Time-frequency (TF) filtering of analog signals has played a crucial role in the development of radio-frequency communications and is currently being recognized as an essential capability for communications, both classical and quantum, in the optical frequency domain. How best to design optical time-frequency (TF) filters to pass a targeted temporal mode (TM), and to reject background (noise) photons in the TF detection window? The solution for ‘coherent’ TF filtering is known—the quantum pulse gate—whereas the conventional, more common method is implemented by a sequence of incoherent spectral filtering and temporal gating operations. To compare these two methods, we derive a general formalism for two-stage incoherent time-frequency filtering, finding expressions for signal pulse transmission efficiency, and for the ability to discriminate TMs, which allows the blocking of unwanted background light. We derive the tradeoff between efficiency and TM discrimination ability, and find a remarkably concise relation between these two quantities and the time-bandwidth product of the combined filters. We apply the formalism to two examples—rectangular filters or Gaussian filters—both of which have known orthogonal-function decompositions. The formalism can be applied to any state of light occupying the input temporal mode, e.g., ‘classical’ coherent-state signals or pulsed single-photon states of light. In contrast to the radio-frequency domain, where coherent detection is standard and one can use coherent matched filtering to reject noise, in the optical domain direct detection is optimal in a number of scenarios where the signal flux is extremely small. Our analysis shows how the insertion loss and SNR change when one uses incoherent optical filters to reject background noise, followed by direct detection, e.g. photon counting. We point out implications in classical and quantum optical communications. As an example, we study quantum key distribution, wherein strong rejection of background noise is necessary to maintain a high quality of entanglement, while high signal transmission is needed to ensure a useful key generation rate.
Photonics provides a promising approach for image processing by spatial filtering, with the advantage of faster speeds and lower power consumption compared to electronic digital solutions. However, traditional optical spatial filters suffer from bulky form factors that limit their portability. Here we present a new approach based on pixel arrays of plasmonic directional image sensors, designed to selectively detect light incident along a small, geometrically tunable set of directions. The resulting imaging systems can function as optical spatial filters without any external filtering elements, leading to extreme size miniaturization. Furthermore, they offer the distinct capability to perform multiple filtering operations at the same time, through the use of sensor arrays partitioned into blocks of adjacent pixels with different angular responses. To establish the image processing capabilities of these devices, we present a rigorous theoretical model of their filter transfer function under both coherent and incoherent illumination. Next, we use the measured angle-resolved responsivity of prototype devices to demonstrate two examples of relevant functionalities: (1) the visualization of otherwise invisible phase objects and (2) spatial differentiation with incoherent light. These results are significant for a multitude of imaging applications ranging from microscopy in biomedicine to object recognition for computer vision.
more » « less- Award ID(s):
- 1711156
- PAR ID:
- 10375475
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Express
- Volume:
- 30
- Issue:
- 16
- ISSN:
- 1094-4087; OPEXFF
- Format(s):
- Medium: X Size: Article No. 29074
- Size(s):
- Article No. 29074
- Sponsoring Org:
- National Science Foundation
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