19

The presence or absence of inversion symmetry in a medium has a direct impact on the types of nonlinear interactions that it can support; specifically, media which do have inversion symmetry cannot support nonlinear effects of even order. The reason for this is that adding an even harmonic to the fundamental will yield an asymmetric dependence of the ...


17

What is it? From Mark Fox's Quantum Optics, an introduction, p.111: The second-order correlation function $g^{(2)}(\tau)$ is the intensity analogue of the first-order correlation function $g^{(1)}(\tau)$ that determines the visibility of interference fringes. (...) $g^{(1)}(\tau)$ quantifies the way in which the electric field fluctuates in time, whereas ...


11

Nonlinear optical elements are called nonlinear precisely because of the behaviour you note: because the optical response of the material does not depend linearly on the driving fields. The response may then have a quadratic or higher dependence on the driver, which is usually written in the form $$ \mathbf P =\varepsilon_0 \chi^{(1)} \mathbf E + \...


8

I think to first order you are looking for the Klein Nishina cross-section. What is important here is that light can inelastically scatter from electrons, but can never be absorbed by a free electron. So instead of the absorption as a function of wavelength, you're really describing the Raman spectrum of an electron, albeit at high energies. https://en.m....


6

I want to know exactly the physical model that what's happening in the crystal which create second harmonic One physically intuitive model for thinking about light-matter interactions is in terms of an energy level picture. In this picture, light propagating through a material can be thought of as series of absorptions and emissions. In one of these cycles ...


6

Correlation functions, such as $g^{(2)}(\tau)$ (or $g^{(1)}(\tau)$, as also mentioned in glance's answer) in quantum optics are employed to evaluate the quantum degree of coherence of an optical source. Frequently discussed examples of sources are lasers (that generally produce coherent light), thermal lamps (that generally produce chaotic light), or an ...


5

In nonlinear optics, the typical approach seems to be: take the relation between the polarization and electric field $P=\epsilon_0 \chi E$ and start adding correctional terms based on the Taylor series. $$P=P_0+\epsilon_0 \chi^{(1)} E+\epsilon_0 \chi^{(2)} E^2 +\epsilon_0 \chi^{(3)} E^3 +...$$ This particular phenomena, second harmonic generation, can only ...


5

If you are not working with very high intensity beams, you are not likely to see nonlinearity effects. However, there are nonlinear effects in glass and they are a limiting factor on the carrying capacity of optical fiber WDM systems, for example. Key words to look at are four-wave mixing, stimulated Brillouin scattering, and cross-phase modulation. Let's ...


5

I like Brandon's very physically intuitive answer: mine is a little drier. It is simply that three waves $E_j(t);\,j=1,2,3$ mix through $n^{th}$ order nonlinearity by way of $n^{th}$ power term $\left(\sum_{j=1}^3 E_j(t) e^{-i\,\omega_j\,t} + E_j(t)^* e^{i\,\omega_j\,t}\right)^n$ in the Taylor series for the input to output transfer function. So in the $n^{...


5

Why not imagine the third-order process as a two-stage second-order process like so:


5

These two processes are fundamentally different processes. The Photon upconversion Wikipedia article has some problems with it, notably by including the image (first imaged below) that is of a two-photon nonlinear optical process. Image from Ref [2] which incorrectly calls this process a two photon excitation upconversion process: A two-photon nonlinear ...


5

There are indeed some subtle but important differences between an SPDC-based heralded source and a true single photon source. In order to understand these differences, consider what a true single-photon source really means. A true single-photon source emits a single excitation at a specified frequency when demanded. So mathematically, the output state ...


5

You're conflating two different views on the description of the attosecond pulse train; in particular, you're flitting back and forth between the time-domain and frequency-domain descriptions, and it's not doing you many favours. Let's look at a few things first: The total field is $$ E(t) = \cdots + E(t-2\pi/\omega)-E(t-\pi/\omega)+E(t)-E(t+\pi/\omega)...


4

There is typically considered to be an uncertainty which softens the matching condition. In the case of momentum, the momentum state is only as well defined as the spatial extent of the interaction allows it to be. If the interaction length is given by $L$, which we can take to be an approximate measure of the position uncertainty $\Delta x$, then the ...


4

I made this little animation for wikipedia a few months ago, partly to clarify this very issue... An electron (purple) is being pushed side-to-side by a sinusoidally-oscillating force, i.e. the light's electric field. But because the electron is in an anharmonic potential energy environment (black curve), the electron motion is not sinusoidal. The three ...


4

As mentioned in the other answers, if the medium is linear then the refractive index is independent of the intensity of light, and the intensity can be related to the electric field amplitude through $I = \frac{nc\varepsilon_0}{2} E_0^2$. However, that does not mean, as the (incorrect) accepted answer implies, that the intensity "depends linearly on $n$". ...


4

Let's see if this explanation works for you. It is more intuitive than rigorous - but maybe it will help. In a "normal" simple harmonic oscillator, the potential well is a parabola, and the restoring force is proportional to the displacement. We know that the equation of motion for such a well is a sinusoid. Now if we make the potential well "more than ...


4

No because solid is a state of matter. Light cannot be considered matter since it is made up of particles which have no mass and I'm pretty sure occupy no space (i.e. photons have no volume). Edit: Since photons are at the quantum level, we can't actually fathom what it would mean for them to occupy space. But on this thread someone pointed out that there ...


4

Frequency mixing is the mechanism. Mental pictures of the form "two photons are absorbed and one bigger photon is emitted" are useful but they're ultimately just not that accurate, unless you're willing to consider any interaction of light with materials (including the dispersion of light by glass) as continuous absorption-and-emission loops. That said, in ...


4

For a closed system, whose time-evolution is unitary and given by the Schrodinger equation, any quantity $S$ quantifying a state's "mixed-ness" (or entanglement entropy, depending on your perspective) that takes the form $S = \text{Tr}\left[ f(\rho) \right]$ for some analytic function $f$ has a value that is identical in the Schrodinger and Heisenberg ...


4

By HHG I mean a process in which many photons are combined into one photon via virtual levels under conservation of energy. This is pretty close to a completely misleading mischaracterization of the use of the term HHG in the literature. The term High-Harmonic Generation (as explained fairly well in e.g. Wikipedia and RP-Photonics, as well as in this ...


4

I wonder whether this is a case where you have a physical intuition about photons which isn't quite working. If we say that 'a photon' has frequency $\omega$ (and energy $\hbar \omega$) then we are saying that the term 'a photon' refers to an excitation of the modes of the electromagnetic field, such that modes at frequency $\omega$ are involved, in a ...


3

Edit: putting the summary of discussion in comments into my answer. Beer-Lambert law assumes that every photon has equal probability to be absorbed by every molecule. It is only valid for sufficiently monochromatic light – that is, the bandwidth of light source should be smaller than the width of the absorption line. When absorption is measured with a ...


3

When an electric field $\mathbf{E}$ interacts with matter, it causes the atoms and molecules to distort and separate into dipole-like blobs, and these dipole blobs then increase the field strength. So, inside of the matter, the total electric field is actually the sum of two components: the external electric field $\mathbf{E}$, plus the electric field ...


3

There are several ways to look at these two effects. Their mechanisms are very similar, but their experimental realizations are rather distinct from one another. Here's one of the physical models, a classical one. Since you ask for physical intuition, I think the classical picture works best. Quantum mechanical models use a different language and tool ...


3

The common optical power on a 4km link is about 1mW, with ~2dB/km loss. with a good-quality single-mod fiber, the non-linear effects are negligible.


3

The Manley-Rowe relation arises from conservation of energy and momentum. For the case of SHG, the presence of the nonlinear optical (NLO) material eliminates the conservation of momentum (any momentum difference between the initial and final photons can be provided by the bulk material). So what's left is conservation of energy. Let $N_\omega$ and $N_{2\...


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