A quantum approach to electromagnetic wave propagation inside a dielectric

Bezgabadi, Abolfazl Safaei; Zarandi, Mahmood Borhani; Bolorizadeh, Mohammad Agha

doi:10.1140/epjp/s13360-020-00637-9

Cited by 7 publications

(5 citation statements)

References 50 publications

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“…The first term in Eq. ( 1 ) which was determined earlier in terms of creation and annihilation operators derived when higher order dispersion term included in the Lagrangian 41 differs from those obtained by Drummond 9 . We also assume the interaction picture and discretize the spatial and wave number dependence; i.e.…”

Section: Theorymentioning

confidence: 79%

“…In order to quantize the pulse propagation in optical fibers, it is necessary to find a canonical Lagrangian leading to the correct Hamiltonian and to the Maxwell’s equations as the Hamilton’s equation of motion. It should be emphasized that in the present work, we include the higher order dispersion terms and the retarded medium response employing the approach recently developed 41 . The present method follows the method developed by Drummond 8 , 9 .…”

Section: Theorymentioning

confidence: 99%

“…One could obtain the Lagrangian and define appropriate creation and annihilation operators applying the method introduced in Ref. 41 , which satisfy the harmonic oscillator commutation relations. The Hamiltonian is: where , , , , and R(t) are mode operators, electric displacement operator, vacuum permittivity, medium permittivity, and response function of the medium (which is absent in Drummond’s works 8 , 9 , 59 , 60 and our earlier works 36 , 40 , 41 ), respectively.…”

Section: Theorymentioning

confidence: 99%

“…The quantum theories used to date for the propagation of electromagnetic wave omit the higher order dispersion terms and the dispersive nature of the nonlinear response 9 , 19 , 36 – 40 . We have developed a theory for canonical quantization of the radiation in the presence of the third order dispersion term 41 . Making use of this quantization scheme and considering that the non-dispersive and instantaneous assumptions of nonlinear response are not suitable for ultra-short pulses, we quantized the supercontinuum generation process.…”

Section: Introductionmentioning

confidence: 99%

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Quantum model for supercontinuum generation process

Bezgabadi

Bolorizadeh

2022

Sci Rep

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A quantum theory is established for the propagation of electromagnetic waves in highly nonlinear dispersive optical fibers. By applying the method recently presented dispersion terms and retarded response of the medium are included for the propagation of light in a fiber in this work. A coupled stochastic generalized nonlinear Schrödinger equation (GNLSE) is obtained via the coherent positive-P representation to describe the supercontinuum generation process. This coupled quantum-stochastic equation is applied to obtain the linearized fluctuation equation for studying quantum noise and the fluctuation in the vicinity of the formed solitons in the supercontinuum generation process in the region of anomalous dispersion. Also, these equations can be used to study the soliton self-frequency shift quantum mechanically. Finally, we simulate the obtained coupled stochastic generalized nonlinear Schrödinger in the mean case and compare our simulation results with experimental results.

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Section: Theorymentioning

confidence: 79%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum model for supercontinuum generation process

Bezgabadi

Bolorizadeh

2022

Sci Rep

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“…In optical communications, the third-order dispersion coefficient (b 3 ) should be considered because it plays an important role [17,31,32]. In this case, one can obtain an equation similar to equation (10) for Gaussian pulse but the functions B and C are replaced by:…”

Section: Discussion On the Theorymentioning

confidence: 99%

Solving nonlinear Schrödinger equation by a new and fast method

Bezgabadi¹,

Bolorizadeh²

2021

Phys. Scr.

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In this paper, a new method is introduced to study pulse propagation in an optical fiber where the governing equation is the Nonlinear Schrödinger equation (NLSE). The method is as accurate as the currently common methods employed, such as the split step Fourier method (SSFM), but faster. Assuming the fiber is isotropic and lossless, the propagation of an input pulse in an optical fiber is investigated. This method is based on the expansion of any pulse shape in terms of complete and normalized functions such as Hermite functions. The propagation of the pulse is then reduced into an inductive relation describing its propagation along with the fiber by the present method. Then, we check the stability of this method in three categories, while the step size could be selected in each step depending on the stability condition. Finally, this method is applied to study pulse evolution along two optical fibers, the pulse broadening, the pulse compression, and generation of new frequencies are observed which its numerical results show good conformity with the available data in the literature.

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Quantum Mechanical Theory and Treatment of NLS Equations for Supercontinuum Generation

Bolorizadeh

Bezgabadi

2022

The Supercontinuum Laser Source

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A quantum approach to electromagnetic wave propagation inside a dielectric

Cited by 7 publications

References 50 publications

Quantum model for supercontinuum generation process

Quantum model for supercontinuum generation process

Solving nonlinear Schrödinger equation by a new and fast method

Quantum Mechanical Theory and Treatment of NLS Equations for Supercontinuum Generation

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