Inquiries about the use of the book should be directed to INTECHOPEN LIMITED rights and permissions department (permissions@intechopen.com). The publisher accepts no responsibility for any damage or injury to persons or property resulting from the use of any materials, instructions, methods or ideas contained in the book.

## Introduction

In the propagation of light and optical instrument design, Huygens-Fresnel diffraction integral (HFDI) (or its advanced versions) and Maxwell's wave equation still remain the essential guide for optical scientists and engineers. Keywords: structured light, hybrid photon, non-interaction of light (NIW), Huygens principle, photoelectric effect, semi-classical model.

## We never “see” light

If the sensing element is inherently quantum mechanical in nature, then the amount of energy ΔEmn¼hνm absorbed by the detector from the EM waves corresponds to the specific quantum transition. The energy in each of the two orthogonal components is the quadratic modulus of the sum of the X component amplitudes and the Y component amplitudes, run separately.

## Light does not “see” light

Jones' matrix has been constructed to find the final energy of a composite light beam as the sum of the two separate energies contained in each of the two orthogonal polarizations. Jones' matrix has been constructed to find the final energy of a composite light beam as the sum of the two separate energies contained in each of the two orthogonal polarizations.

Consequences of assigning detector’s properties to the energy donating entity

## Consequences of ignoring interaction process visualization: the necessity of the hybrid photon model

In the section on "We don't see light," we underlined that detectors see light based on their internal physical properties. In the right segment of Eq. 4), we have “recovered” Einstein's photoelectric energy balancing equation from dipole amplitude excitations due to multitude waves.

## Discussions

Accordingly, the concept of the wave-particle nature of a single photon becomes physically comprehensive and consistent with the experimental evidence. Nevertheless, new events took place in the early twentieth century that supported the particle nature of light.

## The electromagnetic field vector potential 1 Reality of the vector potential

### The radiation vector potential: classical to quantum link

The vector potential of the electromagnetic field 2.1 The reality of the vector potential 2.1 The reality of the vector potential. 46], which proves without a doubt the reality of the vector potential field and its direct influence on the charges.

## Electromagnetic field quantization and the photon description 1 Harmonic oscillator representation of the electromagnetic field

### Electromagnetic field vector potential quantization in QED

Conversely, the zero-point energy expressed by Eq. 33) is useful for the explanation of the spontaneous emission and the Lamb shift in the classical description of radiation. The last equations represent the vector potential and electric field of a large number of modes k of the quantized electromagnetic field in a finite volume V with λk ≪V1=3ð Þ.∀k.

## Quantized vector potential of a single photon

*Photon vector potential amplitude and quantization volume**Photon classical-quantum (wave-particle) physical properties**Photon wave-particle equation and wave function Obviously, the photon vector potential function α ! kλ !r ; t**Electromagnetic field ground state, photons, and electrons-positrons The photon vector potential is composed of a fundamental function Ξ kλ times*

This result is gauge independent as it concerns the natural units of the vector potential. By the same sign, considering circular polarization for the amplitudes of the electric and magnetic fields in Eq. The energy and vector potential uncertainties with respect to time are intrinsic physical properties of the wave-particle nature of the photon.

## Conclusion

This may account for the physical mechanism governing the photon generation during electron–positron (and probably lepton–antilepton) annihilation and that of the electron–positron (lepton–antilepton) pair formation during the annihilation of high-energy gamma photons in the vicinity of very heavy nuclei. Combining the expression j ¼ξ ℏ=4πj je c to the fine structure constant definitionα¼e2=4πε0ℏc allows to directly draw the electron-positron elementary charge e C, a fundamental physical constant which is now expressed exactly through the EFGS amplitudeξ[64, 65]:. This may account for the physical mechanism governing the photon generation during electron–positron (and probably lepton–antilepton) annihilation and that of the electron–positron (lepton–antilepton) pair formation during the annihilation of high-energy gamma photons in the vicinity of very heavy nuclei.

## Photon pair generation using SPDC or SFWM

In both SPDC and SFWM, conservation of energy, linear momentum, and angular momentum must be satisfied. In the next section, we will first introduce the basic principle of SPDC and SFWM for generating photon pairs and then the different materials used for SPDC and SFWM. Finally, we will give a short summary in which some future perspectives for non-classical photon pair generation and possible applications are discussed.

## Various kinds of photon sources generated in SPDC and SFWM Because of the conservation of energy, linear momentum, and angular momen-

### Polarization-entangled photon source

Due to these conservation laws and the quantum interference technology used, two photons in each pair generated in SPDC and SFWM can be correlated in different degrees of freedom, for example polarization, energy-time, orbital angular momentum, positional linear momentum, angular momentum, and photon number and path [1]; we can exploit these freedoms in a specific application scenario in QIST. Therefore, the photon states generated in SPDC and SFWM can be expressed in Fock state basis as [9]:. The photon pair generated in SPDC and SFWM is probabilistic and is indeterminate, which is a disadvantage of photon.

### Time-energy and time-bin-entangled photon source

Then, a pulsed PEPS at 780 nm based on this configuration was developed by Kuzucu and Wong in 2008 [46]. A pulsed PEPS at 1584 nm based on a type II PPKTP was demonstrated by Jin et al. Now, PEPS based on QPM crystals in a Sagnac configuration has become a fundamental tool for many experiments [47–49].

### Orbital angular momentum entangled photon source

A laser with a long coherence time is required to generate a time-energy complex photon pair (see Fig. 3(a)); the time difference between two paths in the UMI should be much larger than the coherent time of a single photon, but much shorter than the coherent time of the pump laser [53]. A similar type of entangled photon source is the time-entangled photon source [56], in which the pulse pump is split into two pulses in the UMI, and then these two pulses have a certain probability to separately generate a pair of photons; the photon pairs generated by these two pulses are indistinguishable after passing through the two UMIs (the time difference of the UMI in the measuring part is the same as the UMI in the pump part, see Fig. 3(b)). The quantum states for a time-energy-entangled or time-bin photon source can be expressed as |Φ SS〉 + e i𝜃𝜃 |LL〉), where S and L represent the short and long arms of the UMIs.

## Methods for characterizing the properties of a nonclassical photon source

The properties and methods for characterizing a 2D entangled source in different degrees of freedom are similar and can be converted from one species to another [48, 68] (see Fig. 4 (images at right)). Whereas for HD entangled source the properties and the characterization methods are quite different. 65] reported on the realization of an 11D entangled source, demonstrating the violation of the Bell inequality.

## Quantum frequency conversion for nonclassical quantum state There are many quantum systems for QIST based on different materials,

It is a measure of photon collection efficiency, filter and transmission losses, and detector efficiency of a single photon. The uniform purity of a single photon indicates that the two-photon spectrum can be factorized into the product of two separate functions of signal and free photons. Experimental setup for measuring the predicted single photon autocorrelation function for a single photon generated from SPDC (figure cited from [74]).

## Discussions and conclusion

Finally, we have theoretically introduced and experimentally demonstrated single-photon frequency conversion in the telecommunication band, which enables switching of single photons between dense wavelength division multiplexing channels. In our work, we used PPLN waveguide chip to realize several kinds of different functions of single-photon frequency conversion to coherent quantum interface. We report single-photon frequency conversion in a telecommunication band based on cascaded quadratic nonlinearity, i.e. SFG and difference frequency generation (DFG), in a PPLN waveguide.

## Methodology and result

### Spectral compression of single-photon-level laser pulse

SFG spectrum of the generated laser pulse (a), central wavelength and compression ratio of output pulses versus optical relative delay (b). The full power of the negatively chirped laser pulse is EN1, as shown in Fig. 6(b). Thus, SFG photons are PSFG∝EN1ES, where ES is the power of a positively chirped laser pulse at the one-photon level.

### Nonlinear interaction between broadband single-photon-level coherent states

We can also confirm that by controlling the power of the negatively chirped laser pulse, considering a laser pulse with a single positive chirped photon level (0.933 photons per pulse). When the relative time delay Δt¼0, the SHG and SFG photons of different situations are obtained by controlling the power of the negatively chirped laser pulse (see Figure 6(a)). To reduce the number of SHG photons in the dark count (3.5 Hz), the power of the negatively chirped laser pulse must be very low.

### Single-photon frequency conversion via cascaded quadratic nonlinear processes

In the experiment, we realized the broadband single photon frequency conversion of the communication band by the type-0 cascade SFG/DFG process. In our experimental scheme, frequency-tunable single-photon frequency conversion can be achieved by adjusting the wavelength of the auxiliary pump light. After the conversion of the single photon frequency, we again measure the entanglement visibility of the converted photon pair, as shown in Figure 13(b).

## Conclusion

In conclusion, we have demonstrated single-photon frequency conversion using a cascaded quadratic nonlinearity in PPLN waveguides chip. Non-inverse propagation of light at the single-photon level is in great demand for applications in quantum networks [1, 2], quantum computers [3], quantum entanglement [4] and quantum measurement [5]. Some feasible schemes based on chiral quantum optics have been proposed to realize non-reciprocity at the single-photon level [ 16 , 17 ], and optical isolators and circulators have been experimentally demonstrated in full quantum regime [ 18 , 19 ].

## Optical chirality and chiral light-matter interaction

A strong constraint in these structures is given by the optical chirality, which is an inherent connection between the local polarization and the direction of light propagation [15]. If quantum emitters are embedded in these structures, a chiral light-matter interaction occurs, leading to emission, absorption, and scattering of photons that depends on the direction of propagation. Consequently, the chiral light-matter interaction can be used to break time symmetry and achieve on-chip single-photon isolation.

## Single-photon isolation using chiral light-matter interaction

### Single-photon isolator based on a nanophotonic waveguide

However, the line widths of dips for left-hand input (blue solid line) are much wider than for right-hand input (red dashed line). Schematic of single-photon insulators. a) Single-photon isolator based on a photonic crystal waveguide asymmetric coupling with a quantum emitter. The numerical simulations of the propagation of a single-photon pulse are performed in [16], which match the analytical forms well (see gray curves in Figure 5a).

## Optical isolation via chiral cross-Kerr nonlinearity

Thus, the backward (forward) moving probe field "sees" the same (opposite) Doppler shift as the switching and coupling one. For a short medium (L=3:33 mm), the transmission of probes moving back and forth can be comparably high, but the phase lagϕbi is always small, specifically about 0:011πatΔp=7:77γ0, as shown in Figure 11b. On the other hand, at the optimal point Δoptp ¼7:77γ0, the phase shift difference, ϕf �ϕb, reaches a) Insulator transfer for forward (blue curves) and backward (red curves) moving probe fields as a function of the probe Δp.

## Conclusions

The strength of the nonlinearity strongly depends on the effective propagations and thus the Doppler shifts. Consequently, these frequency shifts change the optical nonlinearity in a manner that strongly depends on the direction of propagation of the probe field with respect to the switching and coupling fields, leading to the chiral XKerr nonlinearity. The isolation ratio can be significantly improved by large forward transmission by using a longer medium or, equivalently, by increasing the density of atoms.