By R. Kingslake

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Extra resources for Applied optics and optical engineering. Vol. I: Light. Its generation and modification

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3. Write down explicitly the relationship betweenthe polarization and the optical electric fields involved in the processof differencefrequencygenerationwhere the output frequencyis given by the difference betweenthe two input frequencies. 4. What are the requirementsof causalityand reality important at a fundamentallevel? What do theseimply for the complex nature of the responsetensor and susceptibility tensor? 5. Arrive at the units and dimensionsof the coefficients of nth order nonlinear optical susceptibility, from first principles.

13) Further noting that the polarizationdevelopedat time t depends only on the fields applied at times precedingit, the tensorC should vanish for t > t (principle of causality). 14) Chapter 2. 15) Higher Order Polarizations- Time Domain Response In a similar manner,we can considerthe secondorder polarization at time t to arise from the electric field (t~)at the time t~ as well If as the electric field If (t~) at the time t~ to be given by The responsefunction F(2) is a third rank tensor and its componentsFi~22 relate the componentspP) of the secondorder polarization with the two fi eld componentsE j and Ek accordingto From the way the two field componentsappear in the above equation,it is clear that the physical situation would remain unaltered if we interchangeEj (t~) and Ek (t~) so much so the tensor be invariant under the exchangeof componentFi~22 (t : t~, t~)should the pairs(j, t~) and (k , t~).

Dll = -d12 = d26 , d14 = -d25 , d15 = d24 , d16 = d21 = -d22 , d31 = d32 , d33 · D3 group: Only 2 coefficients are independent: dll = -d12 = -d26 , d14 = -d25 · C3v group: The reflection plane is taken to be perpendicularto the X 1 (X axis). There exist 4 independentcomponents , as given by d15 = d24 , d16 = d21 = -d22 , d31 = d32 , d33 · Hexagonalsystem: C6 group: This group has 4 independentcomponents,as given by d14 = -d25 , d15 = d24 , d31 = d32 , d33 . C6v group: Only 3 independent elementsexist in this group, as given by d15 = d24 , d31 = d32 , d33 .

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Applied optics and optical engineering. Vol. I: Light. Its generation and modification by R. Kingslake


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