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    All-Optical Signal Processing Using (2)

    Nonlinearities in Guided-Wave DevicesCarsten Langrock, Student Member, IEEE, Student Member, OSA,Saurabh Kumar, Student Member, IEEE, Student Member, OSA,

    John E. McGeehan, Member, IEEE, Member, OSA,A. E. Willner, Fellow, IEEE, Fellow, OSA, and

    M. M. Fejer, Fellow, OSA

    Invited Paper

    AbstractThe authors present a review of all-optical signal-processing technologies based on (2) nonlinear interactions inguided-wave devices and their applications for telecommunica-tion. In this study, the main focus is on three-wave interactionsin annealed proton-exchanged periodically poled lithium niobatewaveguides due to their suitable properties with respect to non-linear mixing efficiency, propagation loss, and ease of fabrication.These devices allow the implementation of advanced all-opticalsignal-processing functions for next-generation networks with sig-nal bandwidths beyond 1 THz. In this paper, integrated structuresthat will allow for improvements of current signal-processingfunctions as well as the implementation of novel device conceptsare also presented.

    Index TermsDielectric waveguides, nonlinear optics, opticalphase matching, periodically poled lithium niobate (PPLN).


    THE FABRICATION of low-loss single-mode optical fiberhas made possible optical communication links withdemonstrated bandwidths exceeding several terahertz. Cur-rent optical networks are based on time-division multiplexing(TDM), where multiple relatively low-bit-rate streams of datawith the same carrier frequency are interleaved to create asingle high-bit-rate stream or wavelength-division multiplexing(WDM), which involves simultaneous propagation of multipledata signals, each at a different wavelength in a single opticalline. Although these technologies are individually quite mature,increasing the bandwidth further to allow for new services

    Manuscript received December 15, 2005; revised March 21, 2006. This workwas supported in part by the Defense Advanced Research Projects Agencythrough the University of New Mexico Optoelectronic Materials Research Cen-ter under DARPA Prime MDA972-00-1-0024, Intel Corporation, the NationalScience Foundation under Award 0335110, and Crystal Technology, Inc.

    C. Langrock is with the Department of Electrical Engineering, StanfordUniversity, Stanford, CA 94305 USA (e-mail:

    S. Kumar and A. E. Willner are with the Department of Electrical Engineer-ing, University of Southern California, Los Angeles, CA 90089 USA (;

    J. E. McGeehan is with BAE Systems Advanced Technologies, Washington,DC 20037 USA.

    M. M. Fejer is with the Department of Applied Physics, Stanford University,Stanford, CA 94305 USA (e-mail:

    Digital Object Identifier 10.1109/JLT.2006.874605

    such as digital television and the next-generation Internet willrequire the interplay between WDM network topologies [1] andultrahigh-speed TDM.

    WDM systems take advantage of the fortunate coincidenceof the low-loss regime of modern optical fibers and the emissioncross section of rare-earth-doped fiber amplifiers [e.g., erbium-doped fiber amplifiers (EDFAs)] to provide all-optical amplifi-cation, by using data streams with different carrier frequencies.The minimum spacing between these channels is determinedby the bit rate of each stream and the need to reduce crosstalkbetween channels to stay below a desired bit-error rate (BER).By combining TDM and WDM, point-to-point optical linkswith data capacities close to the theoretical maximum can bedesigned. To realize this goal, system designers are faced withseveral challenges critical to the task of interfacing WDM andTDM networks. These include adding/dropping arbitrary chan-nels, resolving wavelength contention, and design of strictlytransparent dispersion-compensated links [2], to name a few.

    Parametric wavelength conversion has been shown to addressthese challenges. Optical frequency (OF) mixers can be consid-ered the optical analog to radio frequency (RF) mixers as shownin Fig. 1. Ultrafast highly efficient all-optical gated mixing [3],nearly arbitrary wavelength conversion [4], and spectral inver-sion for dispersion compensation [5] using OF mixers havebeen demonstrated by several research groups during the lastdecade. Applications of nonlinear mixing go beyond simplewavelength conversion because it lends itself to bit-level digitalsignal processing. Development of optical modules that canassist/replace electronic subsystems that perform simple digitalprocessing functions may be justified if they fulfill any ofthe following criteria: 1) high-speed operation (scalable be-yond 100 Gb/s); 2) parallel operation on multiple wavelengthchannels; and 3) preservation of information (e.g., phase) car-ried in the optical domain, usually lost in opticalelectronicconversion. Nonlinear mixing satisfies all these criteria andtherefore is a suitable platform for development of all-opticaldigital signal-processing techniques.

    This paper is structured as follows. In Section II-A, we givea brief overview of devices for all-optical signal processing

    0733-8724/$20.00 2006 IEEE


    Fig. 1. Comparison between (a) RF and (b) OF mixers.

    in (2) media before we introduce the relevant figures ofmerit with respect to nonlinear processes and guided-wavepropagation in Section II-B. Specific examples focus on pe-riodically poled lithium niobate (PPLN) waveguide devices,but other methods are briefly discussed. We describe signal-processing applications in Section III before concluding bygiving an overview of novel all-integrated device conceptsthat will facilitate next-generation signal-processing function-ality in Section IV.


    A. OF Mixers

    OF mixers operate in close analogy to RF mixers. In thelatter, a strong local oscillator mixes with a (typically) weaksignal, producing an output proportional to the product of thosetwo inputs. For quasi-sinusoidal inputs at frequencies LO ands, respectively, the output frequency is out = LO s;the output is related to the inputs by Vout VLOV s (for thelower sideband). With a continuous-wave (CW) pump, thecarrier frequency is shifted, whereas any amplitude, frequency,and phase information on the envelope is left unchanged. Atoptical frequencies, similar relationships hold for parametricwavelength converters, so that a strong pump can mix witha weak signal to produce an output at the sum or differencefrequency, again preserving the envelope information. Focusingon the difference frequency case most widely used for opticalsignal processing, out = p s, and Eout EpEs , as illus-trated in Fig. 2(a). With a CW pump, the OF mixer performswavelength conversion, the optical analog of conventional RFheterodyne mixing, whereas a pulsed pump transforms thisdevice into a gated mixer. Note that the output is proportionalto the complex conjugate of the input, so that the mixer alsofunctions as a phase conjugator or spectral inverter.

    For a near-degenerate pump frequency, close to twice thatof the signal, we can write s = p/2 + , and the output isthen at out = p/2 , i.e., the output is the mirror image ofthe signal frequency around the degenerate point. With a pumpin the vicinity of 775 nm, outputs can be converted from oneportion of the C-band to another.

    The availability of inexpensive C-band pump sources has ledto a frequency conversion technique that does not require a775-nm pump. This technique relies on the generation of theshort-wavelength pump inside the device via second-harmonicgeneration (SHG) (or sum-frequency generation, SFG) ofa suitable C-band source followed by the above-describeddifference-frequency generation (DFG) between the generatedpump and injected signal shown in Fig. 2(b) [Fig. 2(c)], out =

    Fig. 2. Schematic description of (a) difference-frequency mixing between astrong pump at p and a signal at s, (b) cascaded second-order nonlinearfrequency mixing with single pump via SHG, and (c) with two pumps via SFG.

    2p s (out = (p1 + p2) s). Such a process requiresthe cascaded execution of two (2) processes (SHG/SFG fol-lowed by DFG) and has therefore been termed a cascaded (2)

    process, sometimes written as (2) : (2) [6][8]. Viewed as ablack box, such a device effectively acts as a four-wave mixer(FWM) with a large effective (3). Due to the short devicelength on the order of several centimeters, this quasi-FWMinteraction is essentially free of parasitics such as stimulatedBrillouin scattering (SBS) and other undesired interactionsencountered in true (3) nonlinear devices.

    B. Basic Device Considerations

    The difficulty in implementing OF mixers arises from theweak nonlinearities in available materials. The mixers are, ofnecessity, long compared with the wavelength of the interactingradiation, requiring matching of the phase velocities of thefields at different frequencies participating in the interaction.Even with phase-velocity matching, the pump power requiredfor efficient operation is prohibitive in conventional bulk non-linear media. The use of highly nonlinear materials, like PPLNor AlGaAs, together with the confinement provided by guided-wave geometries, can increase the efficiency by several orders


    of magnitude over that available in bulk interactions, reducingthe required pump powers to the range of 1020 dBm [9].

    In the low-gain and nondepleted pump limit (which will beassumed unless otherwise stated), the output power generatedin a DFG interaction in a waveguide of length L can be writ-ten as