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## Liquid Crystal Displays

Liquid crystal displays are used everywhere, from the simple digital watch that kids these days probably don’t even know about to the screen you are likely reading this from! But how do they work? First, let’s start by comparing them with their predecessor: cathode ray tubes. In the old days, television sets used cathode ray tubes that would spit out electrons that would deflect and produce patterns of light on the screen to produce images. If the kids these days don’t have digital watches, then they certainly won’t remember how these bulky TVs used to work, or even old computer monitors, so I have included an image below.

Come to think of it, many of the lab equipment we use in our lab uses cathode ray tubes. Ah, the simpler times of the 90s!

So how can LCD displays bypass this monstrous use of space? Well, LCD stands for “Liquid Crystal Display”, which gives away the secret element to how these displays can work. Liquid crystals were first discovered in 1888 by Friedrich Reintzer when he noted that this strange substance (he was working with cholesteryl benzoate) seemly had both the properties of a liquid and a solid. Now, the really interesting thing about this material is that in the presence of a voltage (or an electric field, since an electric field is just a voltage/meter), the crystals that may ordinarily be ordered parallel to the voltage become aligned horizontally. Since these crystals have a needlelike shape, the optical properties are then affected by the direction of the crystals with respect to light that may be propagating in the material. This is shown in the figure below.

Now how does this work for an LCD? We will first take the simple example of a black and “white” LCD screen, like the one below.

What is really happening here is that we have a liquid crystal “cell” between two crossed linear polarizers followed by a reflecting mirror. The light that causes the display to light up is just ambient light! We can look at the following image to see how this works.

In our example of the watch, the “unpolarized light” is just natural light, which is unpolarized because it does not have a defined polarization direction. Then it will pass through one polarizer that only lets through the small amount of light that is polarized along the polarization axis of the polarizer (this polarizer is also known as a dichroic crystal, which is covered in another post here). This is shown as the top blue plane in the image above. Next, the light will pass through the nematic cell, which without the presence of a voltage (shown on the left) will turn the light by 90$^\circ$, as shown by the propagation of the green ellipses in the figure above. The second analyzer in the blue plane will then let this light pass through since it is aligned to its axis, and we have light propagating through! With a mirror at the end (not shown), light propagating back through will just emerge the same way it propagated in. Now, in the presence of a voltage, then we have the situation on the right in the figure above where no light is propagated through the second polarizer (analyzer). This is where we get the black portions of the watch screen above: the dark blocks on the screen correspond to where the light was blocked! The other, brighter parts are not connected to the same block, so they do not see any voltage change and can thus propagate back on through unaffected.

Now how does this work for colored light? Since in order to view this website you have to be looking at a screen, see if you can tilt it to an angle where you can see tiny “blocks” sectioning off your screen. Or, if you have ever accidentally cracked your computer/phone screen (not speaking from personal experience here, of course…), you may have noticed the small blocks that appear near the crack. These little blocks compose 3 small LCDs with red, green, and blue filters on them that, with careful control of the voltage applied, can be subtlety changed to form a total of 256 shades.

Voila! LCDs! Hope everyone has a good appreciation for all of those tiny LCDs working so hard for us now!

## Negative Nonlinear Refractive Index

In most of our discussions about the nonlinear refractive index in both the “Nonlinear Optics” section as well as the “Fiber Optics” section, the materials that we dealt with had a positive nonlinear refractive index. However, some of you may be asking yourselves (as I was asking myself as well), is it possible to have a negative nonlinear refractive index? If so, what will physically happen in this case? Can you have solitons form with positive dispersion and a negative nonlinear refractive index? All great questions! In the following article, I have compiled all that I know/can find on the negative nonlinear refractive index, so we can answer these questions together.

WHAT IS THE NEGATIVE NONLINEAR REFRACTIVE INDEX, AND WHERE DOES IT COME FROM?

As a reminder, the nonlinear refractive index is given by the following equation:

$$n_{2E} = \frac{3\chi_{1111}}{8n_0}\label{nonlinear_ref}$$

where $\chi_{1111}$ is the susceptibility in third-order material, and $n_0$ is the refractive index of the material in the absence of an intense light wave. In order for the nonlinear refractive index to be negative, the susceptibility must carry a negative value. According to [1], the sign of the susceptibility has to do with the transitions between the ground state, excited state, and two-photon excited state. When the two photon state dominates, the susceptibility is positive while when the absorption dominates, the susceptibility is negative.

WHICH MATERIALS HAVE A NEGATIVE NONLINEAR REFRACTIVE INDEX?

## Optical Computing

A big buzz-word in the science community at the present moment is “quantum computing”, which would take advantage of quantum phenomena such as superposition of states to provide much faster computing times. However, less talked about but just as cool is the concept of optical computing, which makes use of the properties of photons over electrons.

Because photons can have a specific bandwidth, there is more computing power with which to send data.

## Transverse Modes

Hello everyone! One important concept in optics that can be a bit confusing the first time learning it is transverse modes. First, a mode in free space (or isotropic dielectric medium) is defined as a superposition of plane waves, perpendicular to the direction of propagation. In any waveguide (optical fiber, laser cavity) where a beam is restricted to finite dimensions, however, there are “allowed” modes that depend on the boundary conditions of the waveguide. Each mode corresponds to a single frequency.

Some of the most common modes are discussed below:

Transverse Electro-Magnetic (TEM) Mode – In this case, both the electric and magnetic fields are completely transverse to the direction of propagation of the beam i.e. no dimensionality of the electric or magnetic field in the direction of propagation. In laser cavities, the most common and desired mode is TEM00 mode, which means that the beam is a perfect Gaussian.

Transverse Magnetic (TM) Mode – If a TEM mode meant that there was no dimensionality of electric or magnetic field in the direction of propagation, then a TM mode means that there is no magnetic field in the direction of the beam, but there is an electric field.

Transverse Electric (TE) Mode – As you may have guessed, TE mode means that there is no electric field in the direction of propagation, but there is a magnetic field.

An image of TM and TE modes is shown below (By Courtesy Spinningspark at Wikipedia, CC BY-SA 3.0, https://en.wikipedia.org/w/index.php?curid=39217796)

## The Journey

Hello everyone! This is the first of my (hopefully) many posts to this website. My goal in providing content is to present crazy optical principles in a more relatable fashion. The topics (at least initially) will be more geared towards a graduate level of understanding, but hopefully everyone will find something useful.