Highly linear dual ring resonator modulator for wide bandwidth microwave photonic links

Arash Hosseinzadeh; Christopher T. Middlebrook

doi:10.1364/OE.24.027268

1. Introduction

Microwave photonic links (MPLs) are critical for applications such as wireless-access networks, antenna remoting, and video distribution networks [1–3]. Nonlinear distortions remain as one of the fundamental limitations for full scale implementation of MPL [4, 5]. To evaluate linearity in MPLs, the spur-free dynamic range (SFDR) is a widely accepted performance metric [6]. The dominating distortion in MPLs is the third order intermodulation distortion (IMD3) occurring at frequencies very close to the signal frequencies.

Current MPLs utilize Mach-Zehnder Interferometers (MZI) with sinusoidal transfer function as Electro-optical (E/O) modulators, causing nonlinear distortions. Ongoing research efforts [7–9] have been focused on achieving a highly linear modulator for MPLs using MZI with limited success. To increase the linearity in MZI various approaches have been proposed, namely, dual-parallel MZI [10, 11], cascaded MZI [12], dual-wavelength inputs [13], and dual-polarization inputs [9], and ring resonator assisted MZI [14, 15]. The ring resonator assisted MZI provides higher SFDR overall and is divided in two categories, 1) Resonator-Assisted Mach-Zehnder Interferometer (RAMZI) [7, 14], and 2) Interferometric Modulator with Phase-modulating and Cavity-modulating (IMPAAC) components [8, 15]. In these modulators ring resonators are coupled to the branches of the MZI and the phase response of the ring resonator is used to enhance the linearity of the MZI’s sinusoidal transfer function. The RAMZI and IMPAAC both require a MZI and thus inherit the sinusoidal transfer function, required size, and power requirements. The RAMZI and IMPACC structures add complexity to the fabrication and integration process and their operation is sensitive to the structure properties including loss factor of the ring and coupling coefficient [8, 16]. The main drawback of RAMZI and IMPAAC is the limited linearized bandwidth. SFDR of the standard MZ is ideally independent of the modulation frequency, however by adding a ring resonator to the MZI results a high SFDR in a narrow operational bandwidth [8, 17].

Ring resonator modulator (RRM) attracted interest because of its potential to enhance linearity, reduce the size and power consumption in MPLs [18–22]. The RRM is used as intensity modulators with a Lorentzian shaped transfer function versus applied voltage that yields suppressing of various nonlinear distortions at special bias voltages [23, 24]. Another advantage of the Lorentzian transfer function of the RRM is its repetition in frequency because of the periodicity of the ring resonator resonance in frequency domain. The frequency difference between the two subsequent resonances is the Free-Spectral Range (FSR) of the ring resonator. It has been shown that RRMs with traveling-wave electrodes can provide higher modulation index in compare to MZI modulators in limited bandwidth at higher operational frequencies when velocity mismatch and microwave electrode loss effects are taken into account [25, 26]. Functional RRM has been reported to be operated at multiples of the FSR, up to 165 GHz fabricated by electro-optic polymer material [26]. Despite RRM attractive advantages the implementation of the RRM is very limited mainly because of the resonance dependent function of the RRM and design/fabrication complexity. The RRM impose frequency dependent figure of merits including SFDR, gain and noise figure providing high figure of merits in a narrow bandwidth around the resonance frequency. Moreover figure of merits in RRM is sensitive to the fabrication tolerances and structure properties specifically to the coupling conditions and ring loss factor [27].

A novel E/O modulator, as shown in Fig. 1 is proposed for wide bandwidth applications utilizing a dual ring resonator structure to increase linearity with appropriate bias and RF/Optical feed ratios resulting in a high SFDR over a wide operational bandwidth. The dynamic response of a RRM is first analyzed by deriving analytical equations for nonlinear distortions. Obtained single RRM equations show the operational bandwidth limitations while attempting to maintain a high SFDR. A non-MZI design is proposed utilizing a dual ring resonator modulator that uses RRM linearity combined with specific RF/optical splitting power ratio and 180° phase difference between dual paths demonstrating 3rd order intermodulation distortion suppression which can obtain SFDR ~130 dB.Hz^6/7 at limited operational bandwidth around the resonance frequency while keeping the SFDR > 124 dB.Hz^4/5 independent from operational frequency.

Fig. 1 Schematic of a MPL and using dual ring resonator modulator, F shows the RF power splitting ratio between two modulators. Electrodes can be designed in either lumped or traveling-wave types and depending on the utilized electro-optic material type electrodes locate side-by-side or top-bottom of the optical waveguide. Figure shows lumped electrodes located side-by-side the ring waveguides.

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2. Single ring resonator modulator

The dynamic transfer function of a RRM is determined according to the multiple round-trip approach given by Eq. (1) [26]

{| \frac{E_{o u t} (t)}{E_{i n} (t)} |}^{2} = {| τ - (1 - τ^{2}) \sum_{n = 1}^{\infty} τ^{n - 1} α^{n} \times e^{- i (n θ + δ_{n} \sin (ω_{m} t - n φ))} |}^{2}

where ω_m is the operating microwave angular frequency, t is the time, n is the number of times the beam propagates inside the ring, τ defines the coupling coefficient between output and input, α is the round-trip loss factor of the ring and in this work critical coupling condition [28] is assumed between the ring resonator and the base waveguide with α = τ = 0.8. φ = ω_m/FSR where FSR is defined by c/(n₀L) (c is the speed of light in free space, n₀ is the effective refractive index of the propagating mode and L is the perimeter of the ring). θ is the round trip phase shift due to the steady state refractive index of the ring and applied DC bias voltage as shown in Eq. (2) where k is the propagation constant, r is the electro-optic coefficient of the material, V_dc is the bias voltage, λ is the optical wavelength, Γ is the electrical-optical overlap parameter, and g is the electrode gap. In this paper, steady state phase shift due to the refractive index of the ring is not considered. In Eq. (1) δ_n is the modulation index and in the case of lumped electrode for microwave signal in the form of V(t) = V_msin(ω_mt) is given by Eq. (3). For the calculation purpose the MPL is considered to use laser source at λ = 1.55 μm and modulator is assumed to have L = 6 mm, g = 10 μm, and Γ = 1 while modulator is based on electro-optic polymer materials with n₀ = 1.6 and r = 36 pm/V [29].

θ = k n_{0} L + \frac{π n_{0}^{3} r Γ V_{d c}}{λ g} L

δ_{n} \sin (ω_{m} t - n φ) = \frac{π n_{0}^{3} r Γ V_{m}}{λ g} L \times \frac{\sin (\frac{n φ}{2})}{(\frac{φ}{2})} \times \sin (ω_{m} t - \frac{n φ}{2})

Nonlinearity and IMD3 signal power can be analyzed by calculating output power of harmonic frequencies versus the applied voltage. The 3rd harmonic is the major contribution to IMD3 signal power therefore suppression or cancellation of the 3rd harmonic is the main target to increase SFDR. By writing exp(-i(nθ + δ_nsin(ω_mt - nφ))) part of Eq. (1) in a Bessel expansion, the output power at even and odd harmonics can be obtained as following:

\begin{matrix} {| \frac{E_{o u t} (t)}{E_{i n} (t)} |}_{o d d}^{2} = | τ - (1 - τ^{2}) \sum_{n = 1}^{\infty} τ^{n - 1} α^{n} \\ \times [- \sin (n θ) 2 J_{h} (δ_{n}) \sin (h ω_{m} t - \frac{h n φ}{2}) \\ {- i \cos (n θ) 2 J_{h} (δ_{n}) \sin (h ω_{m} t - \frac{h n φ}{2})] |}^{2} \end{matrix}

\begin{matrix} {| \frac{E_{o u t} (t)}{E_{i n} (t)} |}_{e v e n}^{2} = | τ - (1 - τ^{2}) \sum_{n = 1}^{\infty} τ^{n - 1} α^{n} \\ \times [\cos (n θ) 2 J_{h} (δ_{n}) \cos (h ω_{m} t - \frac{h n φ}{2}) \\ {- i \sin (n θ) 2 J_{h} (δ_{n}) \cos (h ω_{m} t - \frac{h n φ}{2})] |}^{2} \end{matrix}

Using these equations, output powers for fundamental, second, third, and fifth harmonics are calculated in the range of bias voltages and in 1 Hz and 50 MHz frequencies [Fig. 2]. Two critical bias voltages are well noticed (V_A and V_B) at 1 Hz operating frequency [Fig. 2(a)]. At bias point V_A, second and fifth harmonics are suppressed while at V_B, the third harmonic is suppressed. The Lorentzian-shaped transfer function of RRM has a bias point where the output power in third harmonic is minimum while the fundamental signal has considerable amount of power, resulting in higher SFDR compared to MZI modulators. Therefore, V_B is mentioned in literatures as the optimum bias for the RRMs to obtain high SFDR [23, 24]. However, by increasing the RF operating frequency from 1 Hz to 50 MHz the suppressing of the harmonics at V_A and V_B is diminished considerably [Fig. 2(b)] which results in SFDR reduction as shown in Fig. 3.

Fig. 2 Normalized output intensities in fundamental, second-harmonic, third-harmonic and fifth-harmonic frequencies versus bias voltages in (a) 1 Hz, and (b) 50 MHz operating frequencies. Results are for input RF power of −20 dBm and a ring resonator with 6 mm perimeter. Output intensity is in logarithmic scale and normalized versus input RF power.

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Fig. 3 SFDR versus RF operating frequency for RRM, DRRM and MZI. SFDR is calculated for 1 Hz noise bandwidth. RRM is biased at V_B and DRRM is biased at V_A.

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To obtain SFDR, a two tone test and numerical Fourier method is utilized with typical link parameters according to the Table 1 [10]. Figure 3 presents the calculated SFDR for the RRM that is biased at V_B in the range of RF operating frequency up to 5 GHz. Results show that biasing the single RRM at V_B will provide relatively high SFDR at very narrow bandwidths versus MZI modulator. SFDR > 120 dB (1 Hz noise bandwidth) is obtained only in ~20 MHz operational frequency and SFDR drops below MZI level (~110 dB, 1 Hz noise bandwidth) in ~720 MHz operational frequency. Therefore to increase the SFDR at wider bandwidths it is necessary to suppress the 3rd harmonic power utilizing other methods.

Table 1. MPL parameters used in the calculations.

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3. Dual ring resonator modulator

A Dual Ring Resonator Modulator (DRRM) is proposed to cancel the 3rd order harmonic portion of the IMD3 in order to maintain SFDR over a large bandwidth. Equal powers of the 3rd order harmonic are produced by the DRRM with 180° phase difference allowing cancellation of the 3rd order harmonic. However, the cancellation process of the 3rd harmonic slightly suppresses the fundamental signal as quantified later in the paper. To yield the maximum SFDR the optical and RF powers are divided with a specific ratio between the two RRM paths providing minimum cancellation of the fundamental signal.

In single RRM by applying a two tone signal to the Eq. (1) and using Bessel expansions the following relations are obtained for output RF signal and IMD3 powers:

\begin{array}{r} P_{F u n} \propto | τ - (1 - τ^{2}) \sum_{n = 1}^{\infty} τ^{n - 1} α^{n} \times [- \sin (n θ) 2 J_{0} (δ_{n}) J_{1} (δ_{n}) \\ {- i \cos (n θ) 2 J_{0} (δ_{n}) J_{1} (δ_{n})] |}^{2} \end{array}

\begin{array}{r} P_{I M D 3} \propto | τ - (1 - τ^{2}) \sum_{n = 1}^{\infty} τ^{n - 1} α^{n} \times [- \sin (n θ) 2 J_{1} (δ_{n}) J_{2} (δ_{n}) \\ {- i \cos (n θ) 2 J_{1} (δ_{n}) J_{2} (δ_{n})] |}^{2} \end{array}

The fundamental signal power is proportional to the J₀(δ_n)J₁(δ_n) product however the IMD3 signal power is related to the product of Bessel functions, J₁(δ_n)J₂(δ_n). For small RF signals criteria yielding the δ_n ≪ 1 the J₀(δ_n)J₁(δ_n) and J₁(δ_n)J₂(δ_n) products can be expanded as follows:

\begin{array}{l} J_{0} (δ_{n}) J_{1} (δ_{n}) = - δ_{n} + h i g h e r o r d e r s \\ J_{1} (δ_{n}) J_{2} (δ_{n}) = - \frac{1}{16} δ_{n}^{3} + h i g h e r o r d e r s \end{array}

These equations show the output fundamental signal power has approximately linear modulation index dependence while the IMD3 signal power has approximately the cubic modulation index dependence. This relation differences provides a path to suppress IMD3 power by 3rd harmonic cancellation while keeping the fundamental signal suppression at minimum level utilizing DRRM as presented in Fig. 1. Dividing RF and optic powers between two RRMs in order to produce equal powers of 3rd harmonic with 180° phase difference at the detectors yields complete 3rd harmonic cancellation. To illustrate, consider dividing the RF input power between two modulators such that RF input voltage amplitude for one modulator (main) is two times of the RF voltage amplitude for another modulator (secondary). Then the output 3rd harmonic power from the primary modulator is eight times of the 3rd harmonic power from the secondary one. If the optic power is divided between two modulators that primary modulator receives eight times optic power less than the secondary modulator the 3rd harmonic powers from primary and secondary modulators are expected to be equal. By having 180° phase difference in the 3rd harmonic signals from the modulators the 3rd harmonic signal is completely cancelled after combining the outputs of the detectors as shown in Fig. 1. The suggested method can be formulated as following that to cancel the 3rd order harmonic of IMD3 two RRMs are utilized with divided RF power at ratio F²:1 while optical power ratio needs to be the inverse cube of the RF power ratio, i.e. 1:F³. The main modulator is fed by higher RF power while receiving less optical power and the secondary modulator receives less RF power but it is driven with higher optical power. The optical power ratio (1:F³) between the modulators is set by the coupling ratio between the base waveguides of the main and secondary modulators. If the RF and optical power are held at the previously mentioned ratios the 3rd harmonic produced from two modulators is equal and exactly canceled at the output. The output power vs. input power for the fundamental and the IMD3 for RRM and DRRM (both biased at V_A) with F = 3 are shown in Fig. 4. In the DRRM IMD3 power is suppressed more than fundamental signal yielding an enhancement in SFDR as marked in Fig. 4. It is worth mentioning that the IMD3 power versus input power in the RRM has a slope equal to 3 showing 3rd order harmonic contribution in IMD3. Having a linearization process in the DRRM the slope of IMD3 increases to 7, therefore by biasing the modulators at the proper voltages and having DRRM with the proper power ratio of RF and optical powers both 3rd and 5th order harmonics are cancelled.

Fig. 4 Output fundamental and IMD3 powers against the RF input power. Lines are the results for single RRM and dots are for the DRRM. Results are for 6 mm rings biased at V_A. Noise level is at ~-164 dBm in 1 Hz bandwidth.

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To take advantage of the 5th order harmonic suppression modulators are biased at voltages that 5th order harmonic is suppressed (V_A) as shown in Fig. 2. However in order to produce 180° degree phase difference between IMD3 signals at the output modulators need to bias at voltages that are symmetric versus the center of the Lorentzian transfer function as shown in Fig. 5(a) by ± V_A. To confirm 3rd order harmonic cancellation in DRRM harmonic distortions from DRRM calculated and compared to the RRM [Fig. 5(b)]. The Suppression of the 3rd harmonic along with decreasing in fundamental signal power in DRRM is clear. Suppression of the 3rd harmonic in DRRM is maximized at V_A where 5th harmonic suppression happens results in 7th order slope for the IMD3 power change versus RF input power in SFDR diagram [Fig. 4].

Fig. 5 (a) Lorentzian transfer function of a RRM versus bias voltage showing the symmetrical bias points ( ± VA), (b) fundamental and 3rd harmonic distortion in DRRM and RRM versus bias voltage.

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The DRRM provides the 3rd order harmonic cancellation process which is not frequency dependent. In Fig. 3 variation of the SFDR versus operating RF frequency is shown for DRRM. When the operating RF frequency is at resonance frequency the complete suppression of the fifth order harmonic comes with biasing at V_A. Working at frequencies away from the resonance frequency fifth harmonic contribution in IMD3 power increases reducing SFDR, however DRRM maintains complete cancellation of the 3rd harmonic regardless of the operating frequency. Therefore DRRM provides SFDR > 129 dB (1 Hz noise bandwidth) in a relatively narrow operational bandwidth around the resonance frequency (~40 MHz) while keeping SFDR > 124.6 dB (1 Hz noise bandwidth) at unlimited operational bandwidth. The nondispersive 3rd harmonic cancellation using DRRM is a great advantage in comparison with RAMZI or IMPAAC designs since the linearization process in RAMZI and IMPAAC structures is highly sensitive to the operating frequency [8, 17].

It is inevitable that with the DRRM there will be some reduction of the fundamental signal affecting system level figure of merits. The reduction of the fundamental signal is not linearly related to the F-ratio therefore the link figure of merits is analyzed by sweeping the F-ratio as shown in Fig. 6. Optimum figure of merits is obtained at F ~2.4 when minimum cancellation of the fundamental signal occurs yielding improvement in SFDR, gain and noise figure. According to this ratio optical power splitter should be designed to split optical power at 1:2.4³ while RF power is divided in 2.4²:1 ratio.

Fig. 6 Link figure of merits versus F-ratio (a) SFDR, (b) noise figure and gain.

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The main challenge in order to maximize link figure of merits is to design and fabricate optical and RF power splitters precisely. The optical power splitter ratio is set in fabrication step and no control is accessible after fabrication step within the current design. Moreover, depending on the material used in the fabrication, optical power splitter can be vulnerable to the environmental condition. RF power splitting can be controlled in the application step and the RF splitting ratio can be tuned to the desired number after obtaining measurements of optical power splitter in order to satisfy the ratio relations between RF and optical powers. The DRRM imposes a very high tolerance of the SFDR to the RF signal splitting ratio accuracy as shown in Fig. 7. Results are calculated for F = 3 meaning the RF voltage amplitude should be divided in 75% to 25% between the main modulator and the secondary modulator respectively. In order to analyze the tolerance of the DRRM to splitting ratio the voltage amplitude receiving by the second modulator is swept around 25% ratio while keeping the fixed 75% voltage amplitude receiving by the main modulator. To keep the SFDR > 120 dB the RF voltage amplitude needs to be divided in a resolution finer than 0.2% of the input amplitude. Dividing RF signal with high accuracy can be achieved utilizing integration techniques to minimize the fabrication and application tolerances [30].

Fig. 7 SFDR change versus RF voltage amplitude received by the secondary modulator.

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The DRRM inherits operational bandwidth limits from the RRM in terms of the modulation index affecting gain and noise figure. In a RRM three factors can impose the modulation index bandwidth including the electro-optic material response speed, the electrode design, and the resonant characteristic of the ring resonators. By using electro-optic polymer materials the bandwidth limit due to the material response can be negligible since the electro-optic effect in polymers works in high frequencies up to millimeter ranges [26]. In resonance type modulators functionality is limited by the resonance characteristics more than electrode properties [31]. The RRM and consequently the DRRM impose bandwidth limitation to the modulation index based on optical resonance line-width (BW_res). The BW_res can be controlled by the optical resonator structure including size of the ring and coupling parameters and is the trade-off for an increasing in sensitivity [32]. High-Q optical resonances result in an increased modulation efficiency, but more limited RF bandwidth. In Fig. 8 variation of the link figure of merits, gain and noise figure versus operating RF frequency up to 5 GHz is shown for RRM and DRRM. While SFDR improvement in DRRM is clear in Fig. 3, gain and noise figure is slightly diminished due to the fundamental signal reduction as shown in Fig. 8. Unlike RRM, that SFDR is the main limiting factor as shown in Fig. 3, to design a DRRM resonance structures can be defined according to the modulation index required to achieve link gain and noise figure in the desired bandwidth.

Fig. 8 Link figure of merits versus operational bandwidth using RRM and DRRM, (a) gain, and (b) noise figure.

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By using traveling-wave electrodes the capacitance and the transit-time bandwidth limitations due to the lumped electrodes are removed and DRRM can operate at multiple of FSR. A DRRM with lumped electrode can be only operated in baseband up to BW_res/2 while a DRRM with traveling-wave electrodes can work at multiple of FSR while with BW_res bandwidth around the resonance frequency. Utilizing traveling-wave electrodes high frequency operation within RRM is more advantageous in compare to the MZI based modulators when the velocity mismatch and RF loss are taken into account because of the higher modulation index in the BW_res around the resonance frequency [26]. The DRRM inherits the advantages in enhanced modulation index from RRM. Although figure of merits reported in this paper are calculated based on lumped electrode structure the results can be generalized to the traveling-wave electrodes obtaining BW_res around the resonance frequency at multiple FSR. While working with traveling-wave type electrodes microwave electrode loss and material refractive index difference in optical and microwave frequencies should be taken into account since these factors can have detrimental effect on modulation index at multiple FSR operating frequencies [26].

Along with frequency operational bandwidth of a link the SFDR changes in instantaneous bandwidth is another important link parameter which can be calculated using following equation:

S F D R (B) = S F D R (1 H z) - \frac{m - 1}{m} \times 10 \times L o g (B)

where m is the slope of the IMD3 versus input RF power and B is the instantaneous bandwidth. For DRRM operating at frequencies close to the resonance frequency both 3rd and 5th order harmonics are cancelled and m = 7 while at frequencies away from the resonance just 3rd order harmonic is cancelled and m = 5. In Fig. 9 variation of SFDR versus instantaneous bandwidth is presented for the DRRM in comparison with MZI. In order to show the operational frequency effect on SFDR versus instantaneous bandwidth the results for DRRM are presented in 1 Hz and 5 GHz frequencies. The DRRM in comparison with MZI presents ~7–9 dB SFDR improvement in 1 MHz instantaneous bandwidth while improving ~3 dB at 1 GHz instantaneous bandwidth.

Fig. 9 SFDR versus instantaneous bandwidth in MZI and DRRM.

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A comparison between RRM, DRRM and MZI modulators is summarized in Table 2. For these results, operational bandwidths and instantaneous bandwidths are considered ± 5 GHz around the resonance frequency and 1 GHz respectively. Since the RRM and DRRM have frequency dependent function due to the resonance structure the figure of merits is defined in a range for ± 5 GHz operational bandwidth around the resonance frequency. DRRM can provide ~4–15 dB and ~15–20 dB SFDR improvement versus RRM and MZI respectively in 1 Hz instantaneous bandwidth. In 1 GHz instantaneous bandwidth the DRRM maintains ~3 dB SFDR improvement versus MZI. The low improvement in 1 GHz instantaneous bandwidth is related to the higher order harmonic cancellation method yielding higher m in Eq. (9). The presented SFDR improvement comes with the price of the gain and noise figure deteriorating. However it should be stressed that the SFDR is a prevalent figure of merit for increasing performance metrics and wide scale implementation. While linearity of the modulator has the direct critical effect on the SFDR of MPL there are other mechanisms to mitigate degradation of the gain and noise figure including use of higher laser power, higher detector responsivity, and lower laser relative intensity noise. In addition, resonator structure in DRRM can be modified to address gain and noise figure requirements since SFDR is not a limiting factor however, as shown in this paper, main limiting factor of the RRM is the narrow bandwidth of the SFDR. Another advantage of DRRM is very low bias voltage required yielding in lower power consumption in compare to RRM and MZI.

Table 2. DRRM, RRM and MZI figure of merits comparison.

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4. Conclusion

A DRRM is proposed as an electro-optic modulator to obtain high SFDR at wide operational bandwidths for MPLs. Nonlinear distortion in RRMs was analyzed theoretically showing very narrow operational bandwidth around the resonance frequency (~40 MHz) of SFDR > 120 dB (1 Hz noise bandwidth). By dividing the RF and optical powers in specific ratios between two RRMs and proper DC biasing the 3rd harmonic distortion signals at the output have equal powers while being out of phase yielding the IMD3 power suppression independent of the operational frequency. The design takes advantage of 5th harmonic cancellation by proper biasing the modulators at narrow operational bandwidth around the resonance frequency in order to reach SFDR ~130 dB.Hz^6/7 while the 3rd order cancellation method keeps the SFDR > 124.6 dB.Hz^4/5 in frequencies away from resonance frequency. The gain and noise figure of the DRRM design are slightly degraded compared to the RRM because of the fundamental signal reduction and inherit RRM bandwidth limitations. The DRRM offers very low bias voltage (~1.44 V in comparison with 2.49 V for RRM and 4.44 V for MZI) reducing the overall device power consumption. It is worth mentioning although results of this paper were obtained utilizing specifications of the electro-optic polymer material the DRRM can be fabricated based on different material platforms including silicon and LiNbO₃. Currently we are working on the fabrication and measurement of device utilizing electro-optic polymer materials.

Funding

Defense Advanced Research Projects Agency (DARPA) (HR0011-15-C-0082).

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Parameter		Value
Laser power		0.1 W
Laser RIN		−165 dB.Hz
Modulator transmission		−10 dB
Detector responsivity		0.7 A/W
Modulator load resistance		50 Ω
Detector load resistance		50 Ω
Noise Bandwidth		1 Hz

Figure-of-merits	DRRM	RRM	MZI
SFDR (dB)^a	124.6 – 130	109 – 125.6	109.9
SFDR (dB)^b	52.6 – 52.9	49 – 53.6	49.9
Gain (dB)	−39.5 – −34.2	−24.2 – −21.1	−24.2
Noise figure (dB)	43.8 – 49	34 – 37.1	37.1
DC Bias (V)	1.44	2.49	4.44^c

Parameter		Value
Laser power		0.1 W
Laser RIN		−165 dB.Hz
Modulator transmission		−10 dB
Detector responsivity		0.7 A/W
Modulator load resistance		50 Ω
Detector load resistance		50 Ω
Noise Bandwidth		1 Hz

Figure-of-merits	DRRM	RRM	MZI
SFDR (dB)^a	124.6 – 130	109 – 125.6	109.9
SFDR (dB)^b	52.6 – 52.9	49 – 53.6	49.9
Gain (dB)	−39.5 – −34.2	−24.2 – −21.1	−24.2
Noise figure (dB)	43.8 – 49	34 – 37.1	37.1
DC Bias (V)	1.44	2.49	4.44^c

Highly linear dual ring resonator modulator for wide bandwidth microwave photonic links

Abstract

1. Introduction

2. Single ring resonator modulator

3. Dual ring resonator modulator

4. Conclusion

Funding

References and links

Cited By

Figures (9)

Tables (2)

Equations (9)

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