Abstract:
Methods of manufacturing a lasing device are provided by some embodiments, the methods including: creating a silicon micro ring with a predetermined radius and a predetermined first cross-sectional dimension; creating a silicon waveguide with a predetermined second cross-sectional dimension, the silicon waveguide spaced from the silicon micro ring by a predetermined distance; and wherein the predetermined distance, the predetermined radius, the predetermined first cross-sectional dimension, and the predetermined second cross-sectional dimension are determined so that at least one first whispering gallery mode resonant frequency of the silicon micro ring and at least one second whispering gallery mode resonant frequency of the silicon micro ring are separated by an optical phonon frequency of silicon.

Description:
RELATED APPLICATIONS 
     This application is a divisional of U.S. patent application Ser. No. 11/354,725, filed Feb. 15, 2006, which claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Patent Application No. 60/653,556, filed on Feb. 16, 2005, each of which is hereby incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to optical amplification and lasing devices, and methods for manufacturing the devices. More particularly, the present invention relates to low-threshold microcavity Raman lasers, and methods for manufacturing the same. 
     BACKGROUND OF THE INVENTION 
     Stimulated Raman scattering (“SRS”) has a rich and evolving history since the development of the laser. In 1962, SRS effect at infrared frequencies was discovered. This discovery was soon described as a two-photon process with a full quantum mechanical calculation. To account for anti-Stokes generation and higher-order Raman effects, however, coupled-wave formalism was adopted to describe the stimulated Raman effect. Self-focusing was later included to account for the much larger gain observed in SRS. These understandings facilitated the study and design of Raman amplifiers and lasers. For example, low-threshold microcavity Raman lasers have been demonstrated in silica micro spheres and micro disks using excited whispering gallery modes (“WGMs”). Such devices can play an important role in the developing technology of photonic integrated circuits. 
     Because silicon is being considered as a promising platform for photonic integrated circuits, silicon based photonic devices have been increasingly researched. Microscopic passive silicon photonic devices such as bends, splitters, and filters have been developed. Active functionalities in highly integrated silicon devices have been studied, such as optical bistability due to the nonlinear thermal-optical effect and fast all-optical switching with two-photon absorption. 
     Silicon based Raman amplifiers and lasers also have been studied. The bulk Raman gain coefficient g R  in silicon is 10 4  times higher than in silica. Light generation and amplification in planar silicon waveguides with Raman effects have been studied recently. Raman lasing using a silicon waveguide as the gain medium has been demonstrated, where the ring laser cavity is formed by an 8-m-long optical fiber. A Raman laser using an S-shaped 4.8-cm-long silicon waveguide cavity with multi-layer coatings has also been reported, which could be integrated onto CMOS-compatible silicon chips. 
     Despite these advances, microscopic low-threshold Raman amplification and lasing devices on a monolithic silicon chip has yet to be developed. Such devices would support the development towards efficient, all-optical photonic integrated circuits. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention provide all-optical on-chip signal amplification and lasing. In particular, embodiments of the present invention include Raman amplification and lasing devices using on-chip micro ring resonators coupled with waveguides in monolithic silicon. Embodiments of the present invention also provide methods for manufacturing such devices. According to embodiments of the present invention, lasers are designed with geometries so that WGM resonant frequencies of the micro ring resonator match the pump-Stokes frequency spacing of SRS in monolithic silicon. Therefore, one or more pairs of pump and Stokes light can form WGMs in the micro ring resonator. 
     Devices for generating a laser beam are disclosed. In some embodiments, the devices include a silicon micro ring having a radius and a cross-sectional dimension, and at least one silicon optical waveguide having a cross-sectional dimension and disposed at a distance from the micro ring. The distance, the radius, and the cross-sectional dimensions are determined so that at least one pair of whispering gallery mode resonant frequencies of the micro ring are separated by an optical phonon frequency of silicon. 
     Methods of manufacturing a lasing device including a silicon micro ring coupled with a silicon waveguide are disclosed. In some embodiments, the methods include determining a radius and a cross-sectional dimension of the micro ring, a cross-sectional dimension of the waveguide, and a distance between the micro ring and the waveguide, so that at least one pair of whispering gallery mode resonant frequencies of the micro ring are separated by an optical phonon frequency of silicon. The methods also include manufacturing the lasing device by creating the micro ring with the determined radius and cross-sectional dimension, creating the waveguide with the determined cross-sectional dimension, and disposing the micro ring from the waveguide at the determined distance. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The Detailed Description of the Invention, including the description of various embodiments of the invention, will be best understood when read in reference to the accompanying figures wherein: 
         FIG. 1   a  is a top view of a Raman amplification and lasing device in accordance with various embodiments of the present invention; 
         FIG. 1   b  is a cross-sectional view of the Raman amplification and lasing device in  FIG. 1   a;    
         FIG. 2  is a transmission spectrum of a Raman amplification and lasing device according to one example of the present invention; 
         FIG. 3  is a diagram illustrating the WGMs formed by a beam of light in the same example device as used for  FIG. 2 ; 
         FIG. 4  is a diagram illustrating the WGMs formed by another beam of light in the same example device as used for  FIG. 2 ; 
         FIG. 5  is a flow chart illustrating methods for manufacturing a Raman amplification and lasing device according to various embodiments of the present invention; and 
         FIG. 6  is a top view of a fabricated Raman amplification and lasing device according to various embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Devices of various embodiments of the present invention use micro ring resonators as a cavity for producing Raman laser. The strong light confinement of a micro ring resonator enhances the stimulated Raman scattering with low-threshold pump power. 
       FIG. 1   a  is a top view and  FIG. 1   b  is a cross-sectional view of a Raman amplification and lasing device of various embodiments of the present invention, generally at  100 . Device  100  includes an optical micro ring resonator  102  and an optical waveguide  104 , both made of silicon. The cross-sectional view illustrates a cross section of device  100  taken by a plane perpendicular to the sheet and passing through the center of micro ring resonator  102 . 
     In some embodiments, waveguide  104  can be a quasi-transverse electric (“quasi-TE”) single-mode waveguide. As shown, micro ring resonator  102  has radius R. Micro ring resonator  102  and waveguide  104  can have the same width w and height t si . There is a gap s between resonator  102  and waveguide  104 . Resonator  102  and waveguide  104  can be formed on top of a layer of silicon oxide (SiO 2 )  106 . In some embodiments, device  100  can include more than one waveguide disposed at a close distance to resonator  102 . Although waveguide  104  is shown to be straight in  FIG. 1 , it can assume other shapes as known in the art. 
     In operation, pump light can enter the lower end  109  of waveguide  104  in the direction of arrow  108 . This pump light can induce pump light in resonator  102  in the direction of arrow  110  by a coupling effect. When resonator  102  is stimulated, Stokes light in resonator  102  is generated by Raman scattering, which causes Stokes light leaving the upper end of waveguide  104  by the coupling effect. 
     Stimulated Raman scattering in micro ring resonator  102  is a two-photon process related to the optical phonons. The strongest Stokes peak arises from single first-order Raman-phonon (three-fold degenerate) at the Brillouin zone center. The coupling between the pump and Stokes lightwaves in SRS can be described by Maxwell&#39;s equations using nonlinear polarizations P (3) : 
     
       
         
           
             
               
                 
                   
                     
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     The nonlinear polarization P s   (3)  is cast as χ jkmn   (3)  E p  E p * E s , where χ jkmn   (3)  is the third-order fourth-rank Raman susceptibility, and can be calculated in terms of the Raman tensor              i . The E p  and the E s  are electric fields of the pump and Stokes waves respectively.
     In micro ring resonator  102 , it can be shown that the cavity SRS enhancement results from the intensity build up in the cavity, so that the threshold pump power depends on the quality factor Q and also the coupling efficiencies. The intensity build up factor for the cavity mode is:
 
 I   c   /I   0 =( Q λ)/(π 2   nR )  (3)
 
where I 0  is the intensity of the input light, I c  is the effective intensity of the light in the cavity, λ is the light wavelength, n is the refraction index of the micro ring resonator  102  host material, and R is the radius of the micro ring resonator  102 . The effective interaction length is:
 
 L   c =( Q λ)/(2 πn )  (4)
 
     Both pump mode and Stokes mode can be WGMs with quality factors Q p  and Q S , respectively. The condition for Raman lasing is that the gain exceeds the losses:
 
 g   R   ξI   c,pump   &gt;L   c,Stokes   −1   (5)
 
     Assume that the modal volume is V m ≈2πRA, the threshold pump power P th =I 0 A is: 
                     P   th     =           π   2     ⁢     n   2         ξ   ⁢           ⁢     g   R     ⁢     Q   S     ⁢     Q   p         ⁢       V   m         λ   p     ⁢     λ   S                   (   6   )               
where the parameter ξ&lt;1 describes the coupling to the pump mode and the overlap between the pump and Stokes modes, A is the effective cross-sectional area of the cavity mode, and g R  is the bulk Raman gain coefficient of silicon, which is about 70 cm/GW for Stokes radiation in the 1550-nm range.
 
     Because the quality factors Q S  and Q p  of pump mode and Stokes mode are relatively high, threshold power P th  can be made very low. Therefore, by designing a highly confined micro ring resonator  102  that supports pump and Stokes modes, a microscopic low-threshold on-chip amplification and lasing device  100  can be fabricated. 
     The following describes the design of device  100  that supports one or more pump and Stokes modes. Device  100  can be designed by numerically solving Maxwell&#39;s equations (1) and (2) with a boundary condition corresponding to the geometry of device  100 , using a three-dimensional finite-difference time-domain (3D FDTD) method. With a 3D FDTD method, a transmission spectrum of device  100 , resonant wavelengths, WGM field profiles, and quality factor Q of the resonant wavelengths can all be calculated. This can be performed with any software that numerically solves the Maxwell&#39;s equations (1) and (2), such as the FullWAVE™ software provided by RSoft Design Group, Inc. (Ossining, N.Y.). 
     An important goal of the design is to determine iteratively (i.e., fine-tune) the geometry of device  100  so that WGM resonant frequencies of micro ring resonator  102  corresponds to one or more pairs of pump and Stokes frequencies. A pump frequency and a corresponding Stokes frequency are spaced apart by Δv=15.6 THz, which is the optical phonon frequency in monolithic silicon. If a pair of WGM resonant frequencies are separated by 15.6 THz, a pump light having one of the pair of frequencies can be used to generate a Stokes light having the other frequency, and both the pump and the Stokes light can form WGMs in resonator  102 . 
     If it is desirable that device  100  supports pump and Stokes lights with wavelengths close to a predetermined wavelength (e.g., 1550 nm), the geometry of device  100  can be determined iteratively so that wavelengths corresponding to the WGM resonant frequencies of resonator  102  are close to the predetermined wavelength (e.g., within the range of about 1400 nm to about 1600 nm). However, device  100  is not limited by the example provided; device  100  can also be designed to support pump and Stokes lights with wavelengths within other suitable ranges. 
     According to various embodiments of the present invention, a numerical design process can include determine iteratively the geometry of device  100  and calculating the corresponding transmission spectrum of waveguide  104  with, for example, a 3D FDTD method. The drops in the transmission spectrum correspond to WGM resonant frequencies of resonator  102 . From the transmission spectrum, a pump wavelength λ p  can be chosen, such that λ p  corresponds to a drop in the transmission spectrum. Then, the Stokes wavelength can be calculated with λ S =λ p +λ p   2 /(c/Δv−λ p ). Stokes wavelength λ S  should also correspond to a drop in the transmission spectrum. Quality factors Q p  and Q S  can then be calculated with Q=λ/Δλ FWHM  from the transmission spectrum. 
     Determining iteratively the geometry of device  100  can include determining iteratively the radius R of resonator  102 , the width w and the height t Si  of waveguide  104  and micro ring resonator  102 , and the gap s between waveguide  104  and resonator  102 , so that the transmission spectrum of waveguide  104  have certain desired properties. For example, width w and height t Si  can be changed it to shift the high Q resonant spectrum of device  100  to a range close to 1550 nm. A starting point for the iterative determination of width w and height t Si  can be values that support a quasi-TE single-mode waveguide  104 . Radius R can be determined iteratively so that optical phonon frequency (15.6 THz) is an integer multiple of the free spectral range, which is the spacing between the neighboring WGM resonant frequencies of resonator  102  (the WGM resonant frequencies corresponds to drops in the transmission spectrum of the waveguide). Gap s can be determined iteratively to achieve a good electromagnetic coupling efficiency into and out of resonator  102  for different wavelength ranges. 
     As an example, device  100  can be designed with w equals to 350 nm, t Si  equals to 200 nm, s equals to 150 nm, and R equals to 4.9 μm. In this example, the cross-sectional dimension of waveguide  104  as represented by w and t Si  supports a quasi-TE single-mode. Height t oxide  of SiO 2  layer  106  can be 400 nm. The refraction index of silicon and SiO 2  can be n Si =3.48 and n oxide =1.46 respectively. 
       FIG. 2  illustrates the quasi-TE transmission spectrum near 1550 nm of waveguide  104  coupled with resonator  102  according to this example design. As shown, two pump lights (Pump  1  and Pump  2 ) can be selected from the transmission spectrum, with wavelengths λ p1 =1431.8 nm and λ S1 =1546.5 nm. Two corresponding Stokes lights (Stokes  1  and Stokes  2 ) have wavelengths λ p2 =1444.8 nm and λ S2 =1562.5 nm, which also correspond to drops of the transmission spectrum. 
       FIG. 3  illustrates the WGMs of Pump  1  inside micro ring resonator  102  of this example with continuous wave excitation. The white dots  302  in resonator  102  are the locations having stronger Hy field (magnetic field in the Y direction). It can be seen that Pump  1  forms WGMs in resonator  102 . The WGMs of Pump  1  in resonator  102  are caused by Pump  1  in waveguide  104  traveling in the direction of arrow  108  (Z direction). 
       FIG. 4  illustrates the WGMs of Stokes  1  inside micro ring resonator  102  of this example with continuous wave excitation. The white dots  402  in resonator  102  are the locations having stronger Hy field (magnetic field in the Y direction). It can be seen that Stokes  1  forms WGMs in resonator  102  as well. The WGMs of Stokes  1  in resonator  102  are caused by Stokes  1  in waveguide  104  traveling in the direction of arrow  108  (Z direction). 
     Therefore, device  100 , according to the example design, supports the WGMs of both Pump  1  and Stokes  1 . By SRS and coupling, Pump  1  in waveguide  104  can induce WGMs of both Pump  1  and Stokes  1  in micro ring resonator  102 , and hence Stokes  1  in waveguide  104 . Similarly, device  100 , according to the example design, supports the WGMs of both Pump  2  and Stokes  2 . It should be noted that the example geometry of device  100  is not the only geometry that can support WGMs of the required pump and Stokes frequencies. 
       FIG. 5  is a flow chart illustrating various processes for manufacturing Raman amplification and lasing devices of various embodiments of the present invention. At  500 , a suitable geometry of device  100  is determined. At  502 , a layer of polymethylmethacrylate (“PMMA”) can be coated on top of a silicon-on-insulator (“SOI”) wafer. For example, a 200 nm thick 495 495K A6 PMMA can be spin-coated on top of a SOI wafer. At  504 , a design pattern according to the determined geometry can be written on the PMMA layer by electron-beam lithography. At  506 , the exposed PMMA layer can be developed in a solution. For example, a solution of methylbutylisoketone (“MIBK”) and isopropyl alcohol (“IPA”) with MIBK:IPA=1:3 can be used to develop the PMMA layer for about 55 seconds. At  508 , a chrome mask can be transferred on top of the SOI wafer by thermal evaporation. At  510 , the SOI wafer can be etched to form the designs in the wafer, using, for example, inductively coupled plasma (“ICP”) etching. At  512 , the chrome mask can be removed. The wafer can be further packaged to seal the optical devices fabricated on the wafer.  FIG. 6  is a top view of a fabricated Raman amplification and lasing device of various embodiments of the present invention captured by scanning electron microscopy (“SEM”). 
     Other embodiments, extensions, and modifications of the ideas presented above are comprehended and within the reach of one skilled in the art upon reviewing the present disclosure. Accordingly, the scope of the present invention in its various aspects should not be limited by the examples and embodiments presented above. The individual aspects of the present invention, and the entirety of the invention should be regarded so as to allow for modifications and future developments within the scope of the present disclosure. The present invention is limited only by the claims that follow.