**6.4 Results and Discussions**

**6.4.1 In the Absence of the External Magnetic Field**

From (6.32), it can be said that the net electric field characteristics depend on the bias field,
the near-zone electric field, and the field associated with the polarization of the carriers (*E*_{pol})
given as:

*E*_{pol}(*t*)= *P*_{c}(*t*)

κǫ_{0}ǫ_{r} (6.49)

The transient behaviors of the net electric field with the laser pulse, the polarization field, and the radiated near-zone field are shown in Fig. 6.2. From the figure, it is evident that the radiated near-zone electric field mainly causes the reduction in the amplitude of the net electric field.

The amplitude of the radiated far-zone field from a PCA depends on the parameters related to the laser beam, the photoconductive semiconductor material, and the printed antenna geom- TH-2078_126102030

6.4 Results and Discussions

0 1 2 3 4 5 6

0 50 100 150 200 250

0.0 2.0x10

11 4.0x10

11 6.0x10

11 8.0x10

11 1.0x10

12

r

Electric field(kV/m)

Time (ps) net

pol

Peak Power(W)

Laser pulse

0 1 2 3 4 5 6

0.00 0.25 0.50 0.75 1.00 1.25

Electric field (V/m)

Time (ps) pol

Fig. 6.2: Transient behavior of laser pulse, *E*_{net}, electric field due to polarization (*E*_{pol}), and *E*_{r} at
*V**bias*=50 V and*P*=100 mW. The inset figure shows the zoomed view of*E**pol*

etry. To increase the amplitude of the far-zone field, an optimization of the values of these parameters or an optimized combination of the parameters is required. It can be seen in (6.48) that the amplitude of the radiated far-zone electric field depends on the rate of change of the carrier velocities and the carrier densities. The carrier densities mainly depend on the laser beam power, while the carrier velocities on the bias electric field. Thus, varying the laser beam power and the applied bias voltage (within the limit of the thermal and the electrical breakdown, respectively), the amplitude of the radiated far-zone electric field can be improved as shown in Fig. 6.3.

The analytically calculated results of the effect of voltage and laser power on the far-zone electric field are compared with the results from [168] & [169], respectively, and shown in Figs.

6.4 & 6.5. The values of different parameters used for the comparison study are given in Table 6.2 and 6.3.

Table 6.2:Parameters Details for Fig. 6.4

Parameter Value Parameter Value

*L* 100µm [168] *W* 100µm [168]

*f*_{rep} 75 MHz [168] λ 800 nm [168]

τ*l* 150 fs [168] *z**d* 3.5 cm

*P* 90 mW

Values of other parameters have been taken from Table 6.1

The dimension of the gap between the electrodes and the net electric field across it affect the photo-generated carriers density in the PCA. Since the far-zone electric field amplitude is TH-2078_126102030

0 40 80 120 160 0.00

0.05 0.10 0.15 0.20 0.25 0.30

THz

(kV/m)

Average optical input power (mW ) V

bias = 10 V

= 25 V

= 50 V

= 75 V

= 100 V

Fig. 6.3: Radiated far-zone electric field at differ- ent laser input power and DC bias voltage

20 30 40 50 60 70 80 90 100

0.1 1 10

THz

(V/m)

THz

(a.u.)

DC Bias Voltage (V)

Experimental

Analytical

0.1 1 10

Fig. 6.4:Comparison of the analytical and the ex- perimental [168] results of the bias voltage effect on the radiated far-zone electric field

0 20 40 60 80 100 120 140 160 180

0.1 1 10 100

0.1 1 10 100

THz

(a.u.)

Average Optical Input Power (mW )

GaAs:O GaAs:O

GaAs:As

THz

(V/m)

Experimental Analytical

GaAs:As

Fig. 6.5: Comparison of the analytical and the ex- perimental [169] results of the laser input power ef- fect on the radiated far-zone electric field

0 20 40 60 80 100

0.01 0.1 1 10

0.01 0.1 1 10

THz

(V/m)

THz

(a.u.)

DC Bias Voltage (V) L=200 m L=100 m

L=200 m

Experiment Analytical

L=100 m

Fig. 6.6: Comparison of the analytical and the ex- perimental [168] results of the gap length effect on the radiated far-zone electric field

Table 6.3:Parameters Details for Fig. 6.5

Parameter Value Parameter Value

*V*_{bias} (GaAs:O) 100 V [169] *V*_{bias} (GaAs:As) 110 V [169]

*L* 120µm [169] *W* 10µm [169]

ω0 5µm [169] *f*_{rep} 82 MHz [169]

τ_{l} 100 fs [169] λ 760 nm [169]

τ_{n} 0.15 ps *z*_{d} 8 cm

µ*low*,*n* (GaAs:O) 500 cm^{2}V^{−}^{1}s^{−}^{1} µ*low*,*n*(GaAs:As) 200 cm^{2}V^{−}^{1}s^{−}^{1}
µ*low*,*p*(GaAs:O) 100 cm^{2}V^{−}^{1}s^{−}^{1} µ*low*,*p*(GaAs:As) 40 cm^{2}V^{−}^{1}s^{−}^{1}
Values of other parameters have been taken from Table 6.1

proportional to the rate of change of the current density, the parameters which effect the current density also influence the far-zone electric field. Thus, by changing the gap dimensions, the amplitude of the radiated far-zone electric field can be enhanced. Reducing the gap length in- TH-2078_126102030

6.4 Results and Discussions

creases the net electric field and the current density which effectively enhances the amplitude of the far-zone electric field. The result of the gap length effect is compared with the experimental result reported in [168] as shown in Fig. 6.6. The values of different parameters used in the calculations are given in Table 6.4.

Table 6.4:Parameters Details for Fig. 6.6
For*L*=*W*=100µm and *L*=*W*=200µm

Parameter Value Parameter Value

*f**rep* 75 MHz [168] λ 800 nm [168]

τ_{l} 150 fs [168] *z**d* 3.5 cm

Values of other parameters have been taken from Table 6.1

From (6.15) & (6.16), it can be said that the rate of change of the carrier densities mainly depends on the carrier lifetime. A small carrier lifetime supports a fast rate of change, whereas a large value gives a slow rate of change. For the THz frequency generation from the PCA, a fast rate of change of the carrier densities is required which is supported by the small carrier lifetime.

However, a small carrier lifetime provides a low current density compared to the larger values of the carrier lifetime, as the carriers remain available for a very short time to be collected at the electrodes. Increasing the carrier lifetime increases the availability period of the carriers at the gap, which supports a high current density and results in a intense radiation. The analytically calculated results of the carrier lifetime effect are compared with the results from [164] and shown in Fig. 6.7. The parameters values used in the analytical calculations are provided in Table 6.5.

Table 6.5:Parameters Details for Fig. 6.7
Forτ_{e}=0.7 ps and 1.2 ps

Parameter Value Parameter Value

*V*_{bias} 1500 V [164] *L* 5 mm [164]

*W* 5 mm [164] ω_{0} 4 mm [164]

*f*_{rep} 1 kHz [164] µ*low*,*n* 1500 cm^{2}V^{−}^{1}s^{−}^{1} [164]

τ_{l} 200 fs [164] µ_{low,p} 500 cm^{2}V^{−}^{1}s^{−}^{1}

λ 800 nm *z*_{d} 18 cm

Values of other parameters have been taken from Table 6.1 TH-2078_126102030

-0.5 0.0 0.5 1.0 1.5 2.0 -1

0 1 2 3

-1 0 1 2 3

e = 0.7 ps

Time (ps)

THz

(a.u.) THz

(kV/m)

Experiment Analytical

e = 1.2 ps e

= 0.7 ps

e = 1.2 ps

Fig. 6.7: Comparison of the analytical and the experimental [164] results of the carrier lifetime effect on the radiated far-zone electric field