Apr 15, 1996 - Fiber optical parametric amplifiers (OPA's) rely not on properties of doping ions but on the third-order non- linearity of the fiber material.
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Broadband fiber optical parametric amplifiers M. E. Marhic,* N. Kagi,† T.-K. Chiang, and L. G. Kazovsky Department of Electrical Engineering, Stanford University, Stanford, California 94305 Received November 9, 1995 The bandwidth of a single-pump f iber optical parametric amplif ier is governed by the even orders of f iber dispersion at the pump wavelength. The amplif ier can exhibit gain over a wide wavelength range when operated near the f iber’s zero-dispersion wavelength. It can also be used for broadband wavelength conversion, with gain. We have experimentally obtained gain of 10 – 18 dB as the signal wavelength was tuned over a 35-nm bandwidth near 1560 nm. 1996 Optical Society of America
The recent development of doped-fiber optical amplif iers (DFA’s) has provided optical network designers with a useful tool for overcoming fiber and interconnection losses. However, because these amplif iers are based on stimulated emission by doping ions, a typical DFA operates in a wavelength range determined by the type of ion used. For example, the erbium DFA (EDFA) operates near l 1550 nm, with a 35-nm bandwidth. Raman amplifiers that are being developed for amplif ication near 1.3 mm have similar bandwidths.1 The bandwidth available for transmission through optical fibers is of the order of 300 nm, and thus DFA’s may not be adequate to handle the broad spectrum that might be used in future optical communication systems. For this reason it is important to seek other means for making broadband optical amplifiers. Fiber optical parametric amplif iers (OPA’s) rely not on properties of doping ions but on the third-order nonlinearity of the fiber material. Thus they can in principle be operated at an arbitrary center wavelength, corresponding to the zero-dispersion wavelength sl0 d of the fiber used in the OPA. Their bandwidths depend on pump power, fiber nonlinearity, and fiber dispersion; hence there are opportunities for increasing OPA bandwidth that are not available with DFA’s or Raman amplifiers. In addition, the presence of a frequency-shifted idler indicates that such devices can also be used as broadband wavelength converters, possibly exhibiting conversion efficiency greater than 1. In early experiments with fiber OPA’s the emphasis was on achieving frequency conversion with a wide but fixed spacing.2 – 4 Recently parametric gain was studied in communication fibers, as it can arise near l0 and introduce noise by amplifying the amplif ied stimulated emission generated by EDFA’s: a gain of 3.5 dB was measured in an experiment designed to study this aspect.5 Pulsed wavelength conversion by parametric amplification has been investigated, yielding a maximum gain of 5 dB and a 25-nm bandwidth.6 Cw wavelength conversion by parametric amplif ication has been demonstrated, with a conversion eff iciency of 24.6 dB (Ref. 7); the bandwidth was not reported. Recently we obtained gain of as much as 12 dB with a pump power of 180 mW over a 20-nm bandwidth near l0 .8 0146-9592/96/080573-03$10.00/0
In this Letter we explore the potential of single-pump fiber OPA’s to provide broadband optical amplif ication and wavelength conversion. We show that the bandwidth depends only on the even orders of fiber dispersion at the pump wavelength and can reach tens of nanometers for operation near l0 . Consider a strong pump field Ep szd and a smallsignal field Es szd, with respective radian frequencies vp and vs , copropagating in the z direction in a lossless fiber with nonlinear coefficient g (we assume that g . 0, as is the case for silica fibers). Smallsignal theory reveals the existence of parametric gain, which amplif ies the signal, as well as an idler field Ei szd arising at vi 2vp 2 vs .9 Amplif ication can be studied by means of the signal power gain, given by " #2 jEs sLdj2 gP0 11 (1) Gs sLd sinhs gLd . jEs s0dj2 g The parametric gain g is given by9 g2 2DbsDby4 1 gP0 d ,
(2)
and P0 is the pump power. Db is the linear wavevector mismatch determined by the waveguide characteristics, i.e., Db bs 1 bi 2 2bp , where bs , bi , and bp are the respective propagation constants of the signal, the idler, and the pump. Equations (1) and (2) are valid when the pump is not depleted by the nonlinear process, i.e., when the signal is small compared with the pump. The idler conversion efficiency is Gi sLd Gs sLd 2 1. When gL ¿ 1, Gs sLd and Gi sLd are both large and are nearly equal. As a first approximation the gain bandwidth corresponds to g real, which implies that 24gP0 # Db # 0. The gain bandwidth measured in terms of Db is thus of the order of 4gP0 . This shows that the larger P0 , g, or both, the larger is the range of tolerable values of Db, which in turn indicates that a larger frequency difference between the pump and the signal can be tolerated. What the bandwidth is in terms of frequency is determined by the fiber dispersion characteristics. By expanding b in power series near vp , we can put Db in the form ` X b2m (3) Db 2 svs 2 vp d2m , s2md ! m1 where b2m denotes the s2mdth derivative of b at vp . This shows that Db is only a function of u 1996 Optical Society of America
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OPTICS LETTERS / Vol. 21, No. 8 / April 15, 1996
svs 2 vp d2 ; together with Eq. (1) this implies that the gain spectrum s g versus vs d is always symmetric with respect to vp . Also, Eq. (3) shows that the odd dispersion orders play no role in determining the gain spectrum; only the even dispersion orders affect the gain spectrum. This implies that the type of fiber needed to optimize fiber OPA bandwidth is not necessarily the same as the type of fiber needed to reduce linear pulse spreading that is due to dispersion: that is because odd orders of dispersion affect pulse spreading but not fiber OPA bandwidth. One could in principle obtain linear phase matching sDb 0d for all vs if bsvs d had only odd derivatives at vp , i.e., if its graph were symmetric about the point fvp , bsvp dg. This is probably impossible to realize in practice, and thus other ways must be sought to maximize bandwidth. First we consider what happens if Db is dominated in the gain region by the 2mth-order term in Eq. (3). If b2m , 0, gain s g2 . 0d will be available for vs within Dv2m of vp , with #1/2m " 2s2md !gP0 . (4) Dv2m 2 b2m We def ine Dv2m as the bandwidth of the OPA for this case. A natural choice for achieving large bandwidth is to place vp at or near v0 , for which b2 0. We can then distinguish three possibilities: (i) vp precisely at v0 . Then the leading term in Eq. (3) is proportional to b4 . Assuming that it dominates Db, the bandwidth is Dv4 obtained from Eq. (4). (ii) vp close enough to v0 that both second- and fourth-order dispersion must be considered. Then b2 does not vanish, but its sign and magnitude can be chosen to add to or substract from the fourthorder term, thereby possibly allowing for bandwidth optimization. Keeping now only the m 1 and m 2 terms in Eq. (3), we see that Db has a quadratic dependence on u. For b4 , 0, no improvement is possible over Dv4 , because if b2 , 0 the magnitude of Db is larger, and thus g 0 is reached for a smaller u than in possibility (i); if b2 . 0, Db . 0 for small u, which we want to avoid. For b4 . 0, however, the situation is different: If b2 , 0, Db vanishes not only at u 0 but also at umax 212b2 yb4 , and Db is minimum at umax y2. If we require that this minimum be equal to 24gP0 (to have g 0), we can solve for b2 and umax . The bandwidth, which we denote in this case by Dv2, 4 , is given by √ !1/4 p 3gP0 . Dv2, 4 2 2 (5) b4 In this particular case g2 can be expressed in terms of an eighth-order Chebyshev polynomial in svs 2 vp d. (iii) vp far enough from v0 that bandwidth is determined primarily by second-order dispersion. The bandwidth is then given by Dv2 obtained from Eq. (4). We can obtain cases (i)–(iii) in the same fiber by tuning vp near v0 . As an example of case (i), consider a fiber operated near the zero-dispersion wavelength, l0
2pcyv0 1.55 mm, with b4 24.93 3 10255 m21 s4 (the value for bulk silica at this wavelength, obtained from Sellmeier’s equation9). We assume that gP0 3 3 1022 m 21 , which can be achieved with a power of ,15 W in typical silica fibers. Calculating Dv4 , and translating it into wavelength units, we obtain a bandwidth of the order of 52 nm. For a fiber with the opposite value for b4 [case (ii)] one could in principle boost this to 73 nm by optimizing b2 . These numbers are quite respectable and indicate that fiber OPA’s indeed offer good prospects for making wideband optical amplifiers. Figure 1 shows theoretical gain spectra corresponding to different values of lp 2 l0 . We have performed experiments to test the practical feasibility of obtaining such large bandwidths (Fig. 2). Inasmuch as the parametric amplif ier needs high pump power, a pulsed power source was used in our experiments. A DFB laser diode was driven with a train of 20-ns square pulses with a duty cycle of 1y1024. The laser output was amplified by an EDFA and used as a pump. A tunable external-cavity laser diode (ECL; Fig. 2) was used as a signal light source. Pump and signal were combined by a fiber coupler and amplif ied together by a second EDFA. The pump and signal wavelengths were monitored by an optical spectrum analyzer (OSA). The intensity of the signal light was modulated at 400 MHz to permit measurements. A variable optical attenuator (ATT) was used to adjust the signal power. The pump and the signal were launched into the OPA medium, a dispersionshifted fiber (DSF) of length L 200 m. The DSF had l0 1539.3 nm, attenuation constant a 0.23 dBykm,
Fig. 1. Theoretical gain spectra corresponding to the following values: g 2 3 1023 m21 W21 , P0 7 W, L 200 m, b3 1.2 3 10240 s3 m21 , b4 2.5 3 10255 s4 m21 . The labels on the curves are the values of lp 2 l0 .
Fig. 2. Experimental setup. DFB LD, distributed-feedback laser diode.
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In summary, we have shown that the bandwidths of fiber optic parametric optical amplif iers depend only on the even orders of fiber dispersion and that bandwidths of tens of nanometers can readily be obtained by operation near the zero-dispersion wavelength, and we have verif ied these predictions experimentally. Such devices could find applications as broadband amplifiers or alternatively as broadband wavelength converters with high conversion eff iciency.
Fig. 3. Experimental gain spectra. Symbols represent experimental results; curves correspond to theoretically predicted spectra. The input signal power is 212 dBm in both cases.
b4 2.5 3 10255 s4 m21 , and b3 1.2 3 10240 s3 m21 [b3 is used to calculate b2 b3 svp 2 v0 d]. The peak pump power launched into the DSF was 7 W. We conf irmed that stimulated Brillouin scattering in the DSF was negligible by measuring the transmitted and ref lected pump powers. At the end of the DSF a tunable optical bandpass filter (OBPF) was used to select the signal frequency and reject the pump. The output from the filter was detected by an optic-toelectronic converter sOyEd and sent to an oscilloscope. No optical isolator was needed because the parametric gain is unidirectional. We measured the parametric gain in the DSF by monitoring the 400-MHz component of the output signal. The polarization of the signal was adjusted with a polarization controller (PC) to yield the maximum gain. Figure 3 shows our experimental results; the corresponding theoretical gain curves are also shown. The measurements were performed over a wavelength range of the order of 35 nm, limited by the gain bandwidth of the EDFA’s used in the experimental setup. Thus, even in this preliminary experiment, the fiber OPA exhibits a bandwidth greater than that of EDFA’s. The experimental results are in good agreement with theoretical predictions.
This research was supported in part by the U.S. Off ice of Naval Research through grant 4148130-01 and by the National Science Foundation through grant ECS-94175 95. That of T.-K. Chiang was partially supported by a graduate fellowship from Hitachi Ltd. *Permanent address, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois 60208, the address for any correspondence. †Permanent address, General Planning Department, Research & Development Division, Furukawa Electric Ltd., 2-6-1 Marunouchi, Chiyoda-ku, Tokyo, 100, Japan. References 1. S. G. Grubb, presented at the Sixth Topical Meeting on Optical Amplifiers and Their Applications, Davos, Switzerland, June 15 –17, 1995. 2. K. Washio, K. Inoue, and S. Kishida, Electron. Lett. 16, 658 (1980). 3. M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, Appl. Phys. Lett. 41, 1111 (1982). 4. J. P. Pocholle, J. Raffy, M. Papuchon, and E. Desurvire, Opt. Eng. 24, 600 (1985). 5. N. Henmi, Y. Aoki, T. Ogata, T. Saito, and S. Nakaya, J. Lightwave Technol. 11, 1615 (1993). 6. T. Morioka, S. Kawanishi, and M. Saruwatari, Electron. Lett. 30, 884 (1994). 7. S. Watanabe and T. Chikama, Electron. Lett. 30, 163 (1994). 8. N. Kagi, T.-K. Chiang, M. E. Marhic, and L. G. Kazovsky, presented at the Sixth Topical Meeting on Optical Amplifiers and Their Applications, Davos, Switzerland, June 15 –17, 1995. 9. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
