Coherent control of optical spin–orbit interactions
Data files
Feb 16, 2026 version files 331.97 KB
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dataset.zip
305.78 KB
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README.md
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Abstract
Optical spin-orbit interactions (SOI) are an intriguing physical phenomenon where the spin (circular polarization) of light influences and governs its spatial degrees of freedom. Yet, achieving real-time and flexible control over SOI remains a formidable challenge. Here, we propose a coherent control method for the flexible manipulation of optical SOI using a thin isotropic crystal. The output horizontally and vertically polarized waves from the crystal exhibit strong and distinct dependencies on the phase delay between the input signal and control waves, leading to substantial spin-orbit beam shifts. By tuning the relative phase between the signal beam and the control beam, we observe transitions from Gaussian to first-order orbital angular momentum (OAM) vortex modes. The achievable transition speed reaches 11.5 GHz, currently limited by the phase modulator in the control arm. Notably, the dual-port architecture offers coherent and reversible selection of spin–OAM states, with the output port uniquely determined by the phase delay between two counter-propagating input beams. This ultrafast coherent control method opens avenues for advanced manipulation of SOI.
Dataset DOI: 10.5061/dryad.fqz612k5z
Description of the data and file structure
> Dataset Description
> This dataset supports the findings in the manuscript titled "Coherent Control of Optical Spin–Orbit Interactions". The data files provided correspond to the experimental and theoretical results presented in Figures 2, 3, 4, 5, and 6 of the main manuscript. The dataset covers the characterization of the coherent spin-orbit interaction (SOI) effects, including reflection/transmission spectra, phase calculations, spin-orbit beam shifts, system bandwidth, and high-speed optical switching performance.
Files and variables
File: dataset.zip
File Formats and Access
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File Extension:
.csv(Comma Separated Values) -
How to Open: These files are standard text-based data files. They can be opened and viewed using any text editor (e.g., Notepad, TextEdit), spreadsheet software (e.g., Microsoft Excel, Google Sheets), or analyzed using programming languages such as Python (pandas), MATLAB, or R.Dataset Contents & Usage
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List of Files and Variable Definitions
Figure 2 Files (Basic Characterization)
1.
figure2cd_single_incident_processed.csvDescription: Corresponds to Figure 2C and 2D. It contains the theoretical and experimental reflection and transmission spectra for a single plane wave incident on the silicon wafer.
Incident_Angle_deg: The angle of incidence of the beam (theta_1) in degrees.Theory_Reflectance_p: Calculated reflectance (R_p) for horizontally polarized (p-polarized) light.Theory_Transmittance_p: Calculated transmittance (T_p) for horizontally polarized (p-polarized) light.Exp_Transmitted_Power_p_W: Measured optical power transmitted through the wafer for p-polarization, in Watts.Exp_Transmittance_p: Experimental transmittance for p-polarization (normalized).Exp_Reflected_Power_p_W: Measured optical power reflected from the wafer for p-polarization, in Watts.Exp_Reflectance_p: Experimental reflectance for p-polarization (normalized).Theory_Reflectance_s: Calculated reflectance (R_s) for vertically polarized (s-polarized) light.Theory_Transmittance_s: Calculated transmittance (T_s) for vertically polarized (s-polarized) light.Exp_Transmitted_Power_s_W: Measured optical power transmitted through the wafer for s-polarization, in Watts.Exp_Transmittance_s: Experimental transmittance for s-polarization (normalized).Exp_Reflected_Power_s_W: Measured optical power reflected from the wafer for s-polarization, in Watts.Exp_Reflectance_s: Experimental reflectance for s-polarization (normalized).
2.
figure2e_phase_calculations.csvDescription: Corresponds to Figure 2E. It provides the calculated phase relationships relevant to the coherent control mechanism.
Incident_Angle_deg: The angle of incidence (theta_1) in degrees.Cumulative_Phase_delta_deg: The calculated cumulative phase shift (delta) accumulated by the beam during propagation through the wafer thickness, in degrees.Critical_Phase_delta_p_deg: The critical cumulative phase (Delta_p) required for coherent extinction of p-polarized light, in degrees.Critical_Phase_delta_s_deg: The critical cumulative phase (Delta_s) required for coherent extinction of s-polarized light, in degrees.
3.
figure2f_dual_port_incident_processed.csvDescription: Corresponds to Figure 2F. It contains data for the coherent dual-beam configuration (signal + control beams) with a fixed relative phase delay (Delta_varphi = -pi/2). It shows the output intensities at Port 2.
Incident_Angle_deg: The angle of incidence (theta_1) in degrees.Theory_Output_Intensity_Port2_p: Theoretical normalized output intensity for p-polarization at Port 2 (|B_2^p|^2).Theory_Output_Intensity_Port2_s: Theoretical normalized output intensity for s-polarization at Port 2 (|B_2^s|^2).Exp_Output_Power_Port2_p_W: Measured output power for p-polarization at Port 2, in Watts.Exp_Output_Intensity_Port2_p: Experimental normalized output intensity for p-polarization at Port 2.Exp_Output_Power_Port2_s_W: Measured output power for s-polarization at Port 2, in Watts.Exp_Output_Intensity_Port2_s: Experimental normalized output intensity for s-polarization at Port 2.
4.
figure2h_experiment_profile.csvDescription: Corresponds to the experimental data in Figure 2H. It shows the cross-sectional intensity profiles of the output beam for opposite spin states (sigma+ and sigma-) at a fixed incident angle (theta_1 = 8.8deg).
Position_m: Transverse spatial position across the beam profile, in meters.Exp_Intensity_SigmaPlus_Normalized: Measured normalized intensity profile for the sigma+ component.Exp_Intensity_SigmaMinus_Normalized: Measured normalized intensity profile for the sigma- component.
5.
figure2h_theory_profile.csvDescription: Corresponds to the theoretical data in Figure 2H. It provides the calculated beam profiles matching the experimental conditions in the file above.
Position_m: Transverse spatial position across the beam profile, in meters.Theory_Intensity_SigmaPlus_Normalized: Calculated normalized intensity profile for the sigma+ component.Theory_Intensity_SigmaMinus_Normalized: Calculated normalized intensity profile for the sigma- component.
6.
figure2i_experiment_shifts.csvDescription: Corresponds to the experimental data in Figure 2I. It contains the measured spin-orbit beam shifts (transverse displacements) as a function of incident angle.
Incident_Angle_deg: The angle of incidence (theta_1) in degrees.Y-: Individual measurements of the beam centroid shift for the sigma- component, in micrometers (mu m). Multiple columns indicate repeated measurements.Exp_Shift_SigmaMinus_Mean_um: The average centroid shift for the sigma- component, in micrometers.Exp_Shift_SigmaMinus_Std_um: The standard deviation of the shift for the sigma- component, in micrometers.Y+: Individual measurements of the beam centroid shift for the sigma+ component, in micrometers (mu m).Exp_Shift_SigmaPlus_Mean_um: The average centroid shift for the sigma+ component, in micrometers.Exp_Shift_SigmaPlus_Std_um: The standard deviation of the shift for the sigma+ component, in micrometers.
7.
figure2i_theory_shifts.csvDescription: Corresponds to the theoretical prediction in Figure 2I.
Incident_Angle_deg: The angle of incidence (theta_1) in degrees.Theory_Shift_SigmaPlus_um: Calculated transverse beam shift for the sigma+ component, in micrometers (mu m).Theory_Shift_SigmaMinus_um: Calculated transverse beam shift for the sigma- component, in micrometers (mu m).
Figure 3 Files (Coherent Control of SOI)
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figure3b_output_control.csvDescription: Corresponds to Figure 3B. It characterizes the output intensity control at Port 2 by varying the incident angle.
Incident_Angle_deg: The angle of incidence (theta_1) in degrees.Theory_Output_Intensity_Port2_p_Normalized: Calculated normalized output intensity for p-polarization at Port 2.Theory_Output_Intensity_Port2_s_Normalized: Calculated normalized output intensity for s-polarization at Port 2.Exp_Output_Power_Port2_p_W: Measured output optical power for p-polarization at Port 2, in Watts.Exp_Output_Intensity_Port2_p_Normalized: Experimental normalized output intensity for p-polarization.Exp_Output_Power_Port2_s_W: Measured output optical power for s-polarization at Port 2, in Watts.Exp_Output_Intensity_Port2_s_Normalized: Experimental normalized output intensity for s-polarization.
9.
figure3cd_experiment_SigmaMinus_shifts.csvDescription: Corresponds to the experimental data in Figure 3C and 3D for the sigma- component.
Incident_Polarization Angle_deg: The polarization angle of the incident beam, in degrees.X-,X-.1,X-.2: Individual measurements of the beam centroid shift in the X-direction.Y-,Y-.1,Y-.2: Individual measurements of the beam centroid shift in the Y-direction.Exp_Shift_SigmaMinus_X_Mean_um: Average centroid shift in the X-direction for sigma-, in micrometers (mu m).Exp_Shift_SigmaMinus_X_Std_um: Standard deviation of the X-shift.Exp_Shift_SigmaMinus_Y_Mean_um: Average centroid shift in the Y-direction for sigma-, in micrometers (mu m).Exp_Shift_SigmaMinus_Y_Std_um: Standard deviation of the Y-shift.
10.
figure3cd_experiment_SigmaPlus_shifts.csvDescription: Corresponds to the experimental data in Figure 3C and 3D for the sigma+ component.
Incident_Polarization Angle_deg: The polarization angle of the incident beam, in degrees.X+,Y+: Individual measurements of the beam centroid shift in X and Y directions.Exp_Shift_SigmaPlus_X_Mean_um: Average centroid shift in the X-direction for sigma+, in micrometers.Exp_Shift_SigmaPlus_Y_Mean_um: Average centroid shift in the Y-direction for sigma+, in micrometers.
11.
figure3cd_theory_shifts.csvDescription: Corresponds to the theoretical predictions in Figure 3C and 3D.
Incident_Polarization Angle_deg: The polarization angle of the incident beam, in degrees.Theory_Shift_SigmaMinus_X_um: Calculated X-direction shift for the sigma- component, in micrometers.Theory_Shift_SigmaMinus_Y_um: Calculated Y-direction shift for the sigma- component, in micrometers.Theory_Shift_SigmaPlus_X_um: Calculated X-direction shift for the sigma+ component, in micrometers.Theory_Shift_SigmaPlus_Y_um: Calculated Y-direction shift for the sigma+ component, in micrometers.
12.
figure3fg_experiment_profiles.csvDescription: Corresponds to the experimental beam profiles in Figure 3F and 3G.
Position_m: Spatial position along the cross-section (X or Y axis), in meters.Exp_Normalized_Intensity_SigmaMinus_X: Measured intensity profile of the sigm- component along the X-axis.Exp_Normalized_Intensity_SigmaPlus_X: Measured intensity profile of the sigma+ component along the X-axis.Exp_Normalized_Intensity_SigmaMinus_Y: Measured intensity profile of the sigma- component along the Y-axis.Exp_Normalized_Intensity_SigmaPlus_Y: Measured intensity profile of the sigma+ component along the Y-axis.
13.
figure3fg_theory_profiles.csvDescription: Corresponds to the theoretical beam profiles in Figure 3F and 3G.
Position_m: Spatial position along the cross-section, in meters.Theory_Normalized_Intensity_SigmaMinus_X: Calculated intensity profile of the sigma- component along the X-axis.Theory_Normalized_Intensity_SigmaPlus_X: Calculated intensity profile of the sigma+ component along the X-axis.Theory_Normalized_Intensity_SigmaMinus_Y: Calculated intensity profile of the sigma- component along the Y-axis.Theory_Normalized_Intensity_SigmaPlus_Y: Calculated intensity profile of the sigma+ component along the Y-axis.
14.
figure3h_experiment_SigmaMinus_shifts.csvDescription: Corresponds to the experimental data in Figure 3H. It quantifies the shift for the sigma- component as a function of the relative phase delay.
Delta_Phase_pi: Relative phase delay (Delta_varphi) between the signal and control beams, in units of pi radians.X-,Y-: Individual measurements of the beam centroid shift in X and Y directions.Exp_Shift_SigmaMinus_X_Mean: Average centroid shift in the X-direction.Exp_Shift_SigmaMinus_Y_Mean: Average centroid shift in the Y-direction.
15.
figure3i_experiment_SigmaPlus_shifts.csvDescription: Corresponds to the experimental data in Figure 3I. It quantifies the shift for the sigma+ component as a function of the relative phase delay.
Delta_Phase_pi: Relative phase delay (Delta_varphi), in units of pi radians.X+,Y+: Individual measurements of the beam centroid shift in X and Y directions.Exp_Shift_SigmaPlus_X_Mean: Average centroid shift in the X-direction.Exp_Shift_SigmaPlus_Y_Mean: Average centroid shift in the Y-direction.
16.
figure3hi_theory_shifts.csvDescription: Corresponds to the theoretical predictions in Figure 3H and 3I.
Delta_Phase_pi: Relative phase delay (Delta_varphi), in units of pi radians.Theory_Shift_SigmaMinus_X: Calculated X-direction shift for sigma-.Theory_Shift_SigmaPlus_X: Calculated X-direction shift for sigma+.Theory_Shift_SigmaMinus_Y: Calculated Y-direction shift for sigma-.Theory_Shift_SigmaPinus_Y: (Note: HeaderSigmaPinuscorresponds toSigmaPlus) Calculated Y-direction shift for sigma+.
Figure 4 Files (Cavity-Length Dependent SOI)
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figure4b_d_experiment_profile.csvDescription: Corresponds to the experimental data in Figure 4B (and 4D). It shows the measured normalized intensity variation mapping to wafer thickness.
Pixel_Index: The spatial index/position along the measurement axis.Normalized_Intensity: Measured normalized output intensity.
18.
figure4b_d_theory_profile.csvDescription: Corresponds to the theoretical calculation in Figure 4B.
Wafer thickness_um: The thickness of the silicon wafer (d), in micrometers (mu m).Theory_Normalized_Intensity: Calculated normalized output intensity.
19.
figure4c_experiment_lcp_shift.csvDescription: Corresponds to the experimental data in Figure 4C for the sigma- component.
Wafer thickness_d_um: The local thickness of the wafer (d), in micrometers.Y-: Individual measurements of the transverse beam shift in the Y-direction.Exp_Shift_SigmaMinus_Mean_um: Average centroid shift for sigma-, in micrometers (mu ).Exp_Shift_SigmaMinus_Std_um: Standard deviation of the shift for sigma-.
20.
figure4c_experiment_rcp_shift.csvDescription: Corresponds to the experimental data in Figure 4C for the sigma+ component.
Wafer thickness_d_um: The local thickness of the wafer (d), in micrometers.Y+: Individual measurements of the transverse beam shift in the Y-direction.Exp_Shift_SigmaPlus_Mean_um: Average centroid shift for sigma+, in micrometers (mu m).Exp_Shift_SigmaPlus_Std_um: Standard deviation of the shift for sigma+.
21.
figure4c_theory_shifts.csvDescription: Corresponds to the theoretical prediction in Figure 4C.
Wafer thickness_d_um: The thickness of the silicon wafer (d), in micrometers.Theory_Shift_SigmaMinus_Y_um: Calculated transverse shift for sigma-.Theory_Shift_SigmaPlus_Y_um: Calculated transverse shift for sigma+.
22.
figure4e_experiment_profile.csvDescription: Corresponds to the experimental beam profiles in Figure 4E.
Position_m: Transverse spatial position across the beam profile, in meters.Exp_Normalized_Intensity_SigmaMinus: Measured normalized intensity profile for sigma-.Exp_Normalized_Intensity_SigmaPlus: Measured normalized intensity profile for sigma+.
23.
figure4e_theory_profile.csvDescription: Corresponds to the theoretical beam profiles in Figure 4E.
Position_m: Transverse spatial position across the beam profile, in meters.Theory_Normalized_Intensity_SigmaPlus: Calculated normalized intensity profile for sigma+.Theory_Normalized_Intensity_SigmaMinus: Calculated normalized intensity profile for sigma-.
Figure 5 Files (Dynamic Modulation and Bandwidth)
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figure5c_experiment_tuning_curve.csvDescription: Corresponds to the experimental data in Figure 5C. It characterizes the system's ability to modulate output intensity by varying the phase delay.
Delta Phase_pi: The applied relative phase delay (Delta_varphi), normalized by pi.Exp_Normalized_Intensity_Mean: The average normalized output intensity.Exp_Normalized_Intensity_Std: The standard deviation of the intensity measurements.
25.
figure5c_theory_tuning_curve.csvDescription: Corresponds to the theoretical prediction in Figure 5C.
Delta Phase_pi: The applied relative phase delay (Delta_varphi), normalized by pi.Theory_Normalized_Intensity: Calculated normalized output intensity.
26.
figure5d_10mhz_modulation.csvDescription: Corresponds to Figure 5D. Time-domain response under 10 MHz modulation.
Time_s: Time, in seconds.Voltage_Driving_V: Input driving signal voltage, in Volts.Voltage_PD Response_V: Photodetector response voltage (optical output), in Volts.
27.
figure5f_120mhz_pulse.csvDescription: Corresponds to Figure 5F. Time-domain response under 120 MHz pulse modulation.
Time_s: Time, in seconds.Voltage_Driving_V: Input driving signal voltage, in Volts.Voltage_PD Response_V: Photodetector response voltage, in Volts.
28.
figure5f_500mhz_modulation.csvDescription: Corresponds to Figure 5F. Time-domain response under 500 MHz modulation.
Time_s: Time, in seconds/indices.Voltage_Driving_V: Input driving signal voltage, in Volts.Voltage_PD Response_V: Photodetector response voltage, in Volts.
29.
figure5g_10ghz_modulation.csvDescription: Corresponds to Figure 5G. Time-domain response under 10 GHz modulation.
Time_s: Time, in seconds.Voltage_Driving_V: Input driving signal voltage, in Volts.Voltage_PD Response_V: Photodetector response voltage, in Volts.
30.
figure5g_13.5ghz_modulation.csvDescription: Corresponds to Figure 5G. Time-domain response under 13.5 GHz modulation.
Time_s: Time, in seconds.Voltage_Driving_V: Input driving signal voltage, in Volts.Voltage_PD Response_V: Photodetector response voltage, in Volts.
31.
figure5h_system_bandwidth.csvDescription: Corresponds to Figure 5H. It presents the frequency response of the system.
Frequency_Hz: The modulation frequency, in Hertz (Hz).S12_Magnitude_dB: The magnitude of the system's frequency response, in decibels (dB).
Figure 6 Files (Optical Switching)
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figure6c_100mhz_switching.csvDescription: Corresponds to Figure 6C. Coherent optical switching at 100 MHz.
Time_s: Time, in seconds.Voltage_Driving_V: Input driving signal voltage, in Volts.Voltage_Port1_PD Response_V: Photodetector output voltage at Port 1.Voltage_Port2_PD Response_V: Photodetector output voltage at Port 2.
33.
figure6d_10ghz_switching.csvDescription: Corresponds to Figure 6D. High-speed coherent optical switching at 10 GHz.
Time_s: Time scale for the photodetector response columns, in seconds.Voltage_Port1_PD Response_V: Photodetector output voltage at Port 1.Voltage_Port2_PD Response_V: Photodetector output voltage at Port 2.Time_s.1: Time scale for the driving voltage column, in seconds.Voltage_Driving_V: Input driving signal voltage, in Volts.
Contextual Description of Figures
- Figure 2C & 2D: These figures characterize the passive optical response of the silicon wafer under single-beam illumination. They compare the measured and calculated reflection (R) and transmission (T) spectra for horizontally (p) and vertically (s) polarized light as the incident angle is varied. The crossing point of the R and T curves indicates the condition for potential coherent perfect absorption or transparency in a dual-beam setup.
- Figure 2E: This figure illustrates the phase matching conditions required for coherent control. It plots the calculated cumulative phase shift (delta) a beam acquires traversing the wafer and compares it to the critical phase (Delta_{p,s}) required to achieve coherent extinction (destructive interference) at the output ports.
- Figure 2F: This figure demonstrates the result of coherent interference between two counter-propagating beams (signal and control) with a fixed phase delay of pi/2. It shows the normalized output intensity at Port 2, revealing a distinct dip for p-polarization (destructive interference) and a peak for s-polarization (constructive interference) near the critical angle of 7.9 deg.
- Figure 2H: This figure presents the spatial intensity profiles of the output beam, resolved into its two spin components (sigma+ and sigma-). It highlights the "spin-orbit beam shift," where the two spin components spatially separate in opposite transverse directions due to the coherent Spin-Orbit Interaction (SOI) at a specific incident angle (8.8 deg).
- Figure 2I: This figure quantifies the spin-orbit beam shift phenomenon. It plots the transverse centroid displacement (shift) of the sigma+ and sigma- beam components as a function of the incident angle. The data shows that the separation between the two spin states is strongly dependent on the angle of incidence, reaching a maximum near the resonance condition.
- Figure 3B: Illustrates the coherent selection of the operating state. By scanning the incident angle, the system can be tuned to a condition (typically near the Brewster or critical angle) where the coherent interaction allows for maximal control over the output intensity of specific polarization states.
- Figure 3C & 3D: These figures demonstrate the polarization-controlled spin-orbit interaction. They show how rotating the polarization angle of the input beam linearly controls the transverse spatial shift (in both X and Y directions) of the output sigma+ and sigma- beam components. This effectively maps the polarization state (Poincaré sphere) to real-space coordinates.
- Figure 3F & 3G: These figures present the beam profiles under coherent control. They visualize the spatial distribution of the sigma+ and sigma- components along the X and Y axes, confirming that the beam retains its quality while undergoing significant spatial shifts.
- Figure 3H & 3I: These figures demonstrate the phase-controlled spin-orbit interaction. They plot the transverse beam shifts as a function of the relative phase delay (Delta_varphi) between the two coherent input beams. This confirms that the Spin-Orbit Interaction (SOI) and the resulting beam splitting can be continuously modulated and reversed purely by adjusting the phase, without moving any mechanical parts.
- Figure 4B: This figure characterizes the dependence of the system's optical response on the cavity dimension. It plots the output intensity as a function of the silicon wafer thickness (d). The observed fringes (Fabry-Pérot resonances) indicate that the spin-orbit interaction effects can be tuned by slightly varying the thickness or temperature of the crystal.
- Figure 4C: This figure illustrates the thickness-dependent spin-orbit interaction. It shows that the transverse spatial shift (splitting) between the sigma+ and sigma- beam components is not static but oscillates dramatically with the wafer thickness. Large beam shifts (giant SOI) are observed near specific thickness values corresponding to cavity resonances.
- Figure 4E: This figure provides a snapshot of the beam profiles at a chosen thickness where the spin-orbit shift is significant. It confirms that the two spin components are spatially separated into distinct lobes while maintaining their Gaussian-like profile shape, verifying the high quality of the spin-dependent beam splitting.
- Figure 5C: Establishes the static "transfer function" of the device. By sweeping the phase delay slowly, this figure maps the relationship between the control parameter (phase) and the output intensity, which is essential for determining the bias points for linear modulation or switching.
- Figure 5D & 5F: These figures illustrate the temporal dynamic response of the system. They show time-domain traces of the input electrical signal versus the output optical signal at various frequencies (10 MHz, 120 MHz, 500 MHz). This proves that the coherent SOI mechanism is not just a static effect but can be modulated in real-time.
- Figure 5G: Demonstrates the high-speed performance of the system in the microwave frequency range (10 GHz and 13.5 GHz). The clear open eye diagrams or sinusoidal waveforms at these frequencies indicate the system is suitable for high-speed optical communications or signal processing.
- Figure 5H: Provides a quantitative measure of the system bandwidth. By plotting the response magnitude over a wide frequency range (up to nearly 20 GHz), it characterizes the upper frequency limit of the coherent control mechanism, showing it is broadband (11.5 GHz) and limited primarily by the phase modulators rather than the SOI effect itself.
- Figure 6C: Illustrates the low-frequency (100 MHz) coherent switching operation. By modulating the relative phase between the input beams, the optical energy is dynamically routed between Port 1 and Port 2. The waveforms show that when the signal at Port 1 is maximized (constructive interference), the signal at Port 2 is minimized (destructive interference), and vice-versa, demonstrating efficient 1x2 optical switching.
- Figure 6D: Demonstrates the high-speed (10 GHz) coherent switching performance. This figure proves that the proposed spin-orbit interaction based switching mechanism is robust and fast enough to handle data rates compatible with modern optical communication networks (X-band frequencies). The clear anti-phase relationship between the two output ports is maintained even at this high frequency.