Wideband phased array radar systems typically rely on electronic phase shifters to steer the antenna beam. While effective at a single design frequency, this approach introduces beam squint, where the beam pointing angle varies with frequency due to the wavelength dependence of fixed phase shifts (see Appendix). This behavior limits operational bandwidth and degrades angular accuracy in broadband radar systems.

True Time Delay (TTD) beamforming overcomes this limitation by introducing actual time delays between antenna elements, ensuring that the beam direction remains independent of frequency (see Appendix). Photonic implementations of TTD are particularly attractive due to their wide bandwidth, low loss, and precise delay control.

Overview

Understand the simulation workflow and key results

The goal of this example is to demonstrate how a photonic binary‑weighted true time delay beamforming network can be modeled and evaluated using a combined photonic and RF simulation workflow. In this example:

1. A photonic true time delay network is modeled using Lumerical INTERCONNECT.
2. Relative time delays are extracted and converted into RF phase values using Python automation (see Appendix:  Relationship Between Time Delay and RF Phase)
3. Beam steering behavior is evaluated using a patch antenna array simulated in ANSYS HFSS.
4. Conventional phase‑shifter beamforming is compared against photonic true time delay beamforming to clearly illustrate the origin and mitigation of beam squint (see Appendix: Beam Squint in Phase‑Based Radar)

This example provides a practical framework for understanding and evaluating photonic true time delay beamforming concepts using industry‑standard simulation tools.

Note: This article focuses only on the validation results rather than detailing the complete HFSS simulation workflow. The HFSS model is used to compute the far-field radiation patterns of the antenna array based on the extracted delay-derived phase values. For users interested in exploring the full electromagnetic simulation setup and capabilities, additional information on ANSYS HFSS can be found at: Ansys HFSS for Antenna Simulation | Ansys Application Brief

Run and Results

Instructions for running the model and discussion of key results

Step 1: Photonic true time delay network simulation

1. Open the INTERCONNECT project file True_time_delay.icp provided in the example attachment.
   
   Verify that the optical source frequency is set to 193.1 THz and the RF modulation frequency is 10 GHz.
   Inspect the binary‑weighted delay line architecture, where each antenna line consists of five cascaded delay stages with a unit delay \(U = 1\,\text{ps}\), resulting in delay values of 1, 2, 4, 8, and 16 ps. The total delay applied to each antenna channel follows a binary summation relationship (see Appendix: Binary‑Weighted Delay Architecture).
   
   Mach–Zehnder‑based 2×2 optical switches control the routing of the optical signal through the delay network. The bar or cross state of each switch is determined by a state‑dependent digital control logic, in which the switch configuration depends on the transition between consecutive bits in the selected bit sequence rather than a fixed bar or cross interpretation (see Appendix: Optical Switch Control Logic (Bar and Cross States)).
   Note that a fixed pre‑compensation delay is applied to all channels to enable a linear relative delay slope across the antenna array (see Appendix: Pre‑Compensation Delay).

2. Run the simulation to generate time‑domain signals at each antenna output.

   Oscilloscope output showing the time‑domain signals at OSC_1 and OSC_2 for the default delay configuration (00000). The relative displacement between the waveforms illustrates the inter‑element true time delay generated by the photonic beamforming network.

By default, the delay configuration is set to the bit sequence 00000, and the corresponding time‑domain waveforms observed at OSC_1 and OSC_2 are shown in the results image. The relative time shift between these oscilloscope traces illustrates the effective inter‑element time delay for this reference configuration.

Step 2: Delay extraction and phase calculation

1. Run the Python script True_time_delay_delay.py provided in the example attachment and update the file path (see section Important Model Settings) to match the directory of "True_time_delay.icp".

The script is executed for three RF frequencies: 9.5 GHz, 10 GHz, and 10.5 GHz, by automatically updating the modulation source frequency in INTERCONNECT.
For each frequency, the script automatically extracts the relative time delays between adjacent antenna channels (see Appendix True Time Delay Beam Steering) and converts them into corresponding RF phase values using the time‑to‑phase relationship (see Appendix: Relationship Between Time Delay and RF Phase).

Step 3: Validation of beam steering in Ansys HFSS

1. Launch Ansys HFSS and open the project file “Photonic Radar Antenna.aedt” from the attachment.
2. In the Project Manager panel, locate the antenna simulations: RectProbe_ATK9_5GHz (Hybrid Terminal Network), RectProbe_ATK10GHz (Hybrid Terminal Network), and RectProbe_ATK10_5GHz (Hybrid Terminal Network), and double-click the required design to activate it.
    

3. Go to: HFSS → Design Properties → Variables (Local Variables) and locate the array Prog_Phase[].
4. The Prog_Phase[] array contains the phase values corresponding to 32 different bit sequences, where each value represents the phase increment used for beam steering.
5. Each bit sequence (for example, 00000, 10000) maps to one value in the Prog_Phase[] array and determines the phase progression across the antenna array, thereby controlling the beam steering angle.
6. In the same Design Properties window, you can also verify the design frequency corresponding to the selected antenna simulation (9.5 GHz, 10 GHz, or 10.5 GHz).

7. Next, navigate to: HFSS → Fields → Edit Sources to open the excitation window. In the Edit Sources window, observe that each port has: Magnitude = 1 V, Phase = n × (−Prog_Phase[i]) where n is the antenna element index and all phase values are in radians.
8. The negative sign ensures that the applied phase progression results in beam steering in the desired (positive) angular direction.

9. Since the simulation is already solved, directly access the results by navigating to: Results → Gain Plot
10. In the Gain Plot setup, you can select the desired frequency and use the Prog_Phase[] array index as one of the plot axes to select the required bit sequence and visualize the corresponding radiation pattern.

11. In the results corresponding to each simulation, you will observe two gain plots: One corresponding to bit sequence 00000, Other corresponding to bit sequence 10000
12. To export the plotted results, right-click on the gain plot, select Export, and save the data in Excel format for further analysis.

The extracted time delay values are nearly identical across all three frequencies, confirming frequency‑independent true time delay behavior. All extracted delay and phase results are saved automatically in the Results folder included with the example attachment.

Visualization of beam steering behavior

A graphical comparison of beam steering behavior is obtained using conventional phase‑shifter‑based radar and photonic true time delay radar, based on far‑field gain radiation patterns computed for multiple frequencies in Ansys HFSS.

1. For the conventional radar case, a single set of RF phase values is applied to the antenna array and used unchanged at all evaluated frequencies (for example, 9.5 GHz, 10 GHz, and 10.5 GHz). The resulting gain radiation patterns show that the main beam direction shifts with frequency, illustrating beam squint caused by the wavelength dependence of phase‑based steering (see Appendix).
2. For the photonic true time delay radar case, the same physical time delay is maintained across frequency.
   Although the time delay remains constant, the corresponding RF phase values vary with frequency through the phase–delay relationship.
   The resulting gain radiation patterns demonstrate a consistent beam direction across frequency, confirming squint‑free beam steering enabled by true time delay (see Appendix: True Time Delay Beam Steering and Relationship Between Time Delay and RF Phase).

The overlaid radiation patterns clearly highlight the contrast between frequency‑dependent beam pointing in the conventional radar case and frequency‑independent beam pointing in the photonic true time delay case.

HFSS radiation patterns for bit sequences 10000 (MSB->LSB) and 00000 (MSB->LSB) are shown using 10 GHz phase values applied at 9.5, 10, and 10.5 GHz. For both bit sequences, the beam direction shifts with frequency, demonstrating beam squint, which is characteristic of conventional phase-based radar systems.

HFSS radiation patterns for bit sequences 10000 (MSB->LSB) and 00000 (MSB->LSB) are generated using frequency dependent phase values derived from photonic TTD delays. The beam direction remains constant across 9.5, 10, and 10.5 GHz, confirming beam squint free steering, a key feature of photonic radar systems.

Important model settings

Description of important objects and settings used in this model

Script‑dependent configuration parameters

Several model parameters are defined within the Python control script and may need to be updated depending on the Lumerical version, INTERCONNECT project location, and design requirements:

1. Lumerical API path:
   The Python API path must match the installed Lumerical version, for example for 25.2 version:

   sys.path.append(r"C:\Program Files\Lumerical\v252\api\python")

2. INTERCONNECT project file path:
   The script must point to the correct location of the INTERCONNECT design file, for example:

   ICP_PATH = r"D:\Photonic Radar\Python API\True_time_delay.icp"

3. Number of delay bits and antenna lines:
   The delay resolution and array size are controlled by the following parameters:

   M = 5 # number of delay bits

   N = 8 # number of antenna lines

4. Frequency sweep configuration:
   The RF frequencies at which delay and phase extraction are performed are defined as:

   FREQS = [9.5e9, 10e9, 10.5e9]

Modifying these parameters allows the example to be adapted to different array sizes, delay resolutions, RF operating bands, and software installations.

Taking the model further

Information and tips for users that want to further customize the model

Possible extensions include:

1. Increasing delay resolution for finer angular control.
   Beam angular resolution refers to the smallest change in angle that can be achieved between two steering positions, and it depends on the smallest delay element(U) and the number of delay bits used in the system (current system uses 5 bits). It can be improved by reducing the unit delay or increasing the number of delay stages (thereby, increasing number of bits).
2. Beam directivity, on the other hand, describes how narrow and focused the beam is in a given direction and is primarily determined by the number of delay lines (or channels, current system has 8 delay lines). It can be enhanced by increasing the number of delay lines.
3. Extending the configuration to two‑dimensional beam steering involves enabling control of the beam in both azimuth and elevation directions, rather than steering in only a single plane. In a Lumerical-based TTD setup, this is achieved by arranging the delay lines into a two-dimensional array structure instead of a linear array, where independent delay control is applied across both dimensions. This requires additional delay channels and more complex control of delay elements, allowing simultaneous variation of delays along rows and columns, thereby enabling full spatial beam steering and more flexible coverage of the radiation pattern.
4. Including optical loss, noise, and switch non‑idealities
   1. Start with source modeling: Include RIN in the 193.1 THz CW laser to capture input power fluctuations.
   2. Signal propagation: Replace fixed delays with optical waveguides, where delay is governed by physical length. These waveguides naturally introduce propagation loss, phase accumulation, and dispersion.
   3. Switching stage: Add insertion loss in optical switches to account for realistic attenuation and non-ideal behavior.
   4. Detection stage: Incorporate thermal noise in the PIN photodetector to model receiver noise.
   5. Overall impact: This results in a realistic system showing signal degradation, beam distortion, and steering errors.

Appendix

Additional background information and theory

Phase‑Based Beam Steering

In a conventional phased‑array radar, beam steering is achieved by applying a fixed phase shift between adjacent antenna elements.
For an array with element spacing \(d\), the required phase shift \(\Delta\phi\) to steer the beam to an angle \(\theta\) is

$$ \Delta \phi = \frac{2\pi}{\lambda}\, d \sin(\theta) $$ 

where \(\lambda\) is the RF wavelength.

Because the wavelength depends on frequency, this steering condition is inherently frequency‑dependent.

True Time Delay Beam Steering

True time delay beamforming introduces a physical time delay between antenna elements instead of a fixed phase shift.
The required time delay difference \(\Delta\ t\) between adjacent elements is given by

$$ \Delta t = \frac{d \sin(\theta)}{c} $$

where \(c\) is the speed of light.

This expression is independent of frequency, which is the fundamental reason true time delay beamforming does not suffer from beam squint.

Relationship Between Time Delay and RF Phase

For a sinusoidal RF signal at frequency \(f\), a time delay \(\Delta\ t\) corresponds to a phase shift \(\Delta\phi\) given by

$$ \Delta \phi = 2\pi f\,\Delta t $$

In the photonic radar workflow, the time delay remains constant across frequency, while the corresponding phase varies with frequency according to this relationship.

Binary‑Weighted Delay Architecture

The photonic true time delay network uses a binary‑weighted delay architecture.
The total delay applied to a channel is

$$ T_n = \sum_{i=0}^{N-1} b_i\,2^i\,U $$

where:

• \(b_i \in \{0,1\}\) are the digital control bits
• U is the unit delay
• N is the number of delay bits

This architecture enables discrete but scalable delay control.

Binary‑Weighted True Time Delay Beamforming Architecture. (Reference: Ultrabroadband high-resolution silicon RF-photonic beamformer)

Pre‑Compensation Delay

Photonic delay elements can only introduce positive delays.
To maintain a linear relative delay slope across the antenna array, a fixed offset delay is added:

$$ T_{\mathrm{eff},n} = T_{\mathrm{offset}} + T_n $$

This pre‑compensation does not affect relative delays but enables practical implementation without negative delays.

Illustration of delay values 1U to 16U for the first antenna line and their scaled versions across higher index antenna lines, including the pre-compensating delay.

Beam Squint in Phase‑Based Radar

When a fixed phase shift is applied at a frequency different from the design frequency, the resulting beam angle becomes frequency‑dependent:

$$ \theta(f) = \arcsin\!\left(\frac{c\,\Delta\phi}{2\pi f\,d}\right) $$

This frequency dependence explains the beam squint observed in conventional phase‑shifter‑based radar.

Squint‑Free Condition in True Time Delay Beamforming

In true time delay beamforming, the time delay between elements remains constant across frequency.
Although the RF phase varies with frequency, the relative delays between antenna elements are preserved, resulting in

$$ \theta(f) = \theta_0 \text{ (independent of frequency)} $$

This condition leads to squint‑free beam steering, as observed in the HFSS gain radiation patterns.

Optical Switch Control Logic (Bar and Cross States)

Each binary‑weighted delay stage is controlled by a 2×2 optical switch implemented using the INTERCONNECT Optical Switch (X) element. The switch operates in either a bar or cross state, which determines how the signal is routed between input and output ports, rather than directly indicating the presence or absence of delay.

Let the delay configuration be represented by the binary sequence:

$$ \text{Bit_Seq}[m] \in \{0,1\}, \quad m = 0,1,\ldots,M-1 $$

The switch control logic implemented in the script is:

1. For the first delay stage:

$$ \text{control_val} = \begin{cases} 0, & \text{Bit_Seq}[0] = 1 \\ 1, & \text{Bit_Seq}[0] = 0 \end{cases} $$
 

2. For subsequent stages:

$$ \text{control_val} = \begin{cases} 0, & \text{Bit_Seq}[m] = \text{Bit_Seq}[m-1] \\ 1, & \text{Bit_Seq}[m] \ne \text{Bit_Seq}[m-1] \end{cases} $$

The resulting bar or cross state determines the routing of the optical signal with respect to the connected delay arm, depending on the active input port of the switch. As a result, a given bar or cross state does not universally correspond to “delay inserted” or “delay bypassed”, but instead selects the appropriate optical path as designed in the delay network topology.

By applying this transition‑based control logic across all delay stages and antenna channels, the script realizes the desired combination of binary‑weighted delay paths required to generate the target true time delay. This approach follows the same principles used in binary‑weighted photonic true time delay beamforming architectures employing MZI‑based optical switching (see Additional Resources).

Summary of Key Relationships

Notation

Additional resources

1. Martinez-Carrasco, P., Ho, T.H., Wessel, D. et al. Ultrabroadband high-resolution silicon RF-photonic beamformer. Nat Commun 15, 1433 (2024). https://doi.org/10.1038/s41467-024-45743-9