PULSED HIGH PEAK POWER LASERS
9.4 SPACE AND TIME FOCUSING OF LASER LIGHT
9.4.2 Concentrating Light Simultaneously in Time and Space
In order for the light to arrive and add coherently at the same point in time and space at an angleα, we synchronize both the mode-locked pulses from different lasers to arrive together at a pointQin directionαand the light carrier frequencies between different lasers to be in phase at pointQ.
9.4.2.1 Arranging Mode-Locked Pulses to Arrive Simultaneously at the Same Point The mode-locked pulses can be controlled in time by adjusting the timing for the mode-locked shutters (Figure 9.3). Figure 9.7 shows a computer con- trolling themTtime delay for themth mode-locked laser.
174 PULSED HIGH PEAK POWER LASERS
FIGURE 9.7 Array and mode-locked space and time focusing with steering.
9.4.2.2 Synchronizing the Light Carrier Frequency In Figure 9.7, fiber pigtailed laser diodes couple directly into the first column of fiber-connected optical directional couplers,C11toCM1. For the couplers, the first subscript denotes the laser number fromm=1, . . . , Mand the second subscript the coupler column number, 1 or 2, as shown in Figure 9.7 [57, 89, 106].
The synchronization of lasers at light frequencies in an array to perform beam- forming for focusing is achieved by splitting a small percentpof the light emitted by the mth coupler in column 2 into the output of a successive (m+1)th laser in column 1. An isolator is placed in this feedback path to ensure that the (m+1)th laser is synchronized to follow the frequency and phase of themth laser [110]. The percentage of light not coupled back (1−p) passes to a phase controller (or fiber delay line). The phases are set according tot(α)ω0, wheret(α) is determined by equation (9.16) to steer the beam in a fixed directionαfrom the normal to the array.
A beam expander (reverse telescope) (Section 1.3.4) provides a collimated beam that allows beams from all lasers to overlap at the array focus point. As the output beam from a single laser tends to be Gaussian shaped in space with a small radius of curvature, the optics is designed to focus the beam to its minimum waist (Section 2.1).
For a broader frequency band, we should replace the phase controller with a time delay, such as a fiber delay, line with delayst(α).
SPACE AND TIME FOCUSING OF LASER LIGHT 175
FIGURE 9.8 Combining mode-locked lasers in an array.
9.4.2.3 Equations and Simulation for Concentrating Laser Light in Time and Space Using the results of concentrating light in time and 1D space separately from Sections 9.2.1 and 9.4.1, respectively, we now combine these to synchronizeMmode-locked lasers, each havingN modes as shown in Figure 9.8.
The field at a pointQin space is obtained by combining the time and space field equations (9.6) and (9.17), respectively.
E(α, t)=A
n=N−1 n=0
m=M−1 m=0
e−j(m t(α)ω0−n ω t) (9.21)
The powerP(α, t) at pointP for a given angleαand a specific timet is computed from
P(α, t)=E(α, t)E∗(α, t) (9.22)
FIGURE 9.9 Field concentrated in space and time.
176 PULSED HIGH PEAK POWER LASERS
Power at point Qin Figure 9.8 from equations (9.21) and (9.22), for a 1D array, is plotted versus beam angleαand time in Figure 9.9 for a semiconductor laser of cavity lengthd =0.5 cm, laser waveguide refractive indexη=3.5,N=10 modes, M=5 lasers in a linear array, a separation between lasersh=3 cm, and a nominal wavelengthλ=1.04m. The half-power widths of the pulse in time and space are those for combining laser pulses at the array focus pointQ.
ForMlasers, each having N modes, the peak power at the target isMN times greater than that forMnonbeamformed nonmode-locked lasers withNmodes each.
ForN=50 and a 10×10 array of lasers for whichM=100 lasers, the peak is 5000 times greater than that for the nonbeamformed array of nonmode-locked lasers. In the case of 2 W laser diodes in an array, this would provide 5000×2 W or 10 kWpeak power. It is possible to increase the peak power further by using a longer laser, such as a water jacket cooled fiber laser, that exhibits more longitudinal modes. Because of beamforming from an array of lasers, the light intensity at less than or more than the range to point Qis less for the laser array than for a single laser of identical power to the total array. This avoids collateral damage of a weapon system, reduces enemy ability to compromise a communication system, and provides better regional selection for spectrometry.
9.4.2.4 Impact of Atmospheric Turbulence The pulse atQcan be severely distorted in both space and time by atmospheric turbulence: the extent of distortion and subsequent peak power reduction depends on the strength of atmospheric tur- bulence [4, 155] (Section 5.4). For a single laser path, turbulence will spread the pulse in time [87] and generate multipaths for which the varying path lengths cause constructive and destructive interference with time—the reason a star twinkles. The beam expanders in Figure 9.7 expand the diameters of the laser beams, which also reduces the effects of turbulence by averaging over a larger cross section [4, 49, 155].
The optimum beam size and target area are application dependent, for example, in a laser weapon, a larger beam diameter will reduce the influence of turbulence but decrease the intensity at the target and accordingly the damage.
An array of lasers provides a more robust system than a single laser against mul- tipath fading because each laser beam sees different turbulence. Owing to diffraction and turbulence [4, 48], the pulse at the focus pointQwill also wander around and expand in space. This effect may be computed by approximating the output beam with a Gaussian function of standard deviation determined by the optical output aper- ture and the radius of curvature determined to place the beam waist between laser and target. Turbulence is accounted for by computing phase masks as described in Refs [48, 88, 90, 144] and diffraction by propagating between phase masks using a Fourier transform formulation for diffraction (Section 5.4).