Microwave optical links (MOLs), which generate, transport, and process microwave signals in the optical domain, have found various applications in radar, electronic warfare, radio-over-fiber systems, and satellite communication [1, 2]. The transmission of a microwave signal over an MOL can be used to distribute a reference frequency; therefore, the spectral purity of the transmitted signal is of great importance. However, the MOL contributes residual phase noise (RPN) to the reference signal [2-5], and the phase noise of the reference signal could be worsened if the RPN is too close to the signal-phase-noise floor. In general, external modulation offers advantages over direct laser-diode modulation, mainly in terms of bandwidth and linearity range [1, 2], and the intensity modulation direct-detection (IMDD) format with an external Mach–Zehnder modulator (MZM) is arguably the most prevalent architecture presently in use, but this approach leaves the noise induced by the laser’s relative intensity noise (RIN) as an outstanding source of system performance degradation.

As a key component in the IMDD link, the photodetector (PD) could contribute its RPN to the phase noise of the reference signal. Two of the main sources of noise in the photodetection of optical carrier are the conversion of laser RIN into electronic phase noise, and the fundamental shot noise. Shot noise is related to the randomness of the incident photon stream [8, 9], while at higher powers another power-dependent effect, AM-PM conversion, is observed to adversely affect the transition from optical to microwave within the PD [5-12]. That is, the RIN could contribute to the phase noise of the reference signal through such AM-PM conversion, because it produces a change in the RF phase, since the propagation speed of the RF signal (or the PD microwave refractive index) depends on the number of carriers in the semiconductor [5-7]. In the past few years, RIN-induced phase noise in the PD has been studied by defining an AM-PM coefficient as the induced phase variation arising from power fluctuation [3-7]. However, the existing literature has focused on techniques of measuring the AM-PM coefficient for predicting the RIN-induced phase noise; direct, precise measurements of RIN-induced phase noise have not been deeply studied.

In this paper, we propose a new method based on cross-correlation to measure RIN-induced phase noise in an IMDD link. We measure the RIN-induced phase noise in a high-speed PD with different levels of incident optical power, and the results are verified by theory.

The baseband laser RIN can be up-converted to micro-wave phase noise via nonlinearities in the PD. For low RIN levels, the predicted RIN-induced phase noise (in decibels) is given by [5, 6]

where S_RIN(f) is the single sideband (SSB) phase noise spectral density (dBc/Hz) at the RF offset frequency f; RIN(f) is the spectral density of the RIN; P_opt is the laser’s average optical power; and dϕ/dP_opt is the RF phase-to-optical power slope. Thus the AM-PM coefficient (in decibels) of the PD is defined as

Our proposed system for measuring the RIN-induced phase noise, is schematically illustrated in Fig. 1. It is a cross-correlation installation that has two duplicate channels, each of which is constructed as an interferometer with a double-balanced mixer biased at quadrature [13]. The micro-wave signal provided by a reference source is split into four parts; two of them go into the RF input ports of MZM₁ and MZM₂, while the other two provide the additional quadrature signals to drive the mixers. This arrangement ensures that the RIN-induced phase noises are correlated in both channels, while the intrinsic noises generated by the MZMs, PDs, amplifiers, and mixers remain uncorrelated. Finally, the power spectra at the output ports of the mixers, followed by low-pass filters (LPFs), are measured by a two-channel fast Fourier transform (FFT) correlation analyzer.

The microwave source is expressed as

where ω_m and ϕ_m are respectively the angular frequency and phase fluctuation of the microwave source. Then the output of the MZM_i (_i=1, 2) is

where E_o, ω_o, ϕ_o, and n_RIN are respectively the optical intensity, optical frequency, optical phase fluctuation, and relative intensity noise of the laser; ϕ_dc = πV_b/V_π is the DC-bias angle of the MZM, V_b is the DC-bias voltage, V_π is the half-wave voltage, and β = πV_m/V_π is the modulation index at the microwave carrier frequency; and ϕⁱ_MZM is the RPN of MZM_i. Considering only the fundamental products, the output of PD_i is

where A_i is a compound amplitude, ϕ_RIN (t)=α·n_RIN(t) is the RIN-induced phase fluctuation with respect to the LD, α is the AM-PM coefficient of the PD, and ϕⁱ_PD is the RPN of PD_i. If we assume that the two arms of the interferometer are of equal delay, the output of M_i can be expressed as

where kⁱ_ϕ is the phase-to-voltage gain of M_i (which can be determined experimentally), and ϕⁱ_Amp and ϕⁱ_mixer are the RPN of the amplifier and mixer in the i^th channel respectively. Then the cross-spectrum S₁₂(f ) can be obtained by [13]

where V_IF, ₁(f ) and V_IF, ₂(f ) are the Fourier transforms of V_IF, ₁(t) and V_IF,₂(t). In general, FFT analyzers (such as the Agilent 35670A) make use of (7) by replacing the true Fourier transforms with the FFTs of V_IF,₁(t) and V_IF, ₂(t), simultaneously sampled and averaged over N acquisitions. Thus, when dealing with discrete samples, after some lengthy manipulations (7) becomes

where T is the truncation time of one measurement, Φ_RIN is the FFT of ϕ_RIN, Φ_i (i=1, 2) is the FFT of [ϕⁱ_PD(t) +ϕⁱ_Amp(t) + ϕⁱ_mixer (t) + ϕⁱ_MZM(t)], and O(·) means “order of.” Owing to statistical independence, the cross terms decrease proportionally to . Eq. (8) indicates that the cross-correlation process can suppress the uncorrelated phase noise in each channel, while S_RIN (f ), the RIN induced phase noise, is sustained. By averaging N times, the uncorrelated phase noise can be suppressed by a factor of , in theory [13].

In the experiment, the measurement system was constructed according to Fig. 1. A microwave source at 10 GHz was used as the reference. The MOLs consisted of a 1550-nm laser, two independent MZMs, and two independent, high-optical-power-handling PDs (Discovery DSC40S). To achieve a low phase-noise floor, several low-phase-noise amplifiers (HMC606, −150 dBc/Hz at 1 kHz offset and −160 dBc/Hz at 10 kHz offset) were employed. A two-channel FFT correlation analyzer (Agilent 35670A) was used to perform power-spectrum and cross-correlation analysis. The cross-correlated noise floor for 6000 averaged trials of the measurement system is shown in Fig. 2. As we can see, the cross-correlated noise floor is significantly lower than the noise floors for the single channels: approximately 15 dB lower at 1 kHz offset, and 19 dB lower beyond 10 kHz. Therefore, the uncorrelated noise suppression beyond 10 kHz was consistent with the theoretical prediction (5logN = 19 dB, N = 6000), because the RPN spectrum was flat in this frequency range, where the independent channel noises are uncorrelated (white). The smaller noise suppression in the lower frequency range may be explained by the correlation between the low-frequency noises of the two channels. By further increasing the average times, we observed little further reduction in the phase noise level, because the number of averaged spectra sets a statistical limit to the measurement [13].

Figure 3 shows the experimental results for RIN-induced phase noise when the input optical power of the PD was changed from 5 to 30 mW. At low power levels, with increasing optical power the phase noise becomes lower. The phase noise for 18 mW of optical power is about 20 dB lower than that for 5mW, which is about −162 dBc/Hz at 10 kHz offset. However, the phase noise increases when the optical power continues to increase: The phase noise for 30mW of optical power is about 10 dB higher than for 18 mW, which is about −152 dBc/Hz at 10 kHz offset. This phenomenon can be explained by Figs. 4(a) and (b), which illustrate the power and relative phase of the RF signal at the output of the PD, as a function of the RF-modulated optical power at the input of the PD. At low input optical power, the RF power and RF relative phase both increase with input power, but as the input power approaches the PD saturation power, the slopes of the curves both decrease and reach zero at the saturation power, which is about 17-18 mW. As can be seen from eq. (1) and (2), zero slope indicates that the contribution of RIN-induced phase noise is small or zero at the PD, so the RIN-induced phase noise is related to the nonlinearity of the PD, and the best phase noise performance occurs at the saturation point. Thus the experimental results for RIN-induced phase noise using our proposed measurement system are consistent with theory.

In this paper, we present a novel approach for directly measuring a laser’s RIN-induced phase noise in a PD, using a cross-correlation-based method. This method can effectively suppress the RPN of other components in the MOL, which is the uncorrelated phase noise during measurement. By averaging 6000 trials, the uncorrelated phase noise beyond the 10-kHz frequency offset was suppressed by 19 dB, which is consistent with the theoretical prediction. Then the RIN-induced phase noise for different levels of incident optical power was measured, the results showing that minimum AM-PM conversion rate appears at the saturation point of the PD, and that the best RIN-induced phase-noise performance in the measurement is about -162 dBc/Hz at 10 kHz offset. The oversaturated state of the PD may worsen the phase noise, because AM-PM conversion will continue, in part due to saturation and other nonlinearities in the strongly driven PD. This suggests that the proposed method can give a quantitative measure of this kind of up-converted phase noise, and is helpful for designing high-performance microwave photonic systems.