Field Guide to Nonlinear Optics by Peter E. Powers PDF
By Peter E. Powers
This box consultant is designed for these trying to find a condensed and concise resource of key thoughts, equations, and strategies for nonlinear optics. Examples all through this box advisor illustrate basic innovations whereas demonstrating the appliance of key equations. subject matters coated contain technologically vital results, fresh advancements in nonlinear optics, and linear optical houses crucial to nonlinear phenomena, with a spotlight on real-world applicability within the box of nonlinear optics.
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Phase-matching bandwidth may also be written in terms of group velocity. For example, the phase-matching bandwidth Dv2 when v1 is monochromatic is @Dk @k2 @k3 À1 ¼À þ ¼ vÀ1 g3 À vg2 @v2 @v2 @v3 where vÀ1 g is the inverse group velocity, which is related to the group delay df=dv. The bandwidth is 0:886pvg2 vg3 Dv2 ¼ Æ Ljvg2 À vg3 j Large bandwidths occur when the group velocities match. A determination of the bandwidth in these cases is made by plotting sinc2(DkL/2) versus frequency, or by going to a higher order in the Taylor series expansion for the analytic expression.
1 0:443 1 @no 1 @ne 1 @ne À À L l1 @T l1 l2 @T l2 ,uPM l3 @T l3 ,uPM DT ¼ Æ À1 ! À1 0:443 1 @ne 1 @ne 1 @no À À L l1 @T l1 ,uPM l2 @T l2 ,uPM l3 @T l3 e«eþe QPM DT ¼ Æ ! À1 0:443 1 @ne 1 @ne 1 @ne À À L l1 @T l1 ,uPM l2 @T l2 ,uPM l3 @T l3 ,uPM ! À1 0:443 1 @ne Du ¼ Æ L l2 @u l2 , T Du ¼ Æ ! ) Angular acceptance (measured internal to crystal): ! À1 0:443 1 @ne Du ¼ Æ L l1 @u l1 ,T e«oþo ! À1 0:443 1 @ne 1 @ne Du ¼ Æ À L l1 @u l1 ,T l2 @u l2 ,T e«eþo !
Derivatives of the principal indices are evaluated as dn2 dn ¼ 2n ; dl dl therefore; dn 1 dn2 ¼ dl 2n dl For the particular Sellmeier form given above, we obtain an analytic expression: " # dn l B ¼ DÀ 2 dl n ðl À CÞ2 Alternatively, one may evaluate the derivative using numerical differentiation. When evaluating derivatives of the extraordinary index, we use a similar approach. Since ne(u) is written as 1 n2e ðuÞ ¼ cos2 u sin2 u þ 2 n2o nZ derivatives in terms of nÀ2 are convenient. For example, e dnÀ2 2 dne dn n3 dnÀ2 sin 2u 3 1 1 e ¼À 3 and hence, e ¼ À e e ¼ ne 2 À 2 du ne du du 2 du 2 no nZ Similarly, other derivatives required for calculating bandwidths are !
Field Guide to Nonlinear Optics by Peter E. Powers