Nonlinear refraction and absorption: mechanisms and magnitudes

Abstract

We provide an in-depth treatment of the various mechanisms by which an incident light beam can produce an intensity-or flux-dependent change in the refractive index and absorption coefficient of different materials. Whenever possible, the mechanisms are initially traced to single-atom and-molecule effects in order to provide physical understanding. Representative values are given for the various mechanisms. Nine different mechanisms are discussed, starting with the Kerr effect due to atoms and/or molecules with discrete states, including organic materials such as molecules and conjugated polymers. Simplified two and/or three-level models provide useful information, and these are summarized. The nonlinear optics of semiconductors is reviewed for both bulk and quantum-confined semiconductors, focusing on the most common types II-VI and III-V. Also discussed in some detail are the different nonlinear mechanisms that occur in liquid crystals and photorefractive media. Additional nonlinear material systems and mechanisms such as glasses, molecular reorientation of single molecules, the electrostrictive effect, the nuclear effect (vibrational contributions), cascading, and the ever-present thermal effects are quantified, and representative tables of values are given.

MULTIPLE TIME SCALES OPTICAL NONLINEARITIES OF LIQUID CRYSTALS FOR OPTICAL-TERAHERTZ-MICROWAVE APPLICATIONS (Invited Review)

“…This shows that if the interaction time τ in is 10 3 times shorter than τ T , i.e., τ int = 100 ns, the effective n 2 value is ∼10 −9 cm 2 /W, which is in fact much larger than the director axis counterpart (which for similar interaction time yields a nonlinearity about two orders of magnitude smaller) and other mechanisms discussed so far [49]. Laser induced thermal/order parameter change in NLC, therefore, would enable very rapid and efficient one-way optical switching with relatively low threshold intensity requirements.…”

“…Compared to the laser induced orientation nonlinearity of the liquid phase counterpart or anisotropic liquid like CS 2 [49], the orientation nonlinearity of NLC is more than a million times larger. The enormity of the orientation nonlinearity, nevertheless, is accompanied by a rather slow relaxation time.…”

“…In particular, we will investigate all the major mechanisms leading to the so-called optical Kerr effect [49] where the laser induced refractive index change is of the form: Δn = n 2 I [I is the optical intensity and n 2 is the nonlinear index coefficient]. As detailed in the following sections, nonlinear index coefficients characterizing these nonlinear optical processes are among the largest of all known materials, ranging from ∼10 −11 cm 2 /Watt for ultrafast individual molecular electronic nonlinearities to well over 10 3 cm 2 /W for liquid crystalline ordered phase nonlinearities [2][3][4][5].…”

“…In the next few sections, we shall discuss the fundamentals of these mechanisms and their dynamical characteristics, and explore the possibilities of utilizing them for fast responding all-optical switching and modulation operations. For completeness and possibly new applications, we also include a brief discussion of the ultrafast (femtoseconds) molecular electronic nonlinearities [49,[77][78][79][80][81][82][83][84][85] of NLC, as well as the isotropic (liquid) phase nanoseconds orientation nonlinearities [3,52,53].…”

“…To make the final choice, the details for the chosen mechanisms can be obtained from the discussions in preceding sections and the quoted literatures. Enhanced effect [54-57, 63, 64] Director axis reorientation [3,50,65] Flow-reorientation effect [69] Electrostrictiveeffect [67] Laser induced ordering in liquid phase [52] Molecular electronic Nonlinearity [49,78,79] Photorefractive effect [58][59][60][61][62] Thermal and order parameter [71,[73][74][75][76] Figure 13. NLC director axis-distribution (a) inside a photonic crystal inverse opal [8] and (b) around the nanostructures of a negative permeability metamaterial [12].…”