1. Introduction

Four-wave mixing in optical fibers has long been proposed as a useful means of generating tunable coherent radiation [1]. Continuous-wave (cw) and pulsed fiber optical parametric oscillators (FOPOs) based on four-wave mixing have been demonstrated in both conventional optical fibers [2–7] and photonic crystal fibers (PCFs) [8–11]. It has been suggested that in the absence of walk-off, the conversion efficiency for large frequency shift four-wave mixing is limited by the presence of dispersion fluctuations along the length of the fiber [12]. Optical fibers used in modern optical communications systems have a tight specification on their uniformity, and are therefore ideally suited for constructing a widely-tunable FOPO. In this paper we report on an all-fiber optical parametric oscillator providing both high conversion efficiency and a wide wavelength tuning range. It is based on 40 m of dispersion-shifted fiber (DSF) in a synchronously pumped ring cavity. The gain results from modulation instability (MI) in the normal dispersion regime near the fiber’s zero-dispersion wavelength (ZDW). Experimentally we have been able to demonstrate continuous sideband tunability and high conversion efficiency from 1300 to 1500 nm and 1600 to 1860 nm as the pump wavelength is tuned between 1532 and 1556 nm. The linewidth of the generated sidebands are below 1 nm for wavelengths between 1300–1420 nm and 1680–1860 nm without the use of any wavelength selective elements.

2. Theory

In the normal dispersion regime, narrowband MI gain with a wide tuning range is possible when a strong pump propagates near the ZDW of an optical fiber. This effect has been observed in single-mode fiber [13], DSF [14, 15], highly nonlinear fiber [15] and PCF [16,17]. The frequency shift of the generated sidebands depends strongly on the detuning of the pump from the fiber’s ZDW. The phase-matching condition for MI can be written as

where β is the fiber’s linear propagation constant; Ω = ω_a - ω_p = ω_p - ω_s is the sideband frequency detuning; ω_p, ω_a and ω_s are the pump, anti-Stokes, and Stokes frequencies, respectively; γ is the nonlinear interaction coefficient; and P is incident power. Expanding β as a Taylor series around ω_p to fourth-order reduces Eq. (1) to

When β ₄ is negative, large frequency shift MI sidebands can occur in the normal dispersion regime (β2 > 0).

 

Fig. 1. Schematic of the experimental configuration: ECL, external-cavity laser; ISO, isolator; EDFA, Erbium-doped fiber amplifier; PC, polarization controller; WDM, wavelength division multiplexer; DSF, dispersion-shifted fiber.

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3. Experiment

A schematic diagram of our experiment is shown in Fig. 1. The pump source consists of an external-cavity laser (ECL) in a Littman-Metcalf configuration, which is tunable between 1500 and 1600 nm with an output power of 40 mW. The cw output of this laser is modulated with 4-ns pulses at a repetition frequency of ~1 MHz by a Lithium Niobate Mach-Zehnder intensity modulator. The modulator has an extinction ratio of 28 dB. These pulses are then amplified by an Erbium-doped fiber amplifier (EDFA) before being coupled into the cavity through a wavelength division multiplexing (WDM) coupler. The lower wavelength port of the WDM coupler operates between 1250 and 1520 nm while the higher wavelength port operates from 1525 nm and above. The parametric gain fiber is a 40 m long DSF that has a ZDW of 1556 nm and a nonlinear interaction coefficient γ= 2.4 W^-1 km^-1. A 5/95 fused-fiber coupler within the cavity provides 95% output and 5% feedback. The estimated feedback fraction of the oscillator is ~3%, in which we have taken into account the losses in the components. The delay fiber is a 160 m long standard single-mode fiber (SMF-28). This additional fiber allows us to use low duty cycle, and hence high peak power pump pulses. We utilize the wavelength dependent bend loss of SMF-28 to implement a short pass filter in the delay fiber. This ensures only the anti-Stokes wave returns to the gain fiber through the WDM coupler. As a result, the oscillator is only singly resonant with the conversion efficiency independent of the initial phases of the pump and anti-Stokes wave [18]. The operation of the WDM coupler and the splitter were verified between 1250 and 1760 nm using a white light source and a spectrometer. The total cavity length is ~200 m. The repetition rate of the pump is precisely adjusted to synchronize the pump pulse to the succeeding anti-Stokes pulse. When the MI gain exceeds the cavity loss, both sidebands are coherently amplified and eventually a steady-state oscillation is achieved [19]. Maximum conversion efficiency is achieved by adjusting polarization controller PC3 such that the anti-Stokes wave has the same polarization as the input pump inside the DSF. For a 40 THz sideband frequency shift the walk-off between the pump and the sidebands in the DSF is ~5 ps/m. Since the pump pulses are relatively long (4 ns), the effect of walk-off is negligible. We also note that the delay fiber has no effect on the parametric gain as only the anti-Stokes sideband is present.

The typical spectra of the FOPO output are shown in Fig. 2. The peak power coupled into the DSF is 50 W. We tune the FOPO simply by changing the wavelength of the ECL. Since the operating wavelength range of our optical spectrum analyzer ends at 1760 nm, the Stokes waves beyond this wavelength are not shown in Fig. 2. When pumping well inside the normal dispersion regime we observe very sharp MI sidebands. The linewidth of these sidebands increases as we tune the pump wavelength toward the ZDW. This is in agreement with the analytical expressions for the MI gain bandwidth [15]. In the case of perfect phase-matching, the single-pass small-signal gain [20] $G_{\mathrm{dB}}\approx 10{\log }_{10}\left[\frac{1}{4}\exp \left(2\mathrm{\gamma PL}\right)\right]$, where L is the fiber length, is calculated to be ~36 dB in this case. Using this simple formula, the theoretical threshold pump peak power is calculated to be 25 W. The experimental threshold pump peak power of the FOPO is 30 W, in good agreement with the theoretical prediction.

 

Fig. 2. Spectra of the FOPO output for a range of different pump wavelengths. The pump peak power is 50 W.

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Fig. 3. Experimentally measured sideband wavelengths as a function of pump wavelength of the FOPO output (circles). The crosses are calculated from the experimentally measured anti-Stokes wavelengths. Theoretical sideband wavelengths predicted by Eq. (2) (solid curves). Inset, spectrum of the FOPO output at a pump wavelength of 1536.5 nm. The corresponding sideband wavelengths are also shown (stars). The pump peak power is 50 W.

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The tuning range of the FOPO is shown in Fig. 3. The solid curves superimposed on top of the experimentally measured sideband wavelengths (circles) are the phase-matching curves calculated using Eq. (2). The dispersion coefficients of the fiber β ₂, β ₃ and β ₄ were found by fitting the phase-matching curves to the experimentally measured sideband wavelengths. The coefficients were evaluated at 1550 nm and found to be β ₂ = 0.700 ps²/km, β ₃ = 0.177 ps³/km and β ₄ = -8.013×10^-4 ps⁴/km. These dispersion coefficients (β ₂, β ₃ and β ₄), quoted at one pump wavelength, suffice to calculated the phase-matched frequency shift at any other pump wavelength between 1530 and 1565 nm using Eq. (2). The agreement between the experimental and theoretical sideband wavelengths is extremely good. Above 1760 nm the estimated Stokes wavelengths are calculated from the corresponding experimentally measured anti-Stokes wavelengths and shown as crosses. The presence of the Stokes sideband above 1760 nm was confirmed using a high dispersion prism at the FOPO output to spatially separate the pump and the sidebands, and a thermopile detector was scanned across the three dispersed beams. The spectrum recorded by the thermopile detector at pump wavelength 1536.5 nm is shown in the inset of Fig. 3. The sidebands at 1322 and 1833 nm can be clearly seen and these two points are shown as stars in Fig. 3. Above Ω = 34 THz both the anti-Stokes (1305 nm) and the Stokes (1860 nm) sidebands drop very rapidly and beyond 35 THz the oscillator no longer functions. The exact reason for this sharp cut-off is not yet clear as the theoretical phase-matching curve for the Stokes sideband extends well into the infra-red (above 3 μm) with the theoretical limit to the tuning range determined by the asymptotic limits of the fiber’s dispersion. We observe the same limit to the tuning curve in single-pass experiments using 100 m of the same DSF. This fact suggests that this limit is not a result of dispersion fluctuations along the length of the fiber. If dispersion fluctuations were limiting the total tuning range, increasing the fiber length should result a decrease in tuning range [12]. We believe the most likely cause of this limit is the increasingly weak confinement and high bend loss of the DSF at Stokes wavelengths above 1860 nm. Another effect that might limit the ultimate tuning range of the oscillator is the fiber’s higher-order mode cut-off wavelength. For the DSF used in this experiment the cut-off wavelength is specified to be below 1260 nm. As the anti-Stokes sideband does not tune below 1300 nm this limit has not yet been reached by our oscillator.

 

Fig. 4. (a). Internal conversion efficiency versus wavelength of the FOPO (circles). The internal conversion efficiencies calculated from the spectrum in the inset of Fig. 3 are also shown (stars). (b). Linewidth of the sideband as a function of wavelength.

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The experimental internal conversion efficiency from the pump to a single sideband and the spectral width of the sidebands are plotted as a function of wavelength in Fig. 4(a) and 4(b), respectively. Again the range of measurement is limited by the operating wavelength range of our optical spectrum analyzer. Figure 4 shows that between 1300–1420 nm and 1680–1760 nm the linewidth of the sidebands are below 1 nm. The linewidth of the Stokes sideband between 1760 and 1860 nm is also expected to be less than 1 nm as the MI gain bandwidth of the sidebands should be symmetrical in frequency and this leads to an approximate symmetry in wavelength. The internal conversion efficiency from the pump to a single sideband is higher than 10% over the entire tuning range and rises to over 20% at some wavelengths. This gives a total internal conversion efficiency (from the pump to both sidebands) of greater than 40% at some wavelengths. The internal conversion efficiency is calculated by comparing the power of a sideband to that of the single-pass pump power with the oscillator’s feedback loop disconnected. Both powers were measured at the FOPO output. Because of the short duty cycle of the pump pulse (1/250) and the finite modulation depth of the modulator used (28 dB) the average pump power contains a 30% cw component. The internal conversion efficiencies have been corrected to remove this artifact and so the internal conversion efficiency we quote is the conversion efficiency from the pump to the sidebands inside the DSF. The external conversion efficiency (output sideband power/input pump power) can be estimated by measuring the loss of the input pump at the WDM and the loss of the sidebands at the 5/95 coupler. We find that the external conversion efficiency is only 20% below the internal conversion efficiency.

4. Conclusion

In conclusion, we have demonstrated a high-conversion-efficiency widely-tunable all-fiber optical parametric oscillator. The consistent geometric properties and low attenuation of the DSF used in this work have enabled us to observe widely tunable parametric generation in an oscillation configuration. This is an encouraging result suggesting that with suitable fibers and pump lasers, a similar configuration can be expected to yield efficient and widely tunable operation about other central wavelengths.