Ring modulator small-signal response analysis based on pole-zero representation

Abstract

We present a closed-form expression for the small-signal response of a depletion-mode ring modulator and verify it by measurement results. Both electrical and optical behavior of micro-ring modulator as well as the loss variation due to the index modulation is considered in the derivation. This expression suggests that a ring modulator is a third-order system with one real pole, one zero and a pair of complex-conjugate poles. The exact positions of the poles/zero are given and shown to be dependent upon parameters such as electrical bandwidth, coupling condition, optical loss, and sign/value of laser detunings. We show that the location of zero is different for positive and negative detuning, and therefore, the ring modulator frequency response is asymmetric. We use the gain-bandwidth product as a figure of merit and calculate it for various pole/zero locations. We show that gain-bandwidth for the over-coupled ring modulator is superior compared to other coupling conditions. Also, we show that the gain-bandwidth product can be increased to a limit by increasing the electrical bandwidth.

Optical and electrical trade-offs of rib-to-contact distance in depletion-type ring modulators

“…The expected input wavelength-dependent frequency response of the ring modulators [13-15, 19, 28] can be seen from both measurement and simulation results. The difference between frequency responses at positive and negative detunings is a result of loss modulation when modulating the index of the ring resonator [15,19]. Comparing E/O responses of these three rings, the 3dB bandwidth improvements by decreasing d ++ is clear.…”

“…In this study, it is important to pick rings close to the critical coupling condition as the coupling condition (i.e. deep under-or over-coupling) changes the dynamic response of the ring modulator [14,19,22]. Selected rings are indicated with circles in Fig Transmission spectra at through ports of the ring modulators A to D under reverse-biased conditions are shown in Figs.…”

“…This suggests that f Q is the main limiting factor in bandwidth for all three rings. In order to simulate frequency response of the ring modulators, our model presented in [19] is used. From fitted curves to τ l versus voltage shown in Fig 4(a) The RF signal is fed to the device using high speed SG probe.…”

“…This is due to the fact that, in addition to optical ( f Q ) and electrical ( f RC ) bandwidths, carrier wavelength is also important as it may lead to resonance peaking in the frequency response [13][14][15][16][17][18][19]. Small-signal models of ring modulator have been studied previously [13][14][15][16][17][18][19] and can be used to evaluate the effect of various design parameters on ring modulator performance. In this paper, in addition to measurement, we use our small-signal model presented in [19] as a tool to study the effect of d ++ on the frequency response of ring modulators which provides additional insight into frequency response trade-offs.…”

“…Small-signal models of ring modulator have been studied previously [13][14][15][16][17][18][19] and can be used to evaluate the effect of various design parameters on ring modulator performance. In this paper, in addition to measurement, we use our small-signal model presented in [19] as a tool to study the effect of d ++ on the frequency response of ring modulators which provides additional insight into frequency response trade-offs. Also, the rate of increase in bandwidth at the cost of decreasing DC value of the frequency response (DC gain) is calculated based on the electro-optical frequency response and compared across ring modulators with various d ++ .…”