# Modeling and optimization of low chirp LiNbO3 Mach-Zehnder modulators with an inverted ferroelectric domain section

N. Courjal, H. Porte, J. Hauden, P. Mollier, N. Grossard

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N. Courjal, H. Porte, J. Hauden, P. Mollier, N. Grossard. Modeling and optimization of low chirp LiNbO3 Mach-Zehnder modulators with an inverted ferroelectric domain section. Journal of Lightwave Technology, 2004, 22 (5), pp.1338-1343. [hal-00095412](https://hal.science/hal-00095412v1)

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# Modeling and Optimization of Low Chirp LiNbO₃ Mach–Zehnder Modulators With an Inverted Ferroelectric Domain Section

Nadege Courjal, Henri Porte, J. Hauden, P. Mollier, and N. Grossard

**Abstract**—Domain inversion under coplanar waveguide electrodes is proposed to improve the frequency-chirping behavior of Z-cut LiNbO₃ Mach–Zehnder modulators. This is achieved by introducing a phase reversal electrode section in tandem with inverted ferroelectric domains. The method opens the way to broad-band single-drive modulators with predetermined chirp parameter. The experimental results obtained at 10 Gb/s confirm the possibility of lowering the chirp parameter of a Z-cut modulator, while keeping a halfwave voltage lower than 5 V.

**Index Terms**—Chirp modulation, electrooptic modulation, ferroelectric domain inversion, lithium niobate.

## I. INTRODUCTION

IN LONG-HAUL transmission systems, interactions of the frequency chirping with chromatic dispersion can severely distort the transmitted signal and therefore limit the data rates. Because the chirp of electroabsorption modulators or directly modulated lasers tends to be high, a Mach–Zehnder (MZ) configuration is usually used to achieve chirp-free modulation.

Their low optical losses, large extinction ratio and small wavelength dependence makes LiNbO₃ modulators particularly suitable for dense wavelength multiplexing (DWDM) [1] and optical time division multiplexing (OTDM) [2] long haul transmission systems. For X-cut LiNbO₃ devices, the RF electrical fields applied to the optical arms of the MZ structure are symmetric, which results in a chirp-free modulation. On the other hand, Z-cut LiNbO₃ modulators are promising devices because they can provide both a lower driving voltage and a larger bandwidth, particularly if the structure is ridged [3]. However, Z-cut LiNbO₃ modulators use an asymmetric structure to reduce the halfwave voltage (Vπ), so they exhibit a residual chirp parameter. Dual-drive electrodes can appear as an alternative configuration to feature simultaneously a low Vπ and an adjustable chirp parameter [4], but this requires the use of a balanced microwave driver.

In [5], [6], we reported the first demonstration of a single RF drive Z-cut LiNbO₃ modulator featuring a fixed and near zero chirp value. With these preliminary results, we have shown that phase reversal electrode associated with a ferroelectric domain

inverted section can enable flexibility in term of chirp setting. In this paper, we propose a new and optimized modulator designed to work in long haul and high bit rate telecommunication systems. The results reported here with this new device are compared with conventional solutions on single-ended Z-cut modulators. Systems characterization was carried out using 50 km of SMF-28 fiber span at 10 Gb/s.

## II. LOW CHIRP MZ MODULATORS WITH INVERTED FERROELECTRIC DOMAIN SECTION

In external modulators, the application of an electrical modulation signal changes not only the output optical field amplitude but also its phase. The modulation chirp parameter represents the ratio of this phase modulation to the amplitude modulation [7]

$$ \alpha = \frac{\frac{d\varphi}{dt}}{\frac{1}{E} \cdot \frac{dE}{dt}} \qquad (1) $$

where φ and E are phase and magnitude of the output optical field, and t denotes time. In general, α is a function of time, modulation depth and operating bias point of the electrooptic modulator. It can be defined at small signal regime and quadratic bias as

$$ \alpha_{\pi/2} = \frac{\dot{\varphi}_1(t) + \dot{\varphi}_2(t)}{\dot{\varphi}_1(t) - \dot{\varphi}_2(t)} \qquad (2) $$

where φ₁ and φ₂ denote the phase accrued at the outputs of the MZ structure, and the superscript • represents time derivative. In the push-pull configuration, φ₁ and φ₂ are of opposite signs.

For X-cut LiNbO₃ modulators, the optical branches are symmetric with respect to the cross section of the central line [cf. Fig. 1(a)]: $\dot{\varphi}_1 = -\dot{\varphi}_2$. Such a configuration allows a chirp free modulation. Contrary to X-cut modulators, standard single-ended Z-cut LiNbO₃ modulators exhibit an asymmetric structure, as displayed in Fig. 1(b). In this case, the waveguide aligned under the hot line of the central coplanar waveguide (CPW) electrode is submitted to a higher electrical field than the one placed under one of the lateral ground electrodes. This asymmetry causes the chirp value to be

$$ \alpha_{\pi/2}^{S} = \frac{\Gamma_{G} - \Gamma_{C}}{\Gamma_{G} + \Gamma_{C}} \qquad (3) $$

where ΓC and ΓG are the overlap coefficients between the electric and the optical fields in the waveguides located under the

<footnote>N. Courjal is with the Laboratoire d'Optique P.M. Duffieux, UMR CNRS 6603, Université de Franche Comté, Institut des Microtechniques (IMFC), 25030 Besançon Cedex, France (e-mail: nadege.bodin@univ-fcomte.fr).</footnote>

<footnote>H. Porte, J. Hauden, P. Mollier, and N. Grossard are with the Photline Technologies, 25001 Besançon Cedex 3, BP71025 France.</footnote>
central and the ground electrode, respectively, as defined in [8]. Due to the asymmetry induced by the push-pull configuration $-\Gamma_C > \Gamma_G$, so that $\alpha_{\pi/2}^S$ cannot be equal to zero.

We propose to divide the standard structure into two longitudinal sections of opposite spontaneous polarization ferroelectric domain in order to get a symmetric accumulation of phase in both arms. The device is depicted in Fig. 2. One part of the waveguides integrated in the Z-cut substrate is processed to have a ferroelectric domain inversion. In the first section, which is the non inverted one, the central line is centered over the waveguide #1, whereas the waveguide #2 is placed under one of the lateral ground electrodes. In the second section, which is the inverted one, the central line is now placed over the waveguide #2 while the second ground electrode is aligned along the edge of the waveguide #1. Each optical branch is thus submitted to a $\Gamma_C < 0$ overlap coefficient in one section, and to a $\Gamma_G > 0$ overlap coefficient in the other section. The ferroelectric domain inversion compensates for the inversion of polarity of the overlap coefficients because the electrooptic coefficient is positive and equal to $r_{33}$ in the first section, while it is assumed to be negative and equal to $-r_{33}$ in the second region. As a result, we have shown that if the length $L_1$ of the first section equals the length $L_2$ of the second section, a symmetric structure can be realized without sacrifice on the modulation efficiency.

Due to the association of the ferroelectric domain inversion with the phase reversal inversion of electrodes, the optical phase of a light beam propagating through each of the branches of the MZM can be expressed as, respectively

$$ \varphi_1(t) = K \cdot \left( \Gamma_C \cdot \int_0^{L_1} V_Z(y,t) \cdot dy - \Gamma_G \cdot \int_{L_1}^{L} V_Z(y,t) \cdot dy \right) \quad (4) $$

$$ \varphi_2(t) = K \cdot \left( \Gamma_G \cdot \int_0^{L_1} V_Z(y,t) \cdot dy - \Gamma_C \cdot \int_{L_1}^{L} V_Z(y,t) \cdot dy \right) \quad (5) $$

where the integrals account for the transmission of the electrical signal through the optical path in region 1 and 2, respectively, and $V_z(y, t)$ is the voltage applied to the electrodes at a distance $y$ from the beginning of the transmission line. $K = \pi n_{eo}^3 |r_{33}| / \lambda g$ is a constant related to the extraordinary refractive index $n_{eo}$ of lithium niobate, to the electrode gap $g$ and to the wavelength $\lambda$.

In [5], we have shown that a low chirp modulation could be achieved if $L_1 = L_2$ and if the active length is small ($L = 1.4$ cm). A low driving voltage requires however a long active length. In this case, a small index mismatch or an RF attenuation of the electrical field in the line can induce a significant asymmetry between the two arms of the MZ, and produce a significant chirp at high frequencies. The following section aims to model and optimize the structure in case of long electrodes.

### III. MODELING OF MZ MODULATORS WITH INVERTED FERROELECTRIC DOMAIN SECTION

Two main parameters may be responsible for an asymmetry between the two arms of the presented MZ modulator index mismatch, and electrical losses.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Transversal structure of (a) X-cut $LiNbO_3$ modulators. (b) Z-cut $LiNbO_3$ modulators.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Structure of a z-cut MZ modulator with inverted domain.</figcaption></figure>

#### A. Index Mismatch

When the electrical index $N_{el}$ is different from the optical index $n_{eo}$, a time delay per unit length $\Delta t = \Delta n/c$ is induced between the optical wave and the electrical wave through the optical path ($\Delta n = N_{el} - n_{eo}$ denotes the index mismatch, and $c$ is the velocity of light). This time delay causes an asymmetry between the responses of the two MZ arms, since the phase accumulated in the second section is not equal to the phase accumulated in the first section. The asymmetry can be assessed from the integrals in (4) and (5)

$$ \int_{0}^{L_1} V_Z(y,t) \cdot dy = e^{j\omega_0 t} \cdot \frac{\exp\left(\frac{-j2\pi f \cdot \Delta n \cdot L_1}{c}\right) - 1}{\frac{-j2\pi f \cdot \Delta n}{c}} \quad (6) $$

$$ \int_{L_1}^{L} V_Z(y,t) \cdot dy = e^{j\omega_0 t} \cdot \exp\left(\frac{-j2\pi f \cdot \Delta n \cdot L_1}{c}\right) \cdot \frac{\exp\left(\frac{-j2\pi f \cdot \Delta n \cdot L_2}{c}\right) - 1}{\frac{-j2\pi f \cdot \Delta n}{c}} \quad (7) $$
where *f* is the frequency modulation of the electrical signal, and *ω*₀ represents the optical pulsation. In case of a significant index mismatch, (6) is not equal to (7). Thus, the intrinsic chirp parameter becomes

$$ \alpha_{\pi/2} = \alpha_{\pi/2}^{S} \cdot \left| \frac{2 \cdot \exp\left(-\frac{j2\pi f \cdot \Delta n \cdot L_1}{c}\right) - \exp\left(-\frac{j2\pi f \cdot \Delta n \cdot L}{c}\right) - 1}{\exp\left(-\frac{j2\pi f \cdot \Delta n \cdot L}{c}\right) - 1} \right| \quad (8) $$

The intrinsic chirp parameter of a standard single-ended Z-cut modulator does not depend on Δn, as can be seen from (8) by considering L₁ = L. Here, the new modulator configuration exhibits a chirp parameter that changes with Δn. The variation of απ/2 with frequency is depicted in Fig. 3 for different cases of Δn, and L = 2.8 cm. According to this figure, it can be concluded that the index mismatch has to be smaller than 0.1 to benefit from a low chirp parameter (|απ/2| < 0.1) on a 0–10-GHz frequency range.

## B. Electrical Losses

Electrical losses can cause a significant decrease of the voltage propagating through the electrodes: the length of the second section has to be longer than the length of the first section to reestablish symmetry between the two optical branches of the structure. The electrical losses can be modeled by an attenuation coefficient a₀, that stands for the electrical losses in Np/GHz⁰.⁵/cm. In this case, the integrals in (4) and (5) become, respectively

$$ \int_{0}^{L_1} V_Z(y, t) \cdot dy = e^{j\omega_0 t} \cdot \frac{\exp(-a_0 \cdot \sqrt{f} \cdot L_1) - 1}{-a_0 \cdot \sqrt{f}} \quad (9) $$

$$ \int_{L_1}^{L} V_Z(y, t) \cdot dy = e^{j\omega_0 t} \cdot \frac{\exp(-a_0 \cdot \sqrt{f} \cdot L_2) - 1}{-a_0 \cdot \sqrt{f}} \cdot \exp(-a_0 \cdot \sqrt{f} \cdot L_1) \quad (10) $$

These equations lead to the following chirp parameter

$$ \alpha_{\pi/2} = \alpha_{\pi/2}^{S} \cdot \frac{2 \cdot \exp(-a_0 \cdot \sqrt{f} \cdot L_1) - \exp(-a_0 \cdot \sqrt{f} \cdot L) - 1}{\exp(-a_0 \cdot \sqrt{f} \cdot L) - 1} \quad (11) $$

The intrinsic chirp parameter is represented in Fig. 4 with L₁ = L₂ = 1.4 cm. Here, the electrical index matches the optical index. We can see from this figure that a propagation loss of 0.057 Np/GHz⁰.⁵/cm yields a variation of the chirp parameter lower than 0.1 at 10 GHz. This frequency dependence of chirp can be optimized provided that the L₁/L₂ ratio is properly chosen. In fact, it can be seen from (11) that the chirp parameter can be set to zero for a given frequency provided that the length of the second section is long enough to compensate for electrical losses.

Following these preliminary conditions, we have realized a broad-band Z-cut modulator with two sections of opposite ferroelectric domain sign in order to verify the interest of the structure at high frequencies. The modulator was designed for a 10 Gb/s nonreturn to zero (NRZ) modulation.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Variation of the intrinsic chirp parameter απ/2 with frequency for different cases of index mismatch.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Variation of the intrinsic chirp parameter απ/2 with frequency for different cases of electrical attenuation.</figcaption></figure>

## IV. EXPERIMENTAL RESULTS

A modulator with an inverted ferroelectric domain section was fabricated to provide a low driving voltage, low electrical losses and index matching. The L₁/L₂ ratio was chosen to be equal to 0.87 in order to set the chirp parameter to zero at 5 GHz [cf. (11)], which corresponds to the frequency carrier of a NRZ modulation at 10 Gb/s bit rate. The different steps of realization are described in [5].

The 3 dB e-o bandwidth was 15 GHz measured using a vectorial network analyzer and a calibrated detector [Fig. 5(a)]. Fig. 5(b) exhibits electrical reflection losses lower than –10 dB from 0 to 40 GHz. The characteristic impedance Zc and effective electrical index Nel are assessed from the s11 response [Fig. 5(b)]: Nel is calculated to be 2.25, and Zc is estimated to be 38 Ω. The electrical losses are evaluated from the s21 electrical response: a_dB = 0.48 dB/GHz⁰.⁵/cm (i.e., a₀ = 0.055 Np/GHz⁰.⁵/cm). The static half wave voltage is measured to be 4.5 V, the optical losses are very low (–3.9 dB), and the extinction ratio is –25 dB. All these results meet the requirements of a long haul transmission at 10 Gb/s. Moreover, a single-ended Z-cut modulator realized in the same conditions exhibits exactly the same characteristics, so it is confirmed that the inverted ferroelectric domain section is efficient to reestablish the electrooptical properties of the phase reversal modulator without any sacrifice on the efficiency of modulation.

The second step of experimental verifications consisted in measuring the chirp parameter of the presented modulator. This was realized by plotting the frequency transmission response of the modulator after 50 km of a standard fiber at 1550 nm of D = 17 ps/nm/km dispersion parameter. According to a standard method described in [9], the chirp parameter απ/2 can be
<figure><img src="image_6.png" /><figcaption>Fig. 5. Response of the Z-poled modulator. (a) s21 electrooptical response. (b) s11 electrical response.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. Transmission response of the poled Z-cut modulator after 50 km of a standard fiber.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Transmission response of a single-ended Z-cut modulator after 50 km of a standard fiber.</figcaption></figure>

deduced from the resonances that appear in the transmission frequency response by applying (12)

$$f_n^2 \cdot L_f = \frac{c}{2D\lambda^2} \cdot \left( 1 + 2n \pm \frac{2}{\pi} \tan^{-1}(\alpha_{\pi/2}) \right) \quad (12)$$

where $f_n$ is the frequency of the n'th resonance, $L_f = 50$ km is the length of the standard fiber, and $D$ is the dispersion parameter. In (12), the sign + stands for the positive slope of the modulation transfer function (MTF) and the sign - stands for the negative slope of the MTF.

Two kinds of responses are depicted in Fig. 6: the solid gray lines stand for the case where a positive quadratic bias (negative slope) is imposed between the two arms of the modulator, while the dashed lines represent the case where the bias is quadratic and negative (case of a positive slope). If the intrinsic chirp parameter were equal to zero, then the resonances should be exactly the same in both cases. Fig. 6 shows that the first peak for each slope correspond to 8.40 and 8.97 GHz, respectively: the shift of 430 MHz between the two resonances indicates that the chirp can be estimated to $\alpha_{\pi/2} = -0.09$ according to (12).

This result was compared to that obtained with a single-ended Z-cut modulator with no poled section. Fig. 7 represents the transmission response of this single-ended modulator followed with 50 km of a standard SMF-28 fiber. We can see from the figure that the first resonances are located at 7.58 and 9.23 GHz, respectively. This significant shift ($\Delta f = 1.65$ GHz) between the two resonances is due to a non zero chirp parameter: the chirp parameter is measured to be $-0.87$. It can thus be concluded that the poled Z-cut modulator exhibits a chirp parameter that is significantly lower than that of a single-ended Z-cut modulator.

10 Gb/s transmission was then carried out through a fiber of 17 ps/nm/km dispersion. The eye diagram was measured at the output of the device, and after 50 km of a standard fiber. For these measurements, the modulator was driven by a pattern generator delivering a $2^{31} - 1$ frame pattern. An RF modulator driver of 20-GHz bandwidth and 20-dB gain amplified the signal, which was applied to the modulator in order to reach a $5V_p - p$ amplitude modulation at 10 Gb/s PRBS. A dc bias control linearized the signal of modulation on either the positive or negative slope of the modulation transfer function (MTF) of the modulator. The output intensity modulation transmitted in the 50 km of standard single mode fiber was optically amplified with an EDFA. The output light modulation was then collected with a high-speed photo detector of 12-GHz bandwidth. The back-to-back experimental response is depicted in Fig. 8(a) showing a 88% vertical and horizontal opening. Fig. 8(b) and (c) represents the eye diagrams resulting from 50 km of propagation in a standard fiber for a quadratic dc bias corresponding to the negative and positive slope of the transfer curve, respectively. These results show that the signal is submitted to the same distortions whatever the slope of the transfer curve is, which is possible only if the chirp parameter is very low. The resulting dispersion penalty will be the same in both cases.

Conversely, an optical signal generated by a standard single-ended Z-cut modulator does not exhibit the same distortion after a propagation in 50 km of a standard fiber if the sign of the slope is changed: Fig. 9(a), which represents the case of a negative slope, exhibits a more important alteration of the signal than Fig. 9(b), which represents the case of a positive slope. This asymmetry between the positive and negative slope leads to significant differences in the dispersion penalties obtained in both situations. This demonstrates the interest of the new design of poled Z-cut modulator, offering simultaneously the driving
<figure><img src="image_9.png" /><figcaption>Fig. 8. (a) Back-to-back eye diagram at the output of the poled Z-cut modulator. (b) Eye diagram after 50 km of a standard fiber and biasing on the negative slope of the transfer curve (c) Eye diagram after 50 km of a standard fiber and biasing on the positive slope of the transfer curve.</figcaption></figure>

voltage performances of a standard single-ended Z-cut modulator, and the chirp characteristics of a standard X-cut modulator.

The thermal and aging stability of the components were not tested, because the SiO₂ buffer layer was not optimized for stability. However, the ferroelectric domain inversion is predicted to provide stabilization against thermal drift. In fact, a poled section inhibits the built up of charge induced by the pyroelectric effect.

## V. CONCLUSION

Ferroelectric domain inversion associated with electrode inversion has been proposed to fabricate a Z-cut LiNbO₃ modulator with a low chirp parameter (< 0.1), which is significantly lower than that of a standard single-ended Z-cut modulator. The chirp parameter of the presented modulator has been shown to exhibit low frequency dependence if the electrical index matches the optical index and if the electrical losses are

<figure><img src="image_10.png" /><figcaption>Fig. 9. Eye diagram at the output of a single-ended Z-cut modulator after 50 km of standard fiber. (a) Biasing on the negative slope of the transfer curve. (b) Biasing on the positive slope of the transfer curve.</figcaption></figure>

weak. A low chirp Z-cut MZ modulator was realized and tested up to 20 GHz, yielding a 4.5-V half-wave voltage, and a –25 dB extinction ratio. The back-to-back eye diagram at 10 Gb/s bit rate is comparable to that of a standard Z-cut modulator. The 10 Gb/s eye diagrams obtained with a standard single-drive Z-cut modulator after modulation and 50 km of propagation through a dispersive fiber exhibits significant differences in the distortion of the signal if the sign of the slope of the transmission response is not properly chosen, whereas a modulator having a domain inverted section can generate the same signal for both slopes. The low chirp, wide bandwidth and good extinction ratio of this device demonstrate its suitability for long haul 10 Gb/s applications. Work is in progress to extend bandwidth up to 40 GHz.

## ACKNOWLEDGMENT

The authors would like to thank the Photline technical staff and A. Martinez from LOPMD for technical assistance and measurements.
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