Abstract:
A waveguide system includes a first waveguide having surface roughness along at least one surface and a second waveguide substantially identical to the first waveguide and having substantially identical surface roughness along a corresponding side. The first and second waveguides are separated from each other by a predetermined distance and are configured to receive respective first and second light signals having antisymmetric modes. The predetermined distance between the first and second waveguide tends to cause cancellation of at least far-field polarization radiation emanating from the first and second waveguides and resulting from the surface roughness.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     This invention was developed under Contract DE-AC04-94AL85000 between Sandia Corporation and the U.S. Department of Energy. The U.S. Government has certain rights in this invention. 
    
    
     FIELD OF THE INVENTION 
     This application relates to waveguides and in particular waveguides that reduce radiation losses due to optical scattering. 
     BACKGROUND 
     Currently a limitation of the performance of optical microcavities and waveguides is posed by lithographically formed roughness generated through the etch process which defines the sidewalls of waveguides and microcavities, including both microring and photonic crystal cavities. This lithographically formed roughness tends to scatter the light out of the guided optical modes generating optical losses that may be detrimental to the performance of the optical waveguides and cavities. While lithographic roughness can be improved somewhat by using highly controlled lithographic processes there is often no practical way to achieve the low loss level that is desirable for certain highly desirable applications in the context of integrated photonics. 
     SUMMARY 
     The present invention is embodied in a waveguide system including a first waveguide having surface roughness along at least one surface and a second waveguide substantially identical to the first waveguide and having substantially identical surface roughness along a corresponding surface. The first and second waveguides are separated from each other by a predetermined distance and are configured to receive respective first and second light signals having antisymmetric modes. The predetermined distance between the first and second waveguide tends to cause cancellation of at least far-field polarization radiation emanating from the first and second waveguides and resulting from the surface roughness. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and form part of the specification, illustrate the present invention and, together with the description, describe the invention. In the drawings, like elements are referred to by like numbers. 
         FIG. 1  is a perspective drawing of a waveguide that is useful for describing an problem addressed by embodiments of the invention. 
         FIG. 2  is a set of perspective drawings that are useful for describing the problem addressed by the embodiments of the invention. 
         FIG. 3  is a cross-sectional view of the waveguide shown in  FIG. 1  along the lines  3 - 3 ; 
         FIG. 4  is a cross-sectional view of the waveguide shown in  FIG. 1  along the lines  3 - 3  that is useful for describing an embodiment of the invention. 
         FIG. 5  is a perspective graph of the polarization field of a point source that is useful for describing an embodiment of the invention. 
         FIGS. 6A ,  6 B,  7 A and  7 B are cut-away side-plan views of a semiconductor device that may be used in an embodiment of the invention. 
         FIGS. 8 and 9  are cut-away side-plan views of the semiconductor device that are useful for describing an embodiment of the invention. 
         FIG. 10  is a cut-away side plan view of a portion of the semiconductor device that is useful for describing an embodiment of the invention. 
         FIG. 11  is a graph of effective index of refraction versus waveguide separation that useful for describing an embodiment of the invention. 
         FIGS. 12   a , and  12   b  are perspective drawings of an example embodiment. 
         FIGS. 13 and 14  are perspective drawings of example mode converters that may be used in the example embodiment shown in  FIGS. 12   a  and  12   b.    
         FIGS. 15 and 16  are perspective drawings of a one-layer and two-layer photonic crystal cavity device that are useful for describing the structure of an example embodiment. 
         FIGS. 17 and 18  are perspective drawings of a one-layer and two-layer ring resonator device that are useful for describing the structure of an example embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  is a perspective drawing of a portion of a waveguide formed by a photolithographic process. This drawing is taken from an article by T. Barwicz et al. entitled “Three Dimensional Analysis of Scattering Losses Due to Sidewall Roughness and Microphotonic Waveguides,” IEEE J. of Lightwave Tech. vol. 23. no. 9, pp 2719-2732 (2005). The drawing shown in  FIG. 1  exhibits roughness as illustrated by the vertical ridges  102  and  104  along the sides of the waveguide. This roughness is typically caused by unevenness in the mask that is used to form the waveguide. The ridges shown in  FIG. 1  are exaggerated to aid in the description of the invention. 
     In the above-referenced article by Barwicz et al., the waveguide  100  is decomposed into a smooth waveguide  202  and the ridges  204 , as shown in  FIG. 2 . The smooth waveguide does not contribute to the scattering loss radiation and so is ignored in the analysis. Barwicz et al. modeled each of the ridges as a dipole antenna  206  which, combined with the roughness function F rough    208 , models the radiation field exhibited by the edges  204 . 
       FIG. 3  is a cross section of the waveguide  100  along the line  3 - 3  as shown in  FIG. 1 . The waveguide includes the central portion  202  and two ridges  302  and  304 . As described in the Barwicz article, each ridge  302  and  304  acts a dipole antenna generating a polarization current at the boundary.  FIG. 4  is a cross sectional diagram illustrating the polarization radiation pattern  402 . As shown in  FIG. 5 , the radiation pattern  402 ′ generated by a point source with x polarization has the form of a flattened toroid. This radiation pattern may be generated by points along the ridges  302  and  304  to form the pattern  402 , shown in  FIG. 4 . 
     The embodiments of the invention described below cancel this radiation by forming each waveguide as a system of two or more parallel waveguides in which light propagates through the multiple waveguides in an anti-symmetric super mode. In the examples described below, each waveguide includes at least a lower waveguide and an upper waveguide separated by a cladding material. Light is coupled into the waveguide system such that it propagates through the waveguide in an anti-symmetric mode. In one example embodiment, light propagating through the lower waveguide is primarily in the transverse magnetic (TM) mode while light propagating through the upper waveguide is primarily in the transverse electric (TE) mode. As described below with reference to  FIG. 10 , the effect of this construction is essentially to cancel the radiation fields generated by the polarization currents of the two waveguides, greatly reducing polarization radiation emitted by the waveguides, at least in the far field. 
       FIGS. 6 and 6A  are a cut-away views of a cross-section of respective semiconductor wafers that illustrate the construction of an example waveguide. In the example shown in  FIGS. 6A and 6B , layers of material having respective high and low indices of refraction are formed on top of a substrate. In the example shown in  FIG. 6A ,  602  is a silicon substrate and layers  604 ,  608  and  612  are formed of silicon dioxide SiO 2 . The substrate  602  and the intervening layers  606  and  610  are formed of silicon. In this example embodiment, silicon layers  610  and  606  are waveguides covered on top and bottom by cladding layers  604 ,  608  and  612 . These layers have a lower index of refraction than the waveguide layers  606  and  610 . The device shown in  FIG. 6B  is similar to that shown in  FIG. 6A  except that the device in  FIG. 6B  includes two additional high-index layers,  616  and  620  and two additional low-index layers  618  and  622 . 
     The described materials are exemplary. The waveguide system may be formed from other materials commonly used to form semiconductor waveguides, for example, alternating layers of indium phosphide (InP) and Indium Gallium Arsenide phosphide (InGaAsP). Alternatively, multiple layers of deposited amorphous materials such Silicon Nitride, or Bismuth Oxide may be used to form the waveguide system. In addition, dual or multiple layers of crystalline silicon can be used as the core material with a silica cladding formed through use of double or multiple layer silicon on insulator materials (SOI). 
     The item  614  shown in  FIGS. 6A and 6B  is a photo resist mask pattern that is used to form the waveguide in the compound structure. In a typical fabrication process, an etchent may be applied to the semiconductor wafer as shown in  FIG. 6  to selectively remove portions of the semiconductor wafer that are not covered by the mask  614 . This removal operation may be down to stop etch layer (not shown) formed between the layers  602  and  604 . During the etching process, unevenness along the edges of the mask may cause vertical ridges, such as the ridges  102  and  104  shown in  FIG. 1 , on the side surfaces of the waveguide. Alternatively, the pattern may be transferred to a third material, such as nickel which acts as a robust hard-mask during the lithography process. An example process for forming waveguide systems using such a third material is described in an article by T. Barwicz et al. entitled “Microring-resonator-based add-drop filters in SiN: fabrication and analysis,” Optics Express Vol. 12, No. 7, April 2004. 
       FIGS. 7A and 7B  show the devices after the etching operation and after the photo resist  614  has been removed. The example devices shown in  FIGS. 7A and 7B  each includes layers  604 ′,  608 ′ and  612 ′ having a relatively low index of refraction and layers  606 ′ and  610 ′ having a relatively high index of refraction. The device shown in  FIG. 7A  includes the additional high-index layers  616 ′ and  620 ′ as well as the additional low-index layers  618 ′ and  620 ′. The sides of the waveguide layers are subject to the ambient atmosphere which also has a lower index of refraction than the silicon layers  606 ′ and  610 ′. 
     The difference between the index of refraction of the layers  606 ′ and  610 ′ on the one hand and the index of refraction of the layers  604 ′,  608 ′ and  612 ′ and the surrounding atmosphere on the other hand, causes light to propagate through layers  606 ′ and  610 ′ in a mode that depends on the spacing between layers  606 ′ and  610 ′ (i.e., the thickness of layer  608 ′). As shown in  FIGS. 8 and 9 , light may propagate through the two waveguides  606 ′ and  610 ′ in a symmetric mode ( FIG. 8 ) or in an anti-symmetric mode ( FIG. 9 ). Because the roughness on both waveguides  606 ′ and  610 ′ is substantially identical, as it results from the etch process that defines both waveguides, the roughness produced dipole moments may be identical and perfectly in phase in the case of symmetric mode as shown in  FIG. 8  or identical and 180° out phase in the case of the anti-symmetric mode shown in  FIG. 9 . This feature of the waveguide system may be used to effectively cancel the scattering induced radiation emanating from the waveguide, at least in the far field. 
       FIG. 10  shows two waveguides  1002  and  1006  separated by an intervening cladding layer  1004 . In the example shown in  FIG. 10  each of the waveguides  1002  and  1006  has a depth d and width w. The two waveguides  1002  and  1006  are separated by the cladding layer having a depth g and a width w. The plus sign on the waveguide  1002  and the minus sign on the waveguide  1006  indicate that the compound waveguide is operating in the anti-symmetric mode. In this mode the dipoles  1010  on the waveguide  1002  and the dipoles  1012  on the waveguide  1006  exhibit radiation patterns that are 180° out of phase and tend to cancel each other. The inventors have determined that with proper spacing of the waveguides  1002  and  1006  and proper sizing of each of the waveguides  1002  and  1006  at least the far field polarization radiation exhibited by the waveguide and caused by the roughness of the sides of the waveguide may be essentially cancelled. 
     The separation of the waveguides  1002  and  1006  depends on the wavelength of the light being transmitted through the waveguides. Coherent interference between the radiation patterns of the waveguides  1002  and  1006  have some impact on the radiation losses regardless of the separation. However, the largest effect is anticipated where the dipole moment of the scattering system (consisting of the roughness from multiple waveguides) cancels, or is near cancellation. When the dipole moment cancels, or nearly cancels, only the quadripole and higher order multipole moments remain. These moments tend to have much poorer radiation efficiency, and therefore yield lower propagation losses. Broadband cancellation of the of the dipole moment most often occurs when the waveguide separation is smaller than an optical wavelength. 
     As illustrated in  FIG. 11 , however, the structure of the two waveguides in the anti-symmetric mode may not be identical to that of a single waveguide or to the structure waveguides operating in the symmetric mode. This is because the waveguides operating in the anti-symmetric mode may have a lower effective index of refraction and, thus, less confinement of the optical beam than either a single waveguide or a waveguide system operating in the symmetric mode. For a linear waveguide, this effect may be compensated by forming thicker waveguides. Adaptations for specific embodiments on the invention are described below with references to  FIGS. 15-18 . 
       FIG. 11  is a graph of effective refractive index versus waveguide separation which shows that the compound waveguide mode (or super mode) produced by the dual waveguide structure result in a splitting of the effective refractive index of the waveguide system. Each waveguide has a different level of confinement within the high index region of the waveguide system. The symmetric mode has a large field energy between the waveguides while the anti-symmetric mode has a field null yielding weaker modal confinement. As described above, in order to cancel the roughness induced scattering it is desirable to use the anti-symmetric mode. It is noted that the use of the anti-symmetric mode is one example of such a system employing a super mode. Alternatively any multilayer structure such as that shown in  FIG. 7B , having alternating different propagation modes defining more than two waveguide layers can also yield canceling anti-phase radiation in the far field. 
     An example embodiment of the present invention is shown in  FIGS. 12A and 12B . As shown in these Figs., an input waveguide  1202  couples light into a mode converter  1204  which produces light having an anti-symmetric propagation mode in parallel waveguides  1206  and  1208 . In the example, this light is evanescently coupled to a microring resonator optical filter formed by microring resonators  1210  and  1212 . Light at the resonant frequency of the microring resonators  1210  and  1212  is then coupled, also by evanescent coupling, into output waveguides  1214  and  1216 . As described above, the operation of the device shown in  FIGS. 12A and 12B  may be significantly improved over that of a single layer device, because the roughness induced polarization radiation in the paired waveguides  1206 ,  1208 ;  1210 ,  1212 ; and  1214 ,  1216  is essentially cancelled due to the anti-symmetric super mode propagation of light through the waveguides. 
     By adding one or more microring resonators, the example microring resonator device shown in  FIGS. 12   a  and  12   b  may, for example, be used as an add-drop filter as described in an article by Barwicz et al. entitled “Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators,” J. Lightwave Tech. vol. 24, no. 5 May 2006, that describes a single-layer microring resonator device. 
       FIGS. 13 and 14  are examples of mode converters that may be used with the ring resonator system shown in  FIGS. 12A and 12B  or with a photonic crystal cavity structure shown in  FIGS. 15 and 16 , described below. In  FIG. 13 , input waveguide  1302  provides light to parallel ring resonators  1304  and  1306 . By properly spacing the waveguides  1304  and  1306  relative to the waveguide  1302  light propagating in the waveguide  1306  may be in different, antisymmetric modes. Light from the two rings  1306  and  1304  may, in turn, be coupled into the linear waveguides  1310  and  1308  respectively via evanescent coupling. The waveguides  1308  and  1310  form the output of the mode converter  1300 . In order to perform as a mode converter, the converter is designed to have a particular spacing between the two ring resonators  1304  and  1306  and a particular vertical position of the input waveguide  1302  relative to the ring resonators  1304  and  1306 . The design parameters of an example converter are described in an article by P. T. Rakish et al. entitled “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nature Photonics vol. 1 Nov. 2007 www.nature.com/naturephotonics. 
       FIG. 14  is a perspective drawing of an example alternative adiabatic mode converter that may be used with the embodiments of the invention. In this mode converter two waveguides  1402  and  1404  are arranged as shown in  FIG. 14  having a separation S 1  at one side of the two waveguides and a separation S 2  at the other side of the two waveguides the waveguides are also implemented to have different heights and widths. Light is applied to the waveguide  1402  in both the TM and TE modes. Due to the relative height and width of the two waveguides, however, only light in the TE mode propagates through the waveguide  1402  while only light in the TM propagates in the waveguide  1404 . The far ends of the waveguides  1402  and  1404  as shown in  FIG. 14  provide the output of the mode converter. The design parameters for this mode converter are described in an article by M. R. Watts et al. entitled “Integrated mode-evolution-based polarization splitter,” Optics Letters, vol. 30, no. 9, May 2005. 
       FIGS. 15 and 16  illustrate a photonic crystal cavity device that may, for example, implement a high-Q channel drop filter. As shown in  FIG. 15 , a conventional photonic crystal device includes an array of regularly spaced apertures  1504  which form the photonic crystal matrix. Apertures are omitted from a portion of the matrix  1502  to create a cavity, and from a portion  1506  to create a waveguide. These omitted apertures give the device its characteristic as a drop filter. As described above, roughness along the edges of the apertures  1504  may result in unwanted polarization radiation which tends to reduce the efficiency of the device by reducing the optical power of the signals that may be transmitted through the device. A photonic crystal cavity device according to the an embodiment of the subject invention is shown in  FIG. 16 . As shown, parallel photonic crystal devices are separated by a distance suitable to produce a canceling effect for any radiation dipoles caused by roughness in the apertures  1604 . A single-layer photonic device similar to that shown in  FIG. 15  may be used to implement a high-Q channel add/drop filter as described in an article by Y. Akahane et al. entitled “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Applied Physics Letters, vol. 83, no. 8, August 2003. 
     The essential optical characteristics that change in going from the single layer device to a multilayer device are the vertical mode confinement and vertical mode profile. The vertical mode profile impacts the propagation constant and the lateral mode confinement. Thus, in order to recover identical external coupling to the microcavity while reducing the roughness induce scattering losses, the layer thickness hole radius and hole spacing may need to change. In particular it may be desirable to increase the layer thickness to achieve the same modal confinement in order to achieve strong Bragg reflection within the photonic lattice. Furthermore because vertical mode confinement is closely linked to the effective index of refraction and the lateral confinement, it may be desirable to make a small adjustment of the design of the device to ensure proper coupling between photonic crystal cavity and photonic crystal waveguide. For a particular device, such an adjustment may be achieved in a straight forward manner using finite time domain and finite element modeling techniques. 
       FIG. 17  illustrates a microring resonator device that may be used an add or drop filter as is well known. In a single layer device, light propagating through an input waveguide  1702  resonates in a microring resonator  1704  and is provided to in an output waveguide  1706 . This structure may be used to remove (i.e., drop) a wavelength band from the input waveguide  1702  or to add the wavelength band to the output waveguide  1706 . As described above, one or more additional microring resonators may be included in the device. 
       FIG. 18  shows a similar device implemented in the two layer structure as described above. In this device optical energy propagates through input waveguides  1802  and  1804  in an anti-symmetric super mode and is coupled to parallel microring resonators  1806  and  1808  also in the super mode. Finally the optical energy from the resonators  1806  and  1808  is coupled to the output waveguides  1810  and  1812 . 
     To adapt the microring design from a single layer to a dual layer system employing the anti-symmetric super mode, it may be desirable to increase the layer thickness to achieve the same modal confinement that is desirable to implement tight bends within the microring. In addition because the vertical mode confinement is closely linked to the effective index of refraction and the lateral confinement, it may be desirable to implement a small correction in the ring bus coupling gap and the waveguide width. For a particular device, this modification can be achieved in a straightforward manner using finite time domain and finite element modeling techniques. 
     While two embodiments of the invention, a microring resonator device and a photonic crystal cavity device have been described, the subject invention has much broader application and may be used in any optical device having waveguides that are subject to unwanted polarization radiation due to roughness along the waveguide surfaces. To reduce this radiation, the device may be formed as two substantially identical vertically parallel devices having substantially identical waveguides separated by a small distance. Input light to the device is desirably mode-converted to propagate through the vertically parallel devices in an antisymmetric super mode. It may also be desirable to mode convert the light at the output of the device to provide an output signal having, for example, both TE and TM modes. 
     Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention.