               
               
                 3.2–3.6 
                 1.911 
                 1.901 
               
               
                 3.6–4.0 
                 1.902 
                 1.892 
               
               
                 4.0–4.4 
                 1.892 
                 1.882 
               
               
                 4.4–4.8 
                 1.881 
                 1.871 
               
               
                 4.8–5.2 
                 1.869 
                 1.859 
               
               
                 5.2–5.6 
                 1.856 
                 1.846 
               
               
                 5.6–6.0 
                 1.842 
                 1.832 
               
               
                 6.0–6.4 
                 1.827 
                 1.817 
               
               
                 6.4–6.8 
                 1.811 
                 1.801 
               
               
                 6.8–7.2 
                 1.794 
                 1.784 
               
               
                 7.2–7.6 
                 1.777 
                 1.767 
               
               
                 7.6–8.0 
                 1.758 
                 1.748 
               
               
                 8.0–8.4 
                 1.738 
                 1.728 
               
               
                 8.4–8.8 
                 1.718 
                 1.708 
               
               
                 8.8–9.2 
                 1.696 
                 1.686 
               
               
                 9.2–9.6 
                 1.674 
                 1.664 
               
               
                  9.6–10.0 
                 1.650 
                 1.640 
               
               
                 &gt;10.0 
                 1.470 
                 1.470 
               
               
                   
               
            
           
         
       
     
     The Lower Waveguide Cladding LWCL  2110  is made up of silica with a refractive index of n LWCL =1.47. The Upper Waveguide Cladding UWCL is made up of silica with a refractive index of n UWCL =1.47. The Side Waveguide Cladding SWCL is made up of lead silica-titania with a refractive index of distribution given in Table III. 
     For the case of a laterally up-tapered Waveguide Core WC  2145 , the dimensions of the WC are as follows: l HRCSWCa =110 μm, t HRCSWCa =0.3 μm, l HRCVTDWCa =30 μm, t HRCVTDWCaSB =0.3 μm, t HRCVTDCaLB =0 μm, l HRCSWCb =10 μm, w HRCSWCb. =0.3 μm, l HRCLTUWCb =100 μm, w HRCLTUWcbSB =0.3 μm, w HRCLTUCbLB =10 μm, l HRCWSWCb =30 μm and w HRCWSWcb =10 μm. The dimensions of the Lower Refractive index Contrast Waveguide Core LRCWC  2155  are as follows: l LRCWC =170 μm, w LRCWC =10 μm, t LRCWC =10 μm. The Lower Waveguide Cladding LWCL  2110  has a length of l LWCL =170 μm, a width of w LWCL =30 μm and a thickness of t LWCL =2 μm. The Upper Waveguide Cladding UWCL  2160  has a length of l UWCL =170 μm, a width of w UWCL =30 μm and a thickness of t UWCL =2 μm. The two side waveguide claddings SWCL  2176   b  have a length of l SWCL =170 μm, a width of w SWCL =10 μm and a thickness of t SWCL =10 μm. 
     For the case of a laterally down-tapered Waveguide Core WC  2150 , the dimensions of the WC are as follows: l HRCSWCa =10 μm, t HRCSWCa =0.3 μm, l HRCVTDWCa =30 μm, t HRCVTDWCaSB =0.3 μm, t HRCVTDCaLB =0 μm, l HRCSWCb =10 μm, w HRCSWCb. =0.3 μm, l HRCLTDWCb =30 μm, w HRCLTDWCbSB =0.3 μm, w HRCLTDCbLB =0 μm. The dimensions of the Lower Refractive index Contrast Waveguide Core LRCWC  2155  are as follows: l LRCWC =70 μm, w LRCWC =10 μm, t LRCWC =10 μm. The Lower Waveguide Cladding LWCL  2110  has a length of l LWCL =70 μm, a width of w LWCL =30 μm and a thickness of t LWCL =2 μm. The Upper Waveguide Cladding UWCL  2160  has a length of l UWCL =70 μm, a width of w UWCL =30 μm and a thickness of t UWCL =2 μm. The two side waveguide claddings SWCL  2176   c  have a length of l SWCL =70 μm, a width of w SWCL =10 μm and a thickness of t SWCL =10 μm. It should be appreciated by one skilled in the art that all parameter values used in this and other exemplary embodiments are approximate and that the actual values can vary significantly. 
     (ii) General Operation of the Device 
       FIG. 41  shows the results of a computer simulation of the spatial distribution of the electric field strength in the vertical direction for light input from either direction at λ=1.5 μm. The upper graph shows the behavior when light is input into the small light beam input/output port  2171   a ; the mode size at input/output port  2171   a  is 0.3 μm in the vertical direction. As the tapering down section only lies towards the right for the last 30 μm and the cascading beam expansion action occurs on both the left and the right part of the vertical WC taper tip, the computer simulation is thus zoomed into the last 60 μm of the coupler structure. The lower graph is similar. It shows the behavior when light is input to the large light beam output/input port  2177 . Comparing the two graphs demonstrates that the device has good coupling efficiency in both directions. 
     The beam expansion in the lateral direction for the laterally tapered up and laterally tapered down cases are similar to what has been described for exemplary devices  7  and  8  respectively; these cases are not shown in  FIG. 41 . 
     As can be seen from  FIG. 41 , the combined module coupler structure can transform a very small beam of about 0.3 μm in size to a large size beam of about 10 μm in both the vertical and the horizontal directions. Very efficient bidirectional coupling is thus made possible by the supercoupler. 
     (iii) Device Fabrication Procedures 
     An exemplary procedure for fabricating a VSDT+NSVGRIN ICMT device  2100  will now be described with reference to  FIGS. 42A–N . This procedure is given for the purpose of illustration and not limitation, as there are other procedures that can be used to achieve the same fabrication results and other materials systems or device structures that can be utilized to fabricate devices with the same functional capabilities. 
     The VSDT+NSVGRIN ICMT may be fabricated by starting with a Silicon-On-Insulator (SOI) wafer, as shown in  FIG. 42A , which may be fabricated via a commercial process known to those skilled in the art. For an SOI wafer, a silicon layer  2105  is already made on an insulating SiO 2    2110  which is on top on a silicon substrate  2115 . The fabrication of the VSDT+NSVGRIN ICMT structure according to one embodiment is now described. 
     A Si taper may be fabricated by spin-coating a photoresist layer  2120  on the Si waveguide layer  2105 , as shown in  FIG. 42A . A mask pattern with a gray scale transparency along the longitudinal direction and also a laterally tapered up pattern  2125 , as shown in  FIG. 42B , or a laterally tapered down pattern  2130 , as shown in  FIG. 42C , can be used together with UV exposure and photoresist development to make a tapered photoresist pattern that is vertically tapered down and laterally tapered up (pattern  2135  in  FIG. 42D ) or down (pattern  2140  in  FIG. 42E ). Followed by dry etching, indicated in  FIG. 42F , the tapered photoresist pattern  2135  or  2140  may be transferred to the high refractive index Si layer and form the corresponding Si section  2145  or  2150 , shown in  FIGS. 42G–I . The interface between the top Si layer and the lower SiO 2  layer may be used as a natural stop during the dry etching process. A shadow mask based dry etching or a diffusion-limited wet etching may also be used to form the Si taper. 
     To form the top half of the vertically GRIN waveguide  2155 , multiple layers of effective refractive-index-decreasing dielectrics may be deposited on top of the Si taper, as shown in  FIG. 42J . Preferably photosensitive silica is spin-coated so that confinement of light in the horizontal/lateral direction may be easily achieved using UV imprinting. On the very top, a relatively thick (say 2 μm) silica layer  2160  may be deposited to act as an upper cladding. 
     As has already been discussed, to form a dielectric channel waveguide with either a GRIN or step refractive index distribution in the lateral direction to confine light propagation, UV imprinting may be used as the deposited vertically GRIN film can be made photosensitive. In this respect, a step channel mask  2165 , as shown in  FIG. 42K , or a GRIN channel mask  2170 , as shown in  FIG. 42L , may be used to form a single-mode step channel waveguide  2185 , as shown in  FIG. 42M , or GRIN channel glass waveguide  2190 , as shown in  FIG. 42N , to confine light in the horizontal/lateral direction. 
     One skilled in the art will recognize that high efficiency coupling from the buried GRIN channel waveguide to a single mode optical fiber or vice versa is not a problem as the mode size is already designed to match that of a single mode fiber. The chief consideration is the location for this joining. Preferably, the fiber is made to butt-join the GRIN channel waveguide at a fully expanded/collimated location rather than a focused location. The fiber is also preferably located at the first fully expanded location from the tip of the Si taper, in order to reduce light propagation losses in the glass channel waveguide. 
     It should be understood that the above dimensions and exemplary lengths are presented for the purposes of illustrating a useful embodiment of the device  2100  and are not intended to limit other embodiments of any exemplary device, or the device  2100 . A variety of dimensions and sizes can be used, depending on the application desired, as well as the fabrication materials, processes and technologies that are employed. 
     Also, it should be understood that the shapes of the waveguides or the taper (for example the shapes as defined by the surfaces dividing the cladding regions and the core regions) do not generally have to be linear or in the form of straight lines and planar surfaces. Curved shapes and different waveguide dimensions may be utilized as long as they achieve the same functions such as waveguiding or optical mode size transformation with similar topological connections. This applies for all the surfaces of the waveguide structures of the various embodiments of the present invention, including the side surfaces, the top and bottom surfaces, and the input/output surfaces. 
     In addition, it should be understood that the substrate is used to mechanically support the waveguide structures, and can be made up of irregular shapes, or structures, or materials as long as it serves the function of providing mechanical support for the waveguide structures. 
     Furthermore, it should be understood that the output ports can also be used as input ports and the input ports can be used as output ports. This is due to the reciprocal nature of light propagation in passive optical devices and hence the bi-directional nature of the devices. 
     It should be understood to those skilled in the art that the device  2100  can be fabricated on a different substrate other than a silicon substrate. In particular, it can be fabricated directly on InP or GaAs substrates used for making semiconductor photonic devices or integrated circuits and may be fabricated directly at the input/output ports of the photonic devices by sharing the same substrate as the photonic device. 
     (10) Variations of Exemplary Devices and Integration of ICMT with V-(Grooves for Fiber Alignments Platform for Photonic Chips 
     In the above mentioned exemplary combined module ICMTs that involve connecting a vertical sharp-down-taper waveguide core with a lower-refractive-index-contrast vertically graded waveguide, only two cases of placing the taper in the GRIN waveguide have been discussed, namely at the center of a symmetric GRIN waveguide or at the bottom of a half-GRIN waveguide. One skilled in the art will recognize that the GRIN waveguide need not to be restricted to these two cases. For example, the GRIN waveguide may have a refractive index distribution that is similar to the bottom half of a symmetric GRIN profile, and the taper can then be fabricated near the top of the GRIN waveguide. As another example, the GRIN waveguide can be three quarters of a symmetric GRIN profile; as long as the taper is fabricated near the high-refractive-index region of the GRIN profile, cascaded light beam expansion or reduction can be achieved. In fact, the GRIN waveguide may have an arbitrary profile, and the taper may be placed within a relatively large tolerance around the high-index region of the GRIN profile.  FIG. 43  shows the structure and simulation results of light coupling from either side to the other. Note that compared to device  2100  of  FIG. 40A , the Si taper  2210  is now shifted upward into the GRIN region  2220  and is buried above the lower cladding SiO2 layer  2230 . It can be seen that the while the taper to the half GRIN waveguide coupling is basically not changed as compared to the previous case, there is a slight increase in the reverse direction light coupling efficiency. 
     In terms of device fabrication, a silicon waveguide layer may be bonded on top of an X—SiO 2 —Si structure illustrated in  FIG. 44A . X may be a dielectric thin film  2310  with a refractive index equal to the GRIN waveguide core. SiO 2  layer  2320  is a lower cladding layer for the GRIN glass/polymer waveguide, and Si layer  2330  is the substrate. The structure can be easily achieved by, for example, sputtering a glass film  2310  on the SiO2—Si wafer  2320 / 2330 . An ion-implanted silicon wafer with a structure of Si layer  2340  on ion-implanted layer  2350  on Si  2360 , shown in  FIG. 44B , can be flipped over and bonded with the X—SiO2—Si wafer. Si layer  2360  is lifted off as discussed previously, leaving the structure shown in  FIG. 44C . The rest of the fabrication steps are similar to those described above for exemplary device  9 , beginning with fabrication of a tapered waveguide core in Si layer  2340 . 
     With respect to the various combined module ICMTs, at least three basic vertical structure configurations may be manufactured. While the symmetric GRIN waveguide structure offers the best coupling efficiency, it is the most challenging structure to fabricate as there is a need to bond an ion implanted Si wafer to a GRIN dielectric coated SiO 2 —Si wafer. However, it should be understood that the sol-gel spin-coating approach described above is only one exemplary way to fabricate such a structure; modifications of the fabrication process can be made that may simplify the fabrication process. For example, instead of using the sol-gel technique described above, any other thin film deposition technique including flame hydrolysis, sputtering, Ion-Assisted Deposition, evaporation and chemical vapor deposition may be used to deposit the graded refractive index layers. As a result, the wafer-bonding can be relatively easily done as long as the bottom half of the GRIN waveguide is of high quality. 
     One preferred technique for simplifying fabrication is to first deposit a relatively thin dielectric film having a refractive index about equal to that of the GRIN waveguide core onto a SiO2—Si wafer before wafer bonding to an ion implanted Si wafer. For example, sputtering is a well-established process for depositing such films; as a sputtered film is relatively thin, it will be less challenging to wafer-bond an ion implanted Si wafer to a sputtered dielectric-SiO 2 —Si wafer. 
     Another approach is to use a commercially available Si—SiO 2 —Si or SOI wafer, make the top Si waveguide layer into a taper and spin-coat a half GRIN waveguide. Although the resulting light-coupling efficiency is slightly lower as compared to couplers with a full GRIN waveguide, the commercial availability of SOI wafers makes this a simple and easy option in terms of fabrication. 
     In terms of photonic chip mounting and optical fiber alignment with the couplers of the present invention, there are various options.  FIGS. 45A-C  illustrates one process. After the formation of channel waveguides in the vertically GRIN glass waveguide layer  2410  using, for example, UV imprinting, photolithography, as illustrated in  FIG. 45A , can be used to define the Si V-groove wet etching opening  2420 . Selective dry etching of the GRIN glass waveguide layer  2410  and the insulating SiO 2  layer  2430  can then be employed to define a vertical wall  2440  in the GRIN glass waveguide layer, and Si V-grooves  2450  can be wet etched through the dry etched V-groove openings, as shown in  FIG. 45B . To fabricate a photonic chip recess, another photolithography process can be carried out to define the recess/well opening  2460 . Dry etching can be carried out to etch the recess/well to a precise depth.  FIG. 45C  illustrates a section of the completed device. Metal contact pads  2470  as well as electrical conduction paths may be made by metal evaporation. Photonic chip  2480  may be mounted and soldered in the recess/well with slight heating to ensure good adhesion and electrical contact. The silicon wafer with the photonic chips attached and the Si V-grooves already made can be diced into small pieces. Subsequently, optical fiber arrays  2490  can be mounted in the Si V-grooves and fixed. 
     The process is readily adaptable to multiport devices, as illustrated in  FIG. 46 , where photonic chip  2480  may comprise one or more semiconductor optical devices connected by waveguides  2482  to multiport integrated couplers of the present invention  2484 . These devices, in turn, couple to optical fibers  2490 . 
     While the exemplary devices described above use a silicon substrate and a silicon based high refractive index taper, it should be understood that these materials are only meant to illustrate exemplary cases. The embodiments of the present invention also include the use of other suitable materials for the substrate and the high index waveguide core or taper, wherein these suitable materials include compound semiconductor based material such as gallium arsenide, indium phosphide and gallium nitride, or an optical crystal based material such as lithium niobate, lithium tantalate and barium titanate, or a dielectric material such high index glasses. 
     IV. Applications 
     The applications of the mode transformation couplers of the present invention are numerous as the technology addresses the bottleneck of the present photonic integrated circuit (PIC) technologies. Couplers are used in the pigtailing and packaging of almost all semiconductor and optical crystal based photonic devices, especially those with multi-function and multiple ports. One application is in optical communication, where a coupler can be used for the packaging of all kinds of semiconductor and optical crystal based devices including semiconductor lasers, modulators, switches, multiplexers/demultiplexers, amplifiers, power splitters and so on. Presently, there are a number of technologies that are producing these photonic devices, such as III–V-based OEICs, Si-based optical or photonic MEMS, SOI- and SiGe-based integrated optical systems. All these will need mode conversion couplers to link to each other and to the outside world. 
     Another application is the concept of a photonic breadboard on which different integrated photonic chips are mounted and interconnected to one another via couplers of the present invention as shown in  FIG. 47 . Such an optical breadboard can be used to construct a system and test its function or performance before a fully integrated system chip is fabricated. 
     Note that a future trend of photonics is in the integration of multiple functional components on the same chip with multiple input and output ports to be connected to fiber arrays. In addition to optical communication, these chips will basically do the work that today is done by microelectronics chips, but at a much faster speed than their electronic counterparts. It can thus be foreseen that the cost of each component will drastically drop through photonic integration, as has happened for semiconductor-based electronics. The couplers of the present invention together with the associated packaging technology provide a significant reduction in the overall cost of such a multi-port photonic chip. The application areas of these photonic chips are potentially very wide, encompassing, for example, processors, computers, sensors, etc. 
     The foregoing description has provided exemplary embodiments of multiport integrated couplers and processes for fabricating these exemplary devices; these examples are intended to illustrate and not to limit the scope of the invention. One skilled in the art will recognize that various modifications are possible. For example, the waveguides are described with reference to coupling with particular optical devices such as semiconductor optical devices and optical fibers. One skilled in the art will recognize that the utility of the waveguides according to the present invention is not limited to the particular devices mentioned herein; indeed, the waveguides may be used with any optical device, and the dimensions of the waveguides may be varied for optimal matching to the optical device. Therefore, the scope of the present invention should be determined by the following claims, including their full range of equivalents.