Published 07 February, 2020; last updated 08 March, 2021

Group index of light appears to have seen discontinuities of 22 years in 1995 from Coherent Population Trapping (CPT) and 37 years in 1999 from EIT (condensate). Pulse delay of light over a short distance may have had a large discontinuity in 1994 but our data is not good enough to judge. After 1994, pulse delay does not appear to have seen discontinuities of more than ten years.

This case study is part of AI Impacts’ discontinuous progress investigation.

That which is uncited on this page is our understanding, given familiarity with the topic.¹

“Slow Light” is a phenomenon where the speed at which a pulse of light propagates through a medium is greatly reduced. This has potential applications for lasers, communication, and cameras.²

The speed of propagation of the light through the medium referred to as the ‘group velocity‘ of the light, and it is a function of the medium’s refractive index and dispersion (the rate at which the refractive index changes with the frequency of the light).

In most materials—for instance glass, air, or water—the dispersion is low enough that the group velocity is simply the speed of light divided by the index of refraction. In order to slow down light by more than roughly a factor of 3, physicists needed to create optical media with a greater dispersion in the frequency range of interest. The challenge in this was doing so without the medium absorbing most of the light, since most materials exhibit maximum dispersion under conditions of high absorption. This was resolved using exotic phases of matter and sophisticated methods for inducing transparency in them.

Diamonds have a very high index of refraction, and the ability to cut and polish them to achieve good optical quality has existed for hundreds of years³. However there were no light sources available for studying low group velocities until the 1960s, so recorded progress begins then. The first pulsed sources of light that could reasonably be used for the investigation of slow light came about in 1962 with the invention of Q-switching, which is a method for generating series of short light pulses from a laser. We do not know whether early Q-switched lasers could be used for this work, but doubt that any earlier light sources were suitable.

Following Q-switching, progress for slowing light proceeded roughly in four stages:

1. High index materials: For instance, diamonds. There may have been marginally better materials, but we did not investigate because our understanding is that they should at most represent a few tens of a percent of difference, and later gains represent factors of millions to trillions.
2. High absorption media: Materials with very low group velocity at a particular wavelength range, at the cost of very high absorption (losing >99% of the light over <100 microns).
3. Induced transparency: Materials with a narrow window of transparency in spectral regions of low group velocity. This led to rapid increases in total delay of a pulse, both through longer propagation distance and lower speeds.
4. Stopped light: Eventually, group velocity had been lowered to the point that it was possible to destroy the pulse, but store enough information in the medium about it to reconstruct it after some delay. There is room for debate about whether this is really the same pulse of light, however there are applications in which treating is as such is reasonable. We view this as progress in pulse delay, but not group index. After the invention of stopped light, slow light was no longer a major target for progress.

There are several metrics that one might plausibly be interested in in this area. Group velocity is a natural choice because it is simple, but it trades off against absorption. So it is relatively easy to make a medium that has a very low group velocity, but it will absorb too much light to be useful. Because of this, research was more plausibly aimed at some combination of low  group velocity and low absorption.

One simple way to combine absorption and group velocity into a single metric is group velocity with an absorption criterion (say, lowest group velocity in a medium that transmits at least 1% of the light). Another is total time delay of the pulse by the medium, since longer delays can be achieved either by slowing down the pulse more, or slowing it down over a longer distance (requiring lower absorption). Pulse delay seems to have been a goal for researchers, suggesting it tracks something important, making it more interesting from our perspective.

We chose to investigate pulse delay and group index (the speed of light divided by the group velocity).⁴

We collected data from a variety of online sources into this spreadsheet. The sheet shows progress in pulse delay and group index over time as well as our source for each data point, and calculates unexpected progress at each step. Figures 1-3 illustrates these trends.

For comparing points to ‘past rates of progress’ we treat past progress for both pulse delay and group index as exponential, changing to a new exponential regime near 1995 in both cases.⁵

Compared to these rates of past progress, the 1994 point—EIT (hot gas)—could be a very large discontinuity in pulse delay, if there was a small amount of progress prior to it. There probably was, however our estimates of the points leading up to it are so uncertain that it isn’t clear that there was any well-defined progress, and if there was we have not measured it. So we do not attempt to judge whether there is a discontinuity there. Aside from that, pulse delay saw no discontinuities of more than ten years.

Group index has discontinuities of 22 years in 1995 from CPT and 37 years in 1999 from EIT (condensate).

In addition to the size of these discontinuities in years, we have tabulated a number of other potentially relevant metrics here.⁶

These trends are short and not characterized by a clearly established rate prior to any potential change of rate, making changes in apparent rate relatively unsurprising. This means they are both less in need of explanation, and less informative about what to expect in cases where a technology does have a better-established progress trend.

Increasing group index of light does not appear to have been a major research goal prior to the discovery of induced transparency in the mid 1990s. Most of the work up to that point (and, to a lesser, extent after) was directed toward controlling the properties of optical media in general, with group index as one particularly salient parameter that could be controlled, but perhaps at the expense of others. Thus the moderate discontinuities in group index might relate to the hypothesized pattern of metrics that receive ongoing concerted effort tending to be more continuous than those receiving weak or sporadic attention.

Primary author: Rick Korzekwa

Thanks to Stephen Jordan for suggesting slow light as a potential area of discontinuity.

1. Our primary researcher for this page, Rick Korzekwa, has a PhD in physics, with experience in experimental optical physics. In addition, Rick discussed the main ideas in this page with Professor Steve Harris, a researcher responsible for substantial progress on slow light. Prof. Harris has not looked over our conclusions, and any mistakes are Rick’s.
2. “In the future, slowing light could have a number of practical consequences, including the potential to send data, sound, and pictures in less space and with less power. Also, the results obtained by Hau’s experiment might be used to create new types of laser projection systems and night vision cameras with power requirements a million times less than what is presently possible.”
   Cromie, William J., and William J. Cromie. “Physicists Slow Speed of Light.” Harvard Gazette. February 23, 2018. Accessed July 03, 2019. https://news.harvard.edu/gazette/story/1999/02/physicists-slow-speed-of-light/.
3. “The first “improvements” on nature’s design involved a simple polishing of the octahedral crystal faces to create even and unblemished facets, or to fashion the desired octahedral shape out of an otherwise unappealing piece of rough. This was called the point cut and dates from the mid 14th century; by 1375 there was a guild of diamond polishers at Nürnberg.” “Diamond Cut – Wikipedia.” Accessed October 25, 2019. https://en.wikipedia.org/wiki/Diamond_cut.
4. For more on our methodology, see our methodology page.
5. See our methodology page for further explanation of how we measure discontinuities. See our spreadsheet for calculations.
6. See our methodology page for more details.