I read that polarization is directly proportional to electric field in a linear medium. Here we neglect the higher order terms in the Taylor expansion of polarization as the values that non-linear susceptibilities take are very small of the order of 1e-10. But it is said that these terms are considered when light of high intensity is applied to the crystal.
What is not clear to me is that if non-linear phenomena can happen at high intensities in the linear media, why do we need a non-linear medium to observe Second Harmonic Generation and Parametric Down-Conversion?
One more thing is I would like to know if a linear or non-linear medium is the nature of certain crystals or they behave like that depending on the applied intensities.
Every substance must be considered as nonlinear until opposite is proven. In this sense, the medium is called linear if all experiments at all possible intensities have not revealed any signs of any nonlinearity. If the experiments revealed any nonlinearity at available intensities then medium is called nonlinear. The lower intensity is needed to reveal nonlinearity, the higher nonlinearity must be deduced. Hence, all known media called linear ones are simply nonlinear media with very low nonlinearity, below detection threshold. Special case are even order nonlinearity. The must be exactly zero in the media with the centre of inversion. Existence of even order nonlinearity in media where no deviation from inversion symmetry were reveled by all other methods means 1) nonlinear optical test is the most sensitive of all, OR 2) Symmetry breaking happens only under intense laser action
Direct Second Harmonic Generation and Parametric Down-Conversion can only happen in medium with quadratic nonlinearity, which requires the inversion symmetry to be broken.
If the medium has a non-broken inversion symmetry, than you'll be able to observe third-oder nonlinear processes, such as Third Harmonic Generation and Four-Wave-Mixing, however in most cases that will require much higher peak power than Direct Second Harmonic Generation and Direct Parametric Down-Conversion in quadratically nonlinear medium.
While it is possible to arrange Cascaded Second Harmonic Generation and Cascaded Parametric Down-Conversion in medium with zero quadratic nonlinearity, these processes will have even lower efficiency than Third Harmonic Generation and Four-Wave-Mixing (which are already typically harder to get than Direct Second Harmonic Generation and Direct Parametric Down-Conversion in quadratically nonlinear medium).
To summarise: Second order nonlinearity is equal to zero, unless the inversion symmetry in the medium is broken. Third order nonlinearity always remains non-zero, but using third order nonlinearity for efficient frequency conversion typically requires higher powers and/or stronger field confinement compared to using crystals with high second-order nonlinearity.
These fellas are all correct and they have given some valuable detail. I just wanted to point out that this type of "nonlinear" behavior is typical with any phenomena we like to describe with a response function. This response function approach is mainly due to the large set of (sometimes even fundamental) interactions that are required to relate the output vs. the input. In your case, you have stumbled on the common approach to describing the polarization output in response to the E-field input. Basically, if you start in the time domain, then you should have a linear response function in time for responses to small input signals. As you start to more fully describe the system's response to input magnitudes that are no longer small, then you can no longer assume the small input approximation. Then you must include higher-order terms in the Volterra series.
Think of other response functions that we commonly use to describe systems. We can think of the static stress-strain relationship. This can also be written with a correction term for a linear response in time, which is useful for non-static input stress. We can further include nonlinear terms for large time-dependent stresses. There are plenty of macroscopic examples, but I find nonlinear optics interesting because of the complexities in small molecular systems that give rise to all sorts of responses, and yet, we still are small enough to find virtual processes such as spontaneous down-conversion and the like. Note that this has all been discussed in the time domain, where for photons must travel with sinusoidal E/M fields. Thus, we can always look at the electronic response of small quantized systems in the frequency domain for any sinusoidal input.
One reason we use nonlinear materials to produce nonlinear effects is that, even though they will be present in all media in some form or other, the power necessary to produce them can cause structural damage to the media. I have seen a PhD student do this with a downconversion crystal, although he only managed to melt the non-reflective coating before his professor arrived.
Not even free space is linear at high enough intensities since photons interact with each other.
- Badges
- Science topic
- Similar topics
- Filing