Optical Phased Array Beamforming Network

• Optical Phased Array networks are photonic systems that use engineered phase and amplitude modulation to dynamically steer optical beams without mechanical movement.
• They leverage microcomb-based multi-wavelength synthesis, programmable spectral shaping, and dispersive delay lines to overcome beam squint and enable wideband operation.
• Scalable true-time delay architectures with reconfigurable apodization support agile beam pattern control for high-speed communications and defense applications.

An optical phased array (OPA) beamforming network is a photonic system in which the far-field optical radiation pattern is dynamically controlled via engineered phase and amplitude modulation of light in an array of emitters. OPAs enable the precise steering and shaping of optical beams without mechanical movement, fundamentally leveraging interference among coherent emitters with controlled phase profiles. In modern beamforming networks, advanced integration strategies employ microresonator frequency combs, spectral shaping, low-loss dispersive delay lines, and reconfigurable apodization to achieve wideband, wide-angle beam steering with arbitrary pattern synthesis. These architectures are central to advanced phased array antennas for high-speed wireless communications and defense, overcoming fundamental limitations of traditional electronic or purely phase-based beamformers.

1. Principles of True-Time-Delay Beamforming

In a conventional phased array antenna (PAA), beam steering is achieved by introducing frequency-dependent phase shifts at each element. However, this phase shifter approach inherently suffers from the beam-squint problem: the main beam direction drifts with frequency due to the phase–frequency relationship. In contrast, a true-time-delay (TTD) network introduces a fixed temporal delay, $\Delta\tau$, at each antenna element, resulting in a strictly frequency–linear phase advance:

$\Delta\phi = -\omega_{\mathrm{RF}}\Delta\tau$

where $\omega_{\mathrm{RF}}$ is the angular microwave frequency. The resulting beam direction is:

$$\theta_{\max} = \arcsin\left[\frac{c\Delta\phi}{\omega_{\mathrm{RF}}d}\right]$$

where $d$ is the inter-element spacing and $c$ the speed of light. By directly delaying the signal (using, e.g., dispersive fiber), the beam direction is maintained over a wide RF bandwidth, and beam squint is eliminated.

Photonic delay lines implemented with programmable optical dispersion matrices offer ultralow loss and very large bandwidth, enabling integer multiples of delay states (binary weighting), each precisely and independently controlled. These delay lines are typically realized with combinations of low-loss fiber, MEMS optical switches, and specifically engineered dispersion profiles. Integration and control of higher-order dispersion (e.g., compensation of third-order ($\beta_3$) effects) is performed spectrally to maintain phase fidelity.

2. Microcomb-Based Multi-Wavelength Synthesis

The architecture utilizes microresonator-based frequency combs (microcombs) as multi-wavelength sources. A single microcomb—generated in a silicon nitride (SiN) microring (FSR ~231 GHz, loaded Q ≈ $8\times10^5$)—spontaneously emits a series of equidistant, narrow-linewidth lines across the C-band and beyond. Each line acts as an independent carrier capable of being independently delayed, modulated, and recombined.

The dense microcomb spectrum enables simultaneous support for large PAAs: for instance, with a 50 GHz comb line spacing, a comb spanning S, C, and L bands could source over 400 antenna elements, dramatically reducing hardware complexity relative to separate laser arrays.

3. Programmable Apodization and Arbitrary Beam Pattern Control

A central element in beamforming performance is programmable spectral shaping. After phase modulation with the RF signal, each comb line is tailored by a programmable filter which specifies both the amplitude (apodization) and phase correction for each channel. This filter carries out global compensation (for chromatic dispersion and its higher orders) as well as fine per-channel phase and amplitude trimming.

Generation of arbitrary tap coefficients—including positive and negative values crucial for beam pattern engineering—is realized by selective sideband suppression post phase modulation. In the small-signal regime, the sign of the microwave tap is defined by which sideband, upper or lower, is allowed through the shaper. Thus, for each channel, both the magnitude and polarity of the tap can be programmed:

$$E(\theta) \propto \sum_{n=1}^N a_n \exp\left\{ -j [ n \omega_{\mathrm{RF}} d \sin\theta / c - \phi_n ] \right\}$$

where $a_n$ and $\phi_n$ are set via the spectral shaper for apodization and phase correction, respectively.

Key beam profiles—Gaussian, rectangular (sinc-derived), and notched (null or dark beam)—are synthesized through selection of appropriate apodization coefficients, e.g., truncated Gaussian:

$p_n = 10^{-\frac{(n-11)^2}{200}}$

Programmable spectral shaping thus enables both mainlobe control and sidelobe/null steering, essential for adaptive beamforming and interference avoidance.

4. Experimental Metrics and Performance

In the experimental system, 21 C-band comb lines are modulated, spectrally shaped, and routed through a programmable fiber-based binary delay matrix. The operating microwave frequency range is 8–20 GHz, set ultimately by the modulator and shaper bandwidths.

Key performance parameters demonstrated include:

• Beam scanning range: $\pm 60.2^\circ$, realized by selecting among binary delay states ($2^4 = 16$).
• Microwave frequency: 8–20 GHz.
• Supported PAA elements: 21 in the experiment, extensible to >400 with broadband combs.
• Measured mainbeam 3 dB width: 7° near boresight for Gaussian apodization, 25° for rectangular apodization; variable with scan angle and windowing function.
• Notched (dark) beam pattern: achieved by setting one tap's polarity opposite to the remainder, introducing a deep null in a programmable direction.

Extensive amplitude and phase calibration is performed by direct measurement of each channel’s response using the spectral shaper in feedback, with full characterization across the microwave band.

5. Scalability and Integration Prospects

Scaling the system to hundreds or more elements is enabled by broadband microcomb generation and the modularity of spectral shaping. Greater comb line counts allow for:

• Higher spatial resolution and sharper beam definitions.
• Increased degrees of freedom for complex pattern synthesis.
• Support for dynamic null steering and multi-beam operation.
• Reduced per-channel system complexity due to shared architecture.

Integration strategies leveraging CMOS-compatible SiN and other photonic foundry technologies are compatible with monolithic integration of microcombs, phase modulators, programmable spectral filters, and MEMS switches. Bandwidth, insertion loss, and global fidelity constraints must be carefully managed, especially for large comb line counts and in the presence of higher-order dispersion.

6. Theoretical Underpinnings and Control Model

Beam steering by true-time-delay is fundamentally governed by:

$$\theta_{\max} = \arcsin\left[ \frac{c \cdot (-\omega_{\mathrm{RF}}\Delta\tau)}{\omega_{\mathrm{RF}} d} \right]$$

where $\Delta\tau$ is the incremental time delay controlled per channel. The spectrum apodization, beamforming, and delay compensation are dictated by additional relationships:

• Tap coefficient for amplitude shaping: $p_n = 10^{-(n-11)^2/200}$
• Dispersion compensation for higher-order phase: $$\phi(\omega) = \frac{\beta_3 L}{6} (\omega-\omega_0)^3$$

System diagrams typically consist of: [Microcomb Source] → [Phase Modulator] → [Spectral Shaper] → [Programmable Delay Matrix] → [Demultiplexer (channelization)] → [Photodetector Array → Antenna Elements].

7. Application Domains and Impact

The microcomb-based OPA beamforming network extends the state of the art in several application domains:

• Broadband, fast-scanning phased array antennas for high-speed, high-capacity wireless communications, supporting arbitrary beam pattern synthesis.
• Defense radar and electronic warfare systems with adaptive sidelobe/null control, agile beam steering, and large aperture scaling.
• Emerging integrated microwave photonic front-ends, replacing complex RF electronics for large-scale, wideband phased arrays.

By alleviating beam squint, enabling bandwidth-agnostic wide-angle steering, and supporting complex, programmable beam shapes, the photonic TTD architecture with microcomb sourcing establishes a scalable foundation for advanced beamforming networks.

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Table: Experimental Parameters and Achievable Metrics

Parameter	Value / Range	Notes
Comb Line Spacing	231 GHz (FSR) / 50 GHz feasible	SiN microresonator, can reach >400 channels
Supported Elements	21 (exp.), >400 (scalable)	Limited by comb span and shaper bandwidth
Frequency Range	8–20 GHz	Set by modulator and spectral shaper
Beam Scanning Range	$\pm 60.2^\circ$	Controlled by programmable delay states
Mainlobe Width	7° (Gaussian), 25° (rectangular)	Mainlobe 3 dB width near boresight
Apodization Control	Positive/negative programmable	By sideband suppression and amplitude weighting

These metrics directly demonstrate the TTD architecture's superiority in beam fidelity, steerability, and scalability, positioning the photonic OPA beamforming network as a foundational technology for future high-performance antenna systems (Xue et al., 2017).