I think it is a misconception to think, that LN or BBO was "designed" with nonlinear optics in mind. They were not "designed" for that at all. It is rather a kind of coincident, that these crystals are among the materials of choice. If you just think about the nonlinear dipole moments (chi(2) tensors etc.) there are materials with much higher constants out there easily (just look for nonlinear polymers with 100 or 1000 times higher nonlinearities or electro-optic coefficients, which were actually designed/picked with that in mind; look for P. Günters work from Switzerland as an example. Even GaAs has a ~5times higher nonlinearity in a wavelength range compatible with LN). Yet, lithium niobate or BBO or other crystals are still very persistent, which is not just because of its nonlinear properties, but because of a multitude of reasons. Ask yourself, why Silicon is the material of choice for integrated electronics. Certainly, there are materials with better mobility (just think of graphene), or easier to dope or something else, yet Silicon will stay there for a long period of time, due to its availability, technology developed around it etc.

So, let's take a look into LN history. The first mentioning of lithium niobate was in 1928 by norwegian mineralogist William Zachariasian, who was studying the general properties of ABO3 compounds without any nonlinear background at all. The next interest from a physics perspective in LN (and its isostructural compound LT) came in 1949 by B. T. Matthias and J. P. Remeika, who discovered LN among the first solid crystals, which show ferroelectricity. That was an interesting breakthrough, as ferroelectricity at that point was mostly known from complex salts (Rochelle salts). Rochelle salts, however, were water soluble and decomposed a little over room temperature, so not exactly perfect for experimental investigations. And it was a breakthrough to finally show a solid crystal, which displays ferroelectricity. Again, no nonlinear optics at all. Nonlinear optics was only a very poorly studied topic until the invention of the laser in the early 60s, e.g. compare the very early works of Boyd. And it was also Boyd, who chose LN for nonlinear experiments. Yes, at that point (and nowadyas there still is) a hunt for materials with high nonlinear coefficients, but in particular LN was chosen by Boyd as a superior crystal for a different reason. The earliest crystal to do nonlinear optics with lasers were the compounds of KDP and ADP (potassium/ammonium dihydrogen phosphate), which are comparable with LN, but come with a mayor drawback. They are soluable in water, which may is nice to grow crystals from a solution, rather than a high temperature melt, but the crystals will decompose under atmospheric humidity eventually. Lithium niobate, however, has a high melting temperature, a high curie temperature, can be grown from melt nicely at its congruent point, etc. However, LN is also not perfect. The most common LN compound is so called congruent LN, which is the easiest to grow, but comes with an intrinsic Li deficit, which is a major source behind photorefraction. Which is the reason, why other materials, e.g. KTP, have been developed or a lot of effort is put into growing stoichiometric LN or MgO doped LN.

Why is lithium niobate sill so persistent? Lithium niobate is mechanical and chemically stable (high Mohs hardness), it can be homogeneously be grown from melt with the Czrochalski method (in its congruent form), it can be poled for quasi-phase matching (which is a challenge, due to the high voltage, but it can be done), low loss can be fabricated, e.g. by Ti indiffusion or proton exchange, it has a wide transparency window. Still all this properties has not necessarily something to do with its properties for quantum optics. Its interest in optics came originally from its ability as a electro-optic modulator. The modulator market is a huge thing, as the ability to modulate signal is the most important ability for fiber optics communication (and this is still a main driving force; look for recent progress in beyond 100 GHz modulators in thin film LN). Funnily enough, LN has been superseeded by silicon photonics. Silicon may be worse in some aspects, but it can be fabricated on a huge scale driving down prices. Mentioning scaling down prices, the reason for LNs availabilty and relatively cheap price is its use for bulk and acousto-optics filters. Yearly several hundred tons of LN is grown in wafer sizes up to 6 inch and of this - I somewhere read 80% - end up in the RF filter market, rather than in optics. LN may be found in your smartphone or satellite reciever. Compared to modulators (communication) and RF filters the market for quantum optics is small to non-existent. Therefore, those have been the driving forces behind LN, rather than quantum optics. By the way, a very interesting development in LN is the availability of thin film LN (also knowns as LNOI), which is now just starting to become interesting as a platform. But again LNOIs original idea was to make a better platform for modulators and a better platform for RF filters. Quantum/Nonlinear optics is always a side benefit.

These are the reason, why LN is chosen for quantum optics is its availability combined with its good (but not excellent) combination of many favorable properties. I am not even sure, if LN will become the "silicon" of qunatum optics. In fact, I am not even sure, if there is a best material for quantum optics (yet?). If I would need to bet on a "silicon" for quantum optics, I would probably bet on silicon itself. Afterall, it is already available on foundry scale.

I hope that gave a better impression on LNs history and thought processes around it,

Regards,

Michael

PS: If someone has more insight on LN history, I am happy to learn more.

That's an interesting mine of information. You indicate initial interest was from a mineralogist in 1928, so lithium niobate is a naturally occurring crystal? Where do you find this?

Do you have equal detail on BBO?

Unfortunately, I have no significant information on BBO. I can only imagine, that the story is similar, i.e. several compounds including LN were competing and BBO stayed persisting due to not only its nonlinear coefficient, but a combination of various practical and technical considerations (Growth, stability, etc.) as well.

Zachariasen was a mineralogist by profession, i.e. he studied geology in Oslo. But his work would from todays perspective probably considered solid state physics. He did systematic x-ray diffraction analysis.

His PhD thesis is called " Untersuchungen über die Kristallstruktur von Sesquioxyden und Verbindungen ABO3", which is in german. Translated it means something like: "Investigation on the crystal structure of sequioxides and compounds of ABO3 type". Sesquioxides are materials of the general chemical compounds A2O3, where A could be things like Al and O is oxides, while ABO3 are things like A=Li and B=Nb etc. His thesis is about x-ray diffraction analysis of as many compounds as possible of these groups to find structural rules etc. The only thing you can find online readily are summaries of his thesis:

Article Untersuchungen über die Kristallstruktur von Sesquioxyden un...

As far as I understand it, he did grow (or got someone to grow) LiNbO3, as I am not aware of its natural occurence. Early works on the structure of LiNbO3 point to the early works of Zachariasen as early work on the crystal structure. Compare Abrahams for example:

Article Ferroelectric Lithium Niobate. 3. Single Crystal X-Ray Diffr...

Anyway, the early works by Zachariasen is only an interesting side-note. Zachariasen never noted the polar structure or ferroelectricity. This was noted by Matthias and Reimeka, who noted this:

Article Ferroelectricity in the Ilmenite Structure

by the way: While LN is used for nonlinear devices and not really designed for large nonlinear coefficients, there is work trying to optimize compounds for ultra large second order nonliearities or electro-optic coefficients. This has been done for polymers, because in chemistry and with large molecules, there is more flexibility in designing specific properties.

Article Recent progress in second-order nonlinear optical polymers a...

If you just compare the nonlinear coefficients of these molecules with LN, you will find 100 or 1000 times higher nonlinearities easily. By the way, you may now ask, we we are not using nonlinear polymers. People have built extremely efficient nonlinear frequency converters or electro-optic modulators out of this. But polymers have one big issue, which is stability. Large molecules tend to decompose or change their chemical structure under UV light, heat or ambient chemical enviromements. In contrast to this, LN as a crystal stays stable for years. Even domain structures stay stable for years. LN is relatively resistant to scratches, it melts only a way above 1000°C etc. But again, LN is not without its problems. Just search for research directed to address LNs photorefraction (which I think is also one field, where BBO comes in. It takes more power; This is also one of the reasone, why still alternatives are researched, such as KTP). Another limiting factor of LN are the huge mode sizes in indiffused waveguides in bulk samples. This leads to an ultimate limit in its conversion efficiency or requires huge voltages in modulator. However, the advent of thin film LN has addressed this issue. Just compare these two recent articles:

https://www.nature.com/articles/s41586-018-0551-y

https://www.osapublishing.org/optica/abstract.cfm?uri=optica-5-11-1438

A further issue is the smallest poling period for quasi-phase matching, which can be achieved. Currently there is a lot of interest to get sub-micron domain periods, which can be used for counter-propagating frequency conversion processes. However, this has not yet been shown in LN, however in KTP. Check the work by Canalias:

https://www.osapublishing.org/DirectPDFAccess/21E750CC-C4FA-0BB5-4B751B7F4EC1FBF1_223760/ome-1-7-1319.pdf?da=1&id=223760&seq=0&mobile=no

I hope, I could help you.

Regards,

Michael

That's fascinating. My interest centres on trying to understand optimisation of nonlinear crystals in visible bands so i may optimise the magnetic equivalents in the mm-wave band which are likely to be ferrites. Periodic poling with ferrites might be a possibility for increasing efficiency? Many thanks, Neil

One book, which may be interesting for you could be "Nonlinear optical effects and materials" by P Günter. It is already 20 years old, but in various Chapters they discuss their approach to nonlinear polymers, where they hunted for materials with higher and higher Chi(2) constants. Although, I can imagine there are more recent review articles in that field as well.

https://www.springer.com/us/book/9783540650294

What do you mean with "periodic poling of ferrites for increase efficiency"?

Periodic poling in LN and related materials is done to achieve improved phase matching (the method is called Quasi-phase matching) between the interacting beams. If you are not doing phase matching the power tranferred to the signal mode will be limited due to a phase mis-match between the interacting beams. The phase mismatch is a direct result of the dispersion of the refractive index, i.e. light at different wavelength has a different (phase) velocity leading. A periodic structure does provide an extra phase vector to compensate for the phase difference between the beams. The advantage of Quasi-phase matching is, that the phase matching problem can be solved independently from e.g. waveguide design. Traditionally phase matching is performed in a birefringence phase matching scheme. By using an interaction between two different light polarization perfect phase matching between the beams can be achieved, as due to birefringence the same refractive indices are observed for different wavelength (in different polarization). The two major drawbacks are, that ultimately one is limited by the given dispersion and birefringence, if a process is possible or not, and by design always an off-diagonal, usually smaller, tensor element has to be used as the interacting beams are in different polarizations.

If there is an equivalent problem of phase matching and dispersion in mmWave, a periodic structure or periodic poling can help. But that is beyond my knowledge right now.

An equivalent for the mm-wave is exactly what i was referring to for phase matching, however, this whole area is undeveloped, hence my interest in pushing it forward. Many thanks for the book reference, i'll check out for that which i can port to the mm-wave band. Many thanks for your great help. Neil