Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients

Haus, Joseph W.; Soon, Boon Yi; Scalora, Michael; Sibilia, C.; Mel’nikov, Igor V.

doi:10.1364/josab.19.002282

Cited by 25 publications

(16 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To incorporate these effects it is assumed that the detuning and coupling coefficients are complex, see Ref. 11. These losses can be attributed to the higher scattering properties of the high index layer caused by irregular distribution of the liquid crystal within this layer.…”

Section: Results and Analysismentioning

confidence: 99%

Electrically switchable third-harmonic generation in photonic crystals

Markowicz

Tiryaki

Prasad

et al. 2005

Journal of Applied Physics

View full text Add to dashboard Cite

We demonstrate electrically switchable third-harmonic generation in low refractive index contrast one-dimensional photonic crystals pumped by a near-infrared laser beam. A dramatic enhancement of the third-harmonic signal is observed on the short wavelength side of the photonic crystal stop band. The enhancement of the third-harmonic generation disappears when an electric field is applied, revealing the electrical switchability of the third-harmonic generation. The observed phenomenon of enhancement is explained theoretically with a coupled-mode model. We also show that up to a modulation frequency of 10 kHz the switching properties are supported in the photonic crystal.

show abstract

Section: Results and Analysismentioning

confidence: 99%

Electrically switchable third-harmonic generation in photonic crystals

Markowicz

Tiryaki

Prasad

et al. 2005

Journal of Applied Physics

View full text Add to dashboard Cite

show abstract

“…The nonlinear solution has been handled in real space, but due to the complication of N operator matrix, an exponential form has been used in the diagonal part and the off-diagonal part of the nonlinear solution, which has been approximated by using a first-order difference form. Therefore, the nonlinear solution has been expressed as a summation of diagonal part and the off-diagonal part solutions as follows [15]:…”

Section: B Split-step Fourier Transform Methodsmentioning

confidence: 99%

Optical parametric amplification in one-dimensional photonic bandgap structures

et al. 2013

View full text Add to dashboard Cite

In this paper, optical parametric amplification based on the degenerate four-wave mixing principle in a one-dimensional photonic bandgap (PBG) structure has been numerically studied. First, the multiple scale method was introduced to derive a complete set of nonlinear coupled-mode equations for a finite structure with different inhomogeneous nonlinear coefficients than those used in previous works. This finite structure is composed of 680 dielectric layers, which are alternating half-wave/eight-wave films. The wavelengths of the pump, signal, and idler pulses have been determined from the transmission spectrum, which was illustrated by using the transfer matrix method. The parametric interaction of the pump, signal, and idler pulses inside PBG structure has been numerically simulated by using the split-step Fourier transform method. The results of the simulation have shown that the intensities of the signal and idler have exponential growth with respect to the number of layers in the medium. Meanwhile, pump wavevector detuning directly affects the intensities of both pulses due to a band-edge phase-matching condition that might be achieved from only one optimal detuning parameter. Moreover, both the amplification gain and the conversion efficiency of the idler pulse have been shown to be dependent on the bandwidth of the pump pulse spectrum. A very narrow pulse, with a bandwidth much less than the relevant transmission peak, enables the highest amplification and conversion efficiency in this medium because the most efficient phase-matched condition occurs in this situation. Finally, the conversion efficiency grows exponentially with input pump intensity for several input signal intensities. Furthermore, the maximum conversion efficiencies directly vary with input signal intensity.

show abstract

“…To explain the enhancement in PDLC grating, we developed a set of NCEs valid for describing the THG in the structure by using the multiple-scale perturbation analysis (MSPA) [4,15]. First, we begin with the scalar nonlinear wave equation for the total field, as below equation:…”

Section: Multiple-scale Perturbation Analysismentioning

confidence: 99%

“…The average index contrast between high-and low-refractive indices is about 0. 15 [13][14]. In analytical procedure, we applied the multiple-scale perturbation analysis (MSPA) to perturb the nonlinear wave equation and construct a complete set of nonlinear coupled equations (NCEs) valid for THG effect.…”

Section: Introductionmentioning

confidence: 99%

“…In analytical procedure, we applied the multiple-scale perturbation analysis (MSPA) to perturb the nonlinear wave equation and construct a complete set of nonlinear coupled equations (NCEs) valid for THG effect. This set of NCMEs was numerically solved by using split-step Fourier transform technique (SSFTT), which is computational technique with introduction of fast Fourier transform (FFT) algorithm [15][16][17][18]. The numerical solution of NCEs was shown as THG output intensity in forward-and backward-propagating directions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Third-harmonic generation enhancement in polymer-dispersed liquid crystal grating

Wicharn

Buranasiri

2014

Active Photonic Materials VI

View full text Add to dashboard Cite

In this paper, the enhancement of third-harmonic generation in one-dimensional periodic grating structure with lowindex contrast, which is produced by holographic illuminated liquid crystal droplets and called polymer-dispersed liquid crystal grating, with near-infrared pumping has been demonstrated. The observed enhancement process is theoretically explained and modeled with a multi-scale perturbation analysis and split-step Fourier transform technique, respectively. We show that the third-harmonic generation has been enhanced by setting the fundamental frequency wavelength to the long-wavelength band-edge of the first photonic band-gap of this periodic structure and satisfying band-edge phasematched condition. The numerical results show that a dramatic enhancement of the third-harmonic field is observed near the long-wavelength band-edge of the second photonic band-gap. Furthermore, the conversion efficiency of thirdharmonic field of forward-propagating direction is more than of backward-propagating direction by a factor of 600.

show abstract

Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients

Cited by 25 publications

References 23 publications

Electrically switchable third-harmonic generation in photonic crystals

Electrically switchable third-harmonic generation in photonic crystals

Optical parametric amplification in one-dimensional photonic bandgap structures

Third-harmonic generation enhancement in polymer-dispersed liquid crystal grating

Contact Info

Product

Resources

About