Abstract:
A colorless tunable optical dispersion compensator (TODC) comprising a silica arrayed-waveguide grating (AWG) directly coupled to a polymer thermo-optic lens. As a result of its inventive construction, the device exhibits low loss, large tuning range, low electrical consumption and is readily manufactured using standard processes. Additionally, the TODC is fully solid-state and scales to a large figure-of-merit (dispersion range times bandwidth squared).

Description:
FIELD OF THE INVENTION 
   This invention relates generally to the field of optical communications and in particular to a tunable dispersion compensation apparatus. 
   BACKGROUND OF THE INVENTION 
   In long-distance transmission of optical signals, the accumulation of chromatic dispersion in optical fiber presents serious problems. These problems intensify with an increase in bit rate and the distance traveled by the optical signals. Efforts to date that compensate for dispersion have mainly involved the use of dispersion compensating fiber (DCF). 
   Dispersion compensating efforts that employ DCF—while well-proven—are not particularly amenable to integration in existing network elements. This is due—in part—because DCF is employed as a large spool of fiber which occupies significant space in a network office and is not adjustable. In addition, service providers that utilize DCF in their networks must accurately characterize their fiber, deploy more expensive optical amplifiers, and accept additional latency added to links employing the DCF [˜20% additional latency for a fully compensated standard-single-mode fiber (SSMF) link]. Finally, DCF cannot satisfy all of the dispersion compensation requirements of many 40-Gb/s links, consequently, a tunable optical dispersion compensator (TODC) having a small tuning range is often required in addition to the DCF. 
   A TODC employing an arrayed waveguide grating (AWG) and thermo-optic lens was described in U.S. Pat. No. 7,006,730 directed to a “Multichannel Integrated Tunable Thermo-Optic Lens and Dispersion Compensator”). And while the TODC described therein appeared to be an attractive alternative/supplement to DCF, it unfortunately required significant electrical power (7.3 W to tune over 400 ps/nm) and generated relatively high local temperatures thereby negatively impacting its long-term reliability. 
   SUMMARY OF THE INVENTION 
   We have developed, in accordance with the principles of the invention, a tunable optical dispersion compensation apparatus (TODC) which permits the programmable fine tuning of the amount of dispersion compensation applied. Our apparatus comprises a silica arrayed-waveguide grating (AWG) directly coupled to a polymer thermo-optic lens. As a result of its inventive construction, our TODC exhibits low loss, large tuning range, low electrical consumption and is readily manufactured using standard processes. 
   Advantageously, our inventive TODC is fully solid-state, compact, scales to a large figure-of-merit and may be employed in a variety of optical transmission systems while minimizing the need for DCF. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
     A more complete understanding of the present invention may be realized by reference to the accompanying drawing in which: 
       FIG. 1  shows a schematic of a dispersion compensation apparatus constructed according to the present invention; and 
       FIG. 2  shows a schematic of an alternative embodiment of the dispersion compensation apparatus of  FIG. 1 ; 
       FIG. 3  shows a schematic of the embodiment of the dispersion compensation apparatus of  FIG. 1  with additional details; 
       FIG. 4  shows a series of graphs showing measured transmissivity and group delay of the exemplary tunable optical dispersion compensator (not including a circulator) for seven different thermo-optic lens settings at three locations in the C-band wherein resolution bandwith is 10 pm; 
       FIG. 5  is a schematic of an experimental setup used to evaluate the apparatus of  FIG. 1 ; 
       FIG. 6  is a graph showing bit-error rate vs. signal-to-noise ratio of the experimental setup used to evaluate the apparatus of  FIG. 5 ; 
       FIG. 7  shows a schematic of another alternative embodiment of a dispersion compensation apparatus according to the present invention; 
       FIG. 8(   a ) shows a schematic of an “unfolded” variation of a dispersion compensation apparatus according to the present invention; 
       FIG. 8(   b ) shows a schematic of an alternative embodiment of the “unfolded” dispersion compensation apparatus of  FIG. 8(   a ); and 
       FIG. 8(   c ) shows a schematic of yet another alternative embodiment of the “unfolded” dispersion compensation apparatus of  FIG. 8(   a ). 
   

   DETAILED DESCRIPTION 
   Optical switching, multiplexing, and demultiplexing have been accomplished in the past by using an interconnection apparatus having one or more input waveguides communicating with the input of a star coupler. The output of the star coupler communicates with an optical grating comprising a series of optical waveguides, each of the waveguides differing in length with respect to its nearest neighbor by a predetermined fixed amount. The grating is connected to the input of a second star coupler. The second star coupler has one or more output waveguides which form the outputs of the switching, multiplexing, and demultiplexing apparatus. An example of such an interconnection apparatus is disclosed in U.S. Pat. Nos. 5,002,350 and 5,136,671, the entire contents and teachings of which are incorporated herein by reference. 
   The geometry of such an apparatus may be such that a plurality of separate and distinct wavelengths each launched into a separate and distinct input port of the apparatus will all combine and appear on a predetermined one of the output ports. In this manner, the apparatus performs a multiplexing function. The same apparatus may also perform a demultiplexing function. In this situation, a plurality of input wavelengths is directed to a predetermined one of the input ports of the apparatus. Each of the input wavelengths is separated from the others and directed to a predetermined one of the output ports of the apparatus. An appropriate selection of input wavelength also permits switching between any selected input port to any selected output port. Accordingly, these devices are referred to as frequency routing devices. 
   Sharing some common elements with such frequency routing devices,  FIG. 1  shows in schematic form the pertinent details of our inventive tunable dispersion compensation apparatus. The apparatus includes an input/output waveguide port  111  connected to an input circle of a free space region of a slab waveguide  110  (first star coupler). 
   A plurality of output ports extends from an output circle of the free space region of the slab waveguide  110  and is connected to an optical grating  115 . The optical grating  115  comprises a plurality of unequal length waveguides  115 [ 1 ] . . .  115 [N] which provides a predetermined amount of path length difference to a corresponding plurality of input waveguides connected to an input circle of a free space region of another slab waveguide  120  (second star coupler). A half-wave plate  150 , used to reduce overall polarization dependence, is disposed at substantially a mid-point of the grating  115   
   At an opposite, output end of the slab waveguide  120 , positioned adjacent (where output waveguides would be located in a “pure” frequency routing device), is a planar lightwave circuit (PLC)  125  which includes a heating element(s)  130  and a mirror  140 . For our purposes, the PLC is constructed from a material that exhibits a suitable refractive index change upon heating while, at the same time, exhibiting a sufficient thermal conductivity such that it is easily heated. Overall, what is used is a PLC having adequate thermal properties to exhibit a good thermal profile and thus, a preferably parabolic or similar index profile on the required length scale (˜550 um in this case). In this manner, the PLC behaves as a thermo-optic lens by providing a preferred parabolic (or similar) refractive index profile whose magnitude can be electrically (heated) controlled. The total slab length, the length of  120  plus the length of  125  times the refractive index of  125  divided by the refractive index of  120 , is equal to an original slab length of refractive index of  120  where the output waveguides would be located in a “pure” frequency routing device. In other words, the presence of  125  requires that the  120  is shortened accordingly. 
   When configured in this manner, portions of light input to input/output waveguide  111  traverses the first slab waveguide  110 , the grating  115 , the second slab waveguide  120 , traverses the thermo-optic lens PLC  125 , is reflected by the mirror  140 , and subsequently output via input/output waveguide  120  having a majority of its accumulated dispersion compensated. Note that there may be more than one input/output waveguide  111 , for the purpose of adjusting the wavelength of the TODC. 
   In a preferred embodiment, the mirror  140  length along slab  120  will only be equal to or less than the width of the Brillouin zone. This ensures that high spatial diffraction orders from the grating are not reflected back into the grating. In addition, in a preferred embodiment, the mirror  140  is substantially flat as it is easiest to cut and/or polish a flat surface, both for the PLC  125  and for the mirror  140 . As can be appreciated, when the mirror  140  is flat, the device provides negative dispersion when no heating elements in  130  are activated which compensates the dispersion of most single-mode optical fibers, most notable standard single-mode fiber, which has a dispersion of ˜+17 ps/nm/km in the C-band. 
   It may be noted at this point that we may advantageously use the heating elements to adjust focal length and/or add a constant phase since the heat profile includes an offset that may be adjusted as needed. Alternatively, certain ones of the heating elements may be used to generate an offset while others may be used to create the parabolic (or similar) heat profile. As can be readily appreciated by those skilled in the art, through the selective use of our heating elements nearly any suitable heat and/or index distribution may be produced, as needed and/or desired. 
   Turning our attention now to  FIG. 2 , there is shown an alternative embodiment of our inventive tunable dispersion compensator. Shown in  FIG. 2  is an alternative configuration in which a quarter-wave plate  135  is positioned between the PLC  125  and the mirror  140 . This will cause transverse electric polarization to flip to transverse magnetic polarization and vice-versa upon reflection from the mirror and quarter-wave plate, advantageously reducing the polarization dependency of the dispersion compensator. In some cases, this is preferable to the half-wave plate inserted into the middle of the grating, as shown in  FIG. 1 , because the half-wave plate may cause an undesirable back reflection. 
     FIG. 3  shows a schematic of an exemplary tunable optical dispersion compensator (TODC)  300  constructed according to our inventive principles. More particularly, the TODC comprises a silica PLC (˜38×44 mm 2 )  310  having an AWG  320  attached to a much smaller (˜4.2×10mm 2 ) polymer PLC  330  comprising a thermo-optic lens  340 . In this exemplary embodiment, the silica waveguides are substantially 6.0 μm high and exhibit an index contrast of 0.80%, disposed on a silicon substrate. 
   As constructed, the AWG  320  has 44 gratings arms, a free-spectral range of Δf=100 GHz, a grating inlet pitch of a=15 μm, and a star coupler radius of R=7.76 mm (in silica). Thus the width of the central Brillouin zone is 550 μm in the C-band. The gratings arms are brought close together in the grating center, where a thin half-wave plate may be inserted to achieve polarization insensitivity, as shown and described previously. 
   Advantageously, the polymer PLC  330  is a simple slab waveguide on a glass substrate so no core patterning is necessary. The core is 7.5-μm thick and has an index contrast of 0.45%. Both core and cladding are polysiloxane-based materials whose optical properties and overall reliability have been well characterized. (See, e.g., A. W. Norris, J. V. DeGroot, T. Ogawa, T. Watanabe, T. C. Kowalczyk, A. Baugher, and R. Blum, “High reliability of silicone materials for use as polymer waveguides” Proc. SPIE Vol. 5212, p. 76-82, November 2003; and T. C. Kowalczyk and R. Blum, “Polymer variable optical attenuator arrays: pathway from material platform to qualified telecom product”, Proc. SPIE Vol. 5517, p. 50-61, October 2004) 
   As noted before, polymer PLC  330  acts as a thermal lens by exhibiting a parabolic (or similar) refractive index profile whose magnitude and shape can be electrically controlled. We evaluated several possible heater designs and found that a very suitable approach, which is also robust to process variations, is to use a linear array of individually addressable heaters  335 [ 1 ] . . .  335 [ 16 ], as shown in the inset of  FIG. 3 . Thermal simulations showed that despite the discrete nature of the design, a plot of core temperature vs. spatial location along the mirror should be almost perfectly parabolic (standard deviation value of R 2 &gt;99.8%) when 16 individual heater elements are used and as shown in  FIG. 3 . 
   The 16 heaters (2-mm length, 40-μm spacing)  335 [ 1 ] . . .  335 [ 16 ] are patterned on a top surface of the polymeric polysiloxane slab using standard photolithography and connect to traces that fan out to bond pads at the two edges of the polymer PLC. Advantageously, the heaters can be individually addressed and driven with an appropriate power distribution so as to create a parabolic heat distribution, which can be either positive or negative. Because the magnitude of the index change with temperature is ˜35 times higher in this polymer than in silica (the sign of the change is actually opposite that of silica), and the thermal conductivity of the polymer is ˜8 times lower than in silica, the polymer thermo-optic lens consumes ˜1% of the power of a corresponding silica thermo-optic lens. In addition to the much lower power consumption, our inventive approach enables a significantly larger tuning range since there are fundamental limitations on how much power can be applied to the heater electrodes and the corresponding temperature rise. While we have advantageously used polysiloxane in this exemplary embodiment, other materials, polymeric or other, may be used according to our inventive principles. Such other materials should preferably exhibit an index change of at least 2× that of silica and exhibit a thermal conductivity that is less than that of silica. In one particular embodiment, a thermal conductivity that is less than 0.5× that is silica is sufficient. 
   At an end of the 4.2 mm PLC opposite to the AWG, is positioned a small flat mirror  345  that is substantially 550 μm wide. The mirror  345  may be affixed to the PLC with any of a variety of known adhesives and the width of the mirror  345  is substantially equal to or less than the grating Brillouin zone width which—as we have noted earlier—ensures that high diffraction orders from the grating are not reflected back into the grating. 
   The dispersion exhibited when the lens is unpowered (unheated) is given by equation [1] which is expressed as: 
   
     
       
         
           
             D 
             0 
           
           = 
           
             - 
             
               
                 2 
                 ⁢ 
                 Rf 
               
               
                 
                   n 
                   ⁡ 
                   
                     ( 
                     
                       a 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       f 
                     
                     ) 
                   
                 
                 2 
               
             
           
         
       
     
   
   where f is the optical frequency, n is the refractive index, and Δf is the grating free-spectral range. This evaluates to −924 ps/nm in our case at f=194 THz. By way of comparison, an AWG having a flat mirror at one end of one of the star couplers gives negative dispersion, which is what is needed for compensating the dispersion of single mode fiber (SSMF). 
   As can be readily appreciated, we can use the thermo-optic lens to tune the dispersion about this negative bias point. Because the path-length differences in the AWG of our exemplary compensator  300  are so large (˜87-mm path-length difference between the shortest and longest arms), significant phase errors were introduced in the fabrication that varied from device to device. Fortunately, such errors may be compensated to first order by adjusting the AWG focal length. In our exemplary device(s), this was accomplished by cutting the AWG chip in the star coupler to the proper length before attaching the polymer chip. 
   Before inserting the half-wave plate, the AWG polarization-dependent wavelength shift of our exemplary device was 17 pm. When no power is applied to the thermo-optic lens (heater), the dispersion is −918 ps/nm, very close to that predicted by Eq. (1). 
   Using thermal modeling results, an initial estimate of the 16 drive powers of the thermo-optic lens to achieve 0 ps/nm dispersion was generated. The 16 values were then manually adjusted to achieve as close to 0 ps/nm across as wide a bandwidth as possible. Advantageously, the heaters respond quickly and consistently. Accordingly, the resulting set of 16 drive powers was then multiplied by a single variable in order to tune the dispersion to any other desired value (e.g., when the variable is 0 the dispersion is −918 ps/nm, and when the variable is 1.00 the dispersion is 0 ps/nm). Thus the calibration and control are simple. For the measurements presented here, the variable ranged from −0.33 to 1.67. 
   The measured transmissivity and group delay are shown in  FIG. 4  at three locations in the C-band for seven different thermo-optic lens settings. The average dispersion values for the seven cases are −1523, −918, −565, −269, −14, +207, and +394 ps/nm. The limit was set by requiring a reasonable transmissivity passband. The 3-dB transmissivity bandwidths are 29, 39, 54, 66, 76, 65, and 58 GHz, respectively. The lens total power consumptions are 29, 0, 15, 30, 44, 59, and 74 mW, respectively. Measuring with a 10-pm resolution bandwidth, the peak-to-peak group delay ripple (GDR) ±25 GHz from the ITU grid is typically &lt;20 ps, but can be as high as 50 ps in the −1523-ps/nm case. The polarization-dependent loss (PDL) is typically &lt;0.6 dB, but can be as high as 1.2 dB in the −1523-ps/nm case. The differential group delay (DGD) is typically &lt;10 ps, but can be as high as 20 ps in the −1523-ps/nm case. There is a small reflection from the half-wave plate, which is probably the cause for the large GDR, PDL, and DGD. 
   As can be observed, the group delay bandwidth is nearly as wide as the FSR (100 GHz). Thus our exemplary TODC is especially suitable for compensating 40-Gb/s transmitters or non-wavelength locked 10-Gb/s transmitters on a 100-GHz grid. 
   Additionally, the insertion loss (not including a circulator) at the passband peak is ˜7 dB. Approximately 0.7 dB is due to round-trip fiber coupling loss, ˜0.8 dB is due to round-trip waveplate insertion loss, ˜0.6 dB is due to round-trip diffraction loss in the AWG (estimated by simulation), and ˜2.0 dB is due to round-trip propagation and coupling loss in the polymer. The unaccounted for 2.9 dB is likely due to AWG phase errors and can be eliminated with improved fabrication or post-fabrication phase-error adjustment. 
   As mentioned earlier, a possible figure-of-merit for TODCs is dispersion range times bandwidth-squared (bandwidth given by the smaller of the transmissivity 3-dB bandwidth [3 dB being chosen somewhat arbitrarily] or group delay bandwidth), which captures the tradeoff between achievable dispersion and bandwidth. This can be made non-dimensional by giving the dispersion in time/frequency and the bandwidth in frequency. It is a rough measure of the number of adjacent bits that are mixed together by the dispersion if the signal bandwidth occupied the entire TODC bandwidth. Note that this figure-of-merit is different than the one used for DCF, which is the dispersion divided by the loss. 
   The figure-of-merit for the TODC presented here is ˜16 (1312-ps/nm range with &gt;39-GHz bandwidth). As can be appreciated by those skilled in the art, this number is quite large for a PLC TODC. For comparison, we have observed a figure of merit of 5.4 with a 4-stage MZI-based PLC TODC. 
     FIG. 5  shows a 10-Gb/s system experimental setup for comparing our inventive TODC with DCF. With reference to that  FIG. 5 , a 9.953-Gb/s non-return-to-zero signal emitted from a 10-Gb/s pluggable transceiver (XFP)  510  with chirp rated for 800 ps/nm is propagated through 100 km of SSMF  520 . The carrier frequency was 193.498 THz (i.e., 2 GHz off the ITU grid), and the accumulated dispersion was ˜1700 ps/nm. 
   The signal is then amplified  540 , filtered  550 , and passed through either −844 ps/nm of DCF  560  or through the TODC  570 , with its dispersion set to −844 ps/nm. The receiver was another XFP  580  with an avalanche photodiode. 
   Without any dispersion compensation the observed performance was very poor [10 −5  bit-error rate (BER) at 27-dB optical signal-to-noise ratio (OSNR)].  FIG. 6  shows a graph of BER vs. OSNR for the two cases with dispersion compensation, plus the back-to-back case. 
   The performance with the TODC was actually slightly better than with the DCF. This could be from self-phase modulation in the DCF, because the launch power into the DCF was ˜+2 dBm, and the signal is highly dispersed at that point. There was a polarization dependence of ˜0.5 dB in OSNR in the TODC case. DWDM XFPs typically have a ±12.5 GHz end-of-life wavelength accuracy. Although we could not adjust the XFP wavelength, one can see from  FIG. 3  that the bandwidth should be wide enough to accommodate this drift. 
   While we have shown an exemplary embodiment of our inventive tunable dispersion compensation apparatus a number of arrangements of similar apparatus exhibiting our inventive teachings are possible.  FIG. 7  is a schematic of an alternative embodiment of a tunable dispersion compensator wherein the PLC  125  including heating elements  130  is disposed in an optical path “within the body” of the second slab waveguide  120 . 
   With reference now to that  FIG. 7 , the dispersion compensation apparatus  700 , while similar to that shown earlier in  FIG. 2 , does not have the PLC  125  positioned adjacent to the second slab waveguide  120 . Instead, it is positioned in an optical path within the body of the second slab waveguide  120  itself. 
   Advantageously, such a configuration may favorably facilitate the fabrication of our inventive dispersion compensation apparatus as receiving grooves (or other shapes—not specifically shown) are scribed or otherwise formed in the body of the slab waveguide  120  where it/they may receive the suitable materials for effecting the thermo-optic lens. As a result, a substantially more integrated device is realized, exhibiting improved manufacturability. 
   Additional, alternative embodiments are shown in  FIGS. 8(   a )-( c ), wherein “unfolded” dispersion compensation apparatus&#39; are depicted. The unfolded variation generally comprises two frequency routing devices positioned in sequence such that one of the slab waveguides comprising each of the devices are optically coupled, “back-to-back”. According to our inventive teachings, a thermo-optic lens is positioned at the interface between the two frequency routing devices. 
   As shown in  FIG. 8(   a ), a slab waveguide  120  of a frequency routing device is coupled to another frequency routing device. Interposed between and optically coupling the two frequency routing devices, is PLC  125  including heating elements  130  thereby serving as a thermo-optic lens as before. Shown in this  FIG. 8(   a ) is an iris  151  which prevents unwanted optical coupling between the two frequency routing devices. As can be observed from this  FIG. 8(   a ), this apparatus includes a half-wave plate(s)  150 , interposed in the grating arms. 
   A further variation of this dispersion compensation apparatus is shown schematically in  FIG. 8(   b ). More particularly, the half wave plate is combined with iris assembly  150 / 151  and the two elements are collectively interposed between the two frequency routing devices. 
   Finally with respect to the unfolded dispersion compensation apparatus,  FIG. 8(   c ) shows a device in which the PLCs  125  are not positioned at the interface between the two frequency routing devices, rather they are positioned in an optical path within their respective slab waveguide(s)  120 . As before, the PLC  125  includes heating elements  130  thereby producing a thermo-optic lens while improving the manufacturability of the unfolded device. Also shown in this  FIG. 8(   c ) is integrated iris/half wave plate  150 / 151  interposed between the two frequency routing devices. 
   So far we have mainly limited the discussion to compensation of first-order chromatic dispersion. The TODC described here is also capable of compensating high-order dispersion, by using a non-parabolic index distribution in the lens. For example, using a cubic index distribution could compensate for second-order dispersion. Furthermore, the TODC is capable of providing a plain shift in group delay. In this case, the thermooptic lens would have a linear index distribution. 
   At this point, while we have discussed and described our invention using some specific examples, those skilled in the art will recognize that our teachings are not so limited. In particular, different materials—both polymeric and other may be used as thermo-optic PLC devices, where their optical and thermal characteristics are suitable. In addition, while we have used a waveguide grating in our examples shown, other PLC-based gratings such as an echelon diffraction grating could be used as well. Finally, it is noted that the unfolded arrangements described may be advantageously fabricated on the same substrate, (or not as desired) further enhancing their manufacturability. Accordingly, our invention should be only limited by the scope of the claims attached hereto.