Phase matched parametric amplification via four ... - Semantic Scholar
Phase matched parametric amplification via fourwave mixing in optical microfibers MUHAMMAD I.M. ABDUL KHUDUS,1,2,* FRANCESCO DE LUCIA,1 COSTANTINO CORBARI,1,3 TIMOTHY LEE,1 PETER HORAK,1 PIER SAZIO,1 AND GILBERTO BRAMBILLA1 1
Optoelectronics Research Center, University of Southampton, Southampton, SO17 1BJ United Kingdom Photonics Research Centre, Department of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia 3 Renishaw plc, New Mills, Wotton-under-Edge, Gloucestershire, GL12 8JR United Kingdom *Corresponding author: [email protected] 2
Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX
Four-wave mixing (FWM) based parametric amplification in optical microfibers (OMF) is demonstrated over a wavelength range of over 1000 nm by exploiting their tailorable dispersion characteristics to achieve phase matching. Simulations indicate that for any set of wavelengths satisfying the FWM energy conservation condition there are two diameters at which phase matching in the fundamental mode can occur. Experiments with a high-power pulsed source working in conjunction with a periodically poled silica fiber (PPSF), producing both fundamental and second harmonic signals, are undertaken to investigate the possibility of FWM parametric amplification in OMFs. Large increases of idler output power at the third harmonic wavelength were recorded for diameters close to the two phase matching diameters. A total amplification of more than 25 dB from the initial signal was observed in a 6 mm long optical microfiber, after accounting for the thermal drift of the PPSF and other losses in the system. OCIS codes: (190.4370) Nonlinear optics, fibers; (190.4410) Nonlinear optics, parametric processes; (190.4380) Nonlinear optics, four-wave mixing; http://dx.doi.org/10.1364/OL.99.099999
Four-wave mixing (FWM) is a process in which four waves interact via the optical Kerr nonlinearity of a medium, where two photons from one or two ‘pump’ waves (for instance at frequencies , ) are annihilated, and two new photons, called the signal ( ) and idler ( ), are created [1]. One application of FWM is parametric amplification, where the power from one wavelength is transferred to another wavelength via the Kerr effect, which has been demonstrated in a variety of optical fibers, with the highest recorded conversion being 70 dB [1-4]. However, parametric amplification via FWM requires phase matching for efficient energy conversion in order to
compensate for material and waveguide dispersion as well as nonlinear effects, often limiting the bandwidth of the process [5]. A number of schemes were proposed which allowed a broader bandwidth, but the largest realized bandwidth is 900 nm and 300 nm for solid core and microstructured optical fiber, respectively [6,7]. In this letter we demonstrate the possibility of using optical microfibers (OMFs) for FWM parametric amplification over a wavelength band of over 1000 nm by exploiting the tailorable dispersion characteristics of the OMF to optimize the diameter for phase matching. The technique, applicable for both parametric amplification as well as parametric conversion, theoretically allows for the amplification and generation of an almost arbitrary set of wavelengths, as well as the possibility of building fully fiberized light sources in the UV and mid-IR wavelength ranges. OMFs are typically drawn from conventional fibers, most commonly by the flame brushing technique where a section of the fiber is heated to the softening point and pulled to reduce the diameter. By doing so, the optical core of the fiber gradually disappears, and the erstwhile cladding material effectively becomes the core, with air taking the role of the optical cladding. This allows for higher mode confinement, translating into an increased nonlinearity of up to 100 times the original value, as well as relatively low losses of typically < 1 dB [8]. The relatively high nonlinearity and tailorable dispersion has been previously exploited to achieve intermodal third harmonic generation in optical microfibers where energy transfer is achieved by parametric conversion from the fundamental mode at one frequency to a higher order mode at a higher frequency [9,10], as well as an efficient means to achieve parametric conversion [11]. The phase matching and energy conservation conditions for efficient FWM, respectively, can be written as [5]:
(
)+ ( +
)= ( =
)+ ( +
)
(1) (2)
where the subscripts 1,2,3 and 4 refer to the four interacting wavelengths in the FWM process and ( ) is the propagation constant for frequency .
In the case of degenerate d FWM M we have = . Here, we will w assume that light at a all wavelengthss is propagating in i the fundamen ntal mode of the OMF as a this would be th he most efficient mode for FWM. In order to fin nd the OMF dia ameter required to achieve phaase maatching in Eq. (1)), the rigorous eig genvalue equatio ons for a step ind dex refractive index prrofile were solved d for a silica OMF F. The wavelengtths em mployed are harm monics of the fund damental at 1550 0 nm such that th hey au utomatically satissfy Eq. (2). To acccount for both deegenerate and no ondeegenerate FWM, the t wavelengths of the fundamen ntal frequency (FF), seecond harmonic (SH), ( third harmo onic (TH) and fou urth harmonic (FH) weere taken into con nsideration, as sh hown in Fig. 1a.
obtaineed from [12]. T This yields thee predicted phaase matching diameteers for the fund damental modes of the three FW WM schemes discusseed above. It is cllear that for each h FWM scheme, tthere are two phase m matching diameteers at which Eq. ((1) is satisfied, deenoted and , as detailed in Tablle 1. Experimenttally, this translaates into two differen nt diameters at w which FWM ampliification is expectted to occur in an OMFF. Here, we shalll only consider sscheme (A), with h schemes (B) and (C) being studied in n a future work. T These wavelengtths are chosen primariily for experimen ntal reasons, bu ut the technique can be easily extendeed to any numberr of wavelength ccombinations satiisfying Eq. (2), as illusttrated in Fig. 1c ffor degenerate FW WM. It can be seeen that phase matchin ng can be achievved with a widee range of pump p wavelengths ( and ), generating signals spannin ng from the visib ble to near IR wavelen ngths. A plot of th he dispersion of tthe microfiber is shown in Fig. 2 to ind dicate the change of the dispersion n with OMF diameeter. TABLE E I: Phase match hing diameters ffor the three diffferent FWM schemees considered. and denotte the first and ssecond phase match hing diameters, rrespectively. Phase m matching diametter ( m) FWM M scheme and typ pe (A A) Degenerate 0.800 2.886 (B B) Non-degeneraate 1.719 0.790 (C)) Degenerate 0.872 0.530 To in nvestigate this, a Master Oscillat ator Power Amp plifier (MOPA) seeded by a narrow wband continuou us wave (CW)) seed laser (Photon netics Tunics BT T) working in thee telecom C-band wavelength region ((1530–1565 nm)) was employed.. The MOPA systeem (shown in Fig. 3) p produced an outp put at a central w wavelength of 155 50.3 nm with a pulse w width of 5 ns, rep petition rate of 20 00 kHz and averaage powers of n 300 mW and 8 between 800 mW, which ttranslated into peeak powers of between n 300 W and 8 800 W. The pulsses were generaated using an electro--optic modulatorr (EOM), which iss then followed b by an acoustooptic m modulator (AOM)) further along th he chain to remo ove any interpulse am mplified spontan neous emission ((ASE) in the systtem to ensure that thee majority of the power is contain ned in the pulse. T Two fiberized thin film m spectral filters o operating in the C-band were also o employed in order too improve the optical signal-to-n noise ratio (OSNR R) at the final output, required for efficcient second harm monic generation n. Polarization is manaaged by the use off two polarization n controllers (PC) in the MOPA chain.
Fig g. 1. (a) Frequenccies investigated for FWM. The freequencies denoting pu ump, idler and siignal vary with th he scheme for FW WM, as detailed in Taable 1. (b) Rellation between the OMF diam meter and mode prropagation consttants for three different d FWM scchemes; black do ots represent phase matching m diamete ers satisfying Eq. (1). FF, SH, TH an nd FH H represent the fundamental f freq quency, the seco ond harmonic (SH H), the third harmonicc (TH) and the fourth f harmonic (FH), respectiveely. (c)) Degenerate FW WM phase match hed diameter for a set first pum mp waavelength, , (le eft) and five differrent second pump wavelengths, . Th he idler waveleng gth can be calcculated from 1/ = 2/ 1/ . Tw wo distinct sets of o phase matchin ng diameters can be discerned fro om the figure. Three differentt FWM schemess were theoretiically investigateed, naamely, FWM betw ween (A) FF, SH and a TH (degeneraate); (B) FF, SH, TH T an nd FH (non-dege enerate); and (C) SH, TH and FH (degenerate). The T su um of the propag gation constants on each side of Eq. E (1) was plottted forr each FWM sche eme in Fig. 1b. Th he raw data used in i this paper can be
Variation in the d dispersion of the OMF ( ) with wavelength Fig. 2. V for diffferent OMF diam meter ( ). It can be obserrved that the dispersiion profile doess not vary signifi ficantly for 1 m, but changess significantly forr diameters 0.5 m 1 m. The ooutput of the MO OPA was then con nnected to a periodically poled silica fib ber (PPSF) desiigned to be quaasi-phase matcheed (QPM) for efficientt conversion of tthe FF at 1550.3 nm into the SH at 775.15 nm via secoond harmonic gen neration (SHG), w which has a total insertion loss of < 0.5 dB. The PPSF waas fabricated from m a twin-hole Gerrmania doped fused siilica fiber manufaactured by Acreo o Fiberlab. The tw wo holes were
firrst fully filled witth Gallium liquid electrodes by means m of a pressu ure fillling technique siimilar to the one e described in [13]. Tungsten wirres weere then inserte ed at each end of o the two holess before the entiire en nsemble was sea aled with superg glue. The fiber was w then thermaally po oled by applying a positive voltag ge of 7.5 kV on both b the electrod des wh hilst being heated d at 250 °C on a hotplate h [14]. Thee sample was leftt to po ole for 120 min before b the hotpla ate was switched off and allowed to co ool with the high voltage v continuallly applied for a fu urther 60 min. Th his ( ) prrocedure induce es an effective second order susceptibility s un niformly across the silica fiber core by meanss of a third ord der ( ) rectification processs expressed by the t relationship 3 ( ) , wh here ( ) is the third order sussceptibility of siliica and is the t staatic frozen-in electric e field due e to poling [15 5,16]. Quasi-phaase maatching allows th he wavevector mismatch m betweeen the fundamen ntal an nd second harm monics to be compensated c by y modulating the t no onlinearity inducced by poling. This T modulation is achieved by y a peeriodic UV erasure of the poling field by local exxposure to 355 nm n raadiation delivered d as a 200 kHz trrain of 8 ps pulses, focused to a 10 m m×100 m spot size with a tota al fluence of 200 / [17]. Aftter exxposing the poled d fiber to this foccused high-energgy UV radiation, the t resulting free carrrier generation in nside the fiber locally l nullifies the t fro ozen-in electric field f [18]. A spatially period dic exposure of the t ( ) un niformly poled fiber therefore prroduces a modullation of . The T
nd of the PPSF. A byproduct of SH wavvelengths existingg at the output en the SHG G process, howeever, is the geneeration of a sign nal at the TH wavelen ngth, generated d by non-phase matched sum m frequency generattion (SFG), wheree = + . This is similar to the results in [19], and can be explaained by the fact tthat the PPSF is n not perfect and the graating width conta tains slight fluctu uations. The efficciency of this processs is exceedingly ssmall ( ~10 ) aas the PPSF was optimized for SHG and not for the TH wavelength, butt it provides a ‘seeed’ laser with which p parametric ampliification can occu ur. The simultaneous geeneration of thee SH and TH waavelengths, in n to the FF waveelength, allows th he frequency req quirement for addition parameetric amplification n via degeneratee FWM as detailled in scheme (A) of T Table 1 to be auto omatically satisfieed. This is furtherr enhanced as the FF, SSH and TH are co o-polarized and o overlap spatially, both of which are a coonsequence of thee SHG and SFG prrocesses in the PP PSF. Very long pulses were employed d in order to elliminate walk-offf effects. The resultin ng output spectrrum from the P PPSF which has been passed through h a shortpass filteer before taperingg is given in Fig. 4 4.
( )
peeriod of this grating is chose en to allow for QPM Q at the desirred waavelength. The use u of PPSF allow ws for the adop ption of an all-fib ber no onlinear device, and does not su uffer from some constraints of the t more common nonlinear n device es such as theermal instabilities, relatively short intteraction lengthss, high costs, relaatively low damaage threshold, losses due d to diffraction n as well as from m free space opticcal eleements required for alignment an nd walk-off effectss.
Fig g. 3. Schematicc of the experim mental setup ussed to investigaate en nhancement of th he idler signal due e to phase matchiing in OMFs. A total off five amplifiers (Amp#) were employed e in con njunction with tw wo pectral filters in order o to minimizze OSNR and inteer-pulse ASE. Here, sp PP PSF is a periodica ally poled silica fib ber; PC# is a polarrization controlleer. As the PPSF is i highly sensitiive to polarizatiion, the incoming po olarization was co ontrolled by two polarization con ntrollers before an nd aftter the fifth amp plifier (Amp5 in Fig. F 3). To ensuree efficient SHG, the t PP PSF was first directly d connecte ed to the first amplifier (Amp p1) op perating at a CW W power of 30 mW m and the waavelength from the t tuneable seed lase er was changed gradually to see the change in the t PP PSF output. Once e the wavelengtth which producces the highest SH S siggnal is determined, the central wavelengths w of both b spectral filteers weere adjusted accordingly and the e MOPA chain was w reconnected. A pu ump power of 30 00 mW was emp ployed at the MOPA output in ord der to avoid pump dep pletion and any other o undesirable nonlinear effeccts. Att this power levell, the OSNR of the e MOPA output iss more than 50 dB, d su uitable for relativ vely efficient SH HG, producing an a average outp put po ower of more tha an 3 mW at 775 nm. n This resulted d in both the FF an nd
Fig. 4. IInitial output siggnal from the PPSSF after a shortp pass filter. The loss of the filter is wavvelength depend dent, with longerr wavelengths registerring higher lossees, causing the signal at FF (15 550.3) nm to appear smaller than thee SH (755.15 nm)), both shown herre in blue. The idler siggnal (516.75 nm m), shown in red,, is relatively sm mall and is just above th the noise level. Th his is the signal w which will be enh hanced by the OMF, ass shown in Fig. 5. The ooutput from thee PPSF was then spliced to a lenggth of Z-Fiber (Sumitoomo Electric) beefore being conn nected with a sh hortpass filter, designeed to have a lo oss of more thaan 15 dB at 775 nm, and a broadbaand optical specctrum analyzer ((OSA) (Yokogaw wa AQ6315A). The Z-FFiber is then tap pered by using the modified flaame brushing techniq que, which employs a microheatter, with the tap pering profile being ca carefully controlleed in order to saatisfy the adiabaaticity criteria, therebyy minimizing losss [7, 8]. A length h of 6 mm of thee Z-Fiber was tapered d, from an initiall diameter of 12 25 m to a finaal diameter of 0.5 m, in order to fully explore the entirre range of the prredicted phase matchin ng diameters. At the end of the taapering process, tthe OMF has a full lenggth of approximaately 29 mm, with h a waist length o of 6 mm and a waist diiameter of 0.5 m m. The 1.55 m M MOPA source, con nnected to the PPSF, w was launched into to the fiber whistt being tapered. The temporal evolutioon of the outputt spectra at the peak of the idleer wavelength (516.7 n nm) was recordeed with the OSA aas shown in Fig. 5 5. A resolution of 10 nm m was employed d to capture all ssignal power gen nerated at this wavelen ngth. Initiaally, there is a vvery small signaal at the idler w wavelength, as explaineed above. This ssignal does not vary significantlly as tapering takes pllace initially, with h the small variattion being accoun nted for by the taperingg process itself aas well as the theermal drift of thee PPSF. As the OMF d diameter reach hes the first phase matchin ng diameter ( 2.89 m), the ou ncreases by morre than 22 dB. utput intensity in The siggnal then is red duced as the fiber is tapered fu urther, as the
tap pering process re educes the OMF length l at which the t phase matching diaameter occurs, although a due to the t increasing ov verall length of the t microfiber there is i a time-varying g range of diam meters in the OM MF traansition region which w are phase matched m and neaarly phase matcheed, resulting in a grad dual decrease in the t signal. This downward d trend d is ob bserved until the fiber reaches th he second phase matching m diametter ( 0.80 m), where the siignal increases dramatically by ap pproximately 15 dB, reaching the highest recorded d output power. As the fiber is tapered d even more, the signal s monotoniccally decreases un ntil the tapering proce ess stops at a diam meter of 0.5 m. The slight drop in inttensity observed at = 580 s an nd at the end of th he tapering proceess arre due to the OMF F moving inside th he microheater and a approaching its waalls. Additionally y, at the end of processing p there are changes in the t efffective refractive e index associate e to the temperaature change wh hen the taper is taken out o of the microh heater. The inset in Fig. 5 shows the t 12 2 dB increase in idler output bettween the untap pered fiber and the t OM MF with 0.5 m diameter. Fig. 5 in ndicates that if th he tapering proceess is stopped at an OM MF with length of o 6 mm and waisst of approximateely 00 nm, a total ma aximum enhance ement of more th han 20 dB from the t 80 orriginal signal can be achieved, witth the figure bein ng closer to 25 dB B if wee use the output intensity i at 5 m as a baseline.
Figg. 5. Evolution of the idler signall at 516.75 nm with w respect to the t diaameter and the processing time during taperingg. The difference in scaale between the e tapering time axis a (linear) and the diameter axxis (lo ogarithmic) arises from the expon nential profile of the t taper transition regions. Inset: the idler signal befo ore and after thee tapering proceess. Th he data in the inset was measured d with a resolutio on of 0.05 nm and da higgher sensitivity, as a compared to 10 1 nm and a loweer sensitivity for the t maain figure, resultiing in the appare ent discrepancy in i the initial pow wer measurement. The final efficiency was incre eased from ~1 10 to ~10 , co orresponding to a parametric gain n of 25 dB or 4.17 7 dB/mm, by using this method. Thiis is very low w compared to devices such as seemiconductor opttical amplifiers, where w FWM efficiencies in excess of 20 0 dB are possib ble [20], but is comparable to other paramettric am mplifiers and is able a to potentiallly operate acrosss the entire opticcal baandwidth [1-7]. The T final efficiency y can be improveed by increasing the t pu ump-to-signal ra atio, while the overall parameetric gain can be im mproved by the fabrication f of a longer l OMF and d by increasing the t effficiency of the SH HG, where an efficciency of 45% hass been shown to be acchievable [21]. In summary, we w have demonsttrated parametriic amplification via v FW WM in optical miicrofibers. The am mplification is acchieved by tailoring the dispersion of the t OMF by cha anging the diameeter of the OMF to saatisfy the phase matching m requirem ment. An amplificcation of more th han 20 0 dB from in the idler i signal is ach hieved by using an n OMF with a waaist len ngth of 6 mm see eded by a MOPA operating in thee telecom C-band in
conjuncction with a PPSF F which generatees the SH wavelength required for FWM M. Accounting for thermal drift off the PPSF, the to otal maximum FWM eenhancement in n the OMF is aapproximately 25 dB over a wavelen ngth range of 1 1000 nm. In prin nciple, this technique can be extendeed to any waveelength, allowin ng for the relatiively efficient generattion and amplificcation of arbitrarry wavelengths, aassuming that other noonlinear effects ssuch as SPM and X XPM do not domiinate. Fund ding. Engineerring and Physicaal Sciences Reseearch Council (EPSRC C) (EP/L01243X//1). Ackn nowledgment. T The authors wo ould like to than nk Oleksandr Tarasen nko and Waltter Margulis ffrom Acreo Fiberlab who manufaactured the fiber used for the PP PSF as well as Peeter Kazansky, Francessca Parmigiani, Jaames Wilkinson and Senthil Gan napathy at the Optoeleectronics Researcch Centre of the U University of Sou uthampton for access tto the necessary ttechnical facilitiess.
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Optoelectronics Research Center, University of Southampton, Southampton, SO17 1BJ United Kingdom Photonics Research Centre, Department of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia 3 Renishaw plc, New Mills, Wotton-under-Edge, Gloucestershire, GL12 8JR United Kingdom *Corresponding author: [email protected] 2
Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX
Four-wave mixing (FWM) based parametric amplification in optical microfibers (OMF) is demonstrated over a wavelength range of over 1000 nm by exploiting their tailorable dispersion characteristics to achieve phase matching. Simulations indicate that for any set of wavelengths satisfying the FWM energy conservation condition there are two diameters at which phase matching in the fundamental mode can occur. Experiments with a high-power pulsed source working in conjunction with a periodically poled silica fiber (PPSF), producing both fundamental and second harmonic signals, are undertaken to investigate the possibility of FWM parametric amplification in OMFs. Large increases of idler output power at the third harmonic wavelength were recorded for diameters close to the two phase matching diameters. A total amplification of more than 25 dB from the initial signal was observed in a 6 mm long optical microfiber, after accounting for the thermal drift of the PPSF and other losses in the system. OCIS codes: (190.4370) Nonlinear optics, fibers; (190.4410) Nonlinear optics, parametric processes; (190.4380) Nonlinear optics, four-wave mixing; http://dx.doi.org/10.1364/OL.99.099999
Four-wave mixing (FWM) is a process in which four waves interact via the optical Kerr nonlinearity of a medium, where two photons from one or two ‘pump’ waves (for instance at frequencies , ) are annihilated, and two new photons, called the signal ( ) and idler ( ), are created [1]. One application of FWM is parametric amplification, where the power from one wavelength is transferred to another wavelength via the Kerr effect, which has been demonstrated in a variety of optical fibers, with the highest recorded conversion being 70 dB [1-4]. However, parametric amplification via FWM requires phase matching for efficient energy conversion in order to
compensate for material and waveguide dispersion as well as nonlinear effects, often limiting the bandwidth of the process [5]. A number of schemes were proposed which allowed a broader bandwidth, but the largest realized bandwidth is 900 nm and 300 nm for solid core and microstructured optical fiber, respectively [6,7]. In this letter we demonstrate the possibility of using optical microfibers (OMFs) for FWM parametric amplification over a wavelength band of over 1000 nm by exploiting the tailorable dispersion characteristics of the OMF to optimize the diameter for phase matching. The technique, applicable for both parametric amplification as well as parametric conversion, theoretically allows for the amplification and generation of an almost arbitrary set of wavelengths, as well as the possibility of building fully fiberized light sources in the UV and mid-IR wavelength ranges. OMFs are typically drawn from conventional fibers, most commonly by the flame brushing technique where a section of the fiber is heated to the softening point and pulled to reduce the diameter. By doing so, the optical core of the fiber gradually disappears, and the erstwhile cladding material effectively becomes the core, with air taking the role of the optical cladding. This allows for higher mode confinement, translating into an increased nonlinearity of up to 100 times the original value, as well as relatively low losses of typically < 1 dB [8]. The relatively high nonlinearity and tailorable dispersion has been previously exploited to achieve intermodal third harmonic generation in optical microfibers where energy transfer is achieved by parametric conversion from the fundamental mode at one frequency to a higher order mode at a higher frequency [9,10], as well as an efficient means to achieve parametric conversion [11]. The phase matching and energy conservation conditions for efficient FWM, respectively, can be written as [5]:
(
)+ ( +
)= ( =
)+ ( +
)
(1) (2)
where the subscripts 1,2,3 and 4 refer to the four interacting wavelengths in the FWM process and ( ) is the propagation constant for frequency .
In the case of degenerate d FWM M we have = . Here, we will w assume that light at a all wavelengthss is propagating in i the fundamen ntal mode of the OMF as a this would be th he most efficient mode for FWM. In order to fin nd the OMF dia ameter required to achieve phaase maatching in Eq. (1)), the rigorous eig genvalue equatio ons for a step ind dex refractive index prrofile were solved d for a silica OMF F. The wavelengtths em mployed are harm monics of the fund damental at 1550 0 nm such that th hey au utomatically satissfy Eq. (2). To acccount for both deegenerate and no ondeegenerate FWM, the t wavelengths of the fundamen ntal frequency (FF), seecond harmonic (SH), ( third harmo onic (TH) and fou urth harmonic (FH) weere taken into con nsideration, as sh hown in Fig. 1a.
obtaineed from [12]. T This yields thee predicted phaase matching diameteers for the fund damental modes of the three FW WM schemes discusseed above. It is cllear that for each h FWM scheme, tthere are two phase m matching diameteers at which Eq. ((1) is satisfied, deenoted and , as detailed in Tablle 1. Experimenttally, this translaates into two differen nt diameters at w which FWM ampliification is expectted to occur in an OMFF. Here, we shalll only consider sscheme (A), with h schemes (B) and (C) being studied in n a future work. T These wavelengtths are chosen primariily for experimen ntal reasons, bu ut the technique can be easily extendeed to any numberr of wavelength ccombinations satiisfying Eq. (2), as illusttrated in Fig. 1c ffor degenerate FW WM. It can be seeen that phase matchin ng can be achievved with a widee range of pump p wavelengths ( and ), generating signals spannin ng from the visib ble to near IR wavelen ngths. A plot of th he dispersion of tthe microfiber is shown in Fig. 2 to ind dicate the change of the dispersion n with OMF diameeter. TABLE E I: Phase match hing diameters ffor the three diffferent FWM schemees considered. and denotte the first and ssecond phase match hing diameters, rrespectively. Phase m matching diametter ( m) FWM M scheme and typ pe (A A) Degenerate 0.800 2.886 (B B) Non-degeneraate 1.719 0.790 (C)) Degenerate 0.872 0.530 To in nvestigate this, a Master Oscillat ator Power Amp plifier (MOPA) seeded by a narrow wband continuou us wave (CW)) seed laser (Photon netics Tunics BT T) working in thee telecom C-band wavelength region ((1530–1565 nm)) was employed.. The MOPA systeem (shown in Fig. 3) p produced an outp put at a central w wavelength of 155 50.3 nm with a pulse w width of 5 ns, rep petition rate of 20 00 kHz and averaage powers of n 300 mW and 8 between 800 mW, which ttranslated into peeak powers of between n 300 W and 8 800 W. The pulsses were generaated using an electro--optic modulatorr (EOM), which iss then followed b by an acoustooptic m modulator (AOM)) further along th he chain to remo ove any interpulse am mplified spontan neous emission ((ASE) in the systtem to ensure that thee majority of the power is contain ned in the pulse. T Two fiberized thin film m spectral filters o operating in the C-band were also o employed in order too improve the optical signal-to-n noise ratio (OSNR R) at the final output, required for efficcient second harm monic generation n. Polarization is manaaged by the use off two polarization n controllers (PC) in the MOPA chain.
Fig g. 1. (a) Frequenccies investigated for FWM. The freequencies denoting pu ump, idler and siignal vary with th he scheme for FW WM, as detailed in Taable 1. (b) Rellation between the OMF diam meter and mode prropagation consttants for three different d FWM scchemes; black do ots represent phase matching m diamete ers satisfying Eq. (1). FF, SH, TH an nd FH H represent the fundamental f freq quency, the seco ond harmonic (SH H), the third harmonicc (TH) and the fourth f harmonic (FH), respectiveely. (c)) Degenerate FW WM phase match hed diameter for a set first pum mp waavelength, , (le eft) and five differrent second pump wavelengths, . Th he idler waveleng gth can be calcculated from 1/ = 2/ 1/ . Tw wo distinct sets of o phase matchin ng diameters can be discerned fro om the figure. Three differentt FWM schemess were theoretiically investigateed, naamely, FWM betw ween (A) FF, SH and a TH (degeneraate); (B) FF, SH, TH T an nd FH (non-dege enerate); and (C) SH, TH and FH (degenerate). The T su um of the propag gation constants on each side of Eq. E (1) was plottted forr each FWM sche eme in Fig. 1b. Th he raw data used in i this paper can be
Variation in the d dispersion of the OMF ( ) with wavelength Fig. 2. V for diffferent OMF diam meter ( ). It can be obserrved that the dispersiion profile doess not vary signifi ficantly for 1 m, but changess significantly forr diameters 0.5 m 1 m. The ooutput of the MO OPA was then con nnected to a periodically poled silica fib ber (PPSF) desiigned to be quaasi-phase matcheed (QPM) for efficientt conversion of tthe FF at 1550.3 nm into the SH at 775.15 nm via secoond harmonic gen neration (SHG), w which has a total insertion loss of < 0.5 dB. The PPSF waas fabricated from m a twin-hole Gerrmania doped fused siilica fiber manufaactured by Acreo o Fiberlab. The tw wo holes were
firrst fully filled witth Gallium liquid electrodes by means m of a pressu ure fillling technique siimilar to the one e described in [13]. Tungsten wirres weere then inserte ed at each end of o the two holess before the entiire en nsemble was sea aled with superg glue. The fiber was w then thermaally po oled by applying a positive voltag ge of 7.5 kV on both b the electrod des wh hilst being heated d at 250 °C on a hotplate h [14]. Thee sample was leftt to po ole for 120 min before b the hotpla ate was switched off and allowed to co ool with the high voltage v continuallly applied for a fu urther 60 min. Th his ( ) prrocedure induce es an effective second order susceptibility s un niformly across the silica fiber core by meanss of a third ord der ( ) rectification processs expressed by the t relationship 3 ( ) , wh here ( ) is the third order sussceptibility of siliica and is the t staatic frozen-in electric e field due e to poling [15 5,16]. Quasi-phaase maatching allows th he wavevector mismatch m betweeen the fundamen ntal an nd second harm monics to be compensated c by y modulating the t no onlinearity inducced by poling. This T modulation is achieved by y a peeriodic UV erasure of the poling field by local exxposure to 355 nm n raadiation delivered d as a 200 kHz trrain of 8 ps pulses, focused to a 10 m m×100 m spot size with a tota al fluence of 200 / [17]. Aftter exxposing the poled d fiber to this foccused high-energgy UV radiation, the t resulting free carrrier generation in nside the fiber locally l nullifies the t fro ozen-in electric field f [18]. A spatially period dic exposure of the t ( ) un niformly poled fiber therefore prroduces a modullation of . The T
nd of the PPSF. A byproduct of SH wavvelengths existingg at the output en the SHG G process, howeever, is the geneeration of a sign nal at the TH wavelen ngth, generated d by non-phase matched sum m frequency generattion (SFG), wheree = + . This is similar to the results in [19], and can be explaained by the fact tthat the PPSF is n not perfect and the graating width conta tains slight fluctu uations. The efficciency of this processs is exceedingly ssmall ( ~10 ) aas the PPSF was optimized for SHG and not for the TH wavelength, butt it provides a ‘seeed’ laser with which p parametric ampliification can occu ur. The simultaneous geeneration of thee SH and TH waavelengths, in n to the FF waveelength, allows th he frequency req quirement for addition parameetric amplification n via degeneratee FWM as detailled in scheme (A) of T Table 1 to be auto omatically satisfieed. This is furtherr enhanced as the FF, SSH and TH are co o-polarized and o overlap spatially, both of which are a coonsequence of thee SHG and SFG prrocesses in the PP PSF. Very long pulses were employed d in order to elliminate walk-offf effects. The resultin ng output spectrrum from the P PPSF which has been passed through h a shortpass filteer before taperingg is given in Fig. 4 4.
( )
peeriod of this grating is chose en to allow for QPM Q at the desirred waavelength. The use u of PPSF allow ws for the adop ption of an all-fib ber no onlinear device, and does not su uffer from some constraints of the t more common nonlinear n device es such as theermal instabilities, relatively short intteraction lengthss, high costs, relaatively low damaage threshold, losses due d to diffraction n as well as from m free space opticcal eleements required for alignment an nd walk-off effectss.
Fig g. 3. Schematicc of the experim mental setup ussed to investigaate en nhancement of th he idler signal due e to phase matchiing in OMFs. A total off five amplifiers (Amp#) were employed e in con njunction with tw wo pectral filters in order o to minimizze OSNR and inteer-pulse ASE. Here, sp PP PSF is a periodica ally poled silica fib ber; PC# is a polarrization controlleer. As the PPSF is i highly sensitiive to polarizatiion, the incoming po olarization was co ontrolled by two polarization con ntrollers before an nd aftter the fifth amp plifier (Amp5 in Fig. F 3). To ensuree efficient SHG, the t PP PSF was first directly d connecte ed to the first amplifier (Amp p1) op perating at a CW W power of 30 mW m and the waavelength from the t tuneable seed lase er was changed gradually to see the change in the t PP PSF output. Once e the wavelengtth which producces the highest SH S siggnal is determined, the central wavelengths w of both b spectral filteers weere adjusted accordingly and the e MOPA chain was w reconnected. A pu ump power of 30 00 mW was emp ployed at the MOPA output in ord der to avoid pump dep pletion and any other o undesirable nonlinear effeccts. Att this power levell, the OSNR of the e MOPA output iss more than 50 dB, d su uitable for relativ vely efficient SH HG, producing an a average outp put po ower of more tha an 3 mW at 775 nm. n This resulted d in both the FF an nd
Fig. 4. IInitial output siggnal from the PPSSF after a shortp pass filter. The loss of the filter is wavvelength depend dent, with longerr wavelengths registerring higher lossees, causing the signal at FF (15 550.3) nm to appear smaller than thee SH (755.15 nm)), both shown herre in blue. The idler siggnal (516.75 nm m), shown in red,, is relatively sm mall and is just above th the noise level. Th his is the signal w which will be enh hanced by the OMF, ass shown in Fig. 5. The ooutput from thee PPSF was then spliced to a lenggth of Z-Fiber (Sumitoomo Electric) beefore being conn nected with a sh hortpass filter, designeed to have a lo oss of more thaan 15 dB at 775 nm, and a broadbaand optical specctrum analyzer ((OSA) (Yokogaw wa AQ6315A). The Z-FFiber is then tap pered by using the modified flaame brushing techniq que, which employs a microheatter, with the tap pering profile being ca carefully controlleed in order to saatisfy the adiabaaticity criteria, therebyy minimizing losss [7, 8]. A length h of 6 mm of thee Z-Fiber was tapered d, from an initiall diameter of 12 25 m to a finaal diameter of 0.5 m, in order to fully explore the entirre range of the prredicted phase matchin ng diameters. At the end of the taapering process, tthe OMF has a full lenggth of approximaately 29 mm, with h a waist length o of 6 mm and a waist diiameter of 0.5 m m. The 1.55 m M MOPA source, con nnected to the PPSF, w was launched into to the fiber whistt being tapered. The temporal evolutioon of the outputt spectra at the peak of the idleer wavelength (516.7 n nm) was recordeed with the OSA aas shown in Fig. 5 5. A resolution of 10 nm m was employed d to capture all ssignal power gen nerated at this wavelen ngth. Initiaally, there is a vvery small signaal at the idler w wavelength, as explaineed above. This ssignal does not vary significantlly as tapering takes pllace initially, with h the small variattion being accoun nted for by the taperingg process itself aas well as the theermal drift of thee PPSF. As the OMF d diameter reach hes the first phase matchin ng diameter ( 2.89 m), the ou ncreases by morre than 22 dB. utput intensity in The siggnal then is red duced as the fiber is tapered fu urther, as the
tap pering process re educes the OMF length l at which the t phase matching diaameter occurs, although a due to the t increasing ov verall length of the t microfiber there is i a time-varying g range of diam meters in the OM MF traansition region which w are phase matched m and neaarly phase matcheed, resulting in a grad dual decrease in the t signal. This downward d trend d is ob bserved until the fiber reaches th he second phase matching m diametter ( 0.80 m), where the siignal increases dramatically by ap pproximately 15 dB, reaching the highest recorded d output power. As the fiber is tapered d even more, the signal s monotoniccally decreases un ntil the tapering proce ess stops at a diam meter of 0.5 m. The slight drop in inttensity observed at = 580 s an nd at the end of th he tapering proceess arre due to the OMF F moving inside th he microheater and a approaching its waalls. Additionally y, at the end of processing p there are changes in the t efffective refractive e index associate e to the temperaature change wh hen the taper is taken out o of the microh heater. The inset in Fig. 5 shows the t 12 2 dB increase in idler output bettween the untap pered fiber and the t OM MF with 0.5 m diameter. Fig. 5 in ndicates that if th he tapering proceess is stopped at an OM MF with length of o 6 mm and waisst of approximateely 00 nm, a total ma aximum enhance ement of more th han 20 dB from the t 80 orriginal signal can be achieved, witth the figure bein ng closer to 25 dB B if wee use the output intensity i at 5 m as a baseline.
Figg. 5. Evolution of the idler signall at 516.75 nm with w respect to the t diaameter and the processing time during taperingg. The difference in scaale between the e tapering time axis a (linear) and the diameter axxis (lo ogarithmic) arises from the expon nential profile of the t taper transition regions. Inset: the idler signal befo ore and after thee tapering proceess. Th he data in the inset was measured d with a resolutio on of 0.05 nm and da higgher sensitivity, as a compared to 10 1 nm and a loweer sensitivity for the t maain figure, resultiing in the appare ent discrepancy in i the initial pow wer measurement. The final efficiency was incre eased from ~1 10 to ~10 , co orresponding to a parametric gain n of 25 dB or 4.17 7 dB/mm, by using this method. Thiis is very low w compared to devices such as seemiconductor opttical amplifiers, where w FWM efficiencies in excess of 20 0 dB are possib ble [20], but is comparable to other paramettric am mplifiers and is able a to potentiallly operate acrosss the entire opticcal baandwidth [1-7]. The T final efficiency y can be improveed by increasing the t pu ump-to-signal ra atio, while the overall parameetric gain can be im mproved by the fabrication f of a longer l OMF and d by increasing the t effficiency of the SH HG, where an efficciency of 45% hass been shown to be acchievable [21]. In summary, we w have demonsttrated parametriic amplification via v FW WM in optical miicrofibers. The am mplification is acchieved by tailoring the dispersion of the t OMF by cha anging the diameeter of the OMF to saatisfy the phase matching m requirem ment. An amplificcation of more th han 20 0 dB from in the idler i signal is ach hieved by using an n OMF with a waaist len ngth of 6 mm see eded by a MOPA operating in thee telecom C-band in
conjuncction with a PPSF F which generatees the SH wavelength required for FWM M. Accounting for thermal drift off the PPSF, the to otal maximum FWM eenhancement in n the OMF is aapproximately 25 dB over a wavelen ngth range of 1 1000 nm. In prin nciple, this technique can be extendeed to any waveelength, allowin ng for the relatiively efficient generattion and amplificcation of arbitrarry wavelengths, aassuming that other noonlinear effects ssuch as SPM and X XPM do not domiinate. Fund ding. Engineerring and Physicaal Sciences Reseearch Council (EPSRC C) (EP/L01243X//1). Ackn nowledgment. T The authors wo ould like to than nk Oleksandr Tarasen nko and Waltter Margulis ffrom Acreo Fiberlab who manufaactured the fiber used for the PP PSF as well as Peeter Kazansky, Francessca Parmigiani, Jaames Wilkinson and Senthil Gan napathy at the Optoeleectronics Researcch Centre of the U University of Sou uthampton for access tto the necessary ttechnical facilitiess.
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