Waveguide-Mode-Enhanced Millimeter-Wave Photomodulators

I. R. Hooper

Phys. Rev. Applied 17, 034001 – Published 1 March 2022

Abstract

The modulation of millimeter-wave transmission through a silicon wafer upon photoexcitation is typically very inefficient for off-the-shelf low effective charge carrier lifetime wafers, typically requiring tens of kilowatts of photoexciting intensity to generate significant modulation. Here we demonstrate that increasing the light-matter interaction for the millimeter waves using diffractively coupled waveguide modes leads to an increase in photomodulation efficiency of greater than two orders of magnitude, while maintaining the switching speed, of the order of $10 μ s$ , of the bare wafer.

Received 4 December 2021
Revised 26 January 2022
Accepted 3 February 2022

DOI:https://doi.org/10.1103/PhysRevApplied.17.034001

Physics Subject Headings (PhySH)

Interference & diffraction of light Light-matter interaction Metamaterials Photoconductivity Photonics

Devices Elemental semiconductors

Terahertz techniques

Atomic, Molecular & Optical

Authors & Affiliations

I. R. Hooper ^*

Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom

^*i.r.hooper@exeter.ac.uk

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Vol. 17, Iss. 3 — March 2022

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Images

Figure 1
Waveguide mode dispersions. The dispersion relations of the TE and TM waveguide modes supported by an intrinsic silicon wafer that is $670 μ m$ thick. Also shown as dashed lines are the corresponding scattered waveguide modes and light lines resulting from a periodic perturbation with a period of 1.6 mm. These scattered (diffracted) waveguide modes exist within the air light line and can thus be coupled to by incident plane wave radiation.
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Figure 2
Photomodulation of the bare silicon wafer. (a) The TE polarized millimeter-wave transmission through the 150 mm diameter, $670 μ m$ thick, float-zone intrinsic silicon wafer (resistivity greater than $6000$ ohms), used in the DWG modulator when unilluminated, and when photoexcited by $650 {W / m}^{2}$ light from a Thorlabs Solis 623C LED source. The wafer was oriented at a $45^{\circ}$ angle to both the millimeter-wave and optical beams. The peak in transmission at 67 GHz corresponds to the Fabry-Pérot resonance supported within the thickness of the wafer. (b) The time-dynamics upon switch-off of the photoexciting light source at 67 GHz. Also shown are fitted modeled data using a comsol Multiphysics model with the additional semiconductor and rf modules, and an exponential decrease in the change in $Δ T$ with a time constant of $τ = 17$ ms (see main text).
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Figure 3
DWG schematic. A one-dimensional diffraction grating consisting of parallel copper lines was etched into Rogers RO4350B printed circuit board and placed onto a silicon wafer. Also shown are the polar, $θ$ , and azimuthal, $ϕ$ , angles that determine the orientation of the modulator relative to the TE or TM polarized incident millimeter-wave radiation. Here, $ϕ = 0^{\circ}$ corresponds to the grating vector being parallel to the plane of incidence (the orientation shown in the figure). The thickness of the PCB substrate, $t_{sub}$ , copper tracks, $t_{c}$ , and silicon wafer, $t_{Si}$ , were 1.524 mm, $35 μ m$ , and $670 μ m$ , respectively. The period of the grating, $λ_{g}$ , was 2.1 mm, and the track width, $w_{c}$ , was 1.55 mm.
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Figure 4
Angle-dependent spectra. Transmission through the DWG modulator as a function of incident angle and frequency. The first column shows modeled results for the four cases: (a) TE polarized light at $ϕ = 0^{\circ}$ , (d) TM polarized light at $ϕ = 0^{\circ}$ , (g) TE polarized light at $ϕ = 90^{\circ}$ , (j) TM polarized light at $ϕ = 90^{\circ}$ . The second column shows experimental data for the same cases as the first column, while the third column shows equivalent experimental data when the silicon wafer was photoexcited by $650 {W / m}^{2}$ light from a Thorlabs Solis 623C LED source.
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Figure 5
Modulation efficiency. (a) The experimental (solid lines) and modeled (dashed lines) normal incidence TE polarized transmission through the DWG modulator when oriented at $ϕ = 0^{\circ}$ for various photoexcitation intensities. (b) The modulation depth as a function of photoexcitation intensity. Also shown are results extracted from the comsol model of the DWG modulator and of the bare wafer both on (at 67 GHz) and off (at 50 GHz) the Fabry-Pérot resonance supported within its thickness [see Fig. 2].
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Figure 6
Time dynamics of the DWG modulator. The normal incidence TE polarized transmission through the DWG modulator oriented at $ϕ = 0^{\circ}$ as a function of time during switch-off for different photoexcitation intensities. Also shown are exponential curves with various time constants for comparison.
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