Analytical model, analysis and parameter optimization of a super linear electro-optic modulator (SFDR > 130 dB)

Abstract

An analytical model of a super linear optical modulator with high spurious-free-dynamic-range (SFDR > 130 dB) is presented and analyzed. The linear modulator is referred to as IMPACC which stands for Interferometric Modulator with Phase-modulating And Cavity-modulating Components. The modulator is based on a unique combination of a RF-driven phase-modulator (PM) and a ring resonator (RR) within a Mach–Zehnder interferometer (MZI) configuration. Our analysis shows that our design can achieve SFDR values which are ~ 20 dB higher than the standard MZI modulator and 3–5 dB from the Ring Assisted Mach-Zehnder Interferometer (RAMZI) modulator. Both PM and RR in the IMPACC are simultaneously driven by a RF signal of the same frequency, but not necessarily the same amplitudes. The analytical model shows that the combination of these two optical elements, with the proper choice of RF-driving and device parameters, can lead to four important and compelling consequences. First, it offers a wholistic and elegant model in which the standard MZI modulator and the RAMZI modulator are just special cases of IMPACC. Second, the model offers an excellent parameter optimization methodology for fast parameter (internal and/or external) selection and performance evaluation. Third, it provides additional degree of control through the introduction of an external control parameter, the RF power split ratio (F). Lastly, it demonstrates one unique feature of IMPACC such as adaptive SFDR characteristics, where manufacturing tolerances in the transmission coefficient (τ) of the RR can be compensated with proper adjustments of the external parameter of the power split ratio (F).

Introduction

Analog fiber-optic (FO) links are important building blocks for many analog photonic applications. Traditionally, high performance analog FO-links have been used for military-type applications, such as antenna-remoting for phased array antennas, signal distribution for phased array antennas, and other microwave photonics applications [1], [2], [3], [4]. Furthermore, the growing demand for video, data, and voice services over the Internet and the advancement of fiber to the home (FTTH) services for Broadband Access increase the need for high performance analog FO-links for commercial applications. For example, analog FO-links can find applications in cable television (CATV), subcarrier multiplexing (SCM) optical communication systems, Radio-over-Fiber (RoF) communications, and distributed antenna for cellular networks, satellite communication and other platform access systems [5], [6], [7], [8], [9], [10].

Several approaches have been proposed and implemented to offer high performance linear optical intensity modulators using different device configurations such as Mach-Zehnder Interferometer (MZI)-based modulator, coupler-based modulators, and SOA-based modulator [4]. From among these general configurations, the MZI-based modulator is the most well understood and popular. Linearization techniques based on either electrical [11], [12], [13] or optical approaches have been proposed and implemented. The optically linearized MZI-based modulator techniques can be divided further into four groups. The first group can be called dual-signal MZI-based modulator design [14], [15], [16], [17]. It comprises of one modulator but with two optical signals injected in the device (Fig. 1(a)). The two input signal amplitudes and phases must be properly matched with predetermined values of the RF amplitude phase signal. These two injected optical signals could be implemented using (i) two polarizations [14], [15], (ii) two wavelengths [17], or (iii) bi-directional signals [16]. The major advantage of this family of modulators is the relative simplicity and low-cost. Its disadvantages are design inflexibility, non-optimum performance, and tight tolerance requirements.

The second group can be referred to as cascaded modulator design which consists of two or more standard MZI modulators connected in series [18], [19], [20], [21], [22], [23], [24] or in parallel [25], [26] arrangements (Fig. 1(b)). It is a generalization of the principle used in the first group. Its major drawbacks are the tight manufacturing tolerance requirements, higher optical loss, higher cost due to use of multiple modulators, and complicated compensation arrangement.

The third group is generally designated as resonator-assisted MZI (RAMZI) modulators [27], [28], [29], [30], [31], [32], and has received increased interest in recent years ((Fig. 1(c)). The RAMZI uses ring resonator(s) (RRs) instead of the standard phase modulator (PM) which is coupled in the arm(s) of the MZI. This design gives higher SFDR performance but often at higher manufacturing complexity, limited RF bandwidth range, and stricter transmission coefficient control requirement.

The fourth and last group of optically linearized MZI-based modulators was introduced by our group [33], [34], [35], [36], [37], [38], [39], [40], [41]. This modulator design is a family of modulators we referred to as IMPACC which stands for Interferometric Modulators with Phase-modulating And Cavity-modulating Components. There are numerous configurations and variations within the family of IMPACC designs [34]. One specific structure of IMPACC uses a combination of a standard phase modulator (PM) as the phase-modulating component and a ring resonator (RR) as the cavity-modulating component within a MZI structure [33], [35], [37]. The exact positions of the PM and RR relative to one another offer some variations of the implementation (Fig. 1(d)). The critical parameter in the operation of the IMPACC is that the PM and RR are driven by the same frequency RF signal, but with different RF power, controlled by the power split ratio (F) using a variable or fixed RF power splitter (PS).

Recently, we reported on the performance of IMPACC's bandwidth capabilty [38], [39], and effects of non-ideal factors such as the effects on losses in the ring resonator [37], and deviation of the alpha factor [41]. However, a simple model that can provide guidelines to optimize the critical design parameters is important. Hence, the goal of this paper is to focus on the theoretical formulation, rigorous derivation, and detailed performance analysis of IMPACC under the simplified assumptions of ideal electrodes that are frequency independent and lossless. This is a standard approach followed in the literature and helps establish the fundamental treatment of the IMPACC modulator. This simplification also provides important insight on the starting point of optimizing the design of the IMPACC. Our formulation leads to four important results:

• Offers a more wholistic and elegant model for which both the standard MZI modulator and RAMZI modulator are just special cases of IMPACC.

• Provides us with a guideline to perform the important parameter mapping and parameter optimization.

• Provides additional degree of control through the introduction of an external control parameter via RF power split ratio.

• Introduces one unique feature of IMPACC, that is a potential adaptive SFDR characteristic.

This paper is organized as follows. In Section 2, we describe a representative modulator design of IMPACC, and give a rigorous derivation of the formulation amplifier-less FO-link configuration. We also assume short distances (e.g., < 1 km) so that optical dispersion and non-linearity – due to the optical fiber – is negligible and so do not significantly affect the RF performance of the link. References [2], [42], [43] provide review on the basic figures of merit and the important parameters used to describe the FO-link performance. In Section 3, we comment on the generality of our model to describe the standard MZI-based modulator and the RAMZI as special cases of IMPACC. Section 4 focuses on the SFDR performance analysis, where the SFDR evolution, as a function of the optimized modulator parameters, is presented. Section 5 describes what we call the “parameter mapping” — a parameter optimization methodology for identifying the optimum modulator design parameters [35]. Finally, in Section 6, we highlight the advantages of the IMPACC, we comment on the merits of the optimization technique and we propose an adaptive compensation technique for SFDR optimization.