High conversion efficiency fiber opticalparametric oscillator

Y. Q. Xu* and S. G. MurdochPhysics Department, University of Auckland, Private Bag 92019, Auckland, New Zealand

*Corresponding author: yxu079@aucklanduni.ac.nz

Received July 26, 2011; revised September 28, 2011; accepted October 3, 2011;posted October 4, 2011 (Doc. ID 151769); published October 28, 2011

We present a χ�3� fiber parametric oscillator with high conversion efficiency from the input pumpwave to the outputparametric sidebands. By introducing an intracavity filter detuned from the oscillator’s phase-matched frequencyconversion efficiencies considerably higher than those possible when operating at the phase-matched frequency aredemonstrated. Experimentally we are able to obtain a total internal conversion efficiency in excess of 93% from thepump to the Stokes and anti-Stokes sidebands. © 2011 Optical Society of AmericaOCIS codes: 060.2320, 190.4380.

It has long been proposed that the Kerr nonlinearity inoptical fibers can be used to efficiently generate widelytunable coherent light [1]. In the visible and near-IRregion, microstructured optical fiber based parametricoscillators with sideband tuning ranges in excess of150THz have been demonstrated [2,3]. In the telecommu-nication band, a widely tunable oscillator, using a disper-sion shifted fiber (DSF) as its parametric gain medium,has been reported with a tuning range for the parametricsidebands extending from 1.3 to 1:8 μm, and with a con-version efficiency from the pump to the sidebands of upto 40%. [4]. A CW fiber parametric oscillator with a con-version efficiency of 61% has also been reported [5]. Morerecently, by exploiting high power erbium-doped fiberamplifiers, a high power tunable oscillator with an aver-age output power of over 4W in each sideband has beenreported [6]. However, among these works, the subject ofthe optimum conversion efficiency possible in a fiber os-cillator has yet to be fully investigated. It is well knownthat in a single-pump fiber parametric amplifier the opti-mum conversion efficiency from the input pump wave tothe output signal and idler waves does not necessarilyoccur at the phase-matched frequency [7–9]. If a small-signal input is injected into a single-pump parametric am-plifier at the phase-matched frequency, the signal andidler waves initially grow exponentially with the maxi-mum possible parametric gain coefficient. However, asthe pump wave starts to deplete, the power-dependentcomponent of the phase-matching condition starts toevolve. This places a limit on the maximum conversionof the pump to the sidebands, and results in a periodicexchange of energy between the three waves. For aphase-matched signal the maximum possible conversionfrom the pump to the sidebands is only 28% to each side-band (a pump depletion of 56%) [9]. However, if the sig-nal is injected at a detuning with a linear phase mismatchsmaller than the linear mismatch at the phase-matchedfrequency, the phase matching of the parametric processcan actually improve as the pump depletes. In this regimealmost total conversion from the pump to the sidebandsis possible, and experimental pump depletions of 92%and 99% have been reported by exploiting this effect[7,8]. In this Letter, we show how this technique can alsobe exploited to obtain very high conversion efficienciesin a fiber optical parametric oscillator. By building a

singly resonant fiber optical parametric oscillator withan intracavity filter to control the linear phase mismatchparameter of the oscillator we are able to experimentallydemonstrate an internal conversion efficiency in excessof 93%, with 40% conversion into the anti-Stokes (fre-quency up-shifted) sideband and 53% conversion intothe Stokes (frequency down-shifted) sideband. To ourknowledge, this is the highest conversion efficiency ofa fiber-based parametric oscillator yet reported.

We consider a singly resonant ring fiber parametric os-cillator. The ring consists of a dichroic input coupler, aparametric gain fiber, a broadband output coupler, andan intracavity filter to ensure that only one of the para-metric sidebands is fed back into the reflection port ofthe input coupler [6]. For simplicity, we initially neglectthe Raman effect. This allows us to describe the evolu-tion of the pump and two sideband waves propagatingin the parametric gain fiber of the oscillator via theCW coupled-mode equations introduced in Ref. [9]. Wedefine the internal conversion efficiency of the oscillatoras the conversion of the pump to each sideband that oc-curs inside the parametric gain fiber. We also define theexternal conversion efficiency of the oscillator as the ra-tio of the output power of each sideband to the inputpump power. This definition of the external conversionefficiency takes into account of the losses and the outputcoupling of the oscillator. In Fig. 1, the internal conver-sion efficiency of a singly resonant oscillator with a 5%feedback fraction, is plotted as function of the normal-ized linear mismatch κ � −ΔkL=2γP, and the normalizedinput pump power ξ � γPL, where ΔkL � ka � ks − 2kp(ka, ks, and kp are the linear propagation constants ofthree waves), γ is the fiber nonlinearity, P is the inputpump power, and L is the fiber length. From Fig. 1 wecan see that the minimum threshold power for oscilla-tion, with 5% feedback, occurs at the phase-matched fre-quency (κ � 1) and at a normalized power of ξ � 2:5.These values agree with the standard analytic result[6]. Figure 1 also shows that at the phase-matched con-dition (κ � 1, the white dash-dot line in Fig. 1), the max-imum internal conversion to each sideband is only 28%,just as for the single-pass configuration. This occurs atthe normalized power of ξ ∼ 3 (marked with a blackdiamond in Fig. 1). This point corresponds to the maxi-mum flow of power from the pump to the sidebands

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possible at the phase-matched frequency. Beyond thispoint, the power in the sidebands starts to flow back intothe pump. However, Fig. 1 also shows that if we select alinear mismatch of κ ∼ 0:25 (i.e., a value ΔkL four timessmaller than that found at the phase-matched frequency,marked with a white dotted line in Fig. 1), an internalconversion efficiency approaching 50% into each side-band for ξ ∼ 5 − 6 is possible. This corresponds to analmost complete transfer of power from the pump tothe sidebands. The only drawback to operating at thislinear mismatch is that the threshold power is increasedby ∼20% (ξ ∼ 3) due to the reduced small-signal para-metric gain available at this detuning. Continuous tun-ability of the output sidebands is still possible whenoperating in this configuration simply by tuning the pumpwavelength [4]. The above theory considers only a pureKerr nonlinearity, whereas real fibers also possess a Ra-man contribution to the χ�3� nonlinearity. In this case thecoupled-mode equations used in the above simulationsneed to be adjusted to include Raman scattering [10].However, we find that the inclusion of Raman scatteringdoes not significantly alter the results presented above.To investigate the optimum conversion efficiency of

a fiber oscillator experimentally we use an all-fiber para-metric oscillator similar to those presented in Refs. [4–6].The experimental setup is shown as in Fig. 2. The inputpump wave is coupled into the oscillator cavity through afiber WDM with a cut wavelength of 1535 nm, and is

followed by a 54m DSF fiber as a gain medium with azero-dispersion-wavelength (ZDW) of 1553:8 nm, dis-persion parameters β3 � 0:16 ps3=km, β4 � −7:0 ×10−4 ps4=km at the ZDW, and the nonlinear coefficientγ � 2:53W−1 km−1. The splice loss between the single-modefiber and DSF is measured to be 5%. After theDSF, 90% of the light is coupled out of the cavity witha 90=10 fused fiber coupler, chosen to allow high externalconversion efficiency. The remaining light is filtered by afree-space grating filter with a bandwidth of 0:5 nm. Thisfilter selects the anti-Stokes sideband, which is fed backto the cavity through the reflection port of the WDM toform a singly resonant oscillator cavity. A fiber polariza-tion controller is placed just before the WDM to ensurethe fed back anti-Stokes wave is copolarized with the in-put pump. The total cavity round trip transmission of theanti-Stokes wave is measured to be 5% (the same value asin the preceding theory section). The pump for the oscil-lator is a C-band tunable external cavity laser intensitymodulated to form 44 ns pulses with a duty cycle of4% (repetition of 890 kHz synchronized with the cavitylength), then amplified by a 2W erbium-doped fiber am-plifier. The maximum pump peak power is estimated tobe 40W. The pump wavelength is set to 1554:68 nm,which sets β2 � −0:1 ps3=km. The linear transmissionof the input pump through the WDM, parametric gain fi-ber, and the output coupler to the 90% output port is mea-sured to be 73%. The external conversion efficiency ofthe oscillator can be simply calculated by multiplying

ξ

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Fig. 1. (Color online) Internal conversion efficiency, from thepump to each sideband, of a singly resonant ring fiber opticalparametric oscillator as a function of normalized linear mis-match and normalized input power with a resonant sidebandfeedback fraction of 5%.

54 m DSFPG

AM

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EDFA

Powermeter

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WDM99/1

couplerOSA

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Fig. 2. (Color online) Experimental schematic. ECL, externalcavity laser; PG, pulse generator; AM, amplitude modulator; PC,polarization controller; DG, diffraction grating; OSA, opticalspectrum analyzer.

0 0.5 1 1.50

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Fig. 3. (Color online) Internal conversion efficiency of thethree waves as function of normalized linear mismatch at thenormalized power (a) ξ � 3 and (b) ξ � 4:3. The solid line, dashline, and dotted line are the theoretical internal conversion ef-ficiencies of anti-Stokes, Stokes, and pump waves, respectively.The circles, squares, and diamonds are the experimental inter-nal conversion efficiencies of the anti-Stokes, Stokes, and pumpwaves, respectively.

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the internal conversion efficiencies quoted in the sectionthat follows by this linear transmission coefficient.For our first experiment, the input pump peak power is

set to 23W (ξ � 3), slightly above the threshold powerof the oscillator. The phase-matched frequency of theparametric gain can be determined from the single-passdetuning of the spontaneous sidebands in the DSF, and ismeasured to be 4:3THz. The intracavity filter forces theanti-Stokes wave to oscillate at the wavelength selected,allowing us to alter the linear mismatch of the oscillator’sparametric gain. In Fig. 3(a), we plot the experimentallymeasured power of the pump and the sidebands as afunction of the normalized linear mismatch. The opti-mum conversion occurs at κ � 0:7, where we obtain apump depletion of 60%, with 33% converted into Stokessideband and 27% into anti-Stokes sideband. At this pumplevel the optimum conversion efficiency is not too muchhigher than the conversion measured at the phase-matched frequency, κ � 1, where 50% of the pump hasbeen depleted, with 28% converted into Stokes sidebandand 22% into anti-Stokes sideband. The curves in Fig. 3(a)are calculated using the CW coupled-mode theory pre-sented in the theory section, with the effect of Ramanscattering included, as described in Ref. [10]. The param-eter f R, which sets the relative strength of the Kerr andRaman nonlinearities, is set to f R � 0:18. It is the effect ofRaman scattering that results in the small asymmetryobserved between the Stokes and anti-Stokes waves.We then increase the peak power of the pump to 33W,

corresponding to normalized power of ξ � 4:3. This

power gives a phase-matched frequency shift of 5:3THz.In Fig. 3(b), we plot the measured power of the pump andthe sidebands as a function of the linear mismatch κ atthis input power. Figure 3(b) shows that the peak conver-sion efficiency of the oscillator has shifted to a linear mis-match of κ � 0:25. At this point the input pump powerhas been very efficiently converted to the sidebands witha pump depletion of 93%. Again, due to the presence ofRaman scattering, the Stokes wave experiences slightlyhigher conversion of 53% compared to the anti-Stokesconversion of 40%. This is also clearly shown in Fig. 4,where we plot the measured optical spectrum of the out-put of the oscillator at this optimum linear mismatch(solid line, 3:2THz detuning) and at the phase-matchedfrequency (dot-dashed line, 5:3THz detuning). The in-creased conversion efficiency of the oscillator at the op-timum linear mismatch is clearly evident.

In summary, we have demonstrated a high conversionefficiency singly resonant fiber parametric oscillator byuse of a correctly detuned intracavity filter. Maximumpump depletion in excess of 93% has been achieved, with40% conversion into the anti-Stokes wave and 53% con-version into the Stokes wave. This yields an external con-version efficiency for the oscillator of 68% (29% to theanti-Stokes sideband, and 39% to the Stokes sideband).This is considerably higher than the conversion effi-ciency possible when operating the oscillator at itsphase-matched frequency.

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Fig. 4. (Color online) Spectra of the output of the oscillatortaken with the anti-Stokes sideband fed back at a linear mis-match κ � 0:25 (solid line, 3:2THz detuning), and κ � 1(dash-dot line, 5:3THz detuning), at ξ � 4:3.

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