Intrinsic Optical Spatial Differentiation Enabled Quantum Dark-Field Microscopy

By solving the Maxwell’s equations in Fourier space, we find that the cross-polarized component of the dipole scattering field can be written as the second-order spatial differentiation of the copolarized component. This differential operation can be regarded as intrinsic which naturally arises as consequence of the transversality of electromagnetic fields. By introducing the intrinsic spatial differentiation into heralded single-photon microscopy imaging technique, it makes the structure of pure-phase object clearly visible at low photon level, avoiding any biophysical damages to living cells. Based on the polarization entanglement, the switch between dark-field imaging and bright-field imaging is remotely controlled in the heralding arm. This research enriches both fields of optical analog computing and quantum microscopy, opening a promising route toward a nondestructive imaging of living biological systems.

Figure 1

The electromagnetic field emitted by an oscillating dipole. The Hertz vector potential $\tilde{\mathbf{\Pi }}(\mathbf{k})$ is introduced to describe the scattering field $\tilde{\mathbf{E}}(\mathbf{k})$. The scalar potential $\tilde{\varphi }(\mathbf{k})$ is determined by the structure of phase object. Different output field components are obtained by switching the polarizations states (on or off).

Figure 2

The schematic of switchable quantum bright- and dark-field imaging. (a) In the imaging arm, biological cells are centered between two microscope objectives. The polarization of entangled photon pairs is $(1/\sqrt{2})(|HH⟩+|VV⟩)$, the question mark in the heralding arm means polarization selection of idler photons is unknown. The dashed line stands for the electrical path. (b) The switch state on or off of the heralding arm. When the idler photons of the heralding arm are projected to $|H⟩$, it indicates the switch in the on state and leads to a bright-field image. While the heralded photons are projected to $|V⟩$, a dark-field image is obtained with the switch in the off state.

Figure 3

Experimental setup of quantum dark-field microscope. (a) Setup schematic. BDM, broadband dielectric mirror; PPKTP crystal, periodically poled ${\text{KTiOPO}}_4$ crystal; DPBS, dual-wavelength polarization beam splitter; PBS, polarization beam splitter; DM, dichromatic mirror; FC, fiber coupler; BPF, bandpass filter; DHWP, dual-wavelength half wave plate; HWP, half wave plate; QWP, quarter wave plate; SPAD, single photon avalanche detector; ICCD, intensified charge coupled device. The blue (red) light path presents the 405 nm (810 nm) light. The bright-field microscope system is constructed by two confocal microscope objectives ($10\times ,\mathrm{NA}=0.25$). (b) Photon counts of signal side ($u_i$), heralding side ($u_h$), and coincidence ($u_c$) under different pump powers. (c) Coincidence counts as a function of the polarized angle.

Figure 4

Experimental results of SNR in direct imaging and heralded imaging under different pump powers. The inset shows the photon counts of environmental noise detected in direct imaging and heralded imaging with pump power 12 mW. The fraction of the noise photons falling within the gate time is estimated as $ϵ=0.0002$.

Figure 5

Quantum enabled microscopy images of stem-parenchyma cells. (a) and (b) Direct bright-field image and direct dark-field image where the ICCD is internally triggered. (c) and (d) The bright-field image and dark-field image are triggered by the heralding detector. (e)–(h) are taken along the white dashed lines in (a)–(d), respectively. Scale bar, $30\mu \mathrm{m}$.