Interferometric RF-to-Optical Encoding

• Interferometric RF-to-optical encoding schemes are methods that map RF signal characteristics into the optical domain using coherent interference in devices like Mach-Zehnder interferometers.
• These techniques enable high-fidelity RF-over-fiber transmission, frequency conversion, and real-time spectrum analysis by leveraging phase and amplitude modulation.
• They employ advanced architectures, including integrated photonic circuits and acousto-optic systems, to achieve improved conversion gain, resolution, and dynamic modulation fidelity.

An interferometric RF-to-optical encoding scheme is an approach that exploits the coherent superposition of optical fields—with radio-frequency (RF) signals translated onto optical carriers via controlled modulation processes inside interferometric structures. Such schemes underpin a broad set of applications, including high-fidelity RF-over-fiber (RoF) transmission, microwave photonic mixing, all-optical frequency conversion, spectrum analysis, and modulation formats for analog photonic signal processing. Central to these techniques are integrated or fiber-based interferometers (Mach-Zehnder, multimode, or DFT-based) where the RF information, encoded via phase or amplitude, is optically processed and directly mapped to spectral or spatial signatures, often enabling conversion gains, spectral selectivity, and dynamic modulation transfer not accessible by direct intensity modulation alone.

1. Fundamental Principles of RF-to-Optical Interferometric Encoding

The essential mechanism relies on mapping RF signal characteristics onto optical domain observables (phase, amplitude, or spectral intensity patterns) through interference. Key frameworks include:

• Phase Mapping via Nonlinear or Acousto-Optic Effects: In acousto-optic systems, the RF drive modulates the phase of traveling acoustic waves, which transfer their phase to the diffracted optical beam orders as $\phi_\mathrm{opt}^{(n)}(t) = n \phi_\mathrm{rf}(t)$ for diffraction order $n$ (Satapathy et al., 2012). In semiconductor-optical-amplifier Mach-Zehnder interferometers (SOA–MZI), cross-phase modulation (XPM) imprints a RF-induced phase shift on one arm, so interference at the output converts this phase modulation into measurable amplitude or intensity (Kastritsis et al., 2022).
• Mach–Zehnder Interferometry and Generalized Networks: Photonic-integrated circuits (PICs) extend these ideas: an input optical signal is split into $N$ arms, each imparted with an RF-driven phase shift, recombined via a discrete-Fourier-transform (DFT) mesh, enabling arbitrary spectral engineering, sideband selectivity, and frequency conversion (Hasan et al., 2022).
• Dual-Carrier and Speckle-Enhanced Architectures: Advanced schemes employ path-mismatched interferometer topologies to encode the RF spectral content as controlled amplitude oscillations on two optical carriers, mapping the RF spectrum to intensity speckle patterns after propagation through a highly dispersive multimode interferometer (Redding et al., 5 Nov 2025).

2. Architectures and Encoding Topologies

Architectural distinctions arise from the nature of RF–optical interaction and the interferometric arrangement.

Scheme	RF Modulation Mechanism	Interferometric Function
SOA–MZI Switching/Mod	Cross-phase modulation (XPM)	Mach–Zehnder with SOA phase bias/XPM
Acousto-Optic MZI	AOM-driven phase transfer	Mach–Zehnder with AOM in each arm
Universal RF-photonic	EO phase modulation + DFT network	N-arm DFT mesh (generalized MZI)
RF-encoded speckle	Path-mismatched RF interferometer	Multimode interferometer, speckle readout

• SOA–MZI All-Optical RoF Mixing: Utilizes two 3 dB couplers (input/output), SOAs in each arm, phase shifters for bias control, and four fiber-optic ports. Switching architecture introduces RF-controlled XPM in one arm, while the modulation configuration exchanges the roles of pump and signal, directly modulating the output (Kastritsis et al., 2022).
• Acousto-Optic Interferometry: Implements AOMs in interferometer arms, where the electronically controlled RF phase directly modulates the optical phase, enabling programmable fringe visibility and optical phase-noise engineering (Satapathy et al., 2012).
• Universal RF–Photonic Encoder: Incorporates a 1xN splitter, N parallel phase modulators each RF-phase shifted, an N×N optical DFT network, and output ports selectable for SSB/DSB, multiplication, and multi-carrier applications (Hasan et al., 2022).
• PIC-Based Speckle RF Spectrum Analyzer: Deploys a path-mismatched RF interferometer (delaying one arm) to mix the RF signal across two EOM-driven optical carriers; modulated outputs feed into a pair of long/short path-mismatched MMIs, creating a high-dimensional speckle pattern carrying the encoded RF spectrum (Redding et al., 5 Nov 2025).

3. Mathematical Framework and Transfer Functions

The field evolution and transfer characteristics in these encoders are described by explicit operator and matrix formalism:

• Basic Mach-Zehnder Output:

$$E_\mathrm{out}(t) = \frac{E_1(t) + E_2(t)}{\sqrt{2}}$$

where $$E_1(t) = \sqrt{G_1} E_\mathrm{in} e^{j[\phi_{01} + \phi_1(t)]}$$ and $$E_2(t) = \sqrt{G_2} E_\mathrm{in} e^{j[\phi_{02} + \phi_2(t)]}$$, $G_{1,2}$ including gain and cross-gain effects, $\phi_{0n}$ static bias, $\phi_n(t)$ dynamic XPM (Kastritsis et al., 2022).

• Nonlinear Phase Shift via XPM:

$$\phi_1(t) \approx \gamma \cdot P_\text{control}(t) \cdot L_\text{eff}$$

with nonlinear coefficient $\gamma$, $P_\text{control}(t)$ the instantaneous controlling optical power (Kastritsis et al., 2022).

• Generalized N×N DFT Architecture: With input $I$ and DFT matrix $$F_{k,n} = \frac{1}{\sqrt{N}}\, e^{-j\frac{2\pi}{N}(k-1)(n-1)}$$, the output vector is

$$O(t) = T_\text{DFT}\cdot\Phi(t)\cdot T_\text{spl}\cdot I$$

where $$\Phi(t) = \operatorname{diag}(e^{j\phi_1(t)},...,e^{j\phi_N(t)})$$ (Hasan et al., 2022).

• RF-Interferometer Encoding: After recombination in a 90° hybrid, outputs are:

$$\text{RF}_\text{out,1}(\omega_\text{RF}) = \frac{1}{\sqrt{2}} [1 + je^{-j\omega_\text{RF}\tau_\text{RF}}]\ \text{RF}_\text{in}(\omega_\text{RF})$$

$$\text{RF}_\text{out,2}(\omega_\text{RF}) = \frac{1}{\sqrt{2}} [j + e^{-j\omega_\text{RF}\tau_\text{RF}}]\ \text{RF}_\text{in}(\omega_\text{RF})$$

where the splitting and phase delay cause frequency-dependent amplitude encoding, remapped via EOMs to two optical carriers (Redding et al., 5 Nov 2025).

• Speckle Transfer Matrix: The optical detection pattern is modeled as $I = T\,S + \text{noise}$ with $T \in \mathbb{R}^{m \times n}$ experimentally measured across $m$ channels and $n$ RF bins; recovery proceeds via Lasso regularization $Ŝ = \arg\min_S \|T S - I\|_2^2 + \gamma\|S\|_1$ (Redding et al., 5 Nov 2025).

4. Performance Metrics and Experimental Observations

Quantitative performance of interferometric RF-to-optical encoding schemes is characterized by:

Metric	SOA–MZI Modulation	SOA–MZI Switching	Acousto-Optic MZI	PIC Speckle Analyzer
Conversion Gain (CG)	–3 to –7 dB	–8 dB (@m$\sim$0.5)	n/a (phase domain)	>30 dB SNR (@+23 dBm)
Bandwidth (3 dB)	5.5–5.9 GHz	5.5–5.9 GHz	1 MHz (AOM)	10 GHz instant., 10 MHz res.
Linearity (THD)	–20 to –30 dBc	–15 to –25 dBc	n/a	n/a
SFDR	$\sim$80 dB·Hz$^{2/3}$	$\sim$80 dB·Hz$^{2/3}$	n/a	n/a
Optical Resolution	n/a	n/a	0.1–1 rad RMS phase	100 MHz (0.8 pm @1550nm)
SSR (simulated, N=4)	–	–	–	20–30 dB (MMI limits)

• SOA–MZI Architectures: The modulation mode outperforms switching by 3–5 dB in conversion gain and 5–10 dB in linearity due to improved operation within the XPM passband rather than the band-stop region inherent in sample-and-hold (switching) sampling. Modulation also enables simultaneous wavelength conversion (Kastritsis et al., 2022).
• Resolution Limits: In the speckle spectrum analyzer, resolution is set by the combined effect of the RF interferometer FSR (100 MHz) and the optical speckle correlation width (100 MHz), yielding an effective 10 MHz RF resolution across a 10 GHz instantaneous bandwidth (Redding et al., 5 Nov 2025).
• Suppression Performance: The universal RF-photonic encoder with N×N DFT network predicts infinite sideband suppression in ideal conditions; experiments with N=4 achieve ~10–15 dB carrier suppression and 20–30 dB SSR, limited by MMI imbalance and drive index (Hasan et al., 2022).
• Phase-Noise Engineering: Acousto-optic mapping precisely controls optical fringe contrast, allowing the visibility to be analytically tailored as $V_n(\alpha) = \frac{\sin(n\alpha)}{n\alpha}$ (uniform jumps) or $V_n(\sigma) = e^{-n^2\sigma^2/2}$ (Gaussian jumps) (Satapathy et al., 2012).

5. Noise, Crosstalk, and Limitations

System performance is ultimately bounded by physical noise sources, architecture-specific losses, and intrinsic limitations:

• Noise Origins: SOA–MZI architectures are limited by amplified spontaneous emission (ASE), residual pump leakage, and imperfect arm balance, all of which degrade SNR and dynamic range (Kastritsis et al., 2022). Acousto-optic MZIs can exceed the thermal-light $g^{(2)}=2$ bunching limit for appropriate phase-noise parameter choices, with intensity correlations tunable via noise statistics (Satapathy et al., 2012).
• Insertion Loss/Resolution Tradeoff: In PIC-based analyzers, waveguide loss (~10 dB/cm) is precompensated via aggressive power splitting to maintain high-contrast speckle patterns across long interferometers, at the expense of total on-chip insertion loss (~20 dB) (Redding et al., 5 Nov 2025).
• Bandwidth Limitations: SOA–MZIs have 5–6 GHz 3 dB bandwidth, limited by SOA carrier-recovery time. In speckle-based analyzers, the ultimate RF spectral resolution is set by the longer of the RF-interferometer FSR or the optical speckle spread; with lower-loss waveguides (0.1 dB/cm), theoretical RF resolution could approach 1 MHz (Redding et al., 5 Nov 2025).
• DFT Mesh Limitations: Device-level MMIs and phase bias errors (2–5°) in the DFT network lead to SSR degradation and insertion loss on the order of 15 dB (Hasan et al., 2022).

6. Variants, Applications, and Future Directions

Interferometric RF-to-optical encoding is a highly versatile modality underpinning:

• RoF Signal Mixing and Frequency Conversion: SOA–MZI schemes for all-optical upconversion, simultaneous wavelength conversion, frequency multiplication, and high-linearity analog photonic mixing for 5G, antenna remoting, and microwave photonic systems (Kastritsis et al., 2022).
• Programmable Photonic Processors: Universal encoder circuits with DFT networks for software-defined SSB, frequency-multiplied, or multi-carrier signal generation (Hasan et al., 2022).
• Broadband Spectrum Analysis: PIC-integrated speckle analyzers for compact, high-resolution RF analysis in instrumentation, noninvasive sensing, and real-time spectral monitoring; unique in providing 10 GHz instantaneous bandwidth with 10 MHz resolution in a single shot (Redding et al., 5 Nov 2025).
• Optical Phase Noise Control and Quantum Light Generation: Acousto-optic interferometry for tunable dephasing, engineered photon statistics, and nonclassical light sources (Satapathy et al., 2012).

Research trends point to the following advances:

• Integration of higher-index or quantum-dot SOAs for >10 GHz XPM bandwidth (Kastritsis et al., 2022).
• Implementation of multi-tone and interleaved sampling to scale bandwidth and flexibility (Kastritsis et al., 2022).
• Enhanced tuning and calibration methodologies (VOAs, thermal shifters, inverse-designed MMIs) for programmable, fabrication-robust processors (Hasan et al., 2022, Redding et al., 5 Nov 2025).
• Reduction of waveguide loss in silicon photonic platforms (<0.1 dB/cm) for sub-10 MHz RF spectral resolution (Redding et al., 5 Nov 2025).

A plausible implication is that as photonic integration and materials advance, interferometric RF-to-optical encoding will yield fully integrated, low-SWAP, and digitally reconfigurable analog photonic front-ends, making broadband, high-resolution RF-optical signal processing a scalable and widely deployable technology.