Fundamentals and applications featuring the multi-functional properties of the fiber based optical parametric amplifier (FOPA), such as all-optical signal sampling, optical time division demultiplexing, pulse generation, and wavelength conversion are reviewed and discussed.

The amplification in a FOPA is a non-linear phenomenon exploiting the light induced modulation of the fiber refractive index [1]. It is notable that the fiber only serves as a passive medium in contrast to, for instance, Raman, Brillouin or rare-earth doped fiber amplification. Parametric gain in optical fibers is often referred to as a third order parametric process as it is relying on the third order susceptibility c⁽³⁾ of the material. This is in different from the well-investigated parametric processes exploiting the c⁽²⁾ non-linearity in optical materials such as crystals LiNbO₃ and KTP.

Figure 1 Schematic of a FOPA setup. An additional lightwave, the idler is created in the gain process.

Figure 1 shows a typical FOPA configuration. A pump is combined with the signal into the non-linear medium. During the amplification process photons are transferred from the pump wave to the signal wave and to an additional wave, the idler. Due to the relatively high pump powers, stimulated Brillouin scattering (SBS) suppression techniques are commonly needed for the pump wave.

The FOPA response time is limited solely by the relaxation time of the bound electrons in the material. This constant is <10 fs thus enabling ultra fast signal processing applications. It can be shown that when a specific phase condition is maintained throughout the fiber, the FOPA will offer maximum gain. Due to the phase matching condition, the FOPA does not only offer conventional incoherent or phase-insensitive gain but also the important potential of coherent or phase-sensitive parametric amplification. The phase-sensitive amplifier amplifies noise components with the same phase as the signal while attenuating components with the opposite phase. This property has demonstrated many potential signal-processing applications e.g. pulse reshaping, quantum noise suppression and for soliton communication systems: dispersive wave and soliton-soliton interaction reduction [1]. It also has the potential for amplification with 0 dB noise figure. For the phase-insensitive (PI) FOPA, one or two pump light waves with arbitrary phase(s) will interact with a signal light wave. A fourth light wave, the idler, is formed with a phase such that it satisfies the phase matching condition. As the idler adjusts its phase to the injected light waves, the PI FOPA lacks the phase-sensitive features but requirements for its implementation are substantially relaxed.

Except for the obvious feature of providing gain, an FOPA has several properties important for all-optical signal processing applications:

1. High differential gain.

2. Optional wavelength conversion.

3. Wide optical bandwidth.

4. Instantaneous gain response.

5. Operation centered at an arbitrary wavelength.

In the special case when the phase matching condition is maintained over the whole fiber length, L, the parametric gain, G, may be written in dB units as [2]

G=P_pLS-6[dB]

Here g is the fiber nonlinear parameter and S = 8.4g are the differential gain in [dB/W/km]. A typical g value for highly non-linear fiber (HNLF) is 10-15 W^-1km^-1 resulting in a differential gain between 80-130 dB/W/km. Such a steep nonlinear differential gain may advantageously be used in applications such as high power return-to-zero (RZ) pulse generation [3], O-TDM demultiplexing with inherent gain [2,4] and all-optical sampling [5]. Figure 2 (a) shows an overview of the schematics for a RZ pulse generator based on a FOPA. Due to the steep gain slope it is sufficient to use a sinusoidally modulated pump wave while still generating very narrow pulses. Figure 2 (b) shows measured results for a sinusoidally modulated 40 GHz pump wave. The left part shows the optical spectrum for the generated pulses, the upper right figure shows the generated pulses measured by a streak camera with 3.5 ps temporal resolution. The right lower figure shows the same pulses measured over long time persistence (5 min.) with a high bandwidth (45 GHz) optical photo-detector and a 50 GHz sampling oscilloscope.

Figure 2 (a) Schematic of FOPA used for RZ-pulse generation. (b) Left: measured optical spectrum. Righ top: Generated 40 GHz pulses measured with streak camera (3.5 ps resolution). Right low: Generated 40 GHz pulses measured with oscillscope (5 min. persistence).

Common for the above-mentioned applications is that they are using the FOPA as a generic building block to create new functions. Figure 3 (a) shows a schematic for an optical sampling device based on a FOPA [5]. The bandwidth of the sampling device is solely limited by the pulse width of the sampling pulses, in this case 1.6 ps (~600 GHz). The control pump pulses are now asynchronous and “scanning” over the measured pulses. The high sampling bandwidth makes it possible to observe details previously impossible to detect with a conventional electric sampling oscilloscope. Figure 3 (b, left) shows a dispersion-managed soliton sampled after 310 km propagation through a dispersion managed transmission link. Oscillations in the pulse tail show the effect of insufficient b3 compensation. The right figure shows a sampled 300 Gbit/s optical eye diagram.

Figure 3 (a) Schematic of a FOPA used as an optical sampling device. (b, left) Dispersion managed soliton measured after 310 km propagation. (b, right) 300 Gbit/s sampled eye diagram.

A key component for FOPAs operating over a wide bandwidth is the availability of HNLF. The wide operating bandwidth of FOPAs is a direct consequence of the HNLF offering a high differential gain and typically having a low dispersion slope (~0.03 ps/nm²km), thus offering good phase matching over a wide bandwidth. This feature may be used for arbitrary and transparent wavelength conversion [6, 7]. Arbitrary wavelength conversion was until recently only considered a realistic alternative in semiconductor optical amplifiers due to the inherent narrowband operation of third order parametric processes in conventional optical fibers.

One problem for single pumped FOPAs is the high gain ripple. Recent numerical and experimental results demonstrate that it is possible to achieve a flat exponential gain spectrum over a wide wavelength range by using a dual pumping scheme [8].

The fast saturation time of the FOPA gain have been demonstrated usable e.g. for all-optical limiting amplifiers [1,4,9].

Since the first fiber-based parametric amplifier experiments providing net CW gain were only conducted a few years ago [10], there is reason to believe that substantial progress may be made in the future. The further development of “holey fibers” together with new fiber materials may enhance the performance and practical implementation for these amplifiers by offering even higher non-linearities [11].

References
1. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist,” Fiber-based optical parametric amplifiers and their applications”, IEEE Journal on Sel. Top. in Quantum Electronics, vol.8, no.3 , pp. 506 -520, May/June 2002.

2. J. Hansryd and P. A. Andrekson, “O-TDM demultiplexer with 40-dB gain based on a fiber optical parametric amplifier”, IEEE Photon. Technol. Lett., vol.13, no.7 , pp. 732 -734, July 2001.

3. J. Hansryd and P. A. Andrekson, “Wavelength tunable 40GHz pulse source based on fibre optical parametric amplifier”, Electron. Lett., vol.37, no.9 , pp. 584 -585, April 2001.

4. P.-O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Fiber four-wave mixing demultiplexing with inherent parametric amplification”, J. Lightwave Technol., vol.15, no.11, pp.2051-2058, Nov. 1997.

5. J. Li, J. Hansryd, P. -O. Hedekvist, P. A. Andrekson, and S. N. Knudsen, “300 Gbit/s eye-diagram measurement by optical sampling using fiber based parametric amplification”, Optical Fiber Communication Conference 2001, vol. 4, postdeadline paper PD 31, Anaheim, USA, 2001

6. M.C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, L. G. Kazovsky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain”, J. Lightwave Technol., vol.19, no.7, pp. 977-981, July 2001.

7. M. Westlund, J. Hansryd, P. A. Andrekson, P.A., and S. N Knudsen, “Transparent wavelength conversion in fiber with 24 nm pump tuning range”, Electron. Lett., vol.38, no.2, pp. 85 –86, Jan. 2002

8. C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves”, IEEE Journal on Sel. Top. in Quantum Electronics, vol.8, no.3 pp. 538 -547, May/June 2002.

9. A. Takada and W. Imajuku, “Amplitude noise suppression using high gain phase sensitive amplifier as a limiting amplifier”, Electron. Lett., vol.32, no.7, pp. 677-679, March 1996.

10. J.Hansryd, P.A. Andrekson,. “Broadband CW pumped fiber optical parametric amplifier with 49 dB gain and wavelength conversion efficiency”, Optical Fiber Communication Conference 2002, vol. 4, postdeadline paper PD-6, Baltimore, USA, 2000

11. K. M. Kiang, K. Frampton, T. M. Monro, R. Moore, R., J. Tucknott, D.W. Hewak, D. J. Richardson, and H. N. Rutt, “Extruded singlemode non-silica glass holey optical fibres”, Electron. Lett. , vol.38, no.12 , pp.546 –547, June 2002.