超快光学第09章 非线性三阶效应ppt课件.ppt
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1、Third-order nonlinearities: Four-wave mixing,Third-harmonic generationInduced gratingsPhase conjugationNonlinear refractive indexSelf-focusingSelf-phase modulationContinuum generation,Third-harmonic generation,We must now cube the input field:,Third-harmonic generation is weaker than second-harmonic
2、 and sum-frequency generation, so the third harmonic is usually generated using SHG followed by SFG, rather than by direct THG.,Noncollinear third-harmonic generation,We can also allow two different input beams, whose frequencies can be different.So in addition to generating the third harmonic of ea
3、ch input beam, the medium will generate interesting sum frequencies.,Third-order difference-frequency generation: Self-diffraction,Consider some of the difference-frequency terms:,Samplemedium,Signal,w,w,w,The excite-probe geometry,One field can contribute two factors, one E and the other E*. This w
4、ill involve both adding and subtracting the frequency and its k-vector.,This effect is automatically phase-matched!,The excite-probe beam geometry has many applications, especially to ultrafast spectroscopy. The signal beam can be difficult to separate from the input beam, E1, however.,Nonlinearmedi
5、um,Wave plateyielding 45polarization,Signal,w,w,w,Polarization gating,Here field #2 contributes two factors, one E and the other E*. But one is vertically polarized, while the other is horizontally polarized. This yields a signal beam thats orthogonally polarized to the input beam E1.,If E1 is horiz
6、ontally polarized, the signal will be vertically polarized:,This arrangement is also automatically phase-matched. Its also referred to as polarization spectroscopy due to its many uses in both ultrafast and frequency-domain spectroscopy.,The input beam in the signal beam direction is rejected by pol
7、arizer!,The irradiance of two crossed beams is sinusoidal, inducing a sinusoidal absorption or refractive index in the mediuma diffraction grating!,An induced grating results from the cross term in the irradiance:,Many nonlinear-optical effects can beconsidered as induced gratings.,Time-independent
8、fringes,Diffraction off an induced grating,A third beam will then diffract into a different direction.This results in a beam thats the product of E1, E2*, and E3:,This is just a generic four-wave-mixing effect.,Induced gratings,Phase-matching condition:,Assume:,The diffracted beam has the same frequ
9、ency and k-vector magnitude as the probe beam, but its direction will be different.,but,Phase-matching induced gratings,Phase-matching:,z-component:,x-component:,The minus sign is just the excite-probe effect.,The “Bragg Condition”,Induced gratingswith different frequencies,Phase-matching condition:
10、,This effect is called non-degenerate four-wave mixing. In this case, the intensity fringes sweep through the medium: a moving grating.,The set of possible beam geometries is complex. I wrote a thesis on this!,Acousto-optics involves diffracting light off a grating induced by an acoustic wave.,Acous
11、to-optics works because acoustic waves have about the same wavelengths as (visible) light waves. Such diffraction can be quite strong: 70%. Acousto-optics is the basis of useful devices.,An acoustic wave induces sinusoidal density, and hence sinusoidal refractive-index, variations in a medium.,Induc
12、ed gratings with plane waves and more complex beams (of the same frequency),All such induced gratings will diffract a plane wave, reproducingthe distorted wave:,E2 and E3 are plane waves.,Holography is an induced-grating process.,One of the write beams has a complex spatial patternthe image. Differe
13、nt incidence angles correspond to different fringe spacings. Different object views are stored as different fringe spacings.A third beam (a plane wave) diffracts off the grating, acquiring the image infor-mation. Different fringe spacings yield different diffraction angleshence 3D!,The light phase s
14、tores the angular info.,Phase conjugation,When a nonlinear-optical effect produces a light wave proportional to E*, the process is called a phase-conjugation process. Phase conjugators can cancel out aberrations.,The second traversal through the medium cancels out the phase distortion caused by the
15、first pass!,Distorting medium,A phase-conjugate mirror reverses the sign of the phase,A normal mirror leaves the sign of the phase unchanged,Phase conjugation = Time reversal,A light wave is given by:,If we can phase-conjugate the spatial part, we have:,Thus phase conjugation produces a time-reverse
16、d beam!,Degenerate four-wave mixing,Consider only processes with three input frequenciesand an output frequency that are identical.Identical frequencies = degenerate.,Degenerate four-wave mixing gives rise to an amazing variety of interesting effects. Some are desirable. Some are not.Some are desira
17、ble some of the time and not the rest of the time.,Because the k-vectors can have different directions, well distinguish between them (as well as the fields):,Single-field degenerate four-wave mixing,Single-field degenerate four-wave mixing gives rise to “self” effects. These include:Self-phase modu
18、lationSelf-focusing (whole-beam and small-scale)Both of these effects participate in the generation of ultrashort pulses!,If just one beam is involved, all the k-vectors will be the same,as will the fields:,So the polarization becomes:,Degenerate 4WM means a nonlinearrefractive index.,So the refract
19、ive index is:,Recall the inhomogeneous wave equation:,and the polarization envelope (the linear and nonlinear terms):,Substituting the polarization into the wave equation (assuming slow variation in the envelope of E compared to 1/w):,since,Nonlinear refractive index (contd),Usually we define a nonl
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