[Paper Review] Special polarization characteristic features of a three-dimensional terahertz photonic crystal with a silicon inverse diamond structure

Chikara Sakurai|arXiv (Cornell University)|Mar 24, 2017

Photonic Crystals and Applications3 citations

TL;DR

This study investigates polarization anisotropy in a three-dimensional silicon inverse diamond photonic crystal with a complete photonic band gap at ~0.4 THz. Using terahertz time-domain spectroscopy, it experimentally demonstrates that incident S-polarized waves with orientation I(1,0) or I(0,−1) are almost entirely converted into P-polarized reflected waves at 0.38 THz, while I(1,1) and I(1,−1) orientations preserve polarization, indicating strong polarization-dependent response within the band gap.

ABSTRACT

The band structure of an Si inverse diamond structure whose lattice point shape was vacant regular octahedrons, was calculated using plane wave expansion method. A complete photonic band gap was theoretically confirmed at around 0.4 THz. It is said that three-dimensional photonic crystals have no polarization anisotropy in photonic band gap (stop gap, stop band) of high symmetry points in normal incidence. However, it was experimentally confirmed that the polarization orientation of a reflected wave was different from that of an incident wave, [I$(X,Y)$], where $(X,Y)$ is the coordinate system fixed in the photonic crystal. It was studied on a plane (001) at around X point's photonic band gap (0.36 $-$ 0.44 THz) for incident wave direction [001] by rotating a sample in the plane (001), relatively. The polarization orientation of the reflected wave was parallel to that of the incident wave when that of the incident wave was I(1, 1) or I(1, $-$1). In contrast, the former was perpendicular to the latter when that of the incident wave was I(1, 0) or I(0, $-$1) at around 0.38 THz. As far as the photonic crystal in this work is concerned, method of resolution and synthesis of the incident polarization vector is not able to apply to the analyses of rotation of the measured reflected spectra in appearance.

Motivation & Objective

• To investigate polarization anisotropy in a three-dimensional terahertz photonic crystal with a complete photonic band gap.
• To determine whether polarization orientation of the reflected wave differs from that of the incident wave in the photonic band gap region.
• To analyze the behavior of reflected waves under different incident polarization states (I(1,1), I(1,0), I(1,−1), I(0,−1)) on the (001) plane.
• To evaluate the limitations of standard polarization vector resolution and synthesis methods in interpreting the observed spectral rotation.

Proposed method

• Calculated the photonic band structure of the Si inverse diamond structure using the plane wave expansion method with a lattice constant of 300 µm and octahedral voids of 150 µm.
• Fabricated a 48-layer silicon sample with periodic (001) surface patterning to form a 3D photonic crystal with a complete band gap at ~0.4 THz.
• Employed terahertz time-domain spectroscopy (THz-TDS) with a 7° incident angle to measure reflected spectra under controlled incident polarization states.
• Used a 1/2 wave plate to selectively transmit and analyze S- and P-polarized components of the reflected wave, enabling separation of polarization contributions.
• Normalized reflectivity spectra using gold reference and applied spectral decomposition to isolate S-p and P-p components in the reflected signal.
• Performed spectral analysis by comparing reflectivity with and without the wave plate to extract polarization-dependent response characteristics.

Experimental results

Research questions

• RQ1 Does the reflected wave in a 3D Si inverse diamond photonic crystal exhibit polarization anisotropy within the complete photonic band gap at ~0.4 THz?
• RQ2 How does the polarization orientation of the reflected wave depend on the incident wave's polarization direction on the (001) plane?
• RQ3 Why does the polarization of the reflected wave rotate by 90° for certain incident polarization states (e.g., I(1,0)) despite the crystal's high symmetry?
• RQ4 Can standard polarization vector resolution and synthesis techniques explain the observed spectral rotation in the reflected wave?
• RQ5 What is the physical origin of the strong polarization conversion observed at ~0.38 THz for I(1,0) and I(0,−1) incident waves?

Key findings

• A complete photonic band gap (CPB) was confirmed at ~0.4 THz in the Si inverse diamond structure with vacant regular octahedral lattice points.
• For incident polarization I(1,1) and I(1,−1), the reflected wave maintained polarization orientation parallel to the incident wave, indicating no rotation.
• For incident polarization I(1,0) and I(0,−1), the reflected wave exhibited a 90° polarization rotation, with S-p incident waves almost entirely converted into P-p reflected waves at 0.38 THz.
• At 0.38 THz within the BGX (0.36–0.44 THz) band gap, the reflected wave for I(1,0) was predominantly P-polarized, indicating strong polarization conversion.
• The observed polarization rotation cannot be explained by standard polarization vector resolution and synthesis methods, suggesting a non-trivial underlying mechanism.
• Spectral decomposition confirmed that the reflected signal for I(1,0) contained significant P-p component, while for I(1,1) it was dominated by S-p, validating the polarization-dependent response.