A "frequency-doubling" crystal is able to absorb some of
a particular wavelength of light, two photons at a time,
and emit single photons that contain twice the energy
and half the wavelength. A wide variety of such crystals
exist.
We don't want those here, though. What we want is a
slightly
different type of crystal, called a "frequency
summing" crystal. This crystal absorbs photons of two
different wavelengths and adds their different energies
together in emitting new photons. See the link on
frequency tripling for an example of a frequency-
summing crystal.
Here I will assume that an appropriately wide variety of
frequency-summing crystals also exist. We are going to
want three different types of them (all of them
reasonably transparent to infrared and visible light).
Next, according to the linked Wikipedia article, the
human eye responds to wavelengths of light from 390
nanometers (violet) to 700 nanometers (deep red). The
article also shows some pretty good representations of
the three the primary colors --blue, green and red-- as
having wavelengths of 445, 532, and 635 nanometers,
respectively.
So, with those colors as a good-enough starting point for
what follows here, let us assume that our three different
frequency-summing crystals can output light at one of
those three wavelengths.
The visual fanatic may now consider the following
construction: We assemble billions of tiny crystals into a
significant-sized cube. Each tiny crystal is one "voxel" (a
"volume pixel") of our 3D display; its size will be perhaps
a quarter of a millimeter. So, if we want the display to
have a resolution of 2048x2048x2048, then that is
8,589,934,592 voxel crystals, and the overall size of the
display will be 1/4 of 2048 millimeters, or 512
millimeters, about half-a-meter on each side.
However, the preceding description left something
rather important out. Normally one pixel of a regular 2D
display can display any color; the above only outputs 1
color at each voxel. That means the actual resolution, in
terms of full color, would be about 682x682x682 --we'd
need to decrease the voxel size by 1/3, and use
3x3x3=27 times as many voxels as those more-than-8-
billion above, to actually obtain 2048-cubed full-color
resolution, in a half-meter overall cube.
So, let us consider a simpler way. Some 2D displays
(Sony "Trinitron", mostly) used stripes of phosphor, not
individual phosphor dots. Instead of 1 full-color pixel
being made from 3 different-colored phosphor dots, 1
full-color pixel is produced when the horizontally-
scanning electron beam crosses 3 adjacent different-
colored vertical stripes. So, the equivalent for a 3D
display would start by using thin "plates" of frequency-
summing crystal. Each plate could be 512 millimeters
square, and 1/12mm thick, and there would be
2048x3=6144 plates in the full-color stack, half-a-meter
high.
Now we get to talk about the lasers. We want at least 4
and perhaps 6 of them; it depends on the exact
properties of the chosen frequency-summing crystals in
the stack just described above. Suppose that one laser
outputs in the infrared at 710 nanometers; if all three
types of frequency-summing crystals can use that as a
"base" wavelength, then we need 3 more infrared lasers,
such that one crystals adds one wavelength with base-of-
710 to produce 635 nanometers (red), another crystal
adds the base-of-710 to the second wavelength to
produce 532 nanometers (green), and the third crystal
adds the base-of-710 to the third wavelength to produce
445 nanometers (blue).
If the crystals add all-different-wavelengths, then we will
need 6 different infrared lasers, two-at-a-time, for
producing each color of light.
Perhaps you can now see where this Idea is headed.
Since infrared light is invisible, each laser beam can
INDIVIDUALLY be invisibly passed through any part of the
3D crystal-stack with no effect. But if two beams
intersect at an appropriate frequency-summing crystal
plate, then that SPOT of the plate, where the beams
intersect, will start absorbing and adding those photons,
and glow with one color of visible light. Nowhere else
will glow except that single monochrome voxel.
(Note this means you can't illuminate the whole crystal
with, say 710-nanometer infrared light, and pass any
other infrared laser through it, because you will get a
visible line of light as the laser beam is summed with the
background light, in its whole path through the crystal.)
Adjacent spots, in the neighboring crystal layers, can be
illuminated by other pairs of lasers, to get a full-color
voxel. And since the intensities of laser beams can be
adjusted, so can we have different intensities of the
different colors of the full-color voxel (allowing the same
full-spectrum illusion as ordinary 2D color-monitor
systems).
The 4 or 5 or 6 laser beams all need to be fully steerable,
so that any spot in the overall crystal cube can be
excited into glowing by absorbing light from an
appropriate pair of infrared laser beams. You can now
construct a true 3D image of glowing voxels. And since
the glow stops as soon as the beams stop intersecting,
you can also do full-motion video, provided the lasers
can scan the whole crystal cube fast enough. (Or use
even more lasers, and dedicate groups of them to
different portions of the crystal block.)
The final factor to take into account is "refraction". As
light passes through different substances at an angle, its
path gets bent. We will need full information about to
what degree these layers of frequency-summing crystals
affect the path of the infrared laser light, as they scan
through the crystal block at different angles. Signficant
computer power is likely needed, to ensure that, at each
voxel-location that we want to cause to glow, we actually
get laser beams intersecting at that location.
(This effect could possibly be minimized by the
appropriate selection of materials, but just in case we
can't get 3 different frequency-summing crystals that all
have exactly the same index of refraction for different
frequencies of infrared light --the ideal case-- we need
to be prepared to computationally compensate for
different refraction indexes.)
========================
Added March 13, 2013
========================
In the main text above I neglected to mention that the
lasers probably should be located under the crystal cube.
In theory this means the image created inside the cube
would be visible from all sides, and from above the cube.
And since writing the main text, it has occurred to me
that the index-of-refraction problem could be minimized
with one simple and one not-so-simple change.
First, while a stack of crystal plates was described, it is
not essential that that stack be oriented like a typical
stack of pancakes. Four faces of the crystal cube will be
associated with the edges of the crystal plates. One of
those faces could be oriented downward. Now consider
this ASCII sketch:
_________
o
|
|
|
|
o________
The sketch represents the mouths of two laser-aimers
located at each end of the edge of one crystal plate
(turned sideways, with body of plate at right). These
two lasers would create beams that are no wider than
that plate (about 1/12 mm, per the main text), and they
are directed into that plate from that edge.
The aimers, of course, direct the beams into the edge of
plate at a range of angles, such that with two aimers,
the two beams can be caused to intersect anywhere in
that plate.
This pair of lasers/aimers is dedicated to JUST this
single plate in the stack. That would completely
eliminate any index-of-refraction problem with respect
to aiming a laser across multiple plates with different
refraction indexes. So, only at this one place do we
have to worry about how much the beams are refracted,
as they first enter this plate.
With 6144 plates, we would like for there to be 6144
pairs of lasers, each pair associated with just one plate
in the overall stack. That's the not-so-simple thing, of
course. Each laser needs an aimer, see?
============
Added Sept 7, 2015
============
In the annotations to this Idea is mention of the Law of
Conservation of Momentum, and how it could cause the photons
created inside this display to be visible in only one direction,
relative to the display. I'm writing this to suggest a fix for that
problem.
The fix begins by changing the construction of the display to
include phosphors that are transparent to visible light (if any
such thing exists). The different types of frequency-adding
crystals can be changed to a single type. The output of the new
crystals will be UV light. The phosphors will not be transparent
to UV; they will absorb the UV, and emit regular light (different
phosphors for red, green, and blue). The phosphors will be
located inside the crystal at places specifically intended to
receive monodirectional photons generated by nearby spots of
the frequency-adding crystal. The main fact here is that
phosphors radiate in all directions, thus solving the problem
specified.
However, a new problem arises, in that two beams of infrared
light-photons cannot be added to produce UV photons (two
infrared photons simply don't have enough energy for their sum
to equal UV energy). At least one of the lasers, interacting at
some specific location inside a frequency-adding crystal, will
have to be a visible-light laser.
So, this means the lasers can still be located at the bottom of
the display, but the top of the display must be covered with a
light-absorbing material, and viewers won't be allowed to see
the images generated inside the display from above the display
(can't risk harming their eyes with laser light).
Anyway, since the overall substance of the display is
transparent, beams of light passing through it should be
invisible (nothing in there would scatter the light toward the
viewers, see?). It simply comes up from the bottom of the
display and gets absorbed either by the frequency-adding
crystal, or by the material at the top of the display.