This book deals with applications in several areas of science and technology that make use of light which carries orbital angular momentum. In most practical.

**Table of contents**

- Introduction
- OSA | Orbital angular momentum: origins, behavior and applications
- Applications of the orbital angular momentum of light for imaging
- Advances in Optics and Photonics
- Navigation menu

So a quantum interface to bridge the wavelength gap is necessary. There are some experimental realizations of quantum interfaces for single photons with Gaussian shapes 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , either by using second-order nonlinear processes in nonlinear crystals or by third-order nonlinear processes in atomic ensembles 39 , Frequency conversion using nonlinear crystals is much more attractive for practical applications because it can offer wide phase-matching wavelength range, in contrast to using atomic ensembles.

Most of previous experiments used periodically poled LiNbO 3 PPLN bulk crystals or waveguides to perform the frequency conversion, near unity conversion efficiency can be reached in waveguide PPLN crystals and the quantum properties of the single photons are preserved. The frequency conversion of photons with OAM using waveguide crystals is not possible because OAM modes cannot propagate in waveguides. However, our recent studies on the frequency conversion of OAM-carried light offer the possibility for realizing this aim with bulk periodically poled nonlinear crystals 41 , 42 , In this work, we report the first experimental realization of an OAM photonic quantum interface by up-converting a heralded OAM-carried single photons from nm to nm using the cavity-enhanced sum frequency generation SFG.

We clearly demonstrate that the spatial structure of input and output photons exhibits strong similarity. We also show that the coherence properties of the single photons are retained in the conversion process. This primary study will pave the way for high-dimensional quantum information processing, creating a link between different quantum systems that work in different wavelengths by using OAM degree of freedoms of photons. The type-I SFG crystal has a poling period of 9. The nm wavelength corresponding to Rb 85 D1 line, the nm is at telecom band suitable for long distance transmission.

The SFG beam can be used to generate a two-color signal and idler photon source at nm and nm in another crystal which has the same parameter as the SFG crystal.

### Introduction

The bow-tie ring cavity is designed for a single resonance at nm, and the total cavity length is mm. The quantum theory for SFG of continuous waves in second-order nonlinear crystals is shown as follows.

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- Orbital angular momentum of light - Wikipedia!
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- Twisted Photons: Applications of Light with Orbital Angular Momentum;

Three waves are involved in the up-conversion process: The entire conversion process can be described by the following Hamiltonian The Heisenberg equations of motion in the interaction picture are:. N s 0 is the input signal photon number at front face of the crystal. While the theoretical model above is for a Gaussian mode photon, it can naturally be generalized for a photon with OAM. For frequency up-conversion using two Gaussian light beams, the quantum conversion efficiency of the signal light can be expressed as Here, P is the circulating power of the pump beam in cavity, and P max is the pump power that gives unity conversion efficiency.

The expression for P max is:. Please refer to the Supplementary Information for details. For more detailed derivations of Equations 7 and 8 , please refer to the Supplementary Information. To obtain an overview of frequency up-conversion of OAM-carried light, we first perform an experiment using coherent light.

We want to mention the fact that demonstrations of OAM frequency conversion and conservation using classical light are also widely studied in birefringence phase matching crystals 46 , 47 , 48 , The experimental setup is shown in Figure 1a. High conversion efficiency can be achieved by placing a PPKTP crystal inside a ring cavity please refer to materials and methods section for details of the PPKTP crystal and the cavity design. The strong pump beam is provided by a Ti: The cavity is actively locked using the Hansch-Couillaud technique The conversion efficiencies will keep unchanged against the signal power according to the linearity of the SFG process.

We also calculate the quantum conversion efficiency for different OAMs, the results are showed in Figure 2b , where the efficiencies are normalized with respect to the Gaussian mode. The theoretical predictions are well in agreement with experimental results. The differences in the conversion efficiencies for different OAMs are mainly caused by different overlaps between the signal and the pump beams, this can be explained by Equation 8 for further details, please refer to the Supplementary Information.

Differences in conversion efficiency for different OAM modes could be somehow compromised by pre-engineering the focus parameter and amplitude of the input signal beam. Setup for the cavity-enhanced up-converter module a and for up-converting a herald single photon with OAM b L1, L2: InGaAs silicon avalanche detector. Experimental results with strong and attenuated coherent light at single photon level respectively.

We then test our system with attenuated coherent light. The results are shown in Figure 2c—2f , which are obtained using a single-photon-counting camera Andor, ICCD, Belfast, Northern Ireland by setting it in fire-only mode, each image is accumulated with frames and the background is subtracted the dark count is for each pixel in each frame , the exposure time of the ICCD is set to be 1 s. The numbers of frames required for summation to obtain the final images shown in Figure 2c—2f are , , and respectively.

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## OSA | Orbital angular momentum: origins, behavior and applications

The recorded count rates by APD are The typical donut structures can be clearly distinguished for the different OAM-carried input beams in Figure 2c and 2d , the theoretical predictions are showed in Figure 2g—2h. A modified Sagnac interferometer 20 , 27 , 41 is used to generate the OAM superposition, the generated superposition state is:. When we insert another HWP with optical axes placed at The mean photon number of the attenuated light at the input face of the SFG crystal in 1ns detection window is about 0.

The photon pair is prepared by using a nm laser with mW power to pump a type-II PPKTP crystal, generating degenerate signal and idler photons at nm. The non-classical nature of the signal and idler photons can be characterized using the intensity cross-correlation between them 5 , The normalized second-order correlation function are defined as:.

The measurements of consists of first determining the rate of coincidence detections between mode j and k at a time delay. This is effectively a measurement of the non-normalized second-order coherence function, which is the numerator in Equation The normalization is then performed with respect to the rate of coincidences between photons from uncorrelated pairs created at times differing by much more than the coherence time of the photons.

The crystal is described in detail in the Supplementary Information and the performance of the crystal is described in our previous works 52 , 53 , The experimental setup for up-converting a herald single photon with OAM is shown in Figure 1b. We first measure the spatial structure of the up-converted photon by ICCD. Images in Figure 3a—3d show that the photon with both single OAM value and the OAM superposition can be up-converted, as the typical donut shapes and interference patterns are clearly distinguished.

In this experiment, the ICCD has the same settings as used in the previous experiments with the attenuated coherent light. We also measure the cross-correlations for different input OAM states by coupling the up-converted photons into a single mode fiber SMF.

We first perform coincidence measurements between the idler and the up-converted signal photons with the input signal photon in the Gaussian mode. The results are shown in Figure 3f—3i. The deviation of the experimental data from the theoretical fit at the center is a result of the impurity of the up-converted OAM mode, which is mainly caused by misalignment and spontaneous Raman scattering noise, the noises in the up-conversion process is discussed in the Supplementary Information.

We should point out that the filtering of the up-conversion spatial mode using SMF introduces loss in the detection, if the spatial mode is detected directly, the value of the cross-correlation will be even larger. To show that the coherence properties are retained in the conversion process, we let the input signal photon be in the state of Equation 9 , then the up-converted signal photon state is in the form of Equation This method is introduced in refs 20, Usually, the quality of a quantum transforming process is characterized using fidelity of process. The feasible methods are: The present setup is possible for up-conversion of some simple images at ultra-weak power pW level , such as lower-order OAM modes, OAM superposition mode, and simple spatial shapes with spatial symmetry.

We have realized an efficient photonic quantum interface for single photon with both single OAM and OAM superposition. Also, the detailed theoretical description of OAM-carried light up-conversion provides a useful guide for optimizing the conversion process. This primary study will pave the way for high-dimensional quantum information processing in the OAM degree of photons, which create a link between different quantum systems that work in different wavelengths.

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The corresponding wave functions eigenfunctions of OAM operator have the following general expression:. As mentioned in the Introduction, this expression corresponds to waves having a helical wavefront see figure above , with an optical vortex in the center, at the beam axis. Spiral wave plates, made of plastic or glass, are plates where the thickness of the material increases in a spiral pattern in order to imprint a phase gradient on light passing through it.

Although the wave plates themselves are efficient, they are relatively expensive to produce, and are, in general, not adjustable to different wavelengths of light. Another way to modify the phase of the light is with a diffraction grating. A spatial light modulator operates in a similar way to diffraction gratings, but can be controlled by computer to dynamically generate a wide range of OAM states.

Theoretical work suggests that a series of optically distinct chromophores are capable of supporting an excitonic state whose symmetry is such that in the course of the exciton relaxing, a radiation mode of non-zero topological charge is created directly. Most recently, [ when? The geometric phase is modulated to coincide with the spatial phase dependence factor, i.

## Applications of the orbital angular momentum of light for imaging

In this way, geometric phase is introduced by using anisotropic scatterers. For example, a metamaterial composed of distributed linear polarizers in a rotational symmetric manner generates an OAM of order 1. Usually, the conversion efficiency is not high for the transmission-type metasurface.

Alternative solution to achieve high transmittance is to use complementary Babinet-inverted metasurface. Research into OAM has suggested that light waves could carry hitherto unprecedented quantities of data through optical fibres. According to preliminary tests, data streams travelling along a beam of light split into 8 different circular polarities have demonstrated the capacity to transfer up to 2.

Thus the SAM can be measured by transforming the circular polarization of light into a p- or s-polarized state by means of a wave plate and then using a polarizing beam splitter that will transmit or reflect the state of light.

The development of a simple and reliable method for the measurement of orbital angular momentum OAM of light, however, remains an important problem in the field of light manipulation. OAM per photon arises from the amplitude cross-section of the beam and is therefore independent of the spin angular momentum: Where a beam splitter could separate the two states of SAM, no device can separate the N if greater than 2 modes of OAM, and, clearly, the perfect detection of all N potential states is required to finally resolve the issue of measuring OAM.

Beams carrying OAM have a helical phase structure. Interfering such a beam with a uniform plane wave reveals phase information about the input beam through analysis of the observed spiral fringes.

In a Mach—Zender interferometer, a helically phased source beam is made to interfere with a plane-wave reference beam along a collinear path. The path being collinear, these fringes are pure consequence of the relative phase structure of the source beam. Each fringe in the pattern corresponds to one step through: Computer-generated holograms can be used to generate beams containing phase singularities, and these have now become a standard tool for the generation of beams carrying OAM.

This generating method can be reversed: This approach is widely used for the detection of OAM at the single-photon level. The phase of these optical elements results to be the superposition of several fork-holograms carrying topological charges selected in the set of values to be demultiplexed. The position of the channels in far-field can be controlled by multiplying each fork-hologram contribution to the corresponding spatial frequency carrier.

Other methods to measure the OAM of light include the rotational Doppler effect, systems based on a Dove prism interferometer, [15] optical transformations, [16] [17] the measure of the spin of trapped particles, and the study of diffraction effects from apertures. OAM states can be generated in coherent superpositions and they can be entangled , which is an integral element of schemes for quantum information protocols.

## Advances in Optics and Photonics

These states can be generated using parametric down-conversion , and correlations measured using spatial light modulators SLM. From Wikipedia, the free encyclopedia. Type of angular momentum in light. This section may be too technical for most readers to understand.

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We have demonstrated experimentally how spatial filtering of the object field with a spiral phase element in a Fourier plane of the optical path results in a strong and isotropic edge enhancement at the output image. Numerical simulations predict that phase jumps as small as 1 per cent of the optical wavelength could be detected.

Applications of the orbital angular momentum of light for imaging A thesis accepted by Tallinn University of Technology for the Degree of Master of Science Author: