Operation Principle of Proposed AM-Pilot-Tone-Based Post- Detection

A simplified system model is considered in Fig. 2.2. An optical source (denoted by its electric field s(t), representing a CW laser externally modulated by an AM pilot tone with a frequency fp) is launched into a dispersive fiber with a transfer function Hfiber( f ). Only linear dispersion effect is taken into account in this section. The signal at the end of the transmission link is coupled into a DAF, whose constructive or destructive output port has a transfer function H+( f ) or H-( f ). The received r+(t) or r-(t) after the DAF is converted to a photo-current i(t). It should be noted that the actual modulating data does not pass through DAF, only the post-detection path passes through the DAF via a tap coupler as shown in Fig. 2.1(b). The Fourier transforms of all signals are also shown in Fig. 2.2. Note that we ignore the effect of baseband modulation in our calculation because we assume any intermodulation product caused by the beating between the baseband data and the pilot tone would have amplitude much smaller than that of the pilot tone. The effect of pilot tone on data can be small [5], and is not within the scope of this Chapter.

It is well known that after a transmission link and a photo-receiver (without DAF), the magnitude of an AM pilot tone will change with the total accumulated dispersion of the optical link. This is because optical fiber dispersion causes a time delay (and thus relative phase change) between the transmitted upper- and lower-sideband AM pilot tones. Consequently, in a pre-detection scheme we can estimate the total accumulated dispersion by measuring the magnitude of the received pilot tone. The detected chromatic dispersion-dependent RF power of an AM pilot tone can be expressed as [13]

where ℜ is the responsivity, RL is the resistive load of the optical receiver, Po is the average received optical power, m is the rms modulation index of the AM pilot tone, c is the speed of light in vacuum, λ is the operating wavelength, D is the fiber dispersion parameter, and DL is the total accumulated dispersion. When the accumulated dispersion is small, the magnitude of the AM pilot tone remains almost constant, and as a result, the frequency of the pilot tone needs to be increased to improve the resolution sensitivity (ΔPAM/ΔDL, in dB/(ps/nm)). This out-of-band

pilot tone requires a higher bandwidth photo-detector, costly microwave/millimeter- wave components, and reduces the effective system spectral efficiency.

To improve the problems explained above, we use an optical DAF before a photo-detector, as shown in Figs. 2.2 and 2.3. The frequency response of the constructive port of the DAF can be written as

( ) ( )

2

) 2

( = +

= ₊ ^{Φ −}

+ j ⁺ f j e j f

e f H f

H ^πτ (2−2)

Fig. 2.4 illustrates the magnitude and phase response of the DAF at the constructive port, and the frequency spectrum of an optical carrier (fo) and its associated AM pilot tones (fo + fp and fo − fp). The free spectral range (FSR) of the DAF is 1/τ. The basic idea is to let the phase shifts between the optical carrier and the two pilot-tone sidebands be +π/2 and –π/2, respectively, so that these two sidebands have a π phase difference and therefore they could cancel each other (i.e., the received AM pilot tone amplitude is zero) when there is zero fiber dispersion. In addition, the received pilot tone power should change significantly even when only a small residual dispersion is incurred, so that a high dispersion resolution can be obtained. These goals can be achieved when two conditions are satisfied:

(1) τ = τo = 1/(2fp);

(2) The left-hand-side pilot tone, the optical carrier, and the right-hand-side pilot tone are aligned with three successive quadrature points of |H+( f )|², as shown in Fig. 2.4, which implies

4 1 -2

τ

f_o = n (2−3)

where n is an integer. The amplitudes and phases of the three frequency components in Fig. 2.4 can be verified by substituting f in (2−2) with fo +1/(2τo), fo, and fo −1/(2τo), respectively, and use the two conditions given above. As a result, the optical carrier and the two pilot tones all experience a 3 dB optical power loss.

It should be noted that in practical systems, τ may deviate away from τo, i.e., τ

= τo + δτ. This can be observed from the above two conditions that τo = 1/(2fp) and τ

= (2n-1)/(4fo) cannot be always equal for any arbitrary fo , fp and n. As a matter of fact, fo is always given, whileτ needs to be adjusted such that condition (2) is always

satisfied, but not necessarily condition (1). For example, if fo = 193.3 THz, fp = 40 GHz, we obtain τ =τo = 1/(2fp)= 12.5ps, and (2−3) is satisfied by letting n equal to 4833. But when the optical carrier frequency is changed to fo = 191.123 THz, (2−3) is satisfied by letting n equal to 4799 and τ ≈ 12.501ps, i.e., τ ≠τo in this case. We will show the effect of δτ in Fig. 2.5, Fig. 2.6, and (2−13).

The electric field of a pilot tone after passing through a dispersive fiber and a DAF can be written as

The photo-current of fp is obtained by squaring (2−4) and keeping the linear terms at the modulation frequency fp :

( ) ( )

After some mathematical manipulations, it follows that the transfer function of the cascade of a dispersive fiber and a DAF is given by

)

Consequently, the detected RF power of the AM pilot tone after a dispersive transmission link and a DAF can be expressed as

{

}

K is the transmittance of the DAF at the wavelength of the pilot-tone sidebands. Comparing (2−12) to (2−1), we see that the amplitude of the pilot-tone is now related to a sinusoidal function, rather than a cosine function, of the accumulated dispersion. Therefore, the dispersion resolution can be improved significantly around zero dispersion. Note that this sinusoidal dependence on fiber dispersion is similar to those dispersion equalization techniques which utilize PM pilot tone [6],

[11]. The main difference lies in the fact that [6] used a serial PM modulator at the transmitter, [11] used a parallel PM modulator at the transmitter, while this Chapter used an AMZI at the receiver. Therefore, the proposed method in this Chapter has the same advantages mentioned in [6], such as SPM and PMD-tolerant. In terms of complexity, the proposed method is not more complicated than those shown in [6], [11] — those papers have a complicate transmitter design with excessive power loss, while this Chapter has an extra AMZI at the receiver (note that the tapped loss can be easily compensated by an existing pre-amplifier). It is also noted that DAFs have been widely used in optical DPSK demodulation, and are commercially available with thermally tunable optical delay.

As we mentioned previously, there always will be an unavoidable delay variation δτ in practical conditions. Its effect on an AM pilot-tone RF power at different accumulated fiber dispersion DL can be examined by substituting τ fo = (2n-1)/4, τ = τo + δτ and τo = 1/(2fp) into (2−11) (i.e., condition (2) in Section 2.2 is

Based on (2−13), Fig. 2.5 shows the AM pilot-tone power as a function of the normalized delay variation δτ/τ0 at different total residual dispersion DL (0, 0.05, 0.5, 5 and 20 ps/nm), and ℜ=1, Po=0.5 mW, m=0.16, fo=193.3 THz, fp=40 GHz, RL=1. We can see that the maximum AM pilot tone power always occurs at quadrature points of the DAF power transfer function (i.e., δτ/το = 0, ±0.021%, ±0.042%, etc.) when DL≠

0, and the higher the residual dispersion DL, the higher the AM pilot tone power.

The maximum AM pilot-tone power at ±0.021%, ±0.042%, etc., can be explained as follows: As previously discussed, n = 4833 in (2−3) when τ =τo = 1/(2fp)= 12.5ps.

The two nearest quadrature points take place at n = 4832 and 4834, respectively. As a result, δτ/το = (4834-4833)/4833 or (4832-4833)/4833) = ±0.021% if fo is shifted to any of the two neighbor quadrature points. When DL=0, the residual AM pilot tone power is not completely zero except at several points such as δτ/το=0. The non-zero residual AM pilot tone power at DL=0 originates from the cos²(qfp2) term in the square root of (2−10) or (2−13).

Fig. 2.5 shows a small variation range (within ±0.1%) of δτ/το, which means το

is very closely matching 1/(2fp)(this section), or a half of the data-bit-period (Section 2.3). However, sometimes due to fabrication uncertainties of τ in AMZI, and

sometimes due to data rate changes after line coding, there may be a large variation range of δτ/το. In Fig. 2.6, the solid lines are the calculated pilot-tone power as a function of residual dispersion over a much larger variation range of δτ/το (up to 18.75%) based on (2−13). In Fig. 2.6, the frequencies of the pilot tone and optical carrier are 40 GHz and 193.3 THz, respectively; and δτ/το is set to 0% (open triangle), 6.25% (open circle), 12.5% (open diamond), and 18.75% (open square), respectively.

Fig. 2.6 also shows that the smaller δτ/το, and the smaller the residual dispersion, the higher the dispersion resolution around zero accumulated dispersion. In addition, we see that the monitoring window is ±39 ps/nm in the 40 GHz pilot tone-based systems.

This monitoring window is sufficient compared to other detection schemes [5−10].

Fig. 2.6 also shows the simulation data (in various symbols) based on VPItransmission Maker. The key simulation parameters are shown in the figure caption of Fig. 2.6. We can see that these simulation results match well with the theoretically calculated results except that there is a small discrepancy at a normalized delay variation of 0%. This because the simulation took into account the residual chirp in a transmitter MZ modulator due to its limited extinction ratio of 40 dB, while (2−13) does not consider the residual chirp. Fig. 2.6 also shows that a small monitoring error of 10 ps/nm due to SPM is incurred when the fiber launched power is increased from -3 dBm/ch to 12 dBm/ch. As mentioned previously, SPM- and PMD-induced monitoring error can be reduced by lowering the pilot tone frequency, same as the PM-pilot-tone method.

As was shown in Fig. 2.5, the maximum AM pilot tone power always occurs at the quadrature points of a DAF power transfer function when DL≠ 0. Consequently, the DAF differential delay τ should always be adjusted to let the monitored optical wavelength coincide with one of the DAF quadrature points (i.e., condition 2 (Eq.( 2−3)) in Section 2.2 is always satisfied, but not necessarily condition 1). We show in Fig. 2.3 a DAF control loop which can be used to achieve this purpose. This control loop uses a differential optical power detection method which is similar to those commonly adapted for wavelength stabilization [14]. The DC optical power detected at the constructive and destructive ports are

⎪⎭

⎪⎭ of the DAF destructive port given by

( ) ( )

The error signal used to stabilize the DAF in Fig. 2.3 is

⎥⎥

It follows that the zero-crossings of the error signal occur at

fo uses only the DC optical power of the DAF constructive and destructive ports, and is independent of the signal modulation format or data rate.

2.3 Proposed DAF Zero-Dispersion Detection without a Pilot-Tone