Compact and ultra-efficient broadband plasmonic terahertz field detector

Terahertz sources and detectors have enabled numerous new applications from medical to communications. Yet, most efficient terahertz detection schemes rely on complex free-space optics and typically require high-power lasers as local oscillators. Here, we demonstrate a fiber-coupled, monolithic plasmonic terahertz field detector on a silicon-photonics platform featuring a detection bandwidth of 2.5 THz with a 65 dB dynamical range. The terahertz wave is measured through its nonlinear mixing with an optical probe pulse with an average power of only 63 nW. The high efficiency of the scheme relies on the extreme confinement of the terahertz field to a small volume of 10−8(λTHz/2)3. Additionally, on-chip guided plasmonic probe beams sample the terahertz signal efficiently in this volume. The approach results in an extremely short interaction length of only 5 μm, which eliminates the need for phase matching and shows the highest conversion efficiency per unit length up to date.


Supplementary Note 1: THz antenna design and frequency response.
The THz detector comprises of an antenna and a plasmonic slot waveguide filled with a nonlinear material. The collected energy by this antenna can be optimally concentrated into the nonlinear material for maximum detection efficiency. An expression describing the field enhancement (FE), defined as the ratio between the electric field in the plasmonic slot (ETHz,g) and the incident electric field (ETHz,i), as a function of the device parameters was previously derived 1 where Zd is the device's impedance, wslot is the plasmonic slot width, λTHz is the THz wavelength, GR is the antenna gain and Z0 is the free-space impedance. Clearly, the slot width has a strong impact on the efficiency. The nanoscale plasmonic slot can therefore enable optimal field enhancement. In addition, maximum voltage drop (electric field) in the nonlinear material is achieved for a device with a high impedance. This is achieved by exploiting the full-wave resonance of the antenna 2 . Finally, strong resonance, i.e. high impedance, can be achieved with magnetic resonators such as the four-leaf clover antenna. In such a structure, the inductive part comes mainly from the split ring features, and therefore, wider antenna arms can be used to reduce    the two phase shifter arms should come with an opposite orientation in order to achieve push-pull operation 3 . This is achieved by poling the device asymmetrically between the two antennas, see

FE =
The broad frequency response of the antenna can be decomposed into two parts, i.e. high-and low-frequency. The simulated field enhancement of the low-(dashed curves) and high-frequency

Supplementary Note 2: Operation principle of the Mach-Zehnder interferometer.
The working principle of the Mach-Zehnder Interferometer (MZI) is discussed in this section with respect to its sensitivity to an externally applied THz field of amplitude ETHz,g. For this purpose, we assume an input probe intensity in (which is proportional to the square of an electric field in ) which is fed to the MZI. The probe signal is first split and further propagates through the two branches of the interferometer. Subsequently we will show, that the path imbalance between the two branches of the interferometer at zero applied THz field greatly determines the sensitivity of the interferometric detector. The path difference can be given by the phase offset offset = probe pulse in the dielectric waveguide and Δ the geometric path difference between the two branches. We further assume slot to be the length of the plasmonic slot, the attenuation coefficient of the probe intensity in the plasmonic slot and Δ THz = 2π p Δ eff slot = Δ eff slot the phase delay introduced by the in-gap THz electric field ETHz,g. Δ eff can be modulated upon applying an electric field THz,g . Also, it should be noted, that in a MZI that is operated in pushpull operation mode one will induce a phase shift of Δ THz in one arm and a phase shift of −Δ THz in the other arm. The total phase shift thus is 2Δ THz . We assume Δ THz ≪ π 2 to be very small. The electric field and intensity of the probe after the interferometer then is Clearly, since the sensitivity of the output intensity to an incident THz field is highest for sin( offset + 2 Δ THz ) = 1, that is for offset = π/2 (quadrature point).
If the MZI is operated near the maximum transmission point, then offset ≈ 0 and Hence, the intensity modulation contains a quadratic and a linear dependence on the THz electric field. Since typically we have, φ offset > Δ THz , the linear term dominates. A similar behaviour occurs for offset ≈ π.
Conversely, if the MZI is operated near the quadrature point, then offset ≈ π 2 and In case the phase offset between the two MZI arms is offset = π, we are in a destructive operation mode -the so called Null-point operation point. Unfortunately, the intensity modulation around the Null point is then weak. Although the modulation efficiency is maximal, not enough optical power reaches the photodiode to detect the THz field. Conversely, when the phase offset is offset = 0, maximum light reaches the photodiode. However, due to low modulation efficiency , no THz field is detected as well. Furthermore, in the vicinity of the maximum transmission offset = 0, the response of the detector contains linear and quadratic terms (see equation in Supplementary Note 2), as shown in Supplementary Figure 5b. In other words, the detector becomes a photon detector. Finally, when the phase offset is set to offset = π 2 , i.e. quadrature point of the MZI, the intensity modulation becomes largest and a maximal THz field amplitude modulation is detected (see Supplementary Figure 5a). Also, the response of the detector is linear in field, as shown in Supplementary Figure 5b.

Supplementary Note 4: Electric field induced phase modulation.
Here we discuss the induced phase shift of the optical probe signal, i.e. phase modulation, by the applied THz electric field. In an electro-optic material, the phase shift is caused by the change of refractive index Δ mat induced by the applied electric field. The accumulated phase shift over a distance is then given by Δ = • Δ (9) where is the propagation constant. For a small change in refractive index, the phase shift can be rewritten in terms of the group velocity g = Δ Δ ,  (11) where e is the energy velocity 6 , is the permittivity, ℜ the real part and � is the unit vector in z-direction.
The shift in the optical propagation mode 4 due to a small Δ mat is given by where c is the fraction of the total energy of the optical signal that contributes to the nonlinear interaction. In other words, it is the overlap integral between the energy of the optical component aligned to the nonlinear axis of the electro-optic material and the total optical energy 5 : where 0 = is the wavenumber. The linear electro-optic effect introduces a change in the refractive index of the nonlinear material upon an applied electric field THz,g Δ mat = Finally, the induced phase change can be written as We further compare different platforms that are commonly used for coherent detection of the electric field of terahertz (THz) waves with the purpose to evaluate their individual performance and potential for improvement. In that respect, we shall compare electro-optic detection in ZnTe crystal 1 mm, photoconductive detector at 1550 nm, large-area photoconductive detectors at 780 nm, detection in organics combined with a three-dimensional antenna and the organic-plasmonic on-chip detectors. We will resort to distinct scientific reports about the performance of the individual detectors and they will be used to benchmark the different technologies. This study is intended to give an overview over the existing technology and is not aspiring to provide an ultimate comparison as all experiments have been done in different laboratories and in different experimental configurations.
In the different platforms, the electric field of a terahertz wave is measured indirectly, by means of a femtosecond probe. For instance, in electro-optic detection schemes the THz electric field ultimately introduces a modulation of the intensity of the probe beam. Conversely, in photoconductive detection schemes the probe beam generates carriers in a semiconductor which are then accelerated by the THz wave to produce a photocurrent that is finally detected.
In the case of free-space electro-optic detection in ZnTe 110-cut, the intensity modulation is equal to: with p the total probe intensity travelling through the detection crystal, the angular frequency of the probe, opt the refractive index at the probe frequency, int the interaction length between the two beams, and 41 the electro-optic coefficient of ZnTe. Typically, p = 2 mW, opt = 2.8, 41 = 3.9 pm V −1 , int = 1 mm and 0 = 800 nm. Therefore, Δ ( ) p = 6.67 • 10 −7 m V THz ( ).  In the case of the integrated electro-optic THz detector with the MZI configuration featuring a hybrid organic-plasmonic phase modulators one finds: with c g the field energy interaction factor. Typically, p = 10 −4 mW , opt = 1.77 , 33 = 120 pm V −1 , c g = 1.6, = 0.004 mm, FE = 1000 and 0 = 1550 nm. Therefore, We find therefore that the use of a MZI detector featuring hybrid organic-plasmonic phase shifters of a width of 75 nm yields an at least ten times higher electro-optic signal than all other detection schemes at equal probe powers. For shot-noise limited detection, the SNR of the MZI detector is thus at least a factor of 10 higher than the other detection schemes at equal probe powers.
In the case of a photoconductive detector, we find that the photocurrent driven by the terahertz electric field at the electrodes is equal to 8 : where 0 is the electron mobility in the semiconductor and e the elementary charge. Φ( − ) describes the temporal (and thus frequency) response of the semiconductor and is determinded by the carrier lifetime. 12 is the Fresnel transmission coefficient for light from a laser beam of center wavelength and waist of standard deviation Σ . G is the average power entering the semiconductor, ℎ is the Planck's constant and 0 is the speed of light in vacuum.
We summarize different characteristics of the different platforms in Supplementary Table 3. For near-field (NF) measurement possibility but with the probe still propagating through an analyte is marked with yes*. Supplementary Figure 9 shows the dynamic range (DR) as a function of the probe power and the modulation efficiency. The measured DR for the 2.4 THz antenna and the 1 mm long ZnTe crystal are indicated in white for similar measurement specifications. The integrated THz detector has a strong efficiency but a limited probe power. On the contrary, the ZnTe crystal has a low modulation efficiency but a high optical power. Assuming the improvement in optical power as discussed in the method section of the manuscript, an at least equal dynamic range (red point) would be possible for the integrated detector of only 5 µm in length.

Supplementary
Supplementary Figure 9 Dynamic range as a function of the probe power and modulation efficiency.