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All-optical linearized Mach-Zehnder modulator

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Abstract

A practical, broadband, all-optical linearization concept for a Mach-Zehnder modulator (MZM) is proposed and demonstrated. The unique transmitter design includes an amplitude modulated (AM) standard MZM with two optical outputs, where the alternative (or complimentary) output is combined with the laser carrier to create a linearizing optical local oscillator, which when coherently combined with the AM signal fully cancels 3rd order intermodulation distortion components. Using this scheme, record linearity is achieved for a non-amplified RF photonic link, with spurious free dynamic range (SFDR) of 118.5 dB.Hz2/3 and 123 dB.Hz2/3 for single and dual fiber/photodetector schemes.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Analog photonic systems have become increasingly important as RF Photonics applications expand, and as higher order QAM coherent digital systems become more analog-like; requiring a highly linear transmitter. 5G cellular systems using multi-GHz microwave bands at 28 GHz, 39 GHz, and 60 GHz, provide the opportunity of mass market applications for RF photonic links [1], also photonic up- and down-conversion [2], and photonics enabled RF Beamforming [3]. RF photonic links, incorporating high-power, low-noise lasers [4], electro-optic Mach Zehnder modulators (MZMs) [5,6], and high-power, high-speed photodetectors [7], are a key part of analog photonic systems, where spurious free dynamic range (SFDR) is the defining performance parameter. The sinusoidal transfer characteristic of the MZM is the limiting factor in the linearity of an RF photonic link, which is a key part of SFDR, together with system noise. Improving MZM linearity will have a major impact on system performance and will be disruptive in many current RF photonics markets. Additionally, high-volume, low-cost applications for RF photonic links can be best met through photonic integration, most notably the CMOS foundry based Silicon Photonics platform, including heterogeneous integration for required high performance lasers [8] and modulators [6] of an integrated highly linear analog transmitter. Avoiding the large size, weight, power dissipation and cost of discrete components and erbium doped fiber amplifiers (EDFAs) is crucial for high-volume, low-cost products.

Overcoming or linearizing the MZM transfer characteristic, over a wide frequency range, and over a wide range of optical wavelengths, has been a major goal in the RF photonics field for decades, and numerous MZM linearization methods have been suggested and implemented [9]. Linearization techniques can be broadly categorized as electrical, all-optical and mixed. Electrical linearization involves either pre- [10] or post-compensation [11,12], and cascading of modulators [13,14]. The bandwidth of electronic compensation is limited by the speed of electronic processing, and these methods are power consuming. In the “mixed” category, typically two modulators are used to produce complimentary third order intermodulation distortion (IMD3) terms that cancel IMD3 at the detector. A variety of implementations have been used, such as two parallel MZMs [15], polarization multiplexing two separate MZMs [16], dual-parallel MZMs [1719] and others [20]. In all of these schemes that involve more than one modulator, or a specially modified modulator, precise control of multiple DC and RF voltages are required, and IMD3 cancellation takes place at the detector. Since the second harmonic distortion (SHD) terms are not compensated in these schemes unless a balanced photodetector (PD) is used, they are limited in bandwidth to less than an octave. All-optical linearization schemes in which the interference takes place in a ring [21] or a grating [22] in one or both branches of the interferometer are attractive for their simplicity and robustness. They have been successfully implemented on the Silicon Photonics platform [2325], however, the resonant nature of light propagation in rings and gratings limits the bandwidth over which linearization can be achieved. In both Si and III-V modulators IMD3 can potentially be reduced through the interplay of the nonlinearity of the MZI with the intrinsic nonlinearities of the material response [2628]. However, reduction of IMD3 is typically accompanied by an increase of SHD, and linearization requires operation in a region with increased insertion loss. With all the effort devoted to linearization and SFDR expansion of analog links, no technique has been found sufficiently advantageous for widespread use in practical systems.

In this paper we propose, analyze, and demonstrate a novel ultra-wideband, wavelength independent, all-optical technique for full cancellation of IMD3; we combine discrete photonic components to create a linearized transmitter and RF photonic link. We provide linearization results for the cases of a typical system with a single fiber and PD, and also one with dual fibers and a balanced PD. Unlike previously proposed schemes, we simply take advantage of the typically unused complimentary output of a standard MZM with dual outputs, requiring no modified/complex RF driving signal(s). Linearization occurs at the output of the modulator/ transmitter, not at the PD, so no external polarization maintaining (PM) components, e.g. PM fibers, are required. The only additional elements are three simple optical power splitters/combiners that can be easily implemented using integrated optics. This elegant linearization scheme works over an ultra-wideband electrical bandwidth, and due to the absence of resonant components, the optical bandwidth is no different from a standard MZM.

2. Linearized Mach-Zehnder modulator (MZM) concept and theory

Prior to describing the linearization scheme we describe basic RF photonic links, starting with a standard intensity modulated (IM) RF photonic link whose schematic is shown in Fig. 1(a). A high-power, low-noise semiconductor laser provides a singlemode optical carrier into an MZM, which is biased at quadrature (+ 90°, or - 90°) to provide an IM output, the transfer characteristic being sinusoidal versus the modulated phase difference between the arms of the MZM. The output of the MZM includes a large carrier component plus modulated sidebands, which after passing through a system fiber enter a high-power, high-speed PD that provides the electrical RF output. The spectral diagrams in Fig. 1(a) indicate optical components (red) and electrical RF components (blue) in the system for a simple single frequency analysis. The optical signal includes a large optical carrier (DC), modulation components x(t) = V(t)·π/Vπ at frequency ω (where V(t) is the applied modulation waveform and Vπ is the half wave voltage of the MZM), plus 3rd harmonic distortion components x3 at frequency 3ω, and fifth harmonic distortion components x5 at frequency 5ω. This IM scheme is widely used in RF photonics, however, its SFDR is limited by both MZM nonlinearity and system noise, i.e. shot noise in the PD and relative intensity noise (RIN) from the laser. Both noise components are high in IM links due to the large carrier component at the PD. SFDR is often increased in an IM link through a brute force approach of increasing optical power levels, usually by including an erbium doped fiber amplifier (EDFA) [e.g. 15], which also requires a very high-power, high-linearity PD (to avoid PD damage) - this approach adds significant cost, size weight and power, with diminishing returns for improved SFDR as the received power is increased, due to the increase in laser RIN. A much more effective and efficient approach is to improve the linearity of the MZM.

 figure: Fig. 1.

Fig. 1. a) Intensity modulation (IM) RF photonic link including a laser, quadrature biased modulator, and PD, 1b) CC-AM scheme; laser power is split between null-biased modulator (for AM) and Carrier (lower arm); these are coherently combined at quadrature for input to the PD. Spectral diagrams indicate harmonic components in the systems; optical (red), electrical (blue).

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The new linearization scheme is best described in two steps, the first is a move away from the standard IM scheme to a “controlled carrier-amplitude modulation” (CC-AM) scheme [29], which we demonstrate provides ∼ 4 dB of SFDR improvement over a similar IM link. Secondly, the CC-AM scheme is linearized to provide a further increase in SFDR, at least 3 dB higher SFDR in our first experimental demonstrations, providing RF photonic links with > 7 dB SFDR improvement over a standard IM link. A fully integrated device using the Linearized CC-AM scheme should provide even further improvement in SFDR performance.

The CC-AM scheme is shown in Fig. 1(b). The laser power, (1 + a2)P, is split into two (unequal) powers; P to the MZM, and a2P to ‘Carrier’ in the lower arm (e.g. for a 50/50 splitter, a2=1, equal powers go to the MZM and Carrier). The MZM is null-biased, for AM, and its output is coherently combined at quadrature with the Carrier from the lower arm. The choice of the input split ratio is the key to operation. The RF signal V(t) produces phase modulation in each arm x(t) = π V(t) /Vπ. Note that this analysis works for any arbitrary input RF signal and not only for harmonic modulation. The null-biased AM signal from the ‘main’ output of the MZM is;

$${E_s}(t )= {E_0}cos ({\omega _L}t)sin [x(t )]$$
where ωL is the optical frequency, so that Es(t) is made up of an optical carrier with an envelope given by the RF signal. Using a Taylor series expansion for sin(x) gives;
$${E_s}(t )= {E_0}cos ({\omega _L}t)\left[ {x(t )- \frac{1}{6}{x^3}(t )+ \frac{1}{{120}}{x^5}(t )} \right]$$

As expected, this AM signal has no DC component, while it has the modulation signal x(t) plus additional odd powers of x, which for harmonic signals results in odd harmonics (3rd, 5th, and so on), and for two tone signals third and fifth order intermodulation distortion signals, which limit SFDR. It should be noted that if, for example, the term x3(t) is canceled, then all the third order distortions are also canceled no matter what is the actual shape of x(t). The other part of the laser power from the splitter becomes the Carrier or homodyne ‘LO’ signal;

$${E_{LO}} = a{E_0}cos({{\omega_L}t} )$$

The total signal at the PD is found from multiplying these signals (2, 3) together;

$${i_s}(t )\sim aTE_o^2\left[ {x(t )- \frac{1}{6}{x^3}(t )+ \frac{1}{{120}}{x^5}(t )} \right]$$

Equation (4) shows that the output photocurrent follows the input RF signal x(t), with a scaling factor a·T which includes additional losses in the system, 1-T. The third order and fifth order distortion terms are also clearly seen. In comparison to the RF signal, x(t), the third order term is negative with a scaling factor of 1/6, while the fifth order term is positive with a scaling factor of 1/120, these terms are indicated in the spectral diagrams in Fig. 1. These are the terms responsible for IMD3 and fifth order intermodulation distortion (IMD5), respectively.

The CC-AM scheme allows the ratio of Carrier signal to modulation signals to be controlled, in order to optimize and increase SFDR. We denote the ratio of the power to the MZM (P) versus the power to the Carrier (a2P) as R*, where R* = 1/a2. By increasing R* we achieve larger modulation sidebands for CC-AM than in a similar IM system, while the Carrier level and therefore laser RIN at the PD are optimized for maximum SFDR. Additionally, the Carrier signal does not see the insertion loss of the MZM. In order to compare RF Photonic links using IM with CC-AM at different R* ratios, we carried out two-tone intermodulation distortion measurements at 10 GHz, using components described in Section 3, with the same laser power for each of these tests. The two-tone RF signals at 9.995 GHz and 10.005 GHz were combined in an RF coupler, including 6 dB attenuators for each signal before the coupler to increase isolation of signals returning to either of the microwave signal sources (Agilent PSG E8257 units), to avoid adding intermodulation distortion. The output of the coupler passes through a filter to remove second harmonic signals at 20 GHz, and the two-tone signals driving the modulator are ∼ 0 dBm each. Intermodulation distortion components are measured directly on a microwave spectrum analyzer, while the noise floor is calculated by adding together the PD thermal noise, shot noise (based on a photocurrent measurement), and laser RIN (based on a worst case laser RIN value of -165 dBc/Hz [4] and the received optical power at the PD. The plot in Fig. 2 shows the SFDR measurement results. The noise floor varies with optical power/photocurrent, e.g. -161 dBm at 6 mA, and -164.6 dBm for 3 mA photocurrent.

 figure: Fig. 2.

Fig. 2. SFDR versus PD current for IM scheme, and CC-AM scheme with various R* ratios.

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As expected, SFDR for the IM link saturates, in this case at 110.8 dB.Hz2/3 for a PD current of 12 mA, whereas all the CC-AM SFDR curves provide higher SFDR values, even though the PD currents are much lower. For R* values of 6.8 and 15, SFDR values of 114.9 and 114.7 dB.Hz2/3 are found, with associated noise floors of -166 dBm and -168 dBm, ∼ 4 dB SFDR increase over IM, for PD currents of only 2.1 and 1.3 mA. These results demonstrate the advantage of the CC-AM scheme versus the IM scheme. The higher photocurrents in the IM scheme can provide higher RF Gain in the system, which is advantageous in some applications, although system RF Gain can be improved by a good low noise amplifier (LNA) following the PD, whereas system SFDR cannot be improved in the same way.

We now explain the novel linearization scheme [30]. MZMs are known to be implemented using either a Y-junction output coupler with a single output, or a directional (or multimode interference) coupler with two complimentary outputs; one provides the modulated signal and the other is typically unused. The novel linearization scheme shown in Fig. 3 utilizes the (unused) complimentary output of the MZM to achieve broadband linearization. As in the CC-AM scheme, Laser power is split between (upper) modulation and (lower) carrier/local oscillator (LO) arms. The MZM is null-biased so that its (main) output is AM. The complimentary output of the MZM includes the majority of the laser carrier signal input to the modulator (after insertion losses), plus additional (even harmonic) modulation components. This complimentary output, denoted Carrier*, is attenuated, then subtracted from the Carrier in the lower arm from the Input splitter, i.e. added with its carrier component 180° out of phase. When combined, i.e. Carrier – A·Carrier* (where the optimal power scaling coefficient A=1/4 as explained below), they form a new signal, the linearizing local oscillator (LO*), that is combined in the output coupler with the AM signal, and mixed in the PD to create the linearized RF output. A combiner and single PD can be used, as in Fig. 3, for the vast majority of applications with only a single fiber link. The system can use a balanced PD where feasible, using an Output 50/50 coupler - although also requiring dual fibers in the system implementation. The balanced PD system provides improved performance, i.e. increased SFDR and Gain, and reduced Noise Figure (NF), through a higher output RF signal and from RIN and SHD cancellation. The photonic integrated circuit (PIC) can be fabricated in any material currently used for MZM PIC devices, e.g. LiNbO3 [5], III-V [31], Si [32], or alternative versions; thin film LiNbO3 (TFLN) [33], III-V on Si [20], and so on. The complete modulation PIC adds only couplers and DC phase control sections to an MZM device with two outputs. Fabricating the PIC on a single solid substrate provides excellent phase control of the different paths within the Linearized MZM PIC, as required for operation of the MZM device itself.

 figure: Fig. 3.

Fig. 3. Linearized CC-AM RF photonic link; the laser output is split between upper modulation arm and lower Carrier arm. The MZM is null-biased for AM on its main output, providing the Carrier* signal on its alternative output. Carrier* is attenuated, then subtracted from Carrier to create linearizing signal LO*. The AM and LO* signals are coherently combined at quadrature, eliminating IMD3, so that the PD RF output does not include an IMD3 component.

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Considering the Linearized CC-AM scheme in Fig. 3; with the MZM null-biased (AM) for the main output, the complimentary MZM output Carrier* is given by;

$${E^{\ast }}(t )= {E_0}cos ({\omega _L}t)cos [x(t )]$$
which, using a Taylor series expansion for cos(x) gives;
$${E^{\ast }}(t )= {E_0}cos ({\omega _L}t)\left[ {1 - \frac{1}{2}{x^2}(t )+ \frac{1}{{24}}{x^4}(t )} \right]$$

This alternative output has a strong DC carrier signal, plus even harmonics, i.e. second, fourth, and so on. Next, as part of the linearization scheme, to eliminate third order distortion, this signal is attenuated by a/4, providing the signal a/4.Carrier*;

$$a{E_0}cos ({\omega _L}t)\left[ {\frac{1}{4} - \frac{1}{8}{x^2}(t )+ \frac{1}{{96}}{x^4}(t )} \right]$$

This attenuated Carrier* signal includes a DC carrier term, with a scaling factor of a/4, a second order term which has a negative scaling factor of -a/8, and fourth order term which has a positive scaling factor of a/96. Subtracting this attenuated Carrier* signal (Eq. (7)) from the Carrier signal (Eq. (3)) provides the Linearizing LO* signal;

$${E_{LO\ast }} = \frac{3}{4}a{E_0}cos({{\omega_L}t} )\left[ {1 + \frac{1}{6}{x^2}(t )- \frac{1}{{72}}{x^4}(t )} \right]$$

It is important to obtain the correct ratio of Carrier to Carrier* to create LO*, in order to obtain the correct term to linearize the AM signal from the MZM, shown in Eq. (2). Mixing LO* (Eq. (8)) and AM signal (Eq. (2)) and expanding provides the photocurrent, in which the third order term has been eliminated, while the fifth order term is increased by 4x;

$${i_s}\sim 2T{\langle E_s}(t ){E_{LO\ast}\rangle}$$
$$= \frac{3}{2}aTE_0^2{\langle cos ^2}({\omega _L}t)\rangle\left[ {x(t )- \frac{1}{6}{x^3}(t )+ \frac{1}{{120}}{x^5}(t )\ldots .} \right]\left[ {1 + \frac{1}{6}{x^2}(t )- \frac{1}{{72}}{x^4}(t )+ ..} \right]$$
$$= \frac{3}{4}aTE_0^2\left[ {x(t )- \frac{1}{{30}}{x^5}(t )+ ..} \right]$$
$${i_s}(t )= \frac{3}{4}aTE_o^2\left[ {x(t )- \frac{1}{{30}}{x^5}(t )} \right]$$
where the averaging was performed over the response time of the detector which is much longer than the optical period but short enough to respond to the signal. It is also easy to see that in the presence of phase error $\delta \varphi $ between Carrier and Carrier* a third order distortion term ${i_{s3}} = \frac{1}{3}aTE_0^2\sin (\delta \varphi /2)$ will arise; hence keeping the phase shift between Carrier and Carrier* to 180 degrees is crucial for large SFDR. In addition to this, a strong LO current is also formed;
$${i_{LO}}(t )\sim 2T \langle E_{LO\ast }^2\rangle = \frac{9}{8}{a^2}TE_0^2{\langle cos ^2}({\omega _L}t)\rangle{\left[ {1 + \frac{1}{6}{x^2}(t )- \frac{1}{{72}}{x^4}(t )+ ..} \right]^2}$$
$${i_{LO}}(t )= \frac{9}{{16}}{a^2}TE_o^2\left[ {1 + \frac{1}{3}{x^2}(t )} \right]$$

The LO current includes second order distortion, introducing even order harmonics, which limit the linearized modulation bandwidth to less than an octave, although this is sufficient for the 5G application and many others. This SHD can be eliminated through the use of a balanced PD, allowing the linearization scheme to work with a signal bandwidth beyond an octave. From the equations, the key is to have the optimum ratio of the Carrier* to Carrier signal when creating LO*, in order to eliminate IMD3. The ratio of the power of this linearizing LO* signal to the power of the AM signal does not affect linearization. By varying the ratio of Carrier* to Carrier, IMD3 signals can be completely eliminated, as shown in Eq. (9), in which case IMD5 signals will dominate SFDR, although with significantly improved SFDR compared to without linearization. From the analysis, IMD3 is totally eliminated for a ratio of Carrier*/Carrier (C*/C) powers of 1/16, i.e. -12 dB. This C*/C ratio is measured during the experiments, and results validate the analysis, as the linearization/peaking in SFDR is clearly seen for C*/C close to -12 dB. In practice, creating LO* reduces the LO power, as Carrier* is subtracted from Carrier, so there is some penalty associated with the linearization scheme itself.

A two-tone intermodulation distortion analysis for the linearization scheme is included in Supplement 1. This shows a large linearization increase in SFDR for perfect control of the C*/C ratio, e.g. with no phase variations, and also shows SFDR improvement versus C*/C ratio for less ideal control (variation) of this ratio - appropriate for the experimental setup described in Section 3 where optical phase is not well controlled, plus SFDR values more appropriate for a fully integrated device with excellent phase control. These simulated curves are included with the experimental results in Figs. 5 and 6.

3. Experimental setup and results

The novel linearization scheme is a simple but elegant extension to an integrated MZM device; splitting and combining of signals is easily achieved in standard couplers, e.g. directional couplers, while phase control and stability between different signals within the transmitter can be easily achieved in a fully integrated device. However, to validate the scheme would require fabrication of the linearized MZM device, which is very costly and takes considerable time. In order to demonstrate the basic concepts of this scheme in advance of fabricating an integrated version, an experimental setup was devised that includes discrete, commercial “off the shelf” photonic components; i.e. an MZM with two PM fiber outputs, PM couplers, a PM attenuator, interconnected with PM optical fibers, creating the experimental setup shown in Fig. 4.

 figure: Fig. 4.

Fig. 4. Experimental setup to validate the linearized MZM scheme (single fiber/PD scheme) based on fiber interconnected discrete photonic components. MZM and MZI loops are controlled by bias control boards and PZT fiber stretchers to provide the correct control of optical phase.

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A high power 1550 nm laser (Thorlabs ULN15PC), providing a Lorentzian linewidth < 100 Hz and RIN < -165 dBc/Hz [4], is split to provide ∼ +18 dBm each to the MZM (top path) and to the Carrier signal (lower path). An EOSPACE (AX-1 × 2-0MVS-40) MZM is null-biased to provide AM on its main output, with a 1% tap of this output used with a PSI bias control board (PSI-0204-99) to null-bias the MZM. The Carrier* output of the MZM passes through attenuator ‘A’, and is combined with the Carrier signal from the lower path in an 80/20 coupler, i.e. LO* coupler. This coupling ratio was chosen to provide C*/C ratios including the -12 dB optimum value. The LO* coupler provides a main output with 80% Carrier and 20% Carrier*, which for minimum attenuation ‘A’ provides a maximum C*/C ratio of -9.5 dB. The alternative output of the LO* coupler is used with a second PSI bias control board set to minimize the LO* output, i.e. provide Carrier - Carrier*; maximizing the alternative coupler output. The optical phase difference of the two paths within this large Mach Zehnder interferometer (MZI), i.e. the phase difference of the carrier signals of the two paths between the Input 50/50 splitter and the LO* 80/20 coupler, is controlled by a piezoelectric (PZT) PM fiber stretcher (Evanescent 915B), which adds 2.7 m to the length of that arm, controlled by the bias control board.

The AM output of the MZM is combined with the LO* signal in the Output 80/20 coupler, which provides 80% of the AM signal and 20% of the LO* signal to a high-speed PD (Discovery DSC40S). A PZT fiber stretcher in this outer MZI, i.e. the two paths between the Input 50/50 splitter and the Output 80/20 coupler, controls the phase difference of the carrier at the output coupler, controlled by a third PSI bias control board that takes power from the alternative output of the output coupler - this bias control board is set to quadrature. The MZM device and couplers each include one meter PM fiber pigtails, plus the PZT fiber stretchers each add 2.7 m of PM fiber length. These multiple meter fiber lengths within the MZIs make phase difference control between arms of each MZI extremely difficult. A significant effort with multiple setups improved over a year of experiments finally achieved a relatively stable system and repeatable results. Even so, the bias control loops add phase errors that change over time compared to their goal values (i.e. LO* minimized, PD Output at quadrature), especially as phase errors compound in the second MZI from changes in the first MZI. Despite these phase errors, plus any fast phase changes from the fibers not removed by the bias control loops, consistent, repeatable linearization measurements were made using the final experimental setup, stable over the multiple hours needed for a single measurement set of SFDR vs C*/C.

Figure 5 shows results from the experiment shown in Fig. 4, for a single output fiber/PD, together with simulated SFDR3 (broadening value σ = 0.3) and photocurrent curves from Supplement 1. Two-tone measurements were carried out at 10 GHz (∼0 dBm RF each) to provide SFDR results. Without linearization, i.e. using only the CC-AM modulation scheme, with R* = 5 (higher values of R* together with linearization made control loops less stable), an SFDR of 114.8 dB.Hz2/3 was found. This is already 4 dB higher SFDR than the IM link in Fig. 2, which is included for comparison in this figure. The photocurrent without linearization, included at a -40 dB C*/C ratio in the plot for convenience, is 8.7 mA. As the C*/C ratio is increased the photocurrent reduces, as expected, with measurements following the simulated curve. SFDR rises up to a peak value at a C*/C ratio close to -12 dB, agreeing with theory, and demonstrating a 3.4 dB SDFR improvement over the CC-AM scheme. The maximum SFDR is 118.2 dB.Hz2/3, a 7.4 dB SFDR increase over the IM RF photonic link shown in Fig. 2. The PD current at maximum SFDR is 5.3 mA, for a noise floor of -161.6 dBm.

 figure: Fig. 5.

Fig. 5. Experimental results plus simulation result (for σ = 0.3) of SFDR (at 10 GHz) and IPD vs. C*/C for the Linearized CC-AM setup in Fig. 4. Example of SFDR for IM link SFDR included from Fig. 2, plus the SFDR value for CC-AM without linearization is included for comparison.

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The SFDR improvement is achieved even as the photocurrent drops from 8.7 to 5.2 mA. The 3.4 dB SFDR increase over CC-AM alone is significant, the shape versus C*/C fitting well with the simulation curve from Supplement 1 (black dashes in Fig. 5) using a broadening value σ = 0.3, for this discrete component based result. With the excellent phase control expected for a fully integrated device, e.g. using σ = 0.02, a simulated peak SFDR of 122 dB.Hz2/3 would be expected, i.e. 7.2 dB above the CC-AM result, and 11.2 dB above the IM link. The SFDR peak is broadened versus the ideal linearized case versus C*/C, most likely due to phase variations away from optimum over time in the two MZIs, and other limitations of this discrete component based experimental setup. The linearization and significant SFDR increase clearly demonstrates the efficacy of the new linearization technique. In practice, the Input splitter and LO* coupler ratios can be chosen to provide the optimum C*/C ratio, additionally, the Input splitter ratio (e.g. 50/50) could be designed to be tunable to allow C*/C to be optimized. The Gain and NF for this link, at peak SFDR, are -15.6 dB and -28 dB.

The SFDR results in Fig. 5 include three SFDR curves; in these two-tone measurements, F1 is 9.995 GHz, F2 is 10.005 GHz, and IMD3 products are I1 at 9.985 GHz, and I2 at 10.015 GHz. In this set of results the SFDR calculated from F1 and I1, i.e. SFDR F1/I1, and SFDR F2/I2, and also the average values of the two combined, SFDR Fave/Iave, are all almost identical at the different measurements across the C*/C range. However, in some measurement sets, different SFDR values for F1/I1 and F2/I2 were found, e.g. sometimes F1/I1 peaked higher and F2/I2 had a lower peak, and sometimes the opposite occurred. It was not obvious what caused, or how to eliminate, the splitting in the SFDR curves, however, clearly at times the linearizing LO* signal was optimized for one of these values more than the other, maybe due to phase errors/offsets within one and/or the other large MZI. These split SFDR measurements are not expected in a fully integrated linearized-MZM device where the phase differences between arms of the multiple MZIs will be very stable and fixed at the correct values.

A measurement set for a system including two output fibers and a balanced PD, also showing the split in SFDR curves, is shown in Fig. 6. In the experimental setup the couplers were optimized differently than from the single fiber setup in Fig. 4; an Input 80/20 splitter provided 80% of laser power to the MZM (20.2 dBm) and 20% to Carrier (14.2 dBm), a 90/10 LO* coupler passed 90% of Carrier into LO*, subtracting 10% of A·Carrier* (enabling a higher maximum C*/C ratio), and an Output 50/50 coupler was required for the use of a balanced PD. Using an available balanced PD (DSC705) that has lower bandwidth, plus to avoid the need to carefully match the fiber delay paths to the two PDs, a frequency of 1 GHz was chosen for these measurements (∼0 dBm RF per signal) – this also demonstrates the linearization scheme over a wide frequency range. This setup provides an R* value of 4.4, and without linearization an SFDR of 118.7 dB.Hz2/3 was achieved; a high SFDR value due to the CC-AM modulation scheme plus the use of a balanced PD. The non-linearized DC photocurrent from each PD was 7mA (14 mA for 2 PDs) compared to 8.7 mA in the single fiber case, providing a Gain of -7.4 dB (included in Fig. 6), compared to -13.3 dB Gain for the single fiber case.

 figure: Fig. 6.

Fig. 6. Experimental and simulation (for σ = 0.2) results of SFDR (at 1 GHz), and Gain for the Linearized CC-AM setup with two fibers/balanced PD. The SFDR value for CC-AM without linearization is included for comparison.

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The split in SFDR curves shows a maximum SFDR of 124 dB.Hz2/3, a minimum of 120.6 dB.Hz2/3, for an average SFDR of 122.3 dB.Hz2/3, providing SFDR increases from linearization of 5.3 dB (max), 1.9 dB (min), for an average increase of 3.6 dB compared to the CC-AM results, similar to the increase seen in the single fiber/single PD case. The noise floor at peak SFDR is -162 dBm, almost entirely shot noise. The Gain at maximum SFDR is -10 dB, and the NF of the link is -22.2 dB. The simulated curve from Supplement 1 for σ = 0.2 provides a reasonable fit to the experimental results, having a peak SFDR of 123 dB.Hz2/3. Using a small broadening parameter (σ = 0.02) more appropriate for an integrated Linearized CC-AM transmitter would provide a peak SFDR of 126 dB.Hz2/3.

4. Summary

We have proposed and demonstrated a novel linearization technique for an MZM that provides significant improvement in SFDR for an RF photonic link, and will work within a variety of analog photonic systems. The elegant scheme takes advantage of the complimentary, often unused, output of an MZM to create a linearizing LO* signal, which when combined with the AM output of the MZM cancels third order intermodulation distortion components. Using this concept with a non-ideal discrete photonic component implementation of the linearizing scheme, SFDR improvement of 7.4 dB over a typical IM link was demonstrated for a single fiber, single PD system, for a maximum SFDR of 118.2 dB.Hz2/3, while for a dual fiber, balanced PD system, a similar linearization improvement provided an SFDR of 122.3 dB.Hz2/3. The reported measurements are record SFDR results for such RF photonic links obtained without the use of an EDFA, to the best of the authors’ knowledge, and provide the possibility of mass market solutions for high performance, low cost links for use in 5G and other systems.

Funding

Air Force Research Laboratory (FA8650-19-C-1007).

Acknowledgments

The authors acknowledge useful discussions and help with measurements from Jill Morton. The authors acknowledge funding through Air Force SBIR program # FA8650-19-C-1007. The views and conclusions in this paper (AFRL-2021-1525) are those of the authors and should not be interpreted as presenting official policies or position. The U.S. Government is authorized to reproduce and distribute reprints.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Supplementary Material (1)

NameDescription
Supplement 1       Supplemental Document

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. a) Intensity modulation (IM) RF photonic link including a laser, quadrature biased modulator, and PD, 1b) CC-AM scheme; laser power is split between null-biased modulator (for AM) and Carrier (lower arm); these are coherently combined at quadrature for input to the PD. Spectral diagrams indicate harmonic components in the systems; optical (red), electrical (blue).
Fig. 2.
Fig. 2. SFDR versus PD current for IM scheme, and CC-AM scheme with various R* ratios.
Fig. 3.
Fig. 3. Linearized CC-AM RF photonic link; the laser output is split between upper modulation arm and lower Carrier arm. The MZM is null-biased for AM on its main output, providing the Carrier* signal on its alternative output. Carrier* is attenuated, then subtracted from Carrier to create linearizing signal LO*. The AM and LO* signals are coherently combined at quadrature, eliminating IMD3, so that the PD RF output does not include an IMD3 component.
Fig. 4.
Fig. 4. Experimental setup to validate the linearized MZM scheme (single fiber/PD scheme) based on fiber interconnected discrete photonic components. MZM and MZI loops are controlled by bias control boards and PZT fiber stretchers to provide the correct control of optical phase.
Fig. 5.
Fig. 5. Experimental results plus simulation result (for σ = 0.3) of SFDR (at 10 GHz) and IPD vs. C*/C for the Linearized CC-AM setup in Fig. 4. Example of SFDR for IM link SFDR included from Fig. 2, plus the SFDR value for CC-AM without linearization is included for comparison.
Fig. 6.
Fig. 6. Experimental and simulation (for σ = 0.2) results of SFDR (at 1 GHz), and Gain for the Linearized CC-AM setup with two fibers/balanced PD. The SFDR value for CC-AM without linearization is included for comparison.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

E s ( t ) = E 0 c o s ( ω L t ) s i n [ x ( t ) ]
E s ( t ) = E 0 c o s ( ω L t ) [ x ( t ) 1 6 x 3 ( t ) + 1 120 x 5 ( t ) ]
E L O = a E 0 c o s ( ω L t )
i s ( t ) a T E o 2 [ x ( t ) 1 6 x 3 ( t ) + 1 120 x 5 ( t ) ]
E ( t ) = E 0 c o s ( ω L t ) c o s [ x ( t ) ]
E ( t ) = E 0 c o s ( ω L t ) [ 1 1 2 x 2 ( t ) + 1 24 x 4 ( t ) ]
a E 0 c o s ( ω L t ) [ 1 4 1 8 x 2 ( t ) + 1 96 x 4 ( t ) ]
E L O = 3 4 a E 0 c o s ( ω L t ) [ 1 + 1 6 x 2 ( t ) 1 72 x 4 ( t ) ]
i s 2 T E s ( t ) E L O
= 3 2 a T E 0 2 c o s 2 ( ω L t ) [ x ( t ) 1 6 x 3 ( t ) + 1 120 x 5 ( t ) . ] [ 1 + 1 6 x 2 ( t ) 1 72 x 4 ( t ) + . . ]
= 3 4 a T E 0 2 [ x ( t ) 1 30 x 5 ( t ) + . . ]
i s ( t ) = 3 4 a T E o 2 [ x ( t ) 1 30 x 5 ( t ) ]
i L O ( t ) 2 T E L O 2 = 9 8 a 2 T E 0 2 c o s 2 ( ω L t ) [ 1 + 1 6 x 2 ( t ) 1 72 x 4 ( t ) + . . ] 2
i L O ( t ) = 9 16 a 2 T E o 2 [ 1 + 1 3 x 2 ( t ) ]
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