Abstract:
A method and system for increasing the coupling efficiency of optical interconnections between optical elements such as optical fibers, waveguides, and vertical cavity surface emitting lasers (VCSEL) in single mode or multimode.

Description:
BACKGROUND OF INVENTION  
         [0001]    This invention relates to a system and method for the efficient coupling of radiation between optical devices and more particularly from a radiation source to a waveguide.  
           [0002]    When coupling the output of a laser, such as a vertical cavity surface emitting (VCSEL), or a multimode optical fiber into a thin waveguide (e.g., a planar waveguide or an optical fiber), there may be large and unacceptable mode and size mismatches between the laser output mode and the modes that can be supported by the thin waveguide. These mismatches lead to correspondingly large radiation losses between the optical components. Until now these significant losses have been ignored or overcome by simply increasing the output power of the VCSEL so that a desired amount of energy is coupled into the waveguide.  
           [0003]    In the new generation of opto-electronic components one key factor is the size thereof. On the one hand power must be limited to the minimum possible, while on the other, high power is desirable to guarantee good performances such as speed (or bandwidth) and signal/noise ratio. Thus, any power loss is at the expense of device performance. In addition, thermal and cooling issues arise at higher powers. Also, the lifetime of the VCSEL may be impaired if it is overdriven. Yet further, nonlinear or abnormal behavior such as undesired noise, distortion of output signals, etc. may result when a VCSEL has been overdriven.  
           [0004]    Thus, there accordingly remains a need in the art for a system and method for the efficient coupling of radiation from a radiation source to a waveguide, or other optical component, without suffering excessive radiation losses at optical interconnections.  
         SUMMARY OF INVENTION  
         [0005]    An optical coupling system for coupling optical energy between optical devices comprises a waveguide receptive of N-mode radiation from a radiation source where N is an integer. The waveguide comprises a first section receptive of the N-mode radiation from the radiation source and has a thickness of “h”. A second section has a thickness of “t” wherein “t” is less than “h”. A tapered section has a first end thereof with a corresponding thickness of “h” joined with the first waveguide section and a second end thereof with a corresponding thickness of “t” joined with the second waveguide section for coupling the N-mode radiation from the first waveguide section to the second waveguide section. Furthermore, the first section has a width of “q” and the second section a width of “w” less than “q.” The first end of the tapered section has a corresponding width of “q” joined with the first waveguide section and the second end of the tapered section has a corresponding width “w” joined with the second waveguide section.  
           [0006]    In a second embodiment, a cladding has a thickness of “c” and a refractive index of n  w , and is receptive of the N-mode radiation. The second waveguide section has a segment thereof positioned within the cladding and has a thickness of “t”, wherein “t” is less than “c” and a refractive index of n  c  wherein n  c  is greater than n  w .  
           [0007]    In a third embodiment, a waveguide has a refractive index of n  w  and is receptive of the N-mode radiation along an axis. The waveguide comprises a first section receptive of the N-mode radiation and a tapered section receptive of the N-mode radiation from the first waveguide section. A third section is positioned within the tapered section and has a refractive index of n  c  and receptive of the N-mode radiation from the tapered section; wherein n  c  is greater than n  w .  
           [0008]    The tapered section comprises a first aperture having a first cross sectional area receptive of optical radiation and a second aperture having a second cross sectional area less than the first cross sectional area and receptive of the optical radiation from the first aperture. 
       
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0009]    [0009]FIG. 1 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source by way of a prism wherein the waveguide includes a first section, a second section and a tapered section;  
         [0010]    [0010]FIG. 2 shows an arrangement of a waveguide encased in a cladding and receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section, a second section and a tapered section;  
         [0011]    [0011]FIG. 3 is a graphical representation of the normalized power coupled into the waveguide of FIG. 2 as a function of distance therealong;  
         [0012]    [0012]FIG. 4 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section, a second section and a tapered section and the second section has a refractive index different than that of the first section;  
         [0013]    [0013]FIG. 5 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section, a second section, a third section and a tapered section, and the second section has a refractive index different than that of the first section;  
         [0014]    [0014]FIG. 6 is a graphical representation of the normalized power coupled into the waveguide of FIG. 8 as a function of distance therealong;  
         [0015]    [0015]FIG. 7 is a graphical representation of the normalized power coupled into the waveguide of FIG. 5 as a function of distance therealong;  
         [0016]    [0016]FIG. 8 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section, a second section and a tapered section, the second section has a refractive index different than that of the first section and a segment of the second section is positioned within the tapered section;  
         [0017]    [0017]FIG. 9 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section, a second section and a tapered section, the second section has a refractive index different than that of the first section and a wedge-like segment of the second section is positioned within the tapered section;  
         [0018]    [0018]FIG. 10 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section, a second section and a tapered section, the second section has a refractive index different than that of the first section and a wedge-like segment of the second section is positioned within the tapered section;  
         [0019]    [0019]FIG. 11 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section, a second section and a tapered section, the second section has a refractive index different than that of the first section and the second section encompasses the tapered section and the first section;  
         [0020]    [0020]FIG. 12 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section wherein the second section includes a segment thereof positioned within the first section;  
         [0021]    [0021]FIG. 13 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof positioned within the first section, the second section includes a symmetric wedge-like segment;  
         [0022]    [0022]FIG. 14 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof positioned within the first section, the second section includes an asymmetric wedge-like segment;  
         [0023]    [0023]FIG. 15 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof positioned within the first section and the first section is partially truncated;  
         [0024]    [0024]FIG. 16 is a graphical representation of the normalized power coupled into the waveguide of FIG. 15 as a function of distance therealong;  
         [0025]    [0025]FIG. 17 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof including a symmetric wedge-like segment positioned within the first section and the first section is partially truncated;  
         [0026]    [0026]FIG. 18 is a graphical representation of the normalized power coupled into the waveguide of FIG. 17 as a function of distance therealong;  
         [0027]    [0027]FIG. 19 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof including a symmetric wedge-like segment positioned within the first section and the first section is partially truncated;  
         [0028]    [0028]FIG. 20 is a graphical representation of the normalized power coupled into the waveguide of FIG. 19 as a function of distance therealong;  
         [0029]    [0029]FIG. 21 shows an arrangement of a waveguide receptive of N-mode radiation along an axis from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof including a symmetric wedge-like segment positioned within the first section, the first section is partially truncated and the second section is offset from the axis;  
         [0030]    [0030]FIG. 22 is a graphical representation of the normalized power coupled into the waveguide of FIG. 21 as a function of distance therealong;  
         [0031]    [0031]FIG. 23 shows an arrangement of a waveguide receptive of N-mode radiation along an axis from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof including a symmetric wedge-like segment positioned within the first section, the first section is partially truncated and the second section is offset from the axis;  
         [0032]    [0032]FIG. 24 is a graphical representation of the normalized power coupled into the waveguide of FIG. 23 as a function of distance therealong;  
         [0033]    [0033]FIG. 25 shows an arrangement of a waveguide receptive of N-mode radiation along an axis from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof including a symmetric wedge-like segment positioned within the first section, the first section is partially truncated and the second section is offset from the axis;  
         [0034]    [0034]FIG. 26 is a graphical representation of the normalized power coupled into the waveguide of FIG. 25 as a function of distance therealong;  
         [0035]    [0035]FIG. 27 is a graphical representation of the power coupled into the waveguide of FIG. 17 as a function of distance therealong;  
         [0036]    [0036]FIG. 28 shows an arrangement of a waveguide receptive of N-mode radiation from a radiation source wherein the waveguide includes a first section and a second section having a refractive index different than that of the first section and wherein the second section includes a segment thereof including an asymmetric wedge-like segmen positioned within the first section and the first section is partially truncated;  
         [0037]    [0037]FIG. 29 is a graphical representation of the normalized power coupled into the waveguide of FIG. 28 as a function of distance therealong;  
         [0038]    [0038]FIG. 30 shows an arrangement of a waveguide receptive of N-mode radiation along an axis from a radiation source wherein the waveguide includes a first section, a second section and a tapered section and wherein the second section has a refractive index different than that of the first section and the tapered section encompasses a segment of the second section;  
         [0039]    [0039]FIG. 31 is a graphical representation of the normalized power coupled into the waveguide of FIG. 30 as a function of distance therealong;  
         [0040]    [0040]FIG. 32 is a three dimensional view of a waveguide device for coupling optical radiation between optical elements;  
         [0041]    [0041]FIG. 33 is a first configuration of the symmetric wedge-like segment of the second section of the waveguide of FIG. 17;  
         [0042]    [0042]FIG. 34 is a second configuration of the asymmetric wedge-like segment of the second section of the waveguide of FIG. 14;  
         [0043]    [0043]FIG. 35 is a third configuration of the asymmetric wedge-like segment of the second section of the waveguide FIG. 14;  
         [0044]    [0044]FIG. 36 shows an optical beam redirection device as a diffraction grating; and  
         [0045]    [0045]FIG. 37 shows an optical beam redirection device as a concave surface. 
     
    
     DETAILED DESCRIPTION  
       [0046]    Referring to FIG. 1, a first embodiment of an optical coupling system  200  for coupling optical energy between optical devices is shown. The optical coupling system  200  comprises an optical beam redirection device  206  such as a prism (acting as a mirror by total internal reflection) or a lens. The surface of the optical beam redirection device  206  may be planar or non-planar. If, for example, the surface is concaved (FIG. 37), more light may be collected from the VCSEL and coupled into other optical components. The surface of the optical beam redirection device  206  may also be patterned or ruled like an optical diffraction grating (FIG. 36) for optical filtering or wavelength selection. All of these designs can be incorporated into the mirrored surface  206  depending upon the application, the required performance or other needs.  
         [0047]    The optical beam redirection device  206  is receptive of multi-mode radiation  202  (e.g., N-mode radiation where N is an integer) at a distance of “s” from a radiation source  230  such as a vertical cavity surface emitting laser (VCSEL), an edge emitting laser or a multimode optical fiber. The laser output  202  diverges over an approximately symmetric solid angle, X , of about 15 degrees. The optical beam redirection device  206  is placed at the distance “s” so as to capture all or substantially all of the radiation  202  emitted by the laser  230 . A waveguide  214  is receptive of the N-mode radiation  204  from the optical beam redirection device  206 . The waveguide  214  comprises a first section  208  having a thickness of “h”, which is receptive of the N-mode radiation  204  from the optical beam redirection device  206 . A second section  210  of the waveguide  214  has a thickness of “t” wherein “t” is less than “h”. The dimension “h” is approximately 10-100 micrometers (um) and “t” is approximately 2-10 um. A tapered section  212  has a first aperture  226  with a thickness of h joined with the first waveguide section  208  and a second aperture  228  with a thickness of t joined with the second waveguide section  210 , thus coupling the N-mode radiation  204  from the first waveguide section  208  to the second waveguide section  210 . As best understood from FIG. 1, the N-mode radiation  202  may be directed directly into the first section of the waveguide  208 . Also in FIG. 1, the refractive indices of the first and second waveguide sections  208 ,  210  and the tapered section  212  are all equal. As seen in FIG. 35, the tapered section  212  has a length, “I”, of approximately 100-1000 um and also subtends a first angle, α, of about 5 degrees and a second angle, β, perpendicular to the first angle, α, of about 5 degrees measured at or near the second waveguide section  210 .  
         [0048]    Typical material compositions of the optical beam redirection device  206 , the first waveguide section  208 , the second waveguide section  210  and the tapered section  212  are that of special or regular glasses, semiconductors, polymers, optical sol gels, or opto-electrical crystals, etc. The waveguide and tapered structures can be fabricated by using reactive-ion etching (RIE), laser ablation, mechanical sawing, molding, stamping, gray-scale mask lithography and so on.  
         [0049]    In a second embodiment of the invention, as seen in FIG. 2, the waveguide  214 , which has a refractive index of n  w , may be encased within a cladding  216  having a refractive index of n  c , wherein n  c  is less than n w . FIG. 3 depicts a graphical representation at  302  of the normalized power coupled into the second waveguide section  210  of FIG. 2 as a function of distance along the tapered section  212  and the second waveguide section  210 . The maximum normalized power coupled into the second waveguide section  210  of FIG. 2 is about 0.8 normalized units.  
         [0050]    In a third embodiment, as seen in FIGS. 4 and 5, the first waveguide section  208  and the tapered section  212  are defined by the refractive index, n w , and the second waveguide section  210  is defined by the refractive index, n c , wherein n c  is less than n w . In FIG. 5, the second waveguide section  210  includes an additional, elongated top-layer taper  218  which possess the same refractive index as the second waveguide section  210  and extends from the upper surface of the second waveguide section  210  to a point along the tapered section  212 , thus providing improved coupling of power between the first waveguide section  208  and the second waveguide section  210 . FIG. 7 depicts a graphical representation at  306  of the normalized power coupled into the second waveguide section  210  of FIG. 5 as a function of distance along the tapered section  212  and the second waveguide section  210 .  
         [0051]    In a fourth embodiment, as seen in FIGS. 8, 9 and  10  and FIGS. 33, 34 and the second waveguide section  210  includes a segment thereof  220  positioned within the tapered section  212  or within both the tapered section  212  and the first waveguide section  208 . In particular, as seen in FIG. 8, the aforesaid segment  220  comprises a rectangular shaped segment extending a length, “w”, into the tapered section  212  and the first waveguide section  212 . FIG. 6 depicts a graphical representation at  304  of the normalized power coupled into the second waveguide section  210  of FIG. 8 as a function of distance along the tapered section  212  and the second waveguide section  210 . In FIG. 9, the aforesaid segment  220  comprises a wedge  222  having a generally triangular cross section including a base with a thickness of t joined with the second waveguide section  210 . The triangular cross section in FIG. 9 also includes an angled apex 5-10 degrees in opposition to the base subtending an angle, γ, of approximately 5-10 degrees. The triangular cross section in FIG. 9 is generally a right triangle positioned so that the hypotenuse thereof is first receptive of the N-mode radiation  204  from the tapered section  212 , thus coupling the N-mode radiation from the first waveguide section  208  to the second waveguide section  210 . In FIG. 10, the triangular cross section  220  is inclined with respect to the second waveguide section  210  at angle, θ, of between approximately 5-10 degrees. As best understood from FIGS. 8, 9 and  10 , the first waveguide section  208  acts as a waveguide (e.g.; as a core material), while the cladding thereto is a substrate below and air above.  
         [0052]    In a fifth embodiment, as seen in FIG. 11, the second waveguide section  210  encases or envelopes the optical beam redirection device  206 , the first waveguide section  208  and the first tapered section  212  of FIG. 8.  
         [0053]    Referring to FIGS. 12, 1  3  and  14 , and FIGS. 33, 34 and  35 , a sixth embodiment of the optical coupling system  200  is shown. In FIGS. 12, 13 and  14 , the cladding  216 , having a thickness of c and a refractive index of n w , is receptive of the N-mode radiation  204  from the optical beam redirection device  206  along an axis  224 . The second waveguide section  210 , which is symmetric with respect to the axis  224 , has a thickness of “t” (less than “c”), a refractive index of n  c  (greater than n  w ) and a segment thereof  220  positioned within the cladding  216  over a length of b. In FIG. 12, the segment of the second waveguide  220  positioned within the cladding  216  is terminated with a square or rectangular end. In FIGS. 13 and 14, the segment of the second waveguide  220  positioned within the cladding  216  includes a wedge  222 . The wedge  222  has a generally triangular cross section including a base with a thickness “t” joined with the second waveguide section  210  and an angled apex opposed to the base. The wedge  222  is receptive of the N-mode radiation  204  from the optical beam redirection device  206  along the axis  224  for coupling the N-mode radiation  204  from the optical beam redirection device  206  to the second waveguide section  210 . In FIG. 13, the triangular cross section  220  is inclined with respect to the second waveguide section  210  at angle, θ, of between approximately 5-10 degrees. The triangular cross section in FIG. 14 is generally a right triangle positioned so that the hypotenuse thereof is first receptive of the N-mode radiation  204  from the tapered section  212 , thus coupling the N-mode radiation from the first waveguide section  208  to the second waveguide section  210 . As best understood from FIGS. 12, 13 and  14 , in contrast to FIGS. 8, 9 and  10 , the first waveguide section  208  acts as a cladding to the second waveguide section  210 . The use of the first waveguide section  208 , either as a core or a cladding, depends on how it is applied within the whole structure.  
         [0054]    Referring to FIGS. 15, 17 and  19 , a seventh embodiment is shown. In a fashion similar to that shown in FIG. 12, in FIGS. 15, 17 and  19 , the cladding  216 , having a thickness of c and a refractive index of n  w , is receptive of the N-mode radiation  204  from the optical beam redirection device  206  along an axis  224 . The second waveguide section  210 , which is symmetric with respect to the axis  224 , has a thickness of “t” (less than “c”), a refractive index of n  c  (greater than n  w ) and a segment thereof  220  positioned within the cladding  216  over a length of “b”. In FIG. 15, the segment of the second waveguide  220  positioned within the cladding  216  is terminated with a square or rectangular end. FIG. 16 depicts a graphical representation at  308  of the normalized power coupled into the second waveguide section  210  of FIG. 15 as a function of distance along the cladding  216  and the second waveguide section  210 .  
         [0055]    Also in a fashion similar to FIGS. 13 and 14, in FIGS. 17 and 19, the segment of the second waveguide  220  positioned within the cladding  216  includes a wedge  222 . The wedge  222  has a generally triangular cross section including a base with a thickness “t” joined with the second waveguide section  210  and an angled apex opposed to the base. The wedge  222  is receptive of the N-mode radiation  204  from the optical beam redirection device  206  along the axis  224  for coupling the N-mode radiation  204  from the optical beam redirection device  206  to the second waveguide section  210 . FIG. 18 depicts a graphical representation at  310  of the normalized power coupled into the second waveguide section  210  of FIG. 17 as a function of distance along the cladding  216  and the second waveguide section  210 . FIG. 20 depicts a graphical representation at  312  of the normalized power coupled into the second waveguide section  210  of FIG. 19 as a function of distance along the cladding  216  and the second waveguide section  210 .  
         [0056]    However, it is seen in FIGS. 15, 17 and  19 , that the cladding  216  is truncated over a segment thereof having a length “d” wherein the second waveguide section  210  is not enveloped by the cladding  216  over that segment.  
         [0057]    Also as best understood from FIGS. 15, 17 and  19 , in contrast to FIGS. 8, 9 and  10 , the first waveguide section  208  acts as a cladding to the second waveguide section  210 . The use of the first waveguide section  208 , either as a core or a cladding, depends on how it is applied within the whole structure. Still further, as can be seen in FIGS. 18 and 20, the addition of the wedge  222  in FIGS. 17 and 19 respectively, provides a noticeable improvement in the coupling of energy from the cladding  216  into the second waveguide section  210  (about 0.9 normalized units for the arrangement in FIG. 17 and about 0.8 normalized units for the arrangement in FIG. 19), as compared to that seen in FIG. 16 for a second waveguide section  210  with a wedge  222  (about 0.35 normalized units). However, in comparing the coupling in FIGS. 20 and 22, it is seen that the thickness of the second waveguide section  210  has less of an impact on coupling than the addition of the wedge  222 .  
         [0058]    Referring to FIGS. 21, 23 and  25 , a seventh embodiment is shown. In a fashion similar to that shown in FIG. 12, in FIGS. 21, 23 and  25 , the cladding  216 , having a thickness of “c” and a refractive index of n  w , is receptive of the N-mode radiation  204  from the optical beam redirection device  206  along an axis  224 . The second waveguide section  210 , which is symmetric with respect to the axis  224 , has a thickness of t (less than “c”), a refractive index of n  c  (greater than n  w ) and a segment thereof  220  positioned within the cladding  216  over a length of “b”. In FIG. 21, the segment of the second waveguide  220  positioned within the cladding  216  is terminated with a square or rectangular end. FIG. 22 depicts a graphical representation at  314  of the normalized power coupled into the second waveguide section  210  of FIG. 21 as a function of distance along the cladding  216  and the second waveguide section  210 .  
         [0059]    Also in a fashion similar to FIGS. 13 and 14, in FIGS. 23 and 25, the segment of the second waveguide  220  positioned within the cladding  216  includes a wedge  222 . The wedge  222  has a generally triangular cross section including a base with a thickness “t” joined with the second waveguide section  210  and an angled apex opposed to the base. The wedge  222  is receptive of the N-mode radiation  204  from the optical beam redirection device  206  along the axis  224  for coupling the N-mode radiation  204  from the optical beam redirection device  206  to the second waveguide section  210 . FIG. 24 depicts a graphical representation at  316  of the normalized power coupled into the second waveguide section  210  of FIG. 23 as a function of distance along the cladding  216  and the second waveguide section  210 . FIG. 26 depicts a graphical representation at  318  of the normalized power coupled into the second waveguide section  210  of FIG. 25 as a function of distance along the cladding  216  and the second waveguide section  210 .  
         [0060]    Again, it is seen in FIGS. 21, 23 and  25 , that the cladding  216  is truncated over a segment thereof having a length “d” wherein the second waveguide section  210  is not enveloped by the cladding  216  over that segment. However, it is also seen in FIGS. 21, 23 and  25  that the second waveguide section  210  is offset from the axis  224  by a distance Δr.  
         [0061]    As seen in FIGS. 22 and 23, the amount of energy coupled from the cladding  216  into the second waveguide section  210 , for the same offset “r” in the arrangements of FIGS. 21 and 23 respectively, is approximately the same (about 0.6 normalized units) despite a thinner second waveguide section  210  in FIG. 23. Thus, the thickness of the second waveguide section  210  does not dictate the coupling efficiency. However, as seen in FIG. 25, for too large of an offset “ro”, the coupling efficiency is dramatically reduced (to about 0.05 normalized units).  
         [0062]    As shown in FIGS. 22, 24 and  26 , a smaller offset “r” yields a better coupling. However, a certain amount of offset “r” may occur due to fabrication processing, etc. Therefore, innovative solutions are disclosed in FIG. 10 (using a special taper design for “drawing” the energy into a preferred waveguide layer) and in FIG. 33 (using a tapered cladding to “squeeze” the energy into a preferred waveguide layer).  
         [0063]    As best understood from FIGS. 21, 23 and  25 , in contrast to FIGS. 8, 9 and  10 , the first waveguide section  208  acts as a cladding to the second waveguide section  210 . The use of the first waveguide section  208 , either as a core or a cladding, depends on how it is applied within the whole structure.  
         [0064]    In the arrangement of FIG. 17 a symmetric wedge  222  is shown, and in FIG. 28 an asymmetric wedge  222  is shown. The difference in the coupling efficiency between the arrangements of FIGS. 17 and 28 is seen in comparing FIGS. 27 and 29 respectively. In FIG. 27 it is seen that the symmetric wedge  222 , has a higher coupling efficiency (about 0.9 normalized units) than that of FIG. 29 (about 0.8 normalized units).  
         [0065]    In the arrangement of FIG. 25, a symmetric wedge  222  and the second waveguide section  210  are off set by a distance “r” from the axis  224 . As seen in FIG. 26 this arrangement yields a relatively poor coupling efficiency  318  of about 0.05 normalized units. Referring to FIG. 30 an eighth embodiment is shown. In FIG. 30, the cladding  216 , again having a thickness of “c” and a refractive index of n  w , is receptive of the N-mode radiation  204  from the optical beam redirection device  206  along an axis  224 . The tapered section  212  has a first aperture  226  with a thickness of h joined with the cladding  216  and a second aperture  228  opposed to and smaller than the first aperture  226 . Again, as seen in FIG. 32, the tapered section  212  in FIG. 30 has a length, “I”, of approximately 100-1000 um and also subtends a first angle, α, of about 5-10 degrees and a second angle, β, perpendicular to the first angle, α, of about 5-50 degrees. The tapered section  212  is receptive of the N-mode radiation at the first aperture  226  from the cladding  216 . In FIG. 30, the second waveguide section  210  is offset from the axis  224  by a distance “r” and includes a segment  220  thereof positioned and encased within the tapered section  212 . The segment  220  of the second waveguide section  210  positioned within the tapered section  212  includes a wedge  222 . The wedge  222  has a generally triangular cross section including a base with a thickness “t” joined with the second waveguide section  210  and an angled apex opposed to the base. The wedge  222  is receptive of the N-mode radiation  204  from the tapered section  212 . FIG. 31 depicts a graphical representation at  326  of the normalized power coupled into the second waveguide section  210  of FIG. 30 as a function of distance along the tapered section  212  and the second waveguide section  210 . As can be seen in FIG. 31, the coupling efficiency for the arrangement shown in FIG. 30 is an improvement over that shown in FIG. 26 relating to the arrangement of FIG. 25.  
         [0066]    [0066]FIGS. 33, 34 and  35  show various configurations of the wedge-like segment of the second section of the waveguide. In general, the taper and wedge are “gentle” or “slow.” That is, the angles, a and b, of these tapers or wedges are small. Therefore, “h” and “q” are much larger than the waveguide thickness “t” and width “w”. Thus, the angles a and b in FIG. 32 will be then determined accordingly. The length of the wedge-like segment  222  is “k” and the angles θ and γ of FIGS. 33, 34 and  35  are also relatively small. Thus, the wedge-like segment  222  is accordingly elongated in nature. As best understood the tapered section  212  and wedge-like segments  222  are all of an elongated nature wherein the angles a, b, θ and γ are relatively small or acute.  
         [0067]    Any references to first, second, etc., or front or back, right or left, top or bottom, upper or lower, horizontal or vertical, or any other phrase indicating the relative position of one quantity or variable with respect to another are, unless noted otherwise, intended for the convenience of description of the invention, and do not limit the present invention or its components to any one positional or spatial orientation. All dimensions of the components in the attached Figures can vary with a potential design and the intended use of an embodiment without departing from the scope of the invention.  
         [0068]    While the invention has been described with reference to several embodiments thereof, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiments disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.