Generalized model of optical single sideband generation using dual modulation of DML and EAM

Tianwai Bo; Hoon Kim

doi:10.1364/OE.403326

1. Introduction

Optical single sideband (SSB) modulation technique provides an effective way to solve the dispersion-induced RF power fading problem in direct-detection systems. It also doubles the spectral efficiency with respect to the double-sideband (DSB) modulation. Thus, this technique is widely used in radio-over-fiber (RoF) systems and high-speed (e.g., 100 Gb/s) transmissions [1–8].

A common way to generate optical SSB signal is to utilize an in-phase/quadrature modulator or a dual-drive Mach-Zehnder modulator [3–8]. By driving these modulators using a Hilbert transform pair of signal, we can generate an optical SSB signal over a wide range of frequency. Another way to generate the optical SSB signal is to utilize narrow optical filtering [9]. An optical DSB signal can be converted into an SSB signal by filtering out one of its sidebands. However, these schemes suffer from two or more of the following drawbacks: the high insertion loss of the modulator and filter (which, in turn, might require an optical amplifier in the system); high implementation complexity and cost; vestigial sideband due to the finite steepness of optical filter’s skirt; precise wavelength alignment between the DSB signal and optical filter.

The dual modulation of directly modulated laser (DML) and electro-absorption modulator (EAM) was proposed to generate optical SSB signals [10]. In this dual modulation scheme, the DML not only produces the carrier light, but also serves as a phase modulator due to this chirp characteristics. The EAM then imposes the intensity modulation (IM) onto the DML’s output. The major strength of this scheme is that it can be implemented into a monolithically integrated semiconductor device in a highly cost-effective manner. Also, it is capable of producing an optical SSB signal having a relatively high output power. The dual modulation scheme was first demonstrated experimentally for a narrow-band RoF signal, and it was later verified to be effective in synthesizing multi-carrier orthogonal frequency-division multiplexed (OFDM) signals as well as single-carrier baseband signals [10–13]. A prototype of integrated DML and EAM was also developed for the transmission of 10-Gb/s optical SSB OFDM signal [12]. We anticipate that this integrated device can be fabricated as cost-effectively as an electro-absorption modulated laser (EML) since the only difference between the two devices is the direct modulation of laser. The dual modulation scheme can also be used to compensate for the dispersion-induced waveform distortions in baseband transmission [14,15]. The manipulation of the amplitude and phase of light signal in the dual modulation scheme enables us to tailor the electric field such that the electronic pre-compensation can be realized at the transmitter.

Despite these accomplishments, there is no workable theory about the modulation conditions for optical SSB generation using the dual modulation scheme. Although a couple of theoretical models were reported for the dual modulation scheme, they were developed under unrealistic assumptions: the IM of DML is negligible and/or the chirp of EAM is ignored [10,13]. Thus, the optical sideband suppression ratio (OSSR), defined as the optical power ratio between the upper and lower sidebands, is surprisingly limited when we generate the optical SSB signal using these previous models, which will be shown in this paper. To our knowledge, the only practicable way of finding the modulation conditions for optical SSB generation relies on the brute-force search of the amplitudes and phases of a sinusoidal tone fed to the DML and EAM, while sweeping the tone frequency.

In this paper, we develop a generalized model of optical SSB generation for the dual modulation scheme. We first derive closed-form expressions about the modulation conditions for optical SSB generation, taking into account both the IM of DML and non-zero chirp of EAM. We then show that the previously existing models fall into the special cases of our generalized model. The validity of our model is evaluated through numerical simulations and experiments. The results show that the chirp of EAM plays an important role in the estimation of modulation conditions for optical SSB generation. We also show that the OSSR performance could be limited when we utilize the modulation conditions derived from the previously existing models. For example, we successfully generate through experiment a 1-GHz SSB signal having an OSSR higher than 40 dB using our generalized model, but the ratios are measured to be <15 dB when the previously existing models are utilized. Our generalized model estimates the modulation conditions for optical SSB generation accurately over wide ranges of modulation frequency and EAM’s chirp.

2. Generalized model of dual modulation scheme

2.1 Phase response of DML

The direct current modulation of laser always accompanies the frequency modulation. The instantaneous frequency shift of the DML is related to its output power, P(t), and is given by [16]

(1)$$\Delta f = \frac{{{\alpha _{DML}}}}{{4\pi }}\left[ {\frac{d}{{dt}}\ln P(t )+ \kappa P(t )} \right]$$

where α_DML and κ are the linewidth enhancement factor and the adiabatic chirp parameter of the DML, respectively. We assume that a small sinusoidal signal having an angular frequency of ω_m is used to modulate the current of the DML. Then, the electric field of DML’s output can be expressed as

(2)$${E_{DML}}(t )= \sqrt {{P_0}\{{1 + {m_{DML}}({\cos {\omega_m}t} )} \}} \textrm{exp} \{{j\varphi (t )} \}$$

where P₀ denotes the average optical intensity and m_DML is the IM index. Also, φ(t) is the optical phase of the DML’s output, which is given by

(3)$$\varphi (t )= 2\pi \int {\Delta f(t )dt}$$

Using (1), we can approximate the optical phase to

(4)$$\begin{aligned}\varphi (t ) &\approx \frac{{{\alpha _{DML}}{m_{DML}}}}{2}\sqrt {1 + {{\left( {\frac{{\kappa {P_0}}}{{{\omega_m}}}} \right)}^2}} \cos \left( {{\omega_m}t - {{\tan }^{ - 1}}\frac{{\kappa {P_0}}}{{{\omega_m}}}} \right) + \frac{{{\alpha _{DML}}\kappa {P_0}t}}{2} + C \\ &= {m_{PM}}\cos ({{\omega_m}t + {\Phi _{PM}}} )+ \frac{{{\alpha _{DML}}\kappa {P_0}t}}{2} + C \end{aligned}$$

where C is a constant. Also, the phase modulation (PM) index, m_PM, and the phase delay, Φ_PM, are given respectively as

(5)$$\begin{aligned} {m_{PM}} &= \frac{{{\alpha _{DML}}{m_{DML}}}}{2}\sqrt {1 + {{\left( {\frac{{\kappa {P_0}}}{{{\omega_m}}}} \right)}^2}} \\ {\Phi _{PM}} &={-} {\tan ^{ - 1}}\frac{{\kappa {P_0}}}{{{\omega _m}}} \end{aligned}$$

The first term in (4) is the PM response of the DML. A similar expression can be found in [17]. The second and third terms in (4) represent the time-invariant wavelength shift induced by frequency chirp and a constant phase shift, respectively. Thus, they do not contribute to the phase response. In Fig. 1, we plot the PM response and the ratio between the PM and IM indices as a function of modulation frequency when α_DML = 2.5 and κP₀ = 6π GHz. The index ratio decreases rapidly as the frequency increases, but levels off asymptotically at the linewidth enhancement factor of DML. This is because the chirp characteristics of DML are mainly governed by the transient chirp at high frequencies, which is evident from (1). This also explains why the phase delay moves from -π/2 to 0 when the modulation frequency goes up.

Fig. 1. Ratio between the PM and IM indexes (left axis), and the phase change due to PM of the DML (right axis) with respect to the modulation frequency.

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By substituting (4) into (2) and then employing the small-signal approximation, we can express electric field of DML’s output for the fundamental component as

(6)$${E_{DML}}(t )\approx 1 + \frac{{{m_{DML}}}}{2}\cos {\omega _m}t + j{m_{PM}}\sin ({{\omega_m}t + {\varphi_{PM}}} )$$

where φ_PM = π/2 + Φ_PM. Here, we assume that P₀ is 1 without loss of generality. Mathematically, we have an SSB signal when the imaginary part of electric field is a Hilbert transform of the real part. Thus, the conditions for optical SSB generation using a DML become m_DML = 2m_PM and φ_PM = nπ (where n is an integer) [10]. However, these conditions are hardly met in typical DMLs (having α_DML = 2.4 ∼ 5.2 and κ = 3.2 ∼ 15 GHz/mW) [18,19].

2.2 Dual modulation scheme

In the dual modulation scheme, the DML serves mainly as a phase modulator, whereas the EAM functions as an intensity modulator. When the EAM is driven by a sinusoidal signal having an angular frequency of ω_m, the electric field of dual modulation signal can be expressed as

(7)$$E(t )= {E_{DML}}(t )\cdot \sqrt {1 + {m_{EAM}}\cos ({{\omega_m}t + {\varphi_{EAM}}} )} \textrm{exp} \{{j{m_{PM,EAM}}\cos ({{\omega_m}t + {\varphi_{EAM}}} )} \}$$

where m_EAM and m_PM,EAM are the IM and PM indices of EAM, respectively, and φ_EAM is the phase delay of the EAM driving signal with respect to the phase of DML driving signal. Since the chirp parameter of EAM, α_EAM, dictates the relationship between IM and PM indices, we can rewrite (7) as

(8)$$E(t )= {E_{DML}}(t )\cdot \sqrt {1 + {m_{EAM}}\cos ({{\omega_m}t + {\varphi_{EAM}}} )} \textrm{exp} \left\{ {j\frac{{{\alpha_{EAM}}}}{2}{m_{EAM}}\cos ({{\omega_m}t + {\varphi_{EAM}}} )} \right\}$$

By substituting (6) into (8) and then employing the small-signal approximation for m_DML and m_EAM, we have

(9)$$\begin{aligned} E(t ) &\approx 1 + \frac{{{m_{DML}}}}{2}\cos ({{\omega_m}t} )+ \frac{{{m_{EAM}}}}{2}\cos ({{\omega_m}t + {\varphi_{EAM}}} ) \\ &+ j{m_{PM}}\sin ({{\omega_m}t + {\varphi_{PM}}} )+ j\frac{{{\alpha _{EAM}}}}{2}{m_{EAM}}\cos ({{\omega_m}t + {\varphi_{EAM}}} )\end{aligned}$$

To simplify the modeling, we assume to drive the EAM with

(10)$$\cos ({{\omega_m}t + {\varphi_{PM}} + \Delta } )- \frac{{{m_{DML}}}}{{{m_{EAM}}}}\cos {\omega _m}t$$

where Δ is the additional phase delay of EAM driving signal, which will be clear later in this section. The first term is the sinusoidal signal with φ_EAM = φ_PM + Δ and the second term is included in (10) to erase the IM of DML after dual modulation. Then, the output of dual modulation can be expressed using (9) as

(11)$$\begin{aligned} E(t ) &\approx 1 + \frac{{{m_{EAM}}}}{2}\cos ({{\omega_m}t + {\varphi_{PM}} + \Delta } )+ j{m_{PM}}\sin ({{\omega_m}t + {\varphi_{PM}}} ) \\ &+ j\frac{{{\alpha _{EAM}}}}{2}{m_{EAM}}\cos ({{\omega_m}t + {\varphi_{PM}} + \Delta } )- j\frac{{{\alpha _{EAM}}}}{2}{m_{DML}}\cos {\omega _m}t \end{aligned}$$

The imaginary part of (11) can be rewritten as

(12)$${\mathop{\rm Im}\nolimits} \{{E(t )} \}= \frac{1}{2}\sqrt G \sin ({{\omega_m}t + {\varphi_{PM}} + \theta } )$$

where

(13)$$\begin{aligned} G &= 4m_{PM}^2 + \alpha _{EAM}^2m_{EAM}^2 + \alpha _{EAM}^2m_{DML}^2 - 2\alpha _{EAM}^2{m_{DML}}{m_{EAM}}\cos ({\Delta + {\varphi_{PM}}} )\\ &- 4{\alpha _{EAM}}{m_{PM}}{m_{DML}}\sin {\varphi _{PM}} - 4{\alpha _{EAM}}{m_{PM}}{m_{EAM}}\sin \Delta \end{aligned}$$

(14)$$\theta = {\tan ^{ - 1}}\frac{{{\alpha _{EAM}}{m_{EAM}}\cos \Delta - {\alpha _{EAM}}{m_{DML}}\cos {\varphi _{PM}}}}{{2{m_{PM}} - {\alpha _{EAM}}{m_{EAM}}\sin \Delta - {\alpha _{EAM}}{m_{DML}}\sin {\varphi _{PM}}}}$$

Using the Hilbert transform relationship between the real and imaginary parts of the signal, we can finally express the modulation conditions for optical SSB generation as

(15)$${m_{EAM}} = \frac{1}{{\sqrt {1 + \alpha _{EAM}^2} }}\sqrt {4m_{PM}^2 + \alpha _{EAM}^2m_{DML}^2 - 2{\alpha _{EAM}}{\alpha _{DML}}m_{DML}^2}$$

(16)$$\Delta = {\tan ^{ - 1}}{\alpha _{EAM}} - {\tan ^{ - 1}}\frac{{{\alpha _{EAM}}{m_{DML}}\cos {\varphi _{PM}}}}{{2{m_{PM}} - {\alpha _{EAM}}{m_{DML}}\sin {\varphi _{PM}}}}$$

It is very interesting to note that the previous models of dual modulation scheme are the special cases of our generalized model. For example, the IM index of DML and the chirp of EAM were both ignored in [10]. Therefore, m_DML = 0 and α_EAM = 0 in Kim’s model. In these conditions, (15) and (16) become m_EAM= 2m_PM and Δ=0, respectively. Thus, the driving signal of EAM expressed as (10) is simplified to be cos(ω_mt + φ_PM). These are consistent with the conditions reported in [10]. In another model, the IM of DML was taken into consideration, but the chirp of EAM was ignored [13]. Therefore, α_EAM = 0 in Chaibi’s model. In this case, the driving signal of EAM becomes the same as (10) with Δ=0. Table 1 tabulates these special cases of our generalized model. Also listed in this table is another special case (labeled as case III), where the EAM’s chirp is considered, but the IM of DML is ignored. This special case helps to understand the effects of EAM’s chirp on the SSB generation when compared with case I. Equation (8) tells us that the PM of EAM is always in phase with IM. However, the PM imposed by EAM is partially out of phase with the PM produced by DML. This is clearly seen in (11). The third term of (11) is the PM by the DML, whereas the fourth term is the PM by the EAM. For a negligible m_DML [and thus the fifth term in (11)], the phase difference between the third and fourth terms are always larger than 90 degree, regardless of the sign of α_EAM. This implies that the PM of EAM serves to reduce the PM produced by DML. Then, the IM of EAM should be reduced to satisfy the modulation conditions for optical SSB generation. As a result, the net effect of EAM’s chirp is the scaling of m_EAM by a factor of 1/(1+ α²_EAM)^1/2. The phase delay of EAM, φ_EAM, should also be delayed by tan⁻¹α_EAM due to non-zero chirp characteristics of EAM.

Table 1. Special cases of the generalized model

View Table

It is worth noting that the driving signal (10) can be rewritten in a sinusoidal form, as the first and second terms have the same frequency. This explains why the cumbersome probing procedure reported in the previous demonstration works. By brute-force searching the amplitude and phase of the sinusoidal signal driving the DML or EAM on a frequency-by-frequency basis, it is possible to find the modulation conditions for optical SSB generation [13]. Nevertheless, the generalized model developed in this paper not only provides the conditions for optical SSB generation without the cumbersome probing procedure, but also broadens our understanding of dual modulation scheme.

3. Numerical verification

We first conduct numerical simulations to evaluate the validity of our generalized model. For this purpose, we solve the equations (1), (2), (3), and (8) numerically to obtain the electric field of dual modulation signal. It is worth noting that these equations are valid even in the large signal regime [20]. The parameters used for the numerical simulations are as follows: the wavelength of laser = 1550 nm; modulation frequency (ω_m/2π) = 10 GHz; linewidth enhancement factor of DML (α_DML) = 3.8; adiabatic chirp parameter of DML (κ) = 11 GHz/mW, average output power of DML (P₀) = 10 mW; IM index of DML (m_DML) = 0.01. We assume that the transfer curve of EAM is linear with respect to the driving signal. We drive both the DML and EAM with a 10-GHz sinusoidal wave at a sampling rate of 200 Gsample/s.

Figure 2 shows the optical spectra of the signal obtained from numerical simulations. To evaluate the validity of the models, we apply the modulation conditions derived from the models and then measure the OSSRs. Figure 2(a) shows the optical spectrum in the case of chirp-free EAM (i.e., α_EAM = 0) when we apply the modulation conditions derived from Kim’s model (i.e., case I in Table 1). It shows that the lower sideband is suppressed by 23.3 dB, which is limited by the IM of DML. Thus, when Chaibi’s model is applied (i.e., case II in Table 1), the OSSR is improved to 43.3 dB, as shown in Fig. 2(b). However, the OSSR performance is severely deteriorated if the EAM’s chirp is not zero in the previously existing models. As shown in Fig. 2(c) and (d), we have the OSSRs of merely 11.3 and 13.0 dB for α_EAM = 0.5 when Kim’s and Chaibi’s models are utilized, respectively. We also plot the optical spectrum of the signal in Fig. 2(e) when α_EAM = 0.5 and our generalized model is used, but the IM of DML is ignored. In this case, the OSSR is measured to be 22.2 dB. Of course, the limited OSSR should be attributed to the IM of DML. Thus, when we employ the modulation conditions derived from our generalized model, we can improve the OSSR considerably. Figure 2(f) shows that we achieve the OSSR of 42.2 dB when the chirp of EAM is 0.5.

Fig. 2. Simulated optical spectra of optical SSB signals when (a) α_EAM = 0 and Kim’s model is used, (b) α_EAM = 0 and Chaibi’s model is used, (c) α_EAM = 0.5 and Kim’s model is used (d) α_EAM = 0.5 and Chaibi’s model is used, and (e) α_EAM = 0.5 and our generalized model is used, but the IM of DML is ignored, and (f) α_EAM = 0.5 and our generalized model is used.

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Using our theoretical model, we can evaluate the limitation of the previous models. Figure 3 shows the OSSR estimated by our theory as a function of EAM’s chirp when the modulation conditions derived from the previous models are employed. For this purpose, we estimate the magnitude of upper and lower sidebands of the signal from (9), and then calculate the OSSR when we apply the modulation conditions derived from the previously existing models. The parameters of DML used to plot Fig. 3 are identical with those used for Fig. 2. The results show the OSSRs drop rapidly as the chirp value of EAM is away from zero. This is because these models are all developed under the assumption of chirp-free EAM. Thus, we have relatively high OSSRs (e.g., >15 dB) using Kim’s and Chaibi’s models when |α_EAM| < 0.5. For example, the OSSR is estimated to be 12.6 dB at 1-GHz signal for both models when α_EAM is 0.5. It is worth noting that the chirp of EAM has a positive value typically when an EAM is biased at a point where its transfer curve is most linear. In other words, an EAM operates in a chirp-free manner in many cases when it is biased at the tail of its transfer curve. As will be shown later in Section 4, the EAM we utilize in our experimental demonstration exhibits this characteristic. The similar characteristics about the EAM’s transfer curve and their chirp parameters were also reported in [21–23]. Thus, most EAMs suffer from high insertion loss and nonlinearity of their transfer curves when they are biased at a point where the chirp is zero. This implies that most EAMs have positive chirp values, for example, in the range of 0.2 to 1 when they are biased at a point where their transfer curves are quite linear. Figure 3 shows that the OSSR would be limited to less than 10 dB in this range of α_EAM, when the previous models are utilized. The figure also shows that the OSSR performance is dependent upon the modulation frequency. This is due to the frequency-dependent phase response of DML, as shown in (5). Although this frequency dependency was already taken into consideration in the previous models, it makes the OSSR vary with the frequency when combined with non-zero chirp of EAM.

Fig. 3. The OSSR estimated from our generalized model as a function of EAM’s chirp when the modulation conditions derived from the previous models are utilized.

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We also investigate the impacts of amplitude and phase errors of the driving signals on the OSSR performance of dual modulation scheme. The driving signals fed to the DML and EML could be attenuated or delayed unintentionally with respect to the driving conditions we develop in our theory. Figure 4 shows the contour plot of OSSR as function of the amplitude mismatch and phase error. Here, the amplitude mismatch and phase error are defined as the deviation from modulation index ratio, m_EAM/m_DML, expressed in decibel and the phase deviation from our theory expressed in (10) and (16), respectively. Since the modulation conditions for EAM are derived with respect to those of DML, the amplitude mismatch and phase error can be interpreted as the amplitude and phase errors of the signal driving the EAM. The results show that we achieve the OSSR higher than 20 dB when the phase error is less than ±0.2 radian and the amplitude mismatch is smaller than 1.8 dB.

Fig. 4. The OSSR as functions of amplitude mismatch and phase error.

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4. Experiment and results

We carry out experiments to verify our generalized model of the dual modulation scheme. We first measure the chirp characteristics of DML and EAM using the fiber frequency response method reported in [24] and [25]. Figure 5(a) shows the experimental setup. The DML utilized in the experiment has a threshold current of 3.3 mA and emits the optical power of 9.2 dBm at 1547.95 nm when biased at 50 mA. Using the vector network analyzer, we apply a sinusoidal wave to the devices, transmit it over 40-km standard single-mode fiber (SSMF), detect it using a photo-diode (PD) having a 50-GHz bandwidth, and finally measure the frequency response of the link. We also measure the frequency response of the link using 0-km SSMF. This is to measure the frequency-dependent characteristics of the devices (i.e., DML, EAM, and PD) and remove them from the fiber frequency response obtained from the 40-km link. Then, chirp parameters are extracted from the response by using curve fitting with the theoretical model [24]. Figure 6(a) shows the fiber frequency response measured with the DML. Also plotted in this figure is the theoretical curve fitted with α_DML = 2.3 and κ = 4.81 GHz/mW. These chirp parameters give us the minimum mean square error between the measurement and theory.

Fig. 5. Experimental setups for (a) measuring the chirp characteristics of DML and EAM and (b) measuring the optical spectrum

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Fig. 6. (a) Measured frequency response of the DML. (b) The transfer curve the EAM and the corresponding chirp values as a function of bias voltages.

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We utilize an external EAM having an insertion loss of 6.5 dB. Figure 6(b) shows the transfer curve and chirp of EAM as a function of bias voltage. We measure the chirp of EAM by using the fiber frequency response method depicted in Fig. 5(a), as we vary the bias voltage to EAM. It is interesting to note that zero chirp is obtained when the bias voltage is −1.5 V, where the transfer curve drops more than 8.5 dB from its maximum transmittance.

Next, we generate the optical SSB signal using the dual modulation scheme. Figure 5(b) shows the experimental setup. A two-channel arbitrary waveform generator operating at 64 Gsample/s is utilized to generate two sinusoidal waves having the same frequency. This is to adjust the amplitudes and phases of the signals fed to the DML and EAM independently. In order to realize the dual modulation scheme cost-effectively, it is possible to utilize a single-channel signal generator, as demonstrated in [10]. In this case, the output of the signal source is split two ways, one of them is sent to the DML, and the other to EAM with its amplitude and phase adjusted by using an RF attenuator and phase shifter, respectively. In our experimental demonstration, we adjust the amplitude and phase of the signal fed to the EAM with respect to those of the signal sent to the DML, according to the modulation conditions derived from the models. It is worth noting that the path length difference between the DML and EAM is measured to calibrate the actual phase driving the EAM accurately. Finally, we measure the optical spectrum of the signal using the heterodyne receiver, which is composed of a tunable laser (10-kHz linewidth, 9-dBm output power), a polarization controller, a 50:50 optical coupler, and a PD having a 3-dB bandwidth of 50 GHz. The detected signal is digitized by using a real-time oscilloscope operating at 80 Gsample/s and we perform the fast Fourier transformation to obtain the spectrum. The resolution of this spectral analysis is set to be 1 MHz.

We first set the modulation frequency and the bias voltage of EAM to be 1 GHz and −1 V, respectively. At this bias voltage, the transfer curve of EAM is the most linear, but it exhibits the chirp of 0.59. The modulation index of the DML is set to be 1%. Using the chirp parameters of DML and EAM, we adjust the amplitude and phase of the sinusoidal waves driving the DML and EAM based on Kim’s [10] and Chaibi’s [13] models. Figure 7(a) depicts the optical spectrum of the dual modulation signal when we apply Kim’s model to generate the optical SSB signal. The result shows that the lower sideband is suppressed merely 7.6 dB with respect to the upper sideband. Figure 7(b) shows the optical spectrum when we apply the modulation conditions derived from Chaibi’s model. The OSSR is improved slightly in comparison with Fig. 7(a), but it is still limited to <10 dB. On the other hand, when we apply our generalized model, we achieve an OSSR higher than 40 dB, as shown in Fig. 7(c).

Fig. 7. Measured optical spectra of 1-GHz SSB signal when we apply the modulation conditions derived from (a) Kim’s model, (b) Chaibi’s model, and (c) our generalized model.

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Finally, we extract the modulation conditions for optical SSB generation experimentally by searching the amplitude and phase of the signal driving the EAM, and then compare these conditions with the ones derived from our generalized model. Figure 8(a) and (b) show the ratio of m_EAM to m_DML and the relative phase of the signal driving the EAM (with respect to the signal fed to the DML), respectively. The measured data indicate the modulation conditions for OSSR higher than 40 dB. When the modulation frequency is 1 GHz, the measured values agree very well with the theory. When the modulation frequency is high and the EAM’s bias is less than −1.5 V, however, slight discrepancies between our theory and measured values are observed. We attribute them to two factors. Firstly, when the bias of EAM is lower than −1.5 V, the signal power at the output of the EAM becomes less than −12 dBm, which in turn, makes our measurement sensitive to the detector noise. This is because of high loss of EAM and the shallow transfer curve of EAM when its bias voltage is less than −1.5 V. Secondly, the adiabatic chirp parameter of the DML, κ, is a function of modulation frequency. It was shown that κ values decrease with the increased modulation frequency [25]. We confirm that a slightly lower κ value gives us a better match between the theory and measured data when the modulation frequency is high. Nevertheless, the results show that our generalized model agrees with the measured results over wide ranges of modulation frequency and EAM’s chirp.

Fig. 8. Modulation conditions for optical SSB signal. (a) Modulation index ratio between EAM and DML and (b) the phase of EAM driving signal as a function of EAM’s bias voltage.

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5. Summary

We have developed an accurate theoretical model of optical SSB generation for the dual modulation scheme. Unlike the previously existing models, we take into account the intensity modulation of DML and the non-zero chirp of EAM in our model. Thus, the previous models fall into the special cases of our generalized model. We confirm the validity of our model using numerical simulations and experiments. The results show that we can generate an optical SSB signal having a high optical sideband suppression ratio by using the modulation conditions derived from our generalized model over wide ranges of frequency and EAM’s chirp. Thus, we believe that our model can provide a direct and convenient way to synthesize optical SSB signals using the dual modulation scheme.

Funding

National Research Foundation of Korea (2019R1A2C2005367).

Disclosures

The authors declare no conflicts of interest.

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Case	Parameters	m_EAM	φ_EAM	Driving signal of EAM	Ref.
I	m_DML = 0, α_EAM = 0	$2 m_{P M}$	$φ_{P M}$	$\cos (ω_{m} t + φ_{P M})$	[10]
II	m_DML ≠ 0, α_EAM = 0	$2 m_{P M}$	$φ_{P M}$	$\cos (ω_{m} t + φ_{P M}) - \frac{m_{D M L}}{m_{E A M}} \cos ω_{m} t$	[13]
III	m_DML= 0, α_EAM ≠ 0	$\frac{2 m_{P M}}{\sqrt{1 + α_{E A M}^{2}}}$	$φ_{P M} + \tan^{- 1} α_{E A M}$	$\cos (ω_{m} t + φ_{P M}) - \frac{m_{D M L}}{m_{E A M}} \cos ω_{m} t$

Generalized model of optical single sideband generation using dual modulation of DML and EAM

Abstract

1. Introduction

2. Generalized model of dual modulation scheme

2.1 Phase response of DML

2.2 Dual modulation scheme

3. Numerical verification

4. Experiment and results

5. Summary

Funding

Disclosures

References

Cited By

Figures (8)

Tables (1)

Equations (16)

Optics Express