In future high-speed communication systems, ultra-fast all-optical logic gates will play an important rolein signal processing, signal routing, and decisionmaking. In particular, the exclusive-OR (XOR) gateis a common component in optical signal processing.It has been used in various applications, includingdata encoding, high-speed pattern generation, opti-cal correlation, and optical data encryption. XORgates have been implemented via cross-phase modu-lation in a nonlinear loop mirror [1], cross-gain andcross-phase modulation in a semiconductor opticalamplifier (SOA) [2,3] or SOA-Mach–Zehnder interfe-rometer (MZI) [4,5], cross-polarization rotation in ahighly nonlinear fiber [6], four-wave mixing in anSOA or highly nonlinear fiber [7–9], optical para-metric process in a nonlinear fiber [10], and pumpdepletion with sum and difference frequency gen-eration in a periodically poled lithium niobate wave-guide [11]. XOR gates are often used with feedback
as the basis for correlation processing [12], for pseu-dorandom number generation [13], and for building avariety of encryption schemes [14]. In cryptography,combining XOR with feedback is essential in gener-ating long key streams from smaller keys or initiali-zation registers for enciphering in Vernam ciphers.The implementations of block ciphers require XOR,feedback, and feed-forward capabilities. Translatingthese building blocks to the optical domain andusing them together in real applications provides ahigh-speed, electromagnetic-wave-immune, and all-optical means for encryption. However, the opticalimplementations of the above building blocks facevarious practical issues, such as noise accumulationand the propagation of undesirable logic levels.
Various XOR gates with feedback have been pro-posed using an SOA in a Sagnac loop [13] and inan MZI [12] for pseudorandom number generationand correlation. We previously demonstrated anXOR based on cross-polarization rotation in a 40mhighly Ge-doped nonlinear fiber (HDF) [15], the pre-liminary results showing the possibility of using aterahertz optical asymmetric demultiplexer (TOAD)
[16] with optical feedback for signal regeneration andwavelength conversion. The use of nonlinear fiber asthe XOR device offers high-speed operation on the in-coming signals without any unwanted gain depletionthat is observed in the SOA counterparts. The lengthof the Ge-doped nonlinear fiber required for obtain-ing enough nonlinearity is at least 1 order of magni-tude shorter than other silicon-based step-indexnonlinear fiber. In the previous demonstration, theoperation and performance of the XOR gate in feed-back mode was not studied in detail. In this demon-stration, an open eye diagram is experimentallyobtained with the XOR operating in both its sin-gle-pass mode and feedback mode. Because of thelong optical feedback path in the experiment, the out-put bit patterns cannot be displayed on a samplingoscilloscope for the verification of the feedback opera-tion. Thus, the XOR gate with feedback mode is alsosimulated using VPI TransmissionMaker and Com-ponentMaker 8.5. In this work, we study the XORgate in its feedback mode in more detail. From boththe experimental and simulation results presentedin this paper, it is shown that the XOR gate operateswell in its feedback mode. The TOAD successfullyregenerates the signal and converts the wavelengthof the XOR output to the control wavelength forfeedback.
2. Principle and Experiment
The XOR logic with optical feedback is built usingcross-polarization rotation in a highly Ge-doped non-linear fiber, and optical feedback is based on a TOAD.The HDF used for cross-polarization rotation isdoped with 75mol:% GeO2, resulting in a large non-linear coefficient of 35W−1 km−1 [17]. This new typeof nonlinear fiber is desirable because it is very com-patible with standard single mode fibers. Directfusion splicing only results in 0:2dB loss. Justlike standard single mode fibers, HDF is very robustand can be easily put onto a 4 cm fiber spool. Dif-ferent types of nonlinear devices have been demon-strated using the Ge-doped nonlinear fiber, includingoptical switching [18], optical thresholding [19], andwavelength conversion [20]. Cross-polarization rota-tion occurs when a strong control signal and CW sig-nal are launched into a nonlinear media with linearpolarization and have a 45° polarization difference,
as shown in Fig. 1(a). The CW signal rotates inthe other direction if the strong control signal andCW signal have a −45° polarization difference in-stead. A polarizer acts as a polarization shutter byaligning it orthogonally with the CW signal, i.e.,the CW signal is blocked in the absence of the controlsignal. When a control signal is present, a biref-ringence is induced in the nonlinearmedium, leadingto polarization rotation of the CW signal. Theamount of polarization rotation is determined bythe strength of the control signal, and the CW signalis transmitted if a suitable level of the control signalis present. To build an optical XOR gate, two controlsignals are used and are orthogonally polarized, asshown in Fig. 1(b). If only one control signal is pre-sent, the polarization of the CW signal is rotatedand is transmitted through the polarizer, while, ifboth control signals are present with a similar mag-nitude, the overall polarization rotation of the CWlight is zero so that the CW signal is again blockedby the polarizer. This above operation results in anXOR logic operation, where a bit 1 results if and onlyif one of the controls has a bit 1. To build a feedbackpath for the XOR gate, a TOAD is exploited to avoidnoise accumulation and to convert the feedback sig-nal wavelength. The SOA used in our TOAD is sui-table for 10Gb=s applications. The switching windowof the TOAD is determined by the SOA offset in theTOAD, which can be in the terahertz range, while theswitching repetition rate of the TOAD is determinedby the speed of recovery of the SOA. Currently, high-speed SOAs of >40Gb=s are commercially available.
Figure 2 shows a schematic illustration of ourall-optical XOR gate with feedback. The two controlsignals (initial key and signal) at 1550:1nm are gen-erated through intensity modulation of two 5GHzpulsed trains, which are combined at a polarizationbeam splitter to ensure orthogonal polarization. Thecontrols are amplified to 25dBm, combined with CWlight at 1552nm, and launched into a 40m HDF forcross-polarization rotation to occur. At the output ofthe HDF, a polarizer is used as a polarization shutterto observe the XOR output. To complete the feedbackloop for the XOR gate, the XOR output at point A isused to drive the TOAD. The structure of the TOADis shown in the inset of Fig. 2. This XOR output isonly an intermediate output, because there is a
Fig. 1. Schematic illustration of cross-polarization rotation (a) with only one control signal and (b) with two control signals.
residue in bit 0 level, resulting from the nonidenticalcross-polarization modulation induced by the twocontrol signals. The TOAD switches out pulses atλML from point B to point C in the presence of abit 1 in the intermediate output (λcw) at point B, re-sulting in a clean XOR output at point C ðλMLÞ). Theclean XOR output does not consist of any residue inbit 0 level. Part of the clean XOR output is tappedand launched back to the XOR input as the feedback,while the remaining portion is the final XOR out-put at the system output port. The final XOR isthe ultimate output of the XOR gate. The initialkey is continuously supplied to the XOR gate untilthe feedback signal reaches the XOR gate input.Therefore, the length of the initial key is determinedby the length of the feedback, i.e., the shorter thefeedback, the shorter is the initial key needed.
3. Results and Discussion
To verify the operation of our XOR gate, we firstopened the feedback path at point C. Two patterns“10101100” and “01010110” are used as Controls 1and 2, respectively, as shown in Figs. 3(a) and 3(b).Control 1 and Control 2 induce cross-polarizationrotation in the HDF. When the two control signalsare not aligned, XOR operation is not observed. In-stead, it is observed that each of the control pulsesinduces a switching out of the signal at λcw, as shown
in Fig. 3(c). By temporally aligning the two controlsignals, XOR operation represented by the amplitudeof λcw is observed after the polarizer (at point A), asshown in Fig. 3(d). Correct XOR logic is successfullyobtained. It is clearly shown that, when bit 1 of boththe controls are aligned, the cross-polarization ef-fects cancel out each other and result in a bit 0 atthe XOR output. The residue pulse in bit 0 resultsfrom the nonidentical cross-polarization modulationinduced by the two control signals. When the opticalfeedback is formed, the removal of residue pulse inbit 0 is necessary for maintaining the correctnessof XOR operations. A TOAD is used to clean thebit levels and convert the wavelength of the inter-mediate XOR to match the XOR input. The cleanXOR output from the TOAD is shown in Fig. 3(e).Part of the clean XOR output at λML is tapped andlaunched into the polarization beam combiner asthe optical feedback. An optical coupler is used tocouple the initial Control 2 and the feedback. In prac-tice, a decision device would be used to switch theXOR input from the initial Control 2 to the XORfeedback. Figure 3(f) shows a wide-open eye in the
Fig. 2. Schematic illustration of the demonstrated optical XORgate with feedback. EOM, electro-optics intensity modulator;HDF, highly Ge-doped nonlinear fiber; POL, polarizer; TOAD, ter-ahertz optical asymmetric demultiplexer. Fig. 3. (Color online) Measured temporal profiles of the XOR gate
in single-pass mode: (a) Control 1, (b) Control 2, (c) output of theoptical gate when Control 1 and Control 2 are not aligned, (d) in-termediate XOR output when Control 1 and Control 2 are aligned,(e) final XOR output after the TOAD, (f) measured eye diagram ofthe XOR gate in feedback mode.
Fig. 4. (Color online) Simulated temporal profiles: (a) Control 1 with PRBS pattern, (b) Control 2 with first 8 bits as initial input (as shownin the rectangular box) and the rest as XOR feedback, (c) final XOR output.
resulting XOR output when the optical feedbackis employed, indicating that our system has goodperformance. The demonstrated XOR gate is operat-ing at 5Gb=s, which is primarily limited by the repe-tition rate of the mode-locked fiber laser we used inthe experiment. The proposed scheme supports highdata rate operation as the cross-polarization rotationin highly nonlinear fiber is an ultrafast nonlinearresponse; therefore, the ultimate operation speedof the XOR gate is limited by the SOA in the TOADfeedback.
Because of the long pattern period of the XOR out-put, the pattern cannot be recorded experimentallyusing a sampling oscilloscope. We have simulatedthe XOR gate operating in feedback mode usingVPI for the verification of operation. An 8 bit pattern,“01100110,” is used as the initial input for Control 2[Fig. 4(b)], while a pseudorandom bit sequence isused for Control 1 with the first 8 bits as“10010110” [Fig. 4(a)]. The resultant XOR outputis “11110000” [Fig. 4(c)]. The XOR output is thenlaunched back to the device input at Control 2 andis XOR-ed with the incoming Control 1, forming anXOR output operating in its feedback mode. The re-sultant XOR output is shown in Fig. 4(c), indicatingcorrect logic operation of the device in feedbackmode. Figure 5 shows the simulated eye diagramand a wide-open eye is observed.
4. Conclusion
Using cross-polarization rotation in HDF, we de-monstrated an all-optical XOR gate with opticalfeedback. The HDF is very compatible with stan-dard single mode fiber, with low direct-splicing loss.The TOAD in the feedback loop is used for provid-ing a clean XOR feedback for the control of the XORgate and for converting the wavelength to matchthe input requirement. We experimentally showedcorrect operation of the demonstrated XOR gate,and further showed that the eye diagram obtainedfrom the optical XOR gate in feedback mode indi-cates our system has good performance. Simulationis done to prove that the XOR gate in its feedbackmode operates correctly and the eye diagram is con-sistent with the experimental results. XOR gateswith feedback form the building blocks for variouskinds of processing. By successfully building an op-tical XOR with optical feedback, these buildingblocks can potentially be translated to the opticaldomain and can provide a high-speed and all-opticalmeans for processing.
This work was supported in part by the U.S. De-fense Advance Research Projects Agency (DARPA)under Grant MDA972-03-1-0006 and SSC PacificGrant N66001-07-1-2010. The authors would liketo thank Prof. Wade Trappe from WINLAB for thefruitful discussion.
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