Ring-Assisted Mach-Zehnder Interferometer (RAMZI)

• RAMZI is a hybrid photonic structure embedding micro-ring resonators into Mach-Zehnder interferometers to enable precise wavelength interleaving and enhanced modulation.
• It leverages the resonant properties of rings along with the phase stability of MZIs to achieve low-loss filtering, robust fabrication tolerance, and efficient quantum state generation.
• Recent implementations on silicon and lithium niobate platforms demonstrate linearized electro-optic modulation, ultra-high purity photon conversion, and dynamic reconfigurability.

A ring-assisted Mach-Zehnder interferometer (RAMZI) is a hybrid photonic component that embeds one or more micro-ring resonators into the arms of a Mach-Zehnder interferometer (MZI), yielding versatile control over optical filtering, modulation, and nonlinear processes. By leveraging the unique dispersive and resonant characteristics of micro-rings in concert with the broadband, phase-stable MZI architecture, RAMZI devices enable advanced functionalities that surpass conventional interferometric or resonant devices alone. These include ultra-compact and fabrication-robust wavelength interleavers, linearized electro-optic modulation, ultra-high-purity quantum state generation, and efficient quantum frequency conversion. Recent progress spans silicon photonics and thin-film lithium niobate platforms, with demonstrated compatibility with large-scale integration and low-power operation (Rizzo et al., 2022, Shawon et al., 2023, Kundu et al., 2024, Kundu et al., 13 Jan 2025).

1. Fundamental RAMZI Architecture

The canonical RAMZI consists of a balanced (or intentionally asymmetric) two-arm MZI, with at least one arm coupled to a high-Q micro-ring (or racetrack) resonator. The MZI input and output are typically connected via 50:50 multi-mode interference (MMI) couplers or directional couplers, splitting and recombining the optical field. The coupling of a ring into an MZI arm imposes a periodic, frequency-dependent phase response, $\phi_\text{ring}(\omega)$, which modifies the total interferometric transfer function:

$$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$

where $t_i = \sqrt{1 - \kappa_i}$ and $\kappa_i$ are the amplitude transmission and coupling coefficients of the MMIs, and $T_1, T_2$ are the propagation times in the respective arms (Rizzo et al., 2022, Kundu et al., 2024).

The ring-induced phase is given by:

$$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$

where $T_\text{rt}$ is the ring round-trip time, $a$ the round-trip amplitude attenuation, and $\kappa_r$ the ring–bus coupling coefficient.

Variants include the RAMZM, in which both arms are loaded with micro-rings to enable dual-resonant effects and high-speed modulation (Shawon et al., 2023); and the RMZI (also termed RAMZI in lithium niobate literature), featuring periodically poled segments for efficient nonlinear interactions (Kundu et al., 2024, Kundu et al., 13 Jan 2025).

2. Design Principles and Sensitivity Mitigation

RAMZI performance is constrained by fabrication-induced variations in waveguide width, affecting the effective refractive index ($n_\text{eff}$) and, consequently, the phase response and resonance conditions. To suppress sensitivity, recent designs utilize wide (e.g., 1,200 nm) single-mode waveguides with adiabatic Euler bends and wide-body MMIs, achieving a phase sensitivity reduction from

$$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$0

for 400 nm-wide waveguides to $$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$1 — an improvement by over two orders of magnitude (Rizzo et al., 2022). These wide geometries also facilitate robust integration of MMIs (e.g., 3.5 µm × 43.1 µm for 50:50 splitting), eliminating the need for tapers and minimizing fabrication-induced stochastic phase errors.

Novel coupling designs, such as tunable MZI-based couplers and directional coupler-based RAMZI in thin-film LiNbO$$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$2, further enable dynamic control over coupling ratios ($$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$3) across a wide wavelength range and process corner. Periodic poling of lithium niobate in one arm enables quasi-phase-matched nonlinear interactions with minimal propagation loss ($$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$4 dB/cm) (Kundu et al., 2024, Kundu et al., 13 Jan 2025).

3. Spectral, Modulation, and Quantum Performance

Typical RAMZI devices demonstrate the following spectral and modulation properties, depending on implementation:

• Pass-band insertion loss (IL): $$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$5–$$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$6 dB (silicon), $$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$7 dB (RAMZM)
• Extinction ratio (ER): up to $$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$8 dB, with worst-case crosstalk $$H(\omega) = \frac{E_\text{out}(\omega)}{E_\text{in}(\omega)} = \frac{1}{2} \left[t_1 t_2 e^{-j\omega T_1} - \sqrt{\kappa_1 \kappa_2} e^{-j[\omega T_2 + \phi_\text{ring}(\omega)]}\right]$$9 dB
• Pass-band ripple: $t_i = \sqrt{1 - \kappa_i}$0 dB; stop-band ripple $t_i = \sqrt{1 - \kappa_i}$1 dB
• Resonance visibility: $t_i = \sqrt{1 - \kappa_i}$2
• Measured free spectral range (FSR): $t_i = \sqrt{1 - \kappa_i}$3 GHz ($t_i = \sqrt{1 - \kappa_i}$4 nm)
• Full-width at half-maximum (FWHM): $t_i = \sqrt{1 - \kappa_i}$5 GHz ($t_i = \sqrt{1 - \kappa_i}$6 nm)
• Thermal tuning: $t_i = \sqrt{1 - \kappa_i}$7 GHz/K; tuning power $t_i = \sqrt{1 - \kappa_i}$8W (with III–V/Si MOSCAP) (Rizzo et al., 2022)

For linearized optical modulation (RAMZM), the nonlinear, Lorentzian-shaped phase response of the rings is used to counteract the sinusoidal transfer function of the MZI. By biasing at the “linearized” regime ($t_i = \sqrt{1 - \kappa_i}$9, $\kappa_i$0, $\kappa_i$1), third-order intensity modulation distortion is canceled. The result is a measured SFDR of 113.7 dB Hz$\kappa_i$2, exceeding typical lithium niobate MZMs and facilitating low-noise, high-linearity RF-to-optical conversion (Shawon et al., 2023).

Lithium-niobate RAMZI devices achieve $\kappa_i$3 dB quantum squeezing at $\kappa_i$41 mW pump powers with OPO bandwidths of $\kappa_i$5 GHz, and heralded single-photon purity $\kappa_i$6 with heralding efficiency $\kappa_i$7–$\kappa_i$8 at $\kappa_i$9 ps pump duration. In quantum frequency conversion, up to $T_1, T_2$0 external efficiency at $T_1, T_2$1 mW pump and noise photon rate below $T_1, T_2$2 Hz are realized, with bidirectional operation enabled via on-chip thermal tuning (Kundu et al., 2024, Kundu et al., 13 Jan 2025).

4. Nonlinear and Quantum-Enabled RAMZI Architectures

In thin-film lithium niobate (TFLN) platforms, RAMZI architectures (often termed RMZI) integrate periodically poled (PPLN) sections within the ring to enable efficient $T_1, T_2$3 nonlinear processes. The key phase-matching condition for quantum frequency conversion is

$T_1, T_2$4

where $T_1, T_2$5 are the propagation constants for pump, signal, and idler, $T_1, T_2$6 the azimuthal mode number, and $T_1, T_2$7 the poling period. The micro-ring geometry enables resonant field enhancement, reducing pump thresholds for both squeezing and photon conversion well below 1 mW.

The output field is determined by the joint transfer matrix of the MZI and the resonantly loaded ring, with external quality factors adjusted independently by MZI- and ring-heater biasing. Achieved results include squeezing ($T_1, T_2$8 dB at 0.6 mW, up to $T_1, T_2$9 dB at higher power), spectral purity $$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$0 under dual-pulse excitation, heralding rates up to 0.81 MHz/µW, and external frequency conversion efficiency $$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$1 (signal: 727 nm ↔ idler: 1350 nm) (Kundu et al., 2024, Kundu et al., 13 Jan 2025).

5. Reconfigurability, Control, and Integration

Practical RAMZI and RAMZM operation exploits integrated microheaters, electronic feedback, and on-chip monitoring for precision biasing of MZI phases, ring resonances, and coupling ratios. A three-stage convergence algorithm—coupler tuning, ring detuning, and quadrature balancing—enables real-time stabilization against process drift and thermal crosstalk using DAC-driven heaters, Ge photodetectors, and FPGA-based digital control (Shawon et al., 2023). Typical reconfiguration times are $$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$2 s, with autonomous retuning supporting reliable system-on-chip deployment.

Lithium-niobate RAMZI devices employ NiCr microheaters in the oxide cladding for efficient phase bias and resonance alignment. Standardized e-beam lithography and periodic poling methods allow wafer-scale LNOI fabrication, with on-chip grating couplers giving $$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$3 fiber-to-chip efficiency. All reported implementations demonstrate compact footprint (e.g., $$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$4 mm$$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$5 device area for silicon RAMZI (Rizzo et al., 2022), $$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$6 mm$$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$7 RAMZM modulator core (Shawon et al., 2023)), supporting dense photonic integration.

6. Performance Tables

The following table summarizes representative quantitative metrics from recent RAMZI implementations:

Platform	Spectral/Quantum Metric	Value / Performance Range
Silicon (SOI)	Insertion loss (IL)	2–3 dB
	ER / crosstalk	typ. –20 dB, worst –12 dB
	FSR ($$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$8)	$$\phi_\text{ring}(\omega) = -\omega T_\text{rt} + 2\tan^{-1}\left[\frac{[1 - a\sqrt{1-\kappa_r}] \sin(\omega T_\text{rt})}{1 - a\sqrt{1-\kappa_r} \cos(\omega T_\text{rt})}\right]$$91.6 nm (200 GHz)
	σ($T_\text{rt}$0), 1,200 vs 450 nm wg	0.0012 vs 0.010
TFLN	Squeezing (dB)	$T_\text{rt}$1 to $T_\text{rt}$2 dB at $T_\text{rt}$315 mW
	Single-photon purity, heralding	$T_\text{rt}$4, $T_\text{rt}$5–$T_\text{rt}$6
	QFC ext. efficiency, noise rate	$T_\text{rt}$7, $T_\text{rt}$8 Hz at 1 mW
Silicon RAMZM	SFDR	$T_\text{rt}$9 dB Hz$a$0
	EO S21 bandwidth	$a$1 GHz
	Insertion loss (modulator)	$a$2 dB

7. Applications and Implications

RAMZI structures serve as key enablers across several domains:

• Dense wavelength-division multiplexing (DWDM) interleavers with low power and high robustness against fabrication error (Rizzo et al., 2022).
• Linearized and gain-enhanced EO modulation for RF photonics, with performance rivaling or exceeding LiNbO$a$3 MZMs, and drop-in compatibility for PIC-based phased array/radio-over-fiber systems (Shawon et al., 2023).
• Ultra-efficient generation of squeezed light and single photons, meeting stringent requirements for quantum computation/communication protocols (Kundu et al., 2024).
• Bidirectional, near-unity quantum frequency conversion between visible-wavelength quantum memories and the telecom band, with noise floors $a$4 Hz, facilitating scalable quantum repeater and entanglement-distribution networks (Kundu et al., 13 Jan 2025).

RAMZI’s architecture enables the independent control of key photonic degrees of freedom (phase, coupling, resonance) with foundry-compatible fabrication and integrated electronic control, positioning it as a foundational component for advanced classical and quantum photonic systems.