The Optimal Operating Point for Linearizing an Integrated Optical Lithium Niobate Directional Coupler Modulator ^†

Abstract

The influence of an operating point on the linearity of an integrated optical lithium niobate directional coupler modulator was studied. It was found that the optimal setting for the position of an operating point for suppressing the third-order intermodulation distortion depended on the power of the high-frequency modulation signal. Thus, despite the simple design of the device, the directional coupler modulator requires a complex algorithm for setting an operating point to achieve a high linearity of operation. An active system for setting an operating point based on the low-frequency pilot signal and zeroing its third harmonic was used to demonstrate the possibility of linearization when the amplitude of the modulation signal changes. The use of an operating point control system became possible after limiting the drift of the operating point by etching the dielectric buffer layer in the interelectrode gap. The results obtained look promising for high-performance analog optical links.

1. Introduction

This paper is an extended version of our conference paper published in the IEEE International Conference on Electrical Engineering and Photonics (EExPolytech), St. Petersburg, 2020 [1] on the development of the lithium niobate direction coupler modulator and its application in microwave photonics. The technology of integrated optical circuits on lithium niobate substrates [2,3] is one of the basic technologies for the development and production of modern optoelectronic components, primarily high-frequency integrated optical modulators [4,5], which are key components of fiber-optic telecommunication systems that implement the principles of microwave photonics. Microwave photonics is an emerging technology that uses the optical domain to generate, transmit, and process microwave and millimeter wave signals [6,7,8,9,10,11], taking advantage of broad processing bandwidth obtained by converting radio to optical frequencies, the availability of low-loss optical fibers as the transport medium, and the flexibility to adapt the radio frequency (RF) response over decades of frequencies. Important applications include the following: broadband wireless communications (especially with emerging of 5G and 6G networks) [12,13,14,15], radar and antenna remoting [16], sensing [17] and instrumentation including low noise optoelectronic oscillators [18] and electro-optical frequency comb generators [19].

Highly efficient and linearized conversion of RF signals to optical signals is of paramount importance for various applications. Conventional commercially available lithium niobate Mach–Zehnder modulators (LN MZM) have a significant drawback—the third-order intermodulation distortion (IMD3), which occurs when multiple signal tones are used for modulation [7]. Various efforts have been made to improve the linearity of modulators, both electronically and optically. Examples of electronic compensation include pre-distortion compensation [20] and feedforward compensation [21,22]. However, these methods require expensive high-speed optoelectronic components and have a maximum bandwidth of only a few gigahertz. Optical methods, such as those based on a cascaded MZ modulator [23,24,25], an MZ modulator using dual wavelength inputs and dual outputs [26], or a ring resonator assisted MZ modulator [27], provide broadband linearization. However, the disadvantage of optical methods is that improved linearity is achieved at the expense of simple device design. In addition, these complex devices require high thermal stability and precise bias voltage control, which significantly limits their use in practice.

A directional coupler modulator (DCM), on the other hand, had been proven to possess a highly linear transfer function without loss in the simplicity of device design [28,29,30,31]. The principle of the DCM operation is based on coupling between two closely spaced optical waveguides. Light from one waveguide partially penetrates into the other waveguide providing the coupling and transferring of the optical power. The application of the antisymmetric electric field to the interacting waveguides leads, due to the electro-optical effect, to the appearance of a difference in the propagation constants (Δβ) which breaks the phase matching, reduces the coupling coefficient and, in turn, affects the power transfer efficiency. The coupling coefficient between the waveguides linearly depends on the applied electric field and voltage, thus the optical transfer function of the DCM has the form of the sinc function [32].

$$P_{out2}=T\cdot P_{in}\frac{{\sin }^2\left[\frac{\pi }{2}\sqrt{1+3{\left(\frac{v_M}{V_S}\right)}^2}\right]}{1+3{\left(\frac{v_M}{V_S}\right)}^2},$$

(1)

where P_in is the optical power at the modulator input, T is the splitting ratio of the DCM in the absence of an applied voltage, V_S is the characteristic voltage (analogue of half-wave voltage for a Mach–Zehnder modulator). The view of the DCM optical transmittance as a function of applied voltage v_M is shown in Figure 1d. Note that Equation (1) is written for a DCM which, in the absence of voltage, ensures full optical power transfer to the crossed output waveguide, i.e., splitting ratio equal to 1. This case is most suitable for linearization. For directional couplers with a different split ratio, the shape of the transfer function will change.

Unlike a modulator based on a Mach–Zehnder interferometer (MZM), which has a cosine transfer function, for the DCM there is no operating point (or bias voltage), at which all terms corresponding to nonlinear distortions of an even order move to zero. Thus, significant second-order nonlinear terms limit the modulation bandwidth. This is a case of a so-called sub-octave modulator, which produces significant second harmonic distortion and is suitable for use of only one octave of modulation frequency. However, this type of modulator can be used in many applications, such as radar or RoF, where the bandwidth of the transmitted signals is lower than the carrier frequency.

The type of transfer function described by Equation (1) allows the use of DCM as a linearized modulator to suppress third-order intermodulation distortion. The operating point choice is very crucial for effective linearization. A complex shape of the slope of the DCM transfer function places special demands on the accuracy of the bias voltage adjustment. In addition, it is very difficult to implement linearization in a wide frequency range and within a high dynamic range of a modulating signal.

In our preliminary work described in a conference paper [1], we demonstrated the possibility of DCM linearization, the high influence of the operating point, and the dependence of the operating point on the modulation power. The goal of this extended work was to conduct a more detailed investigation of the factors influencing the suppression of third-order intermodulation distortion. Particular attention will be paid to practical aspects related to setting and stabilizing the DCM at the optimal operating point, such as producing a directional coupler with a splitting ratio close to 100% and reducing DC drift of the operating point [33,34,35].

2. Experimental Sample of the Electro-Optical Directional Coupler Modulator

An experimental sample of the DCM (Figure 1c) was fabricated on the base of single-mode channel optical waveguides formed in a lithium niobate substrate using titanium thermal diffusion technology [1]. We chose the X-cut orientation of the crystal substrate (Figure 1a) due to lower DC drift [33]. A thin-film plasmon-polariton polarizer [36] was placed at the input of the modulator to select the TE polarization operating mode, increase the stability of operation, and facilitate the setting and stabilization of the DCM in the linearized mode.

Particular attention was paid to the design of the coupling region. As mentioned above, close to complete (100%) coupling to the cross state in the absence of applied voltage is critical for effective suppression of third-order nonlinearity. The influence of three parameters on the splitting ratio was studied. These are the length of the coupling region (L), the distance between the centers of waveguides in the coupling region (D) and the width of the waveguide channel, determined by the titanium diffusion strip width (W) (see Figure 1a,b). A set of test samples with a series of directional couplers was fabricated and tested. The length of the coupling region was fixed, and the distance between the waveguides and their width were varied. The choice of a sufficiently large length L, equal to 30 mm, was due not only to a decrease in the control voltage, but also to a lower coupling coefficient and less influence of fabrication inaccuracy. Figure 2a shows the experimental dependences of the splitting ratio in the absence of applied voltage on the distance between waveguides made by thermal diffusion from titanium strips 5 and 6 μm wide. Hereinafter, the results were obtained using a TeraXion PureSpectrum™-PS-TNL tunable continuous wave semiconductor laser. In most experiments, the laser was tuned to the center of the telecommunications C-band at a wavelength of 1555 nm. The total coupling to the cross state was achieved at distance D of 16 μm and 19 μm for a titanium stripe of 6 μm and 5 μm, respectively. To fabricate an experimental DCM sample, a configuration was chosen with waveguides at a larger distance D = 19 μm, made of titanium strips W = 5 μm wide, which corresponds to a smaller numerical aperture of the waveguides and a larger modal spot size. Our other work [37] demonstrated that the effect of planar electrodes is stronger for waveguides with higher numerical aperture, so the chosen configuration is less sensitive to electrode displacement and misalignment caused by photolithography inaccuracy, which can lead to differences in waveguide optical loss and applied electric field asymmetry, leading to a change in the transfer function and potentially reducing the effectiveness of suppression of third-order nonlinearity.

Various approaches have been considered to fine-tune the splitting ratio to the desired value of 100%, corresponding to full cross-coupling. Previously, we proposed a method for fine-tuning the splitting ratio of a directional coupler, based on a change in the refractive index due to the photorefractive effect under local laser irradiation [38]. However, this is not suitable because the change in refractive index caused by photorefractive effect decays over time. In this work, we used additive annealing at the same temperature as thermal diffusion of titanium (1021 °C). The shift in the dependence of the splitting coefficient on the distance between the waveguides with additive one-hour high-temperature annealing is shown in Figure 2b. Thus, the directional coupler can be effectively adjusted, but only in the direction of increasing the coupling coefficient. In fabrication of the experimental sample of DCM, we used a series of anneals to consistently achieve complete cross-coupling.

Another feature of DCM, in addition to sub-octave modulation, is the pronounced dependence of the splitting ratio on the wavelength of light. The experimental dependence obtained by tuning the laser wavelength is shown in Figure 3. This means that both the optimal operating point for third-order nonlinearity suppression and the efficiency of its suppression depend on the wavelength of the light, and DCM is not convenient for use in multi-channel WDM systems. But on the other hand, the wavelength of light can be considered as an additional degree of freedom to optimize the suppression of third-order nonlinearity. In this work, we restrict ourselves to investigations at a fixed wavelength of light corresponding to maximum cross-coupling, without applied voltage.

To obtain broadband modulation, high-frequency traveling wave electrodes were fabricated using electroplated silver [39] coated with a thin layer of gold. The electrodes cover the entire length of the coupling region. We used a similar coplanar line configuration that is typically used for Mach–Zehnder modulators on an X-cut lithium niobate substrate. The silicon dioxide-based dielectric buffer layer was used to minimize the mismatch between the phase velocity of the modulating signal and the group velocity of light in the waveguide mode. To ensure the traveling wave mode, a load resistance of 30 Ohms was connected to the end of the coplanar line (see Figure 1b) through a 100 pF capacitor, which made it possible to apply a bias voltage to set the DCM operating point to the same electrodes. It should be noted that, unlike Mach–Zehnder modulators, the DCM modulator did not have separate bias electrodes and the bias voltage was applied simultaneously with the high-frequency modulating voltage through a bias tee. The presence of a dielectric buffer layer was the reason for the unlimited long-term DC drift [34] of the modulator in our previous work [32], which did not allow stabilization of the operating point using an active system with optoelectronic feedback. In this work, the dielectric buffer layer in the interelectrode gaps was removed by dry etching. Etching dramatically changed the long-term behavior of the bias voltage required to maintain the operating point, which generally stabilized within 100–200 s (see Figure 4). Thus, we can use active stabilization with optoelectronic feedback, which improves the accuracy of further third-order nonlinearity suppression measurements.

3. Characteristics of the Experimental Sample of DCM

The experimentally measured transmittance of the DCM versus applied voltage was in good agreement with the theoretical prediction given by Equation (1) (Figure 1d). We associate the shift in the maximum transmission with the influence of the above-discussed inaccuracy of photolithography, which leads to displacement and misalignment of the electrodes relative to the optical waveguides. A rather low value of the characteristic voltage V_S (less than 3 V) was obtained.

By expanding Equation (1) sequentially in terms of the small amplitude of v_M modulation and highlighting the constant bias V_bias, we reach analogically to [32].

$$P_{out2}=T\cdot P_{in}{\left(\frac{\pi }{2}\right)}^2\left[1-\frac{{\pi }^2}{12}\left(1+\frac{3}{V_S^2}\left(V_{bias}^2+2V_{bias}{v}_M+v_M^2\right)\right)\right],$$

(2)

Using this equation, we obtained an expression for the slope of modulation in the dependencies on the bias voltage:

$$P_{out2}=T\cdot P_{in}\frac{{\pi }^4}{8}\frac{V_{bias}{v}_M}{v_S^2},$$

(3)

To evaluate the high frequency performance of the fabricated experimental DCM sample, conventional measurements of spectral dependencies of the electro-optical response and reflection of the modulating signal from the traveling wave electrodes were carried out (Figure 5). The light source was the same as in previous experiments: a TeraXion PureSpectrum™-PS-TNL (by TeraXion, Quebec, QC, Canada) tunable semiconductor laser tuned to a wavelength of 1555 nm. A broadband reverse-biased photodiode (Picometrix P-50A/Z50, by Picometrix LLC, Ann Arbor, MI, USA) was used as a detector. The scattering matrix elements (S11 and S21) were measured using a network analyzer (R&S ZNB40) with standard TOSM calibration. As can be seen in Figure 5c, the frequency bandwidth of the experimental sample was more than 10 GHz at the 3 dB level. The characteristic was taken at the operating point corresponding to the maximum slope of the transfer function. The bias voltage was set using a low-frequency pilot signal by maximizing its transmission. The maximum slope of modulation was observed at V_bias ≈ 0.43 V_S, and it was slightly higher compared to the MZM. Note that the operating point corresponding to the maximum slope had been not optimal for linearization. At the operating point corresponding to the minimum of the third harmonic, the transmission coefficient was much lower.

4. Third-Order Nonlinearity Suppression at Low Frequencies

At first, the experiments were carried out at low frequencies. A DC injector was used to apply a bias voltage from a manually tuned source to the electrodes simultaneously with the modulating signal. Sinusoidal signal at the frequency of 1 kHz was used for modulation. The suppression of the third harmonic of the modulating signal in the output optical signal to a level below the noise of the measuring system was demonstrated by adjusting the bias voltage (Figure 6).

Figure 7 shows two dependencies of the power of the third harmonic on the power of an input modulation signal at different bias voltages (in different operating points). The minima in the dependencies correspond to the complete suppression of third-order nonlinearity. Note that complete suppression occurs only at one specific input power for each measured operating point, and the linearization efficiency generally depends on the power of the modulating signal. At optimal bias voltage, this third harmonic minimum should correspond to zero input power of the modulating signal, and the rate of growth of the third harmonic after the minimum is close to the fifth power. As can be seen in Figure 7 (red curve), the bias voltage Vbias2 ≈ −3.9 V was very close to these conditions. Thus, these conditions ensure an increase in the so-called third-order intercept point [4,6] and are suitable for increasing of the third-order spurious free dynamic range. When the bias voltage is detuned from the optimal operating point by only about 1 V (Vbias1 ≈ −1.8 V), a significant third harmonic appears at a low amplitude of the modulating signal (blue curve), which is almost 20 dB higher than at the optimal operating point.

5. Demonstration of High Frequency Linearization

To define the linearity of the DCM, we performed commonly used third-order intercept point measurements in the two frequencies scheme (Figure 8). Two signals at closely spaced frequencies were applied to the modulator, and the output electrical power spectrum from the photo detector was measured on a frequency spectrum analyzer (Micran SK4M).

Care should be taken to ensure that the nonlinear distortions from the detector, synthesizers, spectrum analyzer or other sources do not exceed the distortions from the modulator. Experiments with R&S SMB 100A and R&S SM 300 RF generators used as radio frequency (RF) sources showed that the isolation of the generators was insufficient, and they interfered with each other creating their own intermodulation distortions that were transmitted to the output of the system. To reduce these distortions, additional 10 dB attenuators were installed in the system after the generators.

In addition, the higher harmonics presenting in the signals from the generators were mixed on the modulator, and the resulting harmonics dominated against the background of suppressed intermodulation distortions from the fundamental frequencies. To suppress the higher harmonics of the generators, two high-frequency filters were developed and produced, which passed only the fundamental frequencies at 176 MHz or 775 MHz. Note that even though the bandwidth of the DCM samples exceeded 10 GHz, we limited ourselves to measurements at these lower frequencies, since at higher frequencies it becomes more difficult from a technical point of view to fulfill the requirements for suppressing nonlinear distortions caused by the measuring system. Nevertheless, these studies allowed us to demonstrate the applicability of the method of using a low-frequency pilot signal to set the DCM to the optimal operating point and linearize its operation at high frequencies as well as to estimate the achievable suppression of third-order nonlinear intermodulation products.

Measurements of the power of the main first harmonic (at 176 MHz and 775 MHz) and higher-order harmonics, namely the second (at 352 MHz and 1550 MHz) and third (at 528 MHz and 2325 MHz), were carried out similarly to measurements for low-frequency signals when only one RF generator was turned on. Figure 9 shows the different harmonics power dependencies on the dc bias (operating point) of the experimental DCM sample. The graph demonstrates that various harmonics can be suppressed by tuning the bias voltage. We were primarily interested in the suppression of third-order nonlinearity (third harmonic).

Then, the third-order intermodulation products were measured. Signals from two RF generators with the same amplitude of 7 dBm was fed to the modulator. For the frequencies of the generators of 775 and 776 MHz, the spectral components of 774, 775, 776 and 777 MHz were measured (Figure 10a). During the measurements, the RF generators had the same power, which resulted in equal power for the two third-order intermodulation terms, so the curves in Figure 10 for the first harmonics (775 and 776 MHz), as well as the curves for the third-order intermodulation terms (774 and 777 MHz) are superimposed on each other. When the bias voltage is close to an operating point corresponding to the suppression of the third harmonic, there is a minimum of third-order intermodulation distortion, in which the ratio between the fundamental and intermodulation components drops by almost 20 dB. The value of the third-order intercept point (OIP3) exceeding 12 dBm was estimated at the optimal operating point of 3.93 V. Note that we use a standard expression for the OIP3 calculation [7].

$$OIPn [\mathrm{dBm}]=\frac{1}{n-1}\left(n\cdot P_{\mathrm{\Omega }} [\mathrm{dBm}]-P_n [\mathrm{dBm}]\right),$$

(4)

which assumes the growth of the third-order intermodulation products as the third power of modulating signal power. Thus, this is a lower estimate since the growth of intermodulation components in the linearized modulator at the optimal operation point proceeds with a higher degree, close to the fifth power of the modulating signal power. This was demonstrated in low frequency measurements and confirmed by measurements of the third-order intermodulation component at 774 MHz and 777 MHz (Figure 10b).

An active system for setting and stabilizing the DCM at the optimal operating point has been developed and fabricated. To set and stabilize an operating point, a low-frequency pilot signal was used at a frequency of 1 kHz, which was mixed with the main high-frequency signal. The criterium for the optimal setting of an operating point was a nulling of third-order harmonics of the low frequency pilot signal. The algorithms and hardware implementation of the system were very similar to the system for setting and stabilizing the Mach–Zehnder modulator (MZM) to the quadrature operating point [40], with the difference that for the DCM it is necessary to zero out the third harmonic, and not the second as for the MZM. It has been demonstrated that third-order nonlinearity can be suppressed by 20 dB at a high frequency of the modulating signal with automatic setting and stabilization of the operating point of the DCM modulator using the developed system.

The theoretical estimate of the noise at the output of a system at a low gain approximation (G << 1) was

$$N=kT+2q{I}_{DC}{R}_0{\left(\left|H_{PD}\right|\right)}^2+RIN\cdot I_{DC}^2{R}_0{\left(\left|H_{PD}\right|\right)}^2=-168 \mathrm{dBm}/\mathrm{Hz}$$

(5)

where I_DC = 3 mA is the constant component of the photocurrent, R₀ = 50 Ohm is the output resistance, kT is the thermal energy, q is the electron charge, RIN = −161 dB/Hz is the relative intensity noise of the used laser diode, and H_PD = 0.5 is the efficiency of the broadband photodetector. A direct measurement of the noise was not possible because the intrinsic noise of the spectrum analyzer exceeded it. By estimating the noise level, the third-order spurious free dynamic range can be calculated [6].

$$SFDR3=\frac{2}{3}\left(OIP3-N\right)$$

(6)

A rather high value of the third-order nonlinear distortion-free dynamic range SFDR3 = 120 dB/Hz^2/3 was obtained continually for the bottom estimate of OIP3 = 12 dBm.

6. Conclusions

To summarize, the influence of an operating point of the lithium niobate directional coupler modulator on the efficiency of the third-order nonlinear intermodulation components suppression was studied. An experimental sample of the DCM based on Ti-indiffused waveguides in single crystal lithium niobate substrates was developed and fabricated. Additive high-temperature annealing was used to adjust the splitting ratio at a zero applied voltage. The possibility of suppressing third-order nonlinearity for both low and high frequencies of the modulating signal was demonstrated. Third-order nonlinearity suppression was observed at a particular bias voltage, which was found lower than at the operating point corresponding to the maximum slope, which allowed increasing dynamic range and reduced optical noise. It was found that the optimal operating point for suppressing the third-order intermodulation distortion depended on the power of the modulating signal. Thus, despite the simple design of the device, it has been concluded that the DCM requires a complicated operating point setting algorithm to achieve a high linearity of operation. An active system for setting the operating point based on the low-frequency pilot signal and zeroing its third harmonic has demonstrated the possibility of linearization when changing the amplitude of the high frequency modulating signal. Removing the dielectric buffer layer in the interelectrode gaps significantly reduced the long-term drift of the DCM and made it possible to use an automatic system for setting and stabilizing the operating point. The ability to achieve a third-order spurious free dynamic range of 120 dB/Hz^2/3 was shown.

The results obtained look promising for high-performance analog optical links. DCM allows for simple technical implementation of the dynamic range extension. The obtained estimate of the third-order spurious free dynamic range of 120 dB/Hz^2/3 is almost 20 dB/Hz^2/3 higher than for the MZM at the quadrature operating point with the same light power and photodetector sensitivity.

However, it should be noted that the practical use of the DCM is fraught with a number of problems. The low gain at the optimal operating point corresponding to the minimum of the third-order intermodulation products, results in a high noise figure > 40 dB, and the high level of second order harmonic distortion leads to limitations in the sub-octave use of the DCM. To fabricate a DCM suitable for effectively suppressing third-order nonlinearity, post-fabrication trimming such as high-temperature additive annealing and etching of the dielectric buffer layer is required, which greatly complicates production.