Table 1 Third-order susceptibility for Si:P and Si:Bi both on and off-resonance

From: Highly efficient THz four-wave mixing in doped silicon

 

Si:P

Si:Bi

\(\hbar\)ω (meV)

32.5

34.0

36.7

39.2

42.5

64.5

 

–

(2p0)

–

 

(2p±)

(3p±)

(2p±)

 

T

R

T

T

R

R

R

L (mm)

0.6

0.5

0.5

0.6

0.5

0.5

1

nD

10

1.0

1.0

10

1.0

1.0

3.4

x

1.6

4.7

5.6

2.3

4.6

3.9

4.9

r0 (mm)

0.53

0.6

0.6

0.53

0.6

0.6

0.64

Ec (μJ)

2.7

4.9

32.3

1.1

1.4

2.1

0.17

f

3.0

28

6.1

6.2

310

27

310

\({\chi }_{\,\text{expt}\,}^{(3)}L\)

0.13

0.80

0.025

0.58

27

1.5

160

\({\chi }_{\,\text{expt}\,}^{(3)}\)

0.22

1.6

0.050

0.96

54

2.9

160

\({\chi }_{\,\text{expt}\,}^{(3)}/{n}_{{\rm{D}}}\)

0.022

1.6

0.050

0.096

54

2.9

46

μeg (e.nm)

–

0.37

–

–

0.71

0.32

0.34

\(\hbar\)/T1 (μeV)

–

11

–

–

5

3.9a

19

\(\hbar\)/T2 (μeV)

–

26

–

–

26

109

44

\(\hbar /{T}_{2}^{* }\) (μeV)

–

115

–

–

115b

194

165

\({\chi }_{\,\text{theory}\,}^{(3)}/{n}_{{\rm{D}}}\)

0.0024

100

0.015

3100

23

18

  1. \(\hbar\)ω is the photon energy, and labels R and T refer to resonant and transparent excitations. Values of μeg are all taken from ref. 29. All values for T1,2 were found from photon echo and pump–probe performed under the DFWM conditions, except: ataken from ref. 21. All values of the half-width, \(\hbar /{T}_{2}^{*}\), were found from the small-signal absorption spectrum, except: bassumed equal to the 2p0 half-width. x is the ratio of the intensities of the pump pulses from Fig. 2. L is the sample thickness and r0 is the spot size. The dimensionless factor f, which is unity for zero loss and infinitely long pulses, appearing in Eq. (3) (and described in detail in the text), was found from integrating the propagation equations. The experimental values of Ec were extracted from Fig. 2. Values of nD are given in units of 1015 cm−3; χ(3)L in units of 10−16 m3 V−2; χ(3) in units of 10−13 m2 V−2; and χ(3)/nD in units of 10−34 m5 V−2. Theoretical predictions are from Eq. (4), and for off-resonance excitation at 36.7 meV, the 2p± contribution was used (it has much higher \({\mu }_{{\rm{eg}}}^{4}\)) while at 32.5 meV we used the 2p0 contribution (it has much smaller Δ)
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