Electronics, Power Electronics, Optoelectronics, Microwaves ...

10-8 Electronics, Power Electronics, Optoelectronics, Microwaves, Electromagnetics, and RadarAbsorptionLight in traveling through media can be absorbed. This can be represented in two ways. The light fluxpropagating through amedium can be written asI ¼ I 0 e a xð 10: 6 Þwhere x is the distance through the medium with incident light flux I 0 . a is the absorption coefficient, usuallystated in cm 1 .Analternative way ofdescribing absorption is to use the imaginary term in the mediarefractive index. The complex refractive index isn ¼ n ð 1 þ i k Þwhere k is the attenuation index. a and k are related asð10: 7 Þa ¼ 4 pl 0nkð 10: 8 ÞCoherenceLight can be partially or fully coherent or incoherent, depending on the source and subsequent filteringoperations. Common sources of light are incoherent because they consist of many independent radiators. Anexample of this is the fluorescent lamp in which each excited atom radiates light independently. There is nofixed phase relationship between the waves from these atoms. In alaser the light is generated in aresonantcavity using alight amplifier and the resulting coherent light has well-defined phase fronts and frequencycharacteristics.Spatial and Temporal Coherence. Spatial coherence describes the phase front properties of light. Abeamfrom asingle-mode laser which has one well-defined phase front is fully spatially coherent. Acollection of lightwaves from anumber of light emitters is incoherent because the resulting phase front has arandomlyindefinable form. Temporal coherence describes the frequency properties of light. Asingle-frequency laseroutput is fully temporally coherent. White light, which contains many frequency components, is incoherent,and anarrow band of frequencies is partially coherent.Laser Beam FocusingThe radial intensity profile of acollimated single-mode TEM 00 (Gaussian) beam from alaser is given by" I ð r Þ¼I 0 exp 2 r !#2w 02 ð 10: 9 Þwhere w 0 is the beam radius (1/e 2 intensity). This beam will diverge as it propagates out from the laser,and thehalf angle of the divergence is given byy 1 = 2 ¼lp w 0ð 10: 10ÞWhen this beam is focused by alens the resulting light spot radius is given byw f ¼ l lp w dð 10: 11Þwhere l is the distance from the lens to the position of the focused spot and w d is the beam radius entering thelens. It should be noted that l > f, the lens focal length, for acollimated beam entering the lens. However, l willbe agreater distance than f if the beam is diverging when entering the lens.