Abstract:
A system for dispersion compensation is provided including a plurality of optical cavities with each including a specific resonant frequency and resonant linewidth. At least one coupling element interconnects the optical cavities. The at least one coupling element defines the coupling strength between the cavities. The optical cavities are interconnected with the at least one coupled element that forms a multi-cavity structure. The multi-cavity structure generates appropriate dispersion properties for dispersion compensation purposes.

Description:
PRIORITY INFORMATION 
   This application claims priority from provisional application Ser. No. 60/300,680 filed Jun. 25, 2001. 

   This invention was made with government support under Grant No. DMR-9808941 awarded by NSF. The government has certain rights in the invention. 

   BACKGROUND OF THE INVENTION 
   The invention relates to the field of optical communications, and in particular to chromatic dispersion using optical resonators. 
   A number of devices have been used for dispersion in communication systems, such as tunable fiber gratings, optical all-pass filters using a ring resonator and virtually imaged phased array devices Tunable fibers can provide high dispersion over large bandwidths, and significant tunability. However, these devices operate in reflection mode that requires an optical circulator to retrieve the reflected signal, which increases the complexity of the device. The optical all-pass filters and the virtually imaged phased array devices exhibit periodic responses, which may not suitable for high bit-rate applications. Also, the all-pass filter designs are based upon a waveguide geometry that tends to exhibit significant polarization mode dispersion, an undesirable characteristics for chromatic dispersion compensation. 
   SUMMARY OF THE INVENTION 
   According to one aspect of the invention, there is provided a system for dispersion compensation. The system includes a plurality of optical cavities with each including a specific resonant frequency and resonant linewidth. At least one coupling element interconnects the optical cavities. The at least one coupling element defines the coupling strength between the cavities. The optical cavities are interconnected with the at least one coupled element that forms a multi-cavity structure. The multi-cavity structure generates appropriate dispersion properties for dispersion compensation purposes. 
   According to another aspect of the invention, there is provided a method for dispersion compensation. The method includes providing a plurality of optical cavities with each including a specific resonant frequency and resonant linewidth. At least one coupling element is provided to interconnect the optical cavities. The at least one coupling element defines the coupling strength between the cavities. Interconnecting the optical cavities with the at least one coupling element form a multi-cavity structure. The method further includes adjusting the overall dispersion of the multi-cavity structure by using certain properties of the optical cavities. 
   According to another aspect of the invention, there is provided a system for dispersion compensation. The system includes a plurality of multi-cavity structure that receives an electromagnetic signal and the electromagnetic signal is cascaded through the multi-cavity structures to perform dispersion compensation. Each of the multi-cavity structures comprises a plurality of optical cavities with each including a specific resonant frequency and resonant linewidth, and at least one coupling element interconnecting the optical cavities, the at least one coupling element defining the coupling strength between the cavities. The interconnection between the optical cavities forms a structure that permits adjusting the overall dispersion of the structure by using the resonant frequency, resonant linewidth, and the coupling strengths of the optical cavities. The multi-cavity structures are arranged such that no mutual coupling occurs between the multi-cavity structures. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIGS. 1   a – 1   c  are schematic diagrams of optical cavities used in accordance with the invention, 
       FIGS. 2   a – 2   d  are graphs of the properties exhibited by optical cavities used in accordance with the invention; 
       FIG. 3  is a schematic diagram of a multi-cavity structure; 
       FIGS. 4   a – 4   d  are graphs demonstrating the characteristics of the multi-cavity structure; and 
       FIG. 5  is a schematic diagram of another embodiment of a multi-cavity for increasing dispersion. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The invention provides a technique for dispersion compensation. The technique is based upon the transmission properties of coupled multi-cavity systems, which eliminates the need of optical circulators and results in significant improvement in cost and device sizes. 
     FIGS. 1   a – 1   c  are schematic diagrams of optical cavities used in accordance with the invention.  FIG. 1   a  shows an optical cavity  2  that includes a waveguide structure  4 , distributed feedback (DFB) grating  6 ,  8 ,  10 , and  12  on top of the waveguide structure  4 . The DFB gratings are used to introduce a phase shift to an electromagnetic signal that enters the waveguide structure  4 . The distance between the DFB gratings  6 ,  8 ,  10 , and  12  can be uniform as shown between grating elements  6  and  8 , or it can also be non-uniform or even overlapping as shown between grating elements  10  and  12 . The distances between grating elements  6 ,  8 ,  10 , and  12  establish a cavity structure with a specific phase shift, delay, and dispersion, which occur to the electromagnetic signal that enters the waveguide structure  4 . 
     FIG. 1   b  shows a photonic crystal structure  14 . The photonic crystal structure  14  includes two embedded optical cavities  24  and  26 , grating elements  20  and  22 , and optical waveguides  16  and  18 . The structure  14  applies the same principles discussed above regarding the cavity  2 . The grating elements  20  and  22  are integral components of the structure  14 . The periodic arrangement of these elements forms a photonic band gap, and confines electromagnetic modes in the cavity region  24  and  26 . The cavity modes then provide specific phase shift, delay, and dispersion properties. The optical waveguides  16  and  18  are coupled with cavities  24  and  26 . As shown in  FIG. 1   b , the electromagnetic signal enters the optical waveguide  16  and leaves through the optical waveguide  18 . Once leaving through the optical waveguides  18 , the electromagnetic signal has incorporated a phase shift, delay, and dispersion that is determined by the cavities  24  and  26  and the coupling strengths between the cavities  24  and  26 . 
     FIG. 1   c  shows a thin film microcavity  28 . The thin film microcavity  28  includes multi-layers  30  and  32  of dielectric mirrors, and the multi-layers  30  and  32  possess different index values. The number of layers can be varied. The microcavity  28  receives an electromagnetic signal. The electromagnetic signal is reflected across the various layers  30  and  32  of the microcavity  28 . Given the layers  30  and  32  can have various index contrast values, the electromagnetic signal experiences an overall phase shift, delay, and dispersion. The DFB cavity  2  and photonic crystal structure  14  are attractive for use in accordance with the invention, because of their compact sizes, and the possibility to directly integrate such cavities on a chip. The multi-layer microcavity  28  offers superior coupling to optical fibers. In addition, when light is incident to the normal of incidence direction, an exact degeneracy can occur due to the rotational symmetry of the structure. Thus, the polarization dependency in principle can be completely eliminated. 
   The invention can also use other types of optical cavities. These optical cavities need to exhibit properties similar to the cavities  2 ,  14 , and  28 , discussed above. These properties will be discussed more hereinafter. Using these optical cavities  2 ,  14 , and  28 , one can create a dispersion compensation module, which results in significant improvement in costs and device sizes. 
     FIGS. 2   a – 2   d  are graphs of the properties exhibited by optical cavities  2 ,  14 , and  28  used in accordance with the invention. While the cavities  2 ,  14 , and  28  are different in structure, they exhibit similar optical properties, as characterized by its transmission function, as discussed hereinafter. A typical transmission function for each of the optical cavities  2 ,  14 , and  28  is shown in  FIG. 2   a . Each of the optical cavities  2 ,  14 , and  28  transmission function is Lorentzian. In order to achieve high transmission, these optical cavities  2 ,  14 , and  28  need to be symmetric in terms of the optical feedback of the mirrors on both sides of the cavities  2 ,  14 , and  28 . The ratio between the resonant wavelength and full width of transmission lineshape at half maximum (FWHM) defines the quality factor Q. In this case, the resonant wavelength, as shown in  FIG. 2   a , is 1.55 μm, the FWHM in frequency is 25 GHz, and the Q factor is 4,000. Such a Q factor can be achieved in the thin film microcavity  28  using Si and SiO 2 . 
     FIG. 2   b  shows a graph  36 , which demonstrates the relationship between phase and wavelength. In particular, the graph  36  defines the phase as a function of wavelength for a single cavity. As the wavelength increases across the resonance, in this case at 1.55 μm, the phase increases from −1.5 μm to 1.5 μm. At resonance, the phase is approximately zero. 
   The delay associated with the electromagnetic wave or optical signal through any the of the cavities  2 ,  14 , and  28  is defined as: 
                   τ   max     =       ⅆ   φ       ⅆ   ω               Eq   .           ⁢   1               
where φ is phase and ω is wavelength. Essentially, the graph  38  of the delay is the derivative of the graph  36  with respect to the frequency, as shown in  FIG. 2   c.    
   The delay exhibits a Lorentzian lineshape, and is at its maximum at the resonant frequency, in this case at 1.55 μm. This indicates that at resonance, light will spend a long time in the cavity before it escapes. The delay decreases when a wavelength is further away from the resonant wavelength. In this case, the maximum delay is at 12 ps. For a single cavity, the maximum delay is defined as: 
                   τ       m   .     ⁢   a   ⁢           ⁢   x       =       Q   ⁢           ⁢   T       2   ⁢   π               Eq   .           ⁢   2               
where T is the optical cycle at the resonant frequency.
 
   The dispersion of an optical system D is defined as 
                 D   =       ⅆ   τ       ⅆ   λ               Eq   .           ⁢   3               
and is calculated for this system, as shown in  FIG. 2   d . The graph  38  is the derivative of the graph  36  with respect to frequency. Also, the dispersion is zero at the resonant frequency, and varies from −82 ps/nm to 82 ps/nm, over a wavelength range of approximately 0.1 nm. The maximum dispersion occurs at a wavelength of approximately 1.55009 micron, and the minimum dispersion occurs at a wavelength of 1.54901 micron.
 
   By tuning the frequency of a cavity, while keeping the signal frequency constant, it is then possible to achieve tuning in the dispersion properties. The tuning can be achieved in a variety of different mechanisms, such as through thermal, electrical, or mechanical means. 
   The Q value defines the optical bandwidth, the dispersion, and delay properties of an optical cavity. The maximum delay scales as Q, while the maximum dispersion scales as Q 2 . In a single cavity system, increasing the bandwidth as is required by the applications in high-bit rate communications systems, also results in the decrease of dispersion. 
   As discussed above, other optical cavities can be used in accordance with the invention. These optical cavities should possess the same properties that have been described with reference to  FIGS. 2   a – 2   d.    
     FIG. 3  is a schematic diagram of a multi-cavity structure  41 . The multi-cavity structure  41  includes optical cavities  42 ,  45 , and  47  and coupling elements  44  and  46 . Given that the multi-cavity structure  41  includes  3  optical cavities, it is consider a 3-cavity structure. In other embodiments, the invention can include more cavity structures. The cavities  42 ,  45 , and  47  are coupled together through the coupling elements  44  and  46 . Also, the number of coupling elements can also vary depending on the optical cavities being used. 
     FIG. 3  also shows each of the cavities  42 ,  45 , and  47  as being thin film microcavities. However, other cavities structures can be used, such as DFB cavities or photonic crystal structures. Also, a combination of the different structures can be used in accordance with the invention, for example, a 3-cavity structure, which includes a thin film microcavity, a photonic crystal structure, and a DFB microcavity. Each of the various cavities individually must exhibit the properties described with reference to  FIGS. 2   a – 2   d . Other optical cavities, beside those described above, can also be used in accordance with the invention. These types of cavities must also demonstrate that they exhibit the properties described in  FIGS. 2   a – 2   d.    
   The coupling elements  44  and  46  are used to interconnect between the optical cavities  42 ,  45 , and  47 , and provide a path for electromagnetic signals leaving a first optical cavity to be directed to a second optical cavity. Also, the coupling elements  44  and  46  allow for mutual inter-mixing of the electromagnetic signals from any two optical cavities to occur within its structures, thus permitting mutual coupling between cavities. 
   In order to increase dispersion without sacrificing the signal bandwidth, it is important to use the multi-cavity system  41 . The cavities  42 ,  48 , and  50  are coupled through coupling element  42  and  44 , which have sufficient coupling strengths to achieve the desired characteristics. For the 3-cavity structure  41 , the coupling constant between the cavities is equal to 0.9 times the decay rate of a one-sided cavity. In other embodiments, the coupling constant can be varied depending on the number of coupled optical cavities. Also, the more optical cavities used in a multi-cavity structure, the dispersion associated with the multi-cavity also increases. 
   An arrangement of cavities of different types can also effect the coupling strength between the various cavities  42 ,  45 , and  47  and their respective coupling constants. However, the coupling constants should not vary significantly from those arrangements that include optical cavities of the same type. The invention provides the flexibility to use different optical cavities without sacrificing signal bandwidth. 
   By tuning the frequency of each of the cavities in the multi-cavity structure  41 , while keeping the signal frequency constant, it is then possible to achieve tuning in the dispersion properties. The tuning can be achieved in a variety of different mechanisms, such as through thermal, electrical, or mechanical means. 
   Another feature of the invention is the presence of large dispersion in high-transmission regions of the optical spectra. This feature allows for low-insertion loss operation. Moreover, with an embodiment using thin films filters at normal incidence, the invention can eliminate polarization mode dispersion associated with certain optical cavities. Since optical cavities can also be constructed in a waveguide geometry, such as photonic crystal microcavities or waveguide gratings, the invention can be designed to be miniaturized to a single wavelength scale. Therefore, allowing photonic circuits to be used in accordance with the invention. 
     FIGS. 4   a – 4   d  are graphs demonstrating the characteristics of the multi-cavity structure  41 .  FIG. 4   a  shows a graph  50  associated with the transmission characteristics of the multi-cavity  41 . As discussed above, the multi-cavity  41  is a 3-cavity structure of thin film microcavities  42 ,  45 , and  47 , as shown in  FIG. 3 . 
   The range of transmission as shown in graph  50  is between approximately 0 and −50 dB. The resonant wavelength is at 1.55 μm. In comparison to the graph  34  of  FIG. 2   a , the range of frequencies with high transmission coefficients in graph  50  are much larger. This is accomplished by having each of the three optical structures  42 ,  45 , and  47  has a resonant frequency at 1.55 μm. However, if each of the optical cavities structures  42 ,  45 , and  47  are to have different resonant frequencies, the resultant frequency of the multi-cavity structure  41  will be different. 
     FIG. 4   b  shows a graph  52  associated with the phase of the multi-cavity structure  41 . The range of the phase as shown in graph  52  is between approximately −11 radian and −2 radian. In comparison to the graph  36  of  FIG. 2   b , the phase of the multi-cavity structure  41  has a larger region. In general, the more optical cavities that are used in a multi-cavity structure, the more the phase will increase. Thus, the multi-cavity structure  41  can accommodate a larger range of phase as compared to a single cavity structure. 
     FIG. 4   c  shows a graph  54  associated with the delay of the multi-cavity structure  41 . The range of the delay as shown in graph  54  is between −1 ps and −50 ps. In comparison to graph  38  of  FIG. 2   c , the range of the delay of the multi-cavity  41  is significantly larger then that of a single cavity structure. The larger the number of optical cavities used in a multi-cavity structure, the larger the range of delay will be. Also, graph  54  shows two minimum values at approximately 1.5499 μm and 1.5501 μm. The graph  52  further shows the delay does not vary very much around the resonant frequency. 
     FIG. 4   d  shows a graph  56  associated with dispersion of the multi-cavity structure  41 . The range of dispersion as shown in graph  56  is between 700 and −700 ps/nm. In comparison with  FIG. 2   d , the multi-cavity  41  has a larger range of dispersion. Also, the dispersion varies from −500 to 500 ps/nm monotonically with the wavelength range of approximately 0.01 nm around the resonant wavelength of 1.55 μm. Within the high transmission frequency range, high dispersion also occurs. The multi-cavity structure  41  can operate with minimal insertion while still achieving high dispersion. 
     FIG. 5  is a schematic diagram of another embodiment for increasing dispersion. A system  57  includes multi-cavity structure  58 ,  60 , and  62 . The multi-cavity structures  58 ,  60 , and  62  are specifically arranged such that there are no mutual coupling among them. In this embodiment, the multi-cavity structures  58 ,  60  and  62  are tilted to ensure that no mutual coupling occurs. Other techniques to prevent mutual coupling can be used. Also, each of the structures  58 ,  60 , and  62  is a thin film multi-cavity structure. Other types of multi-cavity structures can be used in this embodiment. 
   An incident light ray or electromagnetic signal  64  is directed to the first  58  of the multi-cavity structures  58 ,  60  and  62 , and incorporates the dispersion properties associated with the multi-cavity structure  57 . An electromagnetic signal  66  exits the multi-cavity structure  58 , and is directed to the second multi-cavity structure  60 . Within the second multi-cavity structure  60 , the electromagnetic  66  further incorporates the dispersion properties associated the multi-cavity structure  60 . An electromagnetic signal  68  exits the multi-cavity structure  60 , and is directed to the third multi-cavity structure  62 . That electromagnetic signal  68  further includes the dispersion properties of the multi-cavity structure  62 . 
   The resultant electromagnetic signal  70  that passes through all of the multi-cavity structures  58 ,  60 , and  62  is substantially dispersed, and exhibits large dispersion properties. The structure  57  allows for large dispersion to occur, and there is minimal insertion loss, because each of the multi-cavity structures  58 ,  60 , and  62  has low insertion loss as well. 
   Because there is no mutual coupling between the multi-cavity structures, the electromagnetic signals  64 ,  66 , and  68  that are received from each of the multi-cavity structures  58 ,  60 , and  62  have not been exposed to a previous or successor multi-cavity structure. In this case, the total dispersion of the electromagnetic signal becomes the sum of the dispersion of the electromagnetic signal through each of the cavities  58 ,  60 , and  62 , respectively. 
   By tuning the frequency of each of the cavities in the multi-cavity structures  58 ,  60 , and  62 , while keeping the signal frequency constant, it is then possible to achieve tuning in the dispersion properties. The tuning can be achieved in a variety of different mechanisms, such as through thermal, electrical, or mechanical means. 
   The number of multi-cavity structures that can be used can vary. The more multi-cavity structures being used, the resultant light from the arrangement will be more dispersed. Also, these multi-cavity structures will need to be arranged so there are not mutual coupling. 
   The invention can be used to compensate optical signals in optical communications, such as fiber optic lines. The invention does not delineate the signal bandwidth to accomplish the task of tunably compensating an optical signal. The invention is versatile enough to be incorporated onto a chip, or be used in a stand-alone fashion. 
   Although the present invention has been shown and described with respect to several preferred embodiments thereof, various changes, omissions and additions to the form and detail thereof, may be made therein, without departing from the spirit and scope of the invention.