Noise properties of nonlinear semiconductor optical amplifiers

November 15, 1996 / Vol. 21, No. 22 / OPTICS LETTERS

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Noise properties of nonlinear semiconductor optical amplifiers M. Shtaif and G. Eisenstein Department of Electrical Engineering, Barbara and Norman Seiden Advanced Optoelectronics Center, Technion, Haifa 32000 Israel Received August 9, 1996 We demonstrate experimentally and describe analytically two important noise contributions in saturated semiconductor optical amplif iers. The f irst is spontaneous emission power enhancement that is due to the increased and spatially dependent inversion factor. The second is caused by a nonlinear interaction between the saturating signal and the amplif ier noise that, in the optical domain, causes a distinct modification of the noise spectrum over a narrow bandwidth. This modification manifests itself as a noise power decrease in the detected electronic domain.  1996 Optical Society of America

In this Letter we address noise properties of semiconductor optical amplifiers operating in a nonlinear regime, such as the amplif iers intended to be used in all-optical signal-processing applications.1,2 These applications often require deeply saturated amplifiers of which a rigorous quantum mechanical noise analysis is complicated.3 Fortunately, most practical situations involve signals that consist of very large photon numbers, so that the noise problem can be properly described by means of classical electric fields.4 It is well known that a classical description of linear amplifiers yields output electric fields that contain an additive complex white Gaussian noise whose power density spectrum (PDS) equals hv ¯ 0 nsp sG 2 1d, with G being the amplif ier gain and nsp ­ NysN 2 N0 d the inversion factor.5 The carrier density is N , and N0 is its value at transparency. In saturated travelingwave amplif iers, however, this simple formalism does not hold for two main reasons. First, the carrier density, gain coefficient, and inversion factor are all location dependent,6,7 and second, the signal and the amplified spontaneous emission (ASE) noise interact nonlinearly as they propagate along the amplifier, and that interaction correlates different spectral components of the noise so that it can no longer be white.7 Recently, we presented a theoretical analysis, based on classical fields, of noise at the output of a saturated semiconductor optical amplifier.7 In that analysis the amplifier is treated as consisting of inf initesimally short slices of length dz, each of which behaves as a linear amplifier of gain expf gszddzg, with gszd being the local gain coeff icient. Each segment therefore emits white Gaussian noise with a PDS given ¯ 0 nsp gszddz, where by hv ¯ 0 nsp hexpf gszddzg 2 1j ø hv v0 is the optical frequency of the input signal. This simple expression does not represent accurately the noise generated in the part closest to the output facet of a deeply saturated amplifier. It turns out, however, that the contribution of the deeply saturated section to the overall noise is always small because most of the output noise is due to ASE that is generated in the unsaturated sections of the amplif ier (near the input facet) and is amplified while propagating along the amplif ier. For large signal intensities and signal-to-noise ratios, and neglecting linear losses in the amplif ier, we analyzed the nonlinear signal–noise interaction to the first order in the noise amplitude 0146-9592/96/221851-03$10.00/0

and derived analytical expressions for the output PDS of the signal in the optical domain and of the electronically detected signal.7 The noise spectrum in the optical domain has the form SdE s f d ­ GsSM1 1 Se0 d 1

1 1 a2 GjAs f dj2 2

3 fsSM1 1 Se0 dsG 2 1d2 2 2SM1 M2 sG 2 1d 1 SM2 g 2 GjAs f dj2

1 1 GP0 1 2paft P0

3 fsSM1 1 Se0 dsG 2 1d 2 SM1 M2 g .

(1)

SdE s f d contains the contributions of the wideband spontaneous noise, including its enhancement owing to the spatial dependence of nsp , as well as the nonlinear signal –noise interaction. The PDS of the electronically detected signal was also derived in Ref. 7 and takes the form ∑ 2 2 SjEj s f d ­ 2P0 Psat G j1 2 sG 2 1dAs f dj2 sSM1 1 Se0 d ∏ 1 1 P0 1 jAs f dj2 SM2 1 2 jAs f dj2 SM1 M2 . P0 (2) In Eq. (1) f is the frequency detuning from the optical frequency of the injected signal, and in Eq. (2) it is the electronic frequency. The term P0 is the input power normalized to Psat ­ Aeff hv ¯ 0 yGat, with Aeff being the effective waveguide cross-section area, a the differential gain, G the conf inement factor, and v0 the optical frequency of the detected signal. The carrier lifetime is t, and a is the linewidth enhancement factor. The other parameters are def ined as follows: ∑ ∏ aN0 1 g0 aN0 P0 21 ¯ 0 s1 2 G d 1 LnsGd , SM1 ­ hv g0 g0 (3) SM2 ­ hv ¯ 0

∑

aN0 1 g0 aN0 P0 sG 2 G 21 d 1 g0 2g0

∏

3 f2LnsGd 1 G 2 1g 2 2fLnsGd 1 aN0 Lg , 2

(4)  1996 Optical Society of America

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OPTICS LETTERS / Vol. 21, No. 22 / November 15, 1996

∑ µ ∂ aN0 P0 SM1 M2 ­ hv ¯ 0 LnsGd 1 1 g0

As f d ­

∏ aN0 1 g0 21 2 s1 2 G d 1 aN0 L , g0

(5)

P0 , 1 1 GP0 2 i2pf t

(6)

where g0 denotes the small-signal gain coeff icient. The term Se0 s f d represents the PDS of the noise carried by the injected signal. This term was introduced to make the formalism general. Finally, for negligible input noise, the output ASE power at a given optical bandwidth B that is not centered at or near the frequency of the injected signal is PASE ­ BGSM1 . Figure 1(a) shows the calculated optical PDS for several normalized input intensities in the spectral vicinity of the saturating signal. The spectrum is generally asymmetric owing to the Bogatov asymmetry in four-wave mixing transmittivity functions.8 The amplitude of the PDS peaks within a bandwidth that depends on the degree of saturation and is of the order of one to a few gigahertz. For large detunings, the PDS function approaches the value of the wideband noise level. Figure 1(b) shows the calculated electronic PDS, SjEj2 s f d, for several normalized input intensities. The nonlinear interaction manifests itself as a dip in the (electronic) PDS function. Both the depth and the spectral width of this dip depend on the injected optical powers. The depth increases with injected optical power until the gain is saturated ,10 dB, regardless of the small-signal gain value. The bandwidth of the dip increases monotonically with the injected optical power, and it is of the order of s1 1 GP0 dy2pt, as can be seen from Eq. (6). This spectral dip results from the same nonlinear interaction that is responsible for the peak observed in the optical domain PDS, Fig. 1(a). Experimental confirmation of the noise properties was obtained with the experimental setup shown in Fig. 2. A high-power solid-state laser oscillating at 1540 nm with a 10-kHz linewidth and a relative intensity noise of 2174 dByHz served as one of the input sources, and the second source was a standard distributed feedback laser. The 21550-nm amplifier under test had a small-signal gain of 23 dB, a 23-dB output saturation power of 8 mW, and very low mirror ref lectivities (below 0.01%). The amplifier output was filtered by a 1-nm-wide filter and coupled to a p-i-n detector, followed by low-noise AC-coupled electronic amplifiers that fed a rf spectrum analyzer. Power density spectra in the range 0.5–2 GHz measured with the low noise laser serving as a single saturating signal are shown in Fig. 3. The corresponding theoretical predictions are shown by the dashed curve. We obtained the spectra in Fig. 3 by normalizing the measured output by the transmission function of the detection system and then subtracted the electronic noise f loor. The noise of the injected laser (without amplif ication) was measured separately and was also subtracted from the measured result. The source laser contribution was negligible except for

the cases when the amplif ier was deeply saturated. The curves in Fig. 3 are labeled according to the degree of gain compression, where 0 dB means no saturation. At the low saturation level, the output noise spectrum is completely f lat. At high input powers, when the gain is compressed (DG ­ 21 and DG ­ 23 dB in the examples shown) the PDS becomes frequency dependent, and it increases with frequency as predicted by theory. For the largest saturation level shown, DG ­ 216 dB, the measured (and the predicted ) noise increases with moderate frequency. We note that in the case of deep saturation, the measured spectrum deviates somewhat from the theoretical prediction. The next result that we present (for which the lownoise laser served again as the only source) is depicted in Fig. 4(a). We compare measured dependencies on the injected optical power of the gain, the output intensity noise normalized to the output signal power (measured this time in a spectral window of 100 MHz centered at 600 MHz), and the ASE power measured in the presence of a saturating op-

Fig. 1. (a) Calculated PDS of (a) the output signal in the optical domain and (b) the electronically detected signal. The amplifier small-signal gain in the calculations is 23 dB; a ­ 5, t ­ 400 ps.

Fig. 2. Experimental setup: Pol, polarizer, ATT, variable attenuator; P’s, powermeters; BS, beam splitter; SOA, semiconductor optical amplifier.

Fig. 3. Electronically measured PDS in the range of 0.5– 2 GHz for several levels of gain saturation. The theoretical prediction is described by the dashed curve.

November 15, 1996 / Vol. 21, No. 22 / OPTICS LETTERS

Fig. 4. Gain, output ASE power, and noise PDS of a saturating signal normalized to its output power. (a) theory, ( b) experiment.

Fig. 5. Measurements of the ASE power and the normalized PDS of a weak signal in the presence of an intense, saturating field. The PDS is normalized to the signal output power.

tical signal. The ASE power was measured in an optical spectral window of 1-nm bandwidth centered 5 nm away from the injected signal wavelength. The ASE power measurement required careful optical filtering for complete rejection of the amplified signal. The filters that we used permitted a rejection of more than 70 dB. The curves describing the gain and the ASE power overlap perfectly at low levels of saturation, whereas at deep saturation they deviate, and the reduction of gain with input power is more rapid. This results from the fact that the inversion factor depends on the input power and increases along the amplif ier. Examination of the normalized signal spontaneous beat-noise curve shows that it experiences the onset of saturation at much lower input intensities than the gain and the ASE power. This is the result of the nonlinear interaction between the signal and the spontaneous emission as they propagate in the amplifier. The depth of the low-frequency dip in the PDS of the detected signal [Fig. 1(b)] is a function of the injected power. Once this dip is created, the low-frequency portion of the intensity noise decreases much faster than the high-frequency portion. That high-frequency noise, when normalized to P0 G, is proportional to the ASE power [see Eq. (2)].

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Figure 4(b) shows the theoretical calculations that correspond to these experiments and shows generally excellent agreement. We note, however, that the experimental saturation curve is steeper than predicted, probably owing to effects related to scattering waveguide losses, which were neglected in the theoretical analysis. In the final experiment we used two input laser sources, injected simultaneously into the amplifier. The output of a distributed feedback laser was amplif ied by an erbium-doped fiber amplifier and served to saturate the semiconductor optical amplif ier. The low-noise laser, that served here as a probe was attenuated to a level less than 10 dB below the saturating signal. The two sources were detuned by 5 nm, and the noise of the signal at the probe wavelength was measured in the presence of the saturating signal after it was optically filtered. Figure 5 shows the measured intensity noise normalized to the amplified probe power. This noise contribution was also measured in a 100-MHz bandwidth centered at 600 MHz. In the figure the dashed curve shows the output ASE power. It is obvious that the intensity dependence of the normalized noise power is similar to that of the ASE, and there is no nonlinear noise enhancement. This is because the strong nonlinear interaction owing to the saturating signal takes place at a widely detuned wavelength, and a second nonlinear contribution owing to the probe signal’s interacting with the noise is negligibly small because the probe is much weaker than the saturating field. The authors thank Curtis R. Menyuk of the University of Maryland for stimulating discussions. This study was partially supported by Israeli Academy of Sciences grant no. 050-831. References 1. B. Glance, J. M. Wiesenfeld, U. Koren, A. H. Gnauck, H. M. Presby, and A. Jourdan, Electron. Lett. 28, 1714 (1992). 2. R. Schnabel, W. Pieper, M. Ehrhardt, M. Eiselt, and H. G. Weber, Electron. Lett. 29, 2047 (1993). 3. E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, New York, 1994), Chap. 2. 4. J. C. Simone, J. Opt. Commun. 4, 51 (1983). 5. T. Mukai and Y. Yamamoto, IEEE J. Quantum Electron. QE-18, 564 (1982). 6. A. D’Ottavi, E. Iannone, A. Mecozzi, S. Scotti, P. Spano, R. Dall’Ara, J. Eckner, and G. Guekos, IEEE Photon. Technol. Lett. 7, 357 (1995). 7. M. Shtaif and G. Eisenstein, IEEE J. Quantum Electron. 32, 1801. 8. A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, IEEE J. Quantum Electron. QE-11, 510 (1975).