Stefan Reisner and Michael Gutmann, "Numerical treatment of UV-pumped, white-light-seeded single-pass noncollinear parametric amplifiers," J. Opt. Soc. Am. B 16, 1801-1813 (1999)

A technique for numerically simulating second-order nonlinear interactions of light waves modulated spatially and temporally in both amplitude and phase in a uniaxial medium with arbitrary polarization and propagation directions is presented. A three-dimensional grid technique that automatically adapts grid parameters to the evolving sampled amplitudes by means of an analytical fit function is described. By means of spatiotemporal split-step fast-Fourier-transform propagation, diffraction and group-velocity dispersion can be included. We employ this technique for femtosecond noncollinear white-light-seeded parametric amplification in experimental designs presented earlier [Opt. Lett. 22, 1494 (1997); Opt. Lett. 23, 1283 (1998)]. The dependence of phase mismatch on signal wavelength provides a quantitative measure of the achromaticity of phase matching. Our results indicate that the pump pulse characteristics and not phase mismatching limit the amplification and the bandwidth of the parametric amplifier.

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

External and Internal Angles of Incidence and Refractive Indices

Field

External Angle (°)

Internal Angle (°)

n

Signal

-6.28

-3.76

1.666

Idler

+9.97

+5.64

1.656

Pump

-0.03

-0.02

1.657

Table 2

Grid Extensions and Number of Grid Points for Each Coordinatea

Field

x-Direction Interval ${N}_{x}$ (μm)

y-Direction Interval ${N}_{y}$ (μm)

η-Direction Interval
${N}_{\eta}$ (fs)

Pump

(-120, 120) 32

(-120, 120) 32

(-190, 190) 32

Depletion

(-100, 100) 32

(-100, 100) 16

(-130, 230) 32

Seed

(-120, 120) 32

(-100, 100) 16

(-75, 225) 128

Amplification

(-100, 100) 32

(-100, 100) 16

(-75, 225) 128

Idler

(-100, 100) 32

(-100, 100) 16

(-75, 225) 128

Initially all grids except the idler grid have parameters ${u}_{x}={u}_{y}=0;$ the idler grid has nonzero ${u}_{x}.$

Table 3

Investigation of the Effects of Various Factors on the Parametric Amplification by Means of Simulationa

i

${V}_{I}^{(i)}/{V}_{I}^{(0)}$ (%)

Reduction (%)

Effect

0

100

↓ 68

Pump depletion

1

32

↓ 75

Signal–idler temporal walk-off

2

8

↓ 21

Spatial profiles

3

6

↓ 21

Chirp

4

5

↓ 50

Spatial walk-off of idler

5

3

Shown are the reductions of the amplification factor ${V}_{I},$ defined as the ratio of the peak intensities of the amplified signal and the seed field. The figures are based on the amplification factor ${V}_{I}^{(0)}$ predicted by an analytical model assuming plane waves and no pump depletion, which was arbitrarily set to 100%.

Table 4

GVM between Signal and Pump Field, Effective Interaction Length ${L}_{\mathrm{eff}},$ Group Delay β, Chirp Parameter b, and Coupling Coefficient ${\chi}_{\mathrm{eff}}^{(2)}$ for Various Wavelengthsa

${\mathrm{\lambda}}_{\mathrm{signal}}$ (nm)

GVM (fs/mm)

${L}_{\mathrm{eff}}$ (mm)

β (fs/THz)

b (rad/fs^{2})

${\chi}_{\mathrm{eff}}^{(2)}$ (pm/V)

700

134.8

0.49

6.4

9.8

-1.98

620

92.0

0.71

8.1

7.8

-1.97

560

59.0

1.10

9.3

6.8

-1.98

490

23.2

(2.83)

10.8

5.8

-2.04

At 490 nm the effective interaction length is larger than the crystal thickness (2 mm).

Table 5

Signal Bandwidths Estimated $(\mathrm{\Delta}\tilde{\omega})$ and Obtained from Simulation $(\mathrm{\Delta}{\mathit{\omega}}_{\mathrm{FWHM}})$ for Various Signal Wavelengths

Simulation Results: Amplification Factors and Autocorrelation Widths Before
$(\tau _{\mathrm{ac}}{}^{0})$ and After $(\tau _{\mathrm{ac}}{}^{\mathrm{min}})$ Optimal Compression with a Simulated Element of Linear Negative GVD ${\beta}_{\mathrm{opt}}$ for Various Signal Wavelengthsa

The product of autocorrelation width and bandwidth (divided by 2π) is also given.

Tables (6)

Table 1

External and Internal Angles of Incidence and Refractive Indices

Field

External Angle (°)

Internal Angle (°)

n

Signal

-6.28

-3.76

1.666

Idler

+9.97

+5.64

1.656

Pump

-0.03

-0.02

1.657

Table 2

Grid Extensions and Number of Grid Points for Each Coordinatea

Field

x-Direction Interval ${N}_{x}$ (μm)

y-Direction Interval ${N}_{y}$ (μm)

η-Direction Interval
${N}_{\eta}$ (fs)

Pump

(-120, 120) 32

(-120, 120) 32

(-190, 190) 32

Depletion

(-100, 100) 32

(-100, 100) 16

(-130, 230) 32

Seed

(-120, 120) 32

(-100, 100) 16

(-75, 225) 128

Amplification

(-100, 100) 32

(-100, 100) 16

(-75, 225) 128

Idler

(-100, 100) 32

(-100, 100) 16

(-75, 225) 128

Initially all grids except the idler grid have parameters ${u}_{x}={u}_{y}=0;$ the idler grid has nonzero ${u}_{x}.$

Table 3

Investigation of the Effects of Various Factors on the Parametric Amplification by Means of Simulationa

i

${V}_{I}^{(i)}/{V}_{I}^{(0)}$ (%)

Reduction (%)

Effect

0

100

↓ 68

Pump depletion

1

32

↓ 75

Signal–idler temporal walk-off

2

8

↓ 21

Spatial profiles

3

6

↓ 21

Chirp

4

5

↓ 50

Spatial walk-off of idler

5

3

Shown are the reductions of the amplification factor ${V}_{I},$ defined as the ratio of the peak intensities of the amplified signal and the seed field. The figures are based on the amplification factor ${V}_{I}^{(0)}$ predicted by an analytical model assuming plane waves and no pump depletion, which was arbitrarily set to 100%.

Table 4

GVM between Signal and Pump Field, Effective Interaction Length ${L}_{\mathrm{eff}},$ Group Delay β, Chirp Parameter b, and Coupling Coefficient ${\chi}_{\mathrm{eff}}^{(2)}$ for Various Wavelengthsa

${\mathrm{\lambda}}_{\mathrm{signal}}$ (nm)

GVM (fs/mm)

${L}_{\mathrm{eff}}$ (mm)

β (fs/THz)

b (rad/fs^{2})

${\chi}_{\mathrm{eff}}^{(2)}$ (pm/V)

700

134.8

0.49

6.4

9.8

-1.98

620

92.0

0.71

8.1

7.8

-1.97

560

59.0

1.10

9.3

6.8

-1.98

490

23.2

(2.83)

10.8

5.8

-2.04

At 490 nm the effective interaction length is larger than the crystal thickness (2 mm).

Table 5

Signal Bandwidths Estimated $(\mathrm{\Delta}\tilde{\omega})$ and Obtained from Simulation $(\mathrm{\Delta}{\mathit{\omega}}_{\mathrm{FWHM}})$ for Various Signal Wavelengths

Simulation Results: Amplification Factors and Autocorrelation Widths Before
$(\tau _{\mathrm{ac}}{}^{0})$ and After $(\tau _{\mathrm{ac}}{}^{\mathrm{min}})$ Optimal Compression with a Simulated Element of Linear Negative GVD ${\beta}_{\mathrm{opt}}$ for Various Signal Wavelengthsa