I thought I’d muscle in on Swans on Tea’s turf for a post and discuss an interesting optical illusion that is based just as much on optics as on the idiosyncrasies of the eye itself. While stumbling through StumbleUpon.com, I found an interesting collection of images at 2Loop.com showing ‘3D Painted Rooms’. An example of this is shown below the fold, from 2Loop…
In a previous optics basics post, we discussed challenges associated with trying to define the velocity of a localized wave or ‘pulse’ of light. Traditional measurements of the velocity of an object involve measuring how far Δd an object travels in a certain amount of time Δt; then the velocity is simply
velocity = distance/time = Δd/Δt.
But a wave is an extended disturbance, not definitely associated with any particular point in space, and so measuring Δd becomes tricky. If there is a definite feature of the wave (such as a peak), we can define the velocity by measuring how fast the peak moves. If the wave changes shape (i.e. the peak disappears), as happens when waves propagate in matter, it is not immediately clear how one defines wave velocity.
The answer, as discussed previously, seems to be to define a ‘group’ velocity: we can mathematically characterize the velocity of the overall wave signal by
where Δω is the range of temporal frequencies in the wave pulse and Δk is the range of spatial wavenumbers in the pulse. This measure seemed quite good: under most circumstances, the quantity was less than the vacuum speed of light c, and therefore didn’t violate Einstein’s relativity, and those cases where the group velocity was greater than c seemed to always involve a significant attenuation or distortion of the wave.
However, in 2000 researchers Wang, Kuzmich and Dogariu from the NEC Research Institute shocked the physics and optics community by demonstrating* that materials exist for which the group velocity is greater than c, sometimes much greater than c, and the pulse travels at this higher speed without any obvious distortion or attenuation. What was going on?
This was an interesting bit of science news from last week: according to an article on optics.org (free registration required), a research team from Rensselaer Polytechnic Institute and Rice University has fabricated the ‘blackest’ material ever known, which reflects just 0.045% of the light incident upon it. This beats the previous record of 0.16% that was set by a nickel and phosphorous alloy.
There’s a lot of interest in both industry and the military in developing free-space optical communications systems. The basic idea is to use a laser to transmit signals at optical frequencies over distances ranging from a few kilometers to hundreds of kilometers. Potential advantages of such a scheme are the high bandwidth of communications, meaning lots of information can be transmitted very fast, and the highly directional nature of the signal, making it highly secure. Disadvantages of such a scheme include the requirement of direct line of sight between transmitter and receiver, and more significantly the distortion induced in the beam by atmospheric turbulence.
Does one really need a laser to make a viable optical communications system, however? I saw one talk at Photonics West, one of the best talks I’ve seen in a while, which demonstrates pretty convincingly that you do not…
I’m currently in San Jose, at Photonics West, the biggest optics meeting of the SPIE (Society of Photographic Instrumentation Engineers, originally.) I’m only here briefly, and pretty burned out on meetings for the moment. I did see some nice talks that I’ll blog about over the next couple of days.
One session the SPIE provided for students was advice on giving scientific presentations, which is indeed an art and there are plenty of people who never quite figure it out. I thought I’d provide a list of a few of the insights and ‘tricks’ I’ve learned about giving scientific talks at meetings, which will hopefully help someone down the line:
How do we define how fast a wave is going? The question at first glance seems obvious. When we discussed harmonic waves in a previous post, we observed that the velocity of the wave could be measured by measuring how far one of the peaks of the wave travels in a certain amount of time. There are a number of subtle points that arise when talking about wave velocity, however, including the possibility of light traveling at faster than the ’speed of light’! In this post we’ll try and define the velocity of a wave, and explain why the question is not so easy to answer.
To conclude my discussion of optics basics, I want to introduce some of the standard quantities used to describe waves and wave propagation. Unlike previous ‘basics’ posts, this one will necessarily deal with a little bit of algebra and perhaps a little trigonometry.
The simplest wave to deal with from a theoretical point of view is a harmonic wave, one which consists of an infinite sequence of regularly spaced ‘ups and downs’. A portion of such a wave traveling to the right on an extremely long string would appear as:
In part II of my series on ‘What is a wave?’, I addressed one of the two most significant behaviors of waves, namely interference, the ability of a wave to ‘interact’ with itself. The second behavior of waves which is extremely significant is diffraction, and we will address it in this post.
Diffraction may be broadly defined as the tendency of a wave traveling in two or more dimensions to spread out as it propagates. The most significant consequence of this spreading is the ability of waves to ‘bend around corners’ when faced with an obstacle. We all have experienced the diffraction of sound waves: if you and a friend stand on opposite sides of a large building (say a farmhouse) in the middle of an open field, you will be able to talk to each other even though there is no direct ‘line of sight’ between you and your friend, and no ability for the sound waves to reflect off of intermediate surfaces. The sound waves wrap around (diffract around) the outside of the farmhouse, allowing communication.
I was sent a link today to an interesting article about some research done at the University of Central Florida. Researchers have concocted a class of optical beams which appear to follow a curved trajectory in free space propagation. A theoretical picture of the behavior of such a light field on propagation is shown below:
The horizontal axis represents the transverse profile of the beam, while the vertical axis represents the propagation direction. Lighter colors, of course, indicate a brighter field. As one can see, the brightest beam in the wavefield, as well as all the secondary ones to its left, are curving to the right as they propagate!
In the first part of my series on ‘What is a wave?’, I attempted to give a broad definition of a wave, so that we can identify them when we see them. In this part, I will address two of the most important behaviors of waves: interference and diffraction. Interference may be loosely described as the interaction of a wave with itself, or a wave with another wave, while diffraction may be loosely described as the interaction of a wave with other objects.
We will discuss interference in this post, and consider again the wave on a string discussed in part I of this post. A pair of waves are sent down the string to a fixed end, where they are reflected and return to their point of origin. What happens when the waves pass each other? An animation of such an event is displayed below:
