Photoics 2015, 2, 200-213; doi:10.3390/photoics2010200 Review OPEN ACCESS photoics ISSN 2304-6732 www.mdpi.com/joural/photoics All Optical Sigal-Processig Techiques Utilizig Four Wave Mixig Refat Kibria 1,2, * ad Michael W. Austi 1 1 School of Electrical & Computer Egieerig, RMIT Uiversity, Melboure 3000, Australia; E-Mail: Michael.Austi@rmit.edu.au 2 Departmet of Computer Sciece & Egieerig, Shah Jalal Uiversity of Sciece & Techology, Sylhet 3114, Bagladesh * Author to whom correspodece should be addressed; E-Mail: Refat.Kibria@rmit.edu.au or Refat-cse@sust.edu; Tel.: +61-431-180-418; Fax: +61-3-9925-3242. Received: 22 December 2014 / Accepted: 3 February 2015 / Published: 10 February 2015 Abstract: Four Wave Mixig (FWM) based optical sigal-processig techiques are reviewed. The use of FWM i arithmetical operatio like subtractio, wavelegth coversio ad patter recogitio are three key parts discussed i this paper after a brief itroductio o FWM ad its compariso with other oliear mixigs. Two differet approaches to achieve correlatio are discussed, as well as a ovel techique to realize all optical subtractio of two optical sigals. Keywords: four wave mixig (FWM); optical sigal processig; wavelegth coversio; wavelegth regeeratio; patter recogitio; frequecy measuremet 1. Itroductio Because electroic sigal processig systems have a bottleeck of low badwidth, the use of photoic approaches to realize real time sigal processig is becomig icreasigly popular [1 5]. I additio, it is desirable i may practical applicatios that sophisticated sigal processig tasks are doe remotely ad well away from the source of the sigal, e.g., a atea. However, traditioal approaches to implemet a photoic sigal processig uit do ot isolate the trasmitter from the receiver [2,6] as a Mach-Zehder modulator (MZM) is typically used to perform the multiplicatio required for the correlatio fuctio.
Photoics 2015, 2 201 I recet days, oliear optical mixig like FWM is becomig a key iterest of research as it ca be used to overcome the curret limitatios. The aim of this paper is to report recet ivestigatios o the use of oliear FWM i Highly Noliear Fibre (HNLF) to achieve the desired sigal processig. Furthermore, the use of FWM is exteded to employ it to realize egative accumulatio optically ad thus remove the eed for the use of electroic processig eve whe subtractio betwee optical sigals is required. The preferece of FWM over other fibre based oliear effects like self-phase modulatio (SPM) or cross-phase modulatio (XPM) is also discussed as it is a istataeous pheomeo ad is therefore trasparet to bit rate ad data format of the sigal [7]. Sectio 2 cotais a isight o FWM. This paper heavily covers the utilizatio of FWM pheomeo ad a detailed aalytical explaatio as well as iheret properties of FWM are provided ad discussed i this sectio. Sectio 3.1 presets a practical implemetatio of a patter recogitio techique utilizig FWM. Optical mixig of template wavelegths with a pump wavelegth, which has bee modulated by a iput bit stream, i order to produce copies of the iput sigal at the output idler wavelegths, is doe i a legth of HNLF [8]. The results show that a correlatio fuctio is achieved optically. Sectio 3.2 illustrates a useful extesio of the cocept of Sectio 3.1 by selectig the template with a software cotrolled optical processor istead of physically turig o/off the laser diodes as was doe i the experimet of Sectio 3.1. This approach allows a true remotig of the trasmitter. Sectio 3.3 discusses a optical techique for the cocept of egative accumulatio of optical power optically. The FWM property is exploited to achieve subtractio betwee two optical sigals. Whe the relative phase differece betwee two pump wavelegths is π/2 radias, i the mixig process the geerated idler has a phase differece of π radias with respect to other idlers at the same frequecy ad this π radias phase shift leads to egative accumulatio of the sigal optically. Sectio 4 summarizes the work udertake i the research, draws some coclusios ad metios possible future work. 2. Four Wave Mixig FWM is a oliear effect arisig from a third-order optical oliearity, as is described by a χ (3) coefficiet. The cocept of three electromagetic fields iteractig to produce a fourth field is cetral to the descriptio of all FWM processes. It is a oliear pheomeo which allows optical wavelegth coversio. It ca occur if at least two differet frequecy compoets propagate together i a oliear medium such as a HNLF or a semicoductor optical amplifier (SOA). I the area of sigal processig, optical FWM has bee used to perform frequecy coversio [9], spatial iformatio processig [10] ad frequecy measuremet [11]. The origi of the FWM process lies i the oliear respose of boud electros of a material to a applied optical field. To uderstad the FWM effect, let us cosider a WDM sigal, which is a sum of moochromatic plae waves. Followig the approach described i [12], we ca cosider the total electric field of a sigal as a summatio of plae waves as i Equatio (1); E = E p cos(ω p t k p z) p=1 (1)
Photoics 2015, 2 202 where Ep is the amplitude, p is the frequecy ad kp is the propagatio costat of the optical fields. The oliear polarizatio is give by P l = ε 0 X (3) E 3 (2) As i [12], by cosiderig the total electric field as that expressed by Equatio (1), Equatio (2) becomes, P l = E 0 X (3) E p cos(ω p t k p z) E q cos(ω q t k q z)e r cos(ω r t k r z) p=1 q=1 r=1 By expasio of Equatio (3) we get, P l = 3 4 ε 0X (3) (E 2 p + 2 E p E q ) E p cos(ω p t k p z) P=1 q p + 1 4 ε 0X (3) E p 3 cos(3ω p t 3k p z) p=1 + 3 4 ε 0X (3) E p 2 E q cos{(2ω p ω q )t (2k p k q )z} p=1 q p + 3 4 ε 0X (3) 2 E p E q cos{(2ω p + ω q )t (2k p + k q )z} p=1 q 1 p q r p q r p q r p q r p q r p q r p q r p q r cos ω ω ω t k k k z 6 cos ω ω ω t k k k z ε χ (4) 4 cos ω ω ω t k k k z cos ω ω ω t k k k z 3 0 E peqer p1 q p rq The first term i Equatio (4) icludes itesity depedet refractive idex terms which represet the effect of SPM ad XPM. The secod, third ad fourth terms ca be eglected because of a phase mismatch which evolves betwee the optical fields as they propagate alog the fibre. The reaso behid this phase mismatch is that i a optical fibre the propagatio costat is frequecy depedet so that k(3ω) 3k(ω). Whe there is a varyig phase mismatch betwee the propagatig waves the couplig of eergy betwee waves with distace averages to zero. The phase mismatch ca also be uderstood as the mismatch i phase betwee differet sigals travellig withi the fibre at differet group velocities. These terms ca be eglected because they cotribute little effect. The last term I Equatio (4) represets the pheomeo of FWM [13]. If the wavelegths i the WDM system are closely spaced so that the relative fibre dispersio is small, or they are located ear the zero dispersio wavelegth of the fibre, the the propagatio costats of the wavelegth chaels are early costat ad the phase-matchig coditio is early satisfied. Whe this is so, the power geerated at these sum ad differece frequecies ca be quite sigificat [14]. (3)
Photoics 2015, 2 203 FWM is ofte used for wavelegth coversio i photoic sigal processig applicatios. Amog the various oliear pheomea exploited for fibre-based wavelegth coversio, FWM is regarded as advatageous due to its trasparecy both i terms of modulatio format ad bit rate [15]. FWM-based wavelegth coverters have bee demostrated i a rage of optical fibres icludig W- type soft glass fibre [16], highly oliear photoic crystal fibre [17] ad HNLF [18]. Figure 1 below is a demostratio of FWM effect i a HNLF. I basic terms, FWM is the mixig of three wavelegths to produce a fourth wavelegth such that 4 = 1 + 2 3. Note that for the special case whe 1 = 2, two frequecies ca produce a third such that 4 = 21 3. Commoly, a high power pump laser at p ca be used to covert a sigal frequecy s to a ew frequecy at 2p s, which is ofte kow as the idler frequecy, i. I terms of wavelegth, i 2p s. Similarly, a idler ca be produced at 2s p. Figure 1. Illustratio of the Four Wave Mixig (FWM) process i a Highly Noliear Fibre (HNLF). As discussed above, FWM requires phase matchig of the propagatig waves. This requires small chromatic dispersio i the fibre ad/or small wavelegth spacig betwee the propagatig waves. FWM mixig efficiecy scales iversely with wavelegth or chael spacig whe the fibre dispersio is o-zero. The wavelegth spacig must decrease as the fibre dispersio icreases i order to maitai a give mixig efficiecy. Figure 2 is a plot of calculated FWM mixig efficiecy as a fuctio of chael spacig for various values of fibre dispersio. It ca be prove i theory ad is evidet i Figure 2 that the smaller the dispersio or the smaller the wavelegth spacig, the larger the FWM mixig efficiecy.
Photoics 2015, 2 204 3. Utilizatio of FWM Figure 2. Variatio i mixig efficiecy with wavelegth spacig [19]. This sectio discusses photoic wavelegth coversio ad patter recogitio techiques usig FWM i a legth of HNLF. FWM has bee used to mix wavelegth chaels with a pump wavelegth which has bee modulated by a iput bit stream i order to produce copies of the iput sigal at the output idler wavelegths [8,20]. These idler wavelegths are differetially delayed ad summed at a photoreceiver to produce the required correlatio fuctio. 3.1. Time Spectral Covolutio Based Patter Recogitio A microwave photoics based approach to realize ultrafast correlatio is becomig popular cosiderig the potetial very broad badwidth of photoic techologies. I recet years, umerous research groups have worked i this particular area. Oe approach which uses FWM for this purpose is discussed i detail here. The cocept of obtaiig a correlatio from a time-spectral covolutio was first proposed by Park ad Azaa i [2]. The covolutio process is defied by the Equatio (5). r(t) s(t) = r(t)s(t τ)dt For correlatio of bit patters, the discrete form of the correlatio fuctio is more appropriate. Below is the equatio which was preseted as Equatio (5) to represet correlatio for discrete sigals. c rs () = r[k]s[k ] k I this ew system, the bit patter o oe wavelegth is copied oto several other wavelegths usig wavelegth coversio; i particular, FWM wavelegth coversio is used. The proposed method is show i Figure 3. A pump wavelegth is first modulated by the ukow iput bit stream. This part of the system is called the trasmitter (TX) ad ca be doe at a remote locatio. The modulated pump is the set to the receiver (RX) where it is mixed with a umber of CW wavelegth (5) (6)
Photoics 2015, 2 205 chaels i a legth of HNLF. FWM i the HNLF creates umerous idler wavelegths, each with a copy of the iput bit stream. The referece bit patter or template is represeted by the idler wavelegths which are created durig the FWM process. These are determied by the choice of the CW wavelegth chaels which are mixed with the pump wavelegth. The idler wavelegths are filtered ad differetially delayed with delays correspodig to multiples of a bit period ad the summed at a photoreceiver to provide the correlatio fuctio. Figure 3. Illustratio of the workig priciple of the proposed HNLF based correlatio scheme. The correlatio fuctio for matched ad mismatched iput bit patters is demostrated. I Figure 4, the solid blue lie shows the measured correlatio fuctio at the photoreceiver output whe all three idler wavelegths are preset ad the iput bit patter (1011) matches the referece bit patter. Whe there is a match betwee the iput bit patter ad the referece bit patter, a correlatio peak occurs at the middle of the correlatio fuctio, which is at the ed of the origial bit patter (bit 4). The height of the correlatio peak is equal to the height of a detected 1 multiplied by the umber of 1 s i the template, which i this case is 3 (3 0.125 V = 0.375 V). Figure 5 demostrates the output correlatio fuctio with a mismatched iput patter. Here the iput patter is 1000 which is differet from the referece patter 1011. It is a large mismatch case ad the peak of the output correlatio fuctio for the mismatched patter is oly 1 uit which is equal to the amplitude of oly oe 1 of the system. I this case this is 1 0.125 V = 0.125 V. Figure 6 compares the measured output for the matched iput matched (iput 1011) with a worstcase mismatched iput (iput 1010). This worst-case iput was determied from a truth table exercise. As is visible i the Figure 6 the correlatio peak for the matched case is at least 1 uit larger tha that for a mismatched sigal.
Photoics 2015, 2 206 Figure 4. Correlatio output with matched iput sigal 1011. Figure 5. Correlatio output with a mismatched iput sigal 1000. Figure 6. Correlatio output with matched iput 1011 ad worst-case mismatched iput sigal 1010.
Photoics 2015, 2 207 3.2. Remote Trasmitter Correlatio Usig FWM I Sectio 3.1 a correlatio techique based o FWM was discussed. I that techique, the template, represeted by wavelegths λ1 λ4, was selected by physically turig laser diodes o or off. I this sectio, a oliear mixig based correlatio scheme is discussed where the template is selected usig software cotrol of a optical processor. This is a key differece. Because of the software cotrolled filterig of wavelegths, chagig ad cotrollig the template patter ca be doe from a remote locatio as show i Figure 7. As i 3.1, this scheme uses FWM i a legth of HNLF to mix a umber of CW laser wavelegths with a pump wavelegth which has bee modulated by a iput bit stream i order to produce copies of the iput sigal at the output idler wavelegths [21]. The MZM was biased such that the drive voltage produced a maximum o-off cotrast or eyeopeig for the modulated sigal. The modulated pump wavelegth is the trasmitted to the receiver. The trasmitter could be located several km from the receiver if the fibre losses are small ad the received sigal ca be amplified to a useful power level. Figure 7. Characterizatio ad experimetal set-up. I Figure 8, the thick solid lie shows the measured correlatio fuctio at the photoreceiver output whe all three idler wavelegths are preset ad the iput bit patter (1011) matches the referece bit patter. Whe there is a match betwee the iput bit patter ad the referece bit patter, a correlatio peak occurs at the middle of the correlatio fuctio, which occurs at the ed of the origial bit patter. The height of the measured correlatio peak is equal to the height of a 1 detected for each wavelegth (0.6 V) multiplied by the umber of 1 s i the template, which i this case is 3 (3 0.6 V = 1.8 V). The dotted plots i Figure 8 show the measured correlatio fuctios for all possible mismatched coditios. The height of the correlatio peak is always smaller tha that for the matched case. The
Photoics 2015, 2 208 maximum output for a mismatched sigal is 2 0.6 = 1.2 V. The results achieved here are similar to those obtaied usig the scheme i [2,20]. Figure 8. Measured correlatio outputs for all possible combiatios of iput bit patters. The solid lie idicates the output for a matched bit patter whilst the dotted lies are for mismatched bit patters. 3.3. Optical Subtractio Usig FWM Subtractio is a widely used pheomeo required for various sigal processig tasks. I photoic correlatio schemes such as [21,22], a high speed balaced photoreceiver is typically used to obtai the differece betwee two optical sigals. The sigal processig to achieve a correlatio is the doe i the electroic domai. However, a iheret bottleeck of electroic systems is their limited badwidth. Optical wavelegths for the mixig process are selected carefully followig the priciple of [23], so that the mixig product for several pump ad sigal wavelegths produces idlers at the same wavelegth. Chagig the phase of pump wavelegths produces a subtractio of power at the idler wavelgth. The key cocept of achievig optical egative accumulatio i this work, is to utilize the iheret property of four wave mixig to achieve the subtractio of two optical sigals optically. FWM of sigal ad pump wavelegths creates idlers at sum ad differece wavelegths which carry iformatio from the origial wavelegths. If a umber of sigal ad pump wavelegths are selected such that the sigal wavelegths have a separatio of twice that of the pump wavelegths, the FWM of each sigal ad pump will create idlers at a commo target wavelegth, as show i Figure 9. The optical power at this target idler wavelegth depeds o the relative phase of each mixig term at that wavelegth. Subtractio of a idler ca be achieved if the pump of that mixig product has a π/2 radias phase shift with respect to the other pumps. The resultat idler for that particular mixig term will have a π radias phase differece with respect to the other idlers ad their sum will be a subtractio betwee two optical sigals by subtractio of electric fields.
Photoics 2015, 2 209 Figure 9. Priciple of operatio. (a) Selectio of wavelegths based o the scheme i [23] for additio; (b) Illustratio of the subtractio process by applyig a π/2 relative phase shift to oe pump wavelegth. I Figure 9, the sigal wavelegths are S1 ad S2 (= S1 + ΔS) ad the pump wavelegths are P1 ad P2 (= P1 + ΔS/2). I terms of frequecy, the sigal frequecies are ωs1 ad ωs2, where ωs2 = ωs1 + ΔωS, ad the pump frequecies are ωp1 ad ωp, where ωp2 = ωp1 + ΔωS/2. Four wave mixig of ωp1 ad ωs1 produces a idler frequecy at 2ωP1 ωs1 ( 2P1 S1). Likewise, FWM of ωp2 ad ωs2 produces a idler at 2(ωP1 + ΔωS/2) (ωs1 + ΔωS) = 2ωP1 + ΔωS ωs1 ΔωS = 2ωP1 ωs1 ( 2P1 S1). If the pump wavelegths are i phase (Figure 9a), the resultat idlers add at the commo wavelegth. If P2 has a phase shift of /2 radias compared to P1 (Figure 9b), the mixig product due to P2 has a phase shift of radias compared to the mixig product due to P1 resultig i subtractio of the optical fields. 3.3.1. Simulatio Verificatio of the Proposed Cocept A simulatio of this proposed cocept was performed usig VPItrasmissioMaker 9.0 software (Figure 10). A WDM comb geerator is used as a optical source to obtai wavelegths with a determiistic phase relatioship. A Waveshaper (optical processor or filter) was desiged to pass sigal wavelegths i oe arm ad pump wavelegths i the other arm. The Waveshaper ca also chage the phase of a pump wavelegth as required. The pump ad sigal wavelegths are the combied ad fed ito a legth of HNLF. The output of the HNLF cotais the oliear FWM products. The comb geerator is a mode locked laser with all the wavelegths locked i phase. A badpass filter is used to pass oly the mixig products at the required idler wavelegth ad elimiate all other wavelegth compoets. The power level at the target idler is moitored usig a Optical Spectrum Aalyzer (OSA) to observe the additio ad subtractio processes.
Photoics 2015, 2 210 3.3.2. Simulatio Results Figure 10. Simulatio schematic to achieve optical subtractio. Figure 11 shows the simulatio results whe the sigal ad pump wavelegths are all i phase. I Figure 11a sigal λs1 ad pump λp1 mix ad geerate a idler at 2λP1 λs1 with a power level of 30 dbm. Likewise i Figure 11b, λs2 ad λp2 geerate a idler at the same wavelegth with the same power level of 30 dbm. Whe λs1, λs2, λp1 ad λp2 are all preset, the optical fields of the two idlers add i phase, resultig i a power level of 24 dbm, a 6 db power icrease caused by a doublig of the optical field. Figure 11. Simulatio results illustratig the optical additio process. (a) Sigal wavelegth λs1 ad pump wavelegth λp1 geerate a idler at 2λP1 λs1; (b) λs2 ad λp2 mix ad geerate a idler at the same wavelegth 2λP1 λs1; (c) λs1, λs2, λp1 ad λp2 geerate two idlers at the same wavelegth which add i phase, producig a 6 db icrease i optical power.
Power [dbm] Photoics 2015, 2 211 Figure 12 shows the simulatio results whe the phase of pump λp2 is phase shifted by 90 (π/2 radias) with respect to λp1. As before, the mixig of λs1 ad λp1 produces a idler at 2λP1 λs1 with a power level of 30 dbm, as does the mixig of λs2 ad λp2. However, the two idlers are ow 180 ( radias) out of phase. Whe λs1, λs2, λp1 ad λp2 are all preset, the optical fields of the idlers subtract ad produce a power level of 80 dbm. -10-30 -50-70 -90-10 -30-50 -70-90 -10-30 -50-70 -90 2λ P1 -λ S1 (a) (b) (c) λ P2 λ P1 λ S2 λ S1 1552.8 1553.5 1554.1 Figure 12. Simulatio results illustratig the optical subtractio process. (a) Sigal wavelegth λs1 ad pump wavelegth λp1 geerate a idler at 2λP1 λs1; (b) λs2 ad λp2, which is 90 phase shifted with respect to λp1, geerate a idler at the same wavelegth as i a) but with a 180 phase shift; (c) λs1, λs2, λp1 ad λp2 mix ad geerate two idlers at the same wavelegth which are 180 out of phase, producig a subtractio. 4. Coclusios The aim of this paper was to itroduce readers to the recet implemetatio of FWM to achieve correlatio of a iput bit stream with a referece template patter. The use of a correlator with egative accumulatio i a applicatio, such as serial time-ecoded amplified microscopy (STEAM), will be a excitig forthcomig research i ultrafast image processig. Ackowledgmets Wavelegth [m] The authors gratefully ackowledge the cotributio of Professor Ara Mitchell ad Lam Bui for their isightful commets.
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