Dumb Question #215

[Tony]

Sorry but sometimes things pop in my head....

So say you have a high DF hologram (say 90%) narrow band.
You blast it with a light source that has infinite intensity.
You start low and turn the knob it gets brighter and brighter
Is there a point where the hologram saturates? In other words is there a point where it no longer able to defract the incoming light?

Thanks

[BobH]

At some point you'll melt the medium. Before that, I expect it to mush into a diffuser. Try it with an absorption hologram and a few Watts of raw laser beam. A metal shim hologram will last longer.

[Dinesh]

Well, this question has a lot of overtones to it!

From a practical point of view, Bob's right that on both counts: at some point you'll melt the medium, however, long before that, you'll craze the emulsion and destroy the fringe integrity making a diffuser.

From a theoretical point of view, there's an inherent inconsistency in the description. The efficiency is:
eta = I/I_0
where I is the light diffracted by the hologram. However, if I_0 were infinity, then strictly speaking, eta is undefined. From an intuitive perspective (shop floor arithmetic?) anything divided by infinity would be zero, so the efficiency is zero, not 90%. Strange things happen when you do arithmetic with infinity or zero!

Another problem is that you'll get non-linear responses. The basic theory of holography (or any optical process at low laser powers) is that the response of the medium is linear. This means that the bound electrons oscillate with a frequency very similar to the driving frequency, ie the incoming optical field, and so the light is propagated with the incoming frequency. This is why light goes through a transparent medium without changing colour. There's a reason why the beam propagates forwards also, but that's another story. When the laser power gets very high, there are non-linear terms in the frequency response of the bound electrons. An incoming optical field with a frequency w generates, not only w, but also w squared, w cubed etc. These non-linear terms will cause 4 wave mixing with the fringes already present. In fact, I suspect that as the incoming optical field goes towards infinity, the number of non-linear terms will increase and causing N wave mixing. Another non-linear effect is that you may cause amplification, which will generate a laser like field (without an oscillator - mirrors - you won't sustain laser action, but the non-linear terms will generate short, sharp coherent radiation).

At very high energies, the dispersion equation also becomes non-linear. This means that the refractive index becomes non-linear. Effectively, you'll create a birefringent material (maybe trirefringent depending on the molecular structure of the medium). This will cause polarisation effects.

There are probably other effects (intermolecular collisions due to excessive kinetic energies?), but these are all that occur to me off the bat.

You see, not a dumb question at all!

[Johnfp]

I think Tony is asking when will the hologram not refract light anymore. I would simply ask the same question but instead of a hologram use a lens. Now, of course in negating the physical effects of the medium itself, the answer to me is, "There is no point at which the hologram will not diffract the light anymore, practically speaking anymore then a lens would saturate."

But as Bob and Dinesh points out:
Infinite intensity, phycial properties, etc...does change things.

[Dinesh]

I think Tony is asking when will the hologram not refract light anymore.

Holograms don't refract light, they diffract it. the two phenomena are very different, but, in holography, sometimes a refractive effect is used to model the diffractive effect. Such is the case when the hologram is modeled as a series of tiny lenses. Sometimes holograms are modeled as zone plates. This seems to rely on refraction because zone plates are transparent, but the zone plate works because of Fresnel diffraction.

Now, of course in negating the physical effects of the medium itself, the answer to me is, "There is no point at which the hologram will not diffract the light anymore, practically speaking anymore then a lens would saturate."

The problem is that you can't negate the physical effects of the medium, because the physical effects of the medium are what transmit the light in the first place! Without the physical effects, light would not transmit. Thus, it's the physical medium that determines the index - through the dispersion equations - which in turn determines Snell's Law. In all media, there is a band of frequencies where there is no refraction but just absorption, this is called the anomalous region where the refractive index goes complex. In silver chloride, for example, the anomalous region is roughly in the far IR

The way light transmits inside a transparent medium is that the electric field of the light hits a molecule of the medium. This E field drives the molecule into a vibration mode. The vibrating molecule then transmits a light wave of it's own. This "new" light wave, from the vibrating molecule, interferes constructively with the original light wave but only in the forward direction (in the backwards and sideways directions there is destructive interference and so no light is transmitted backwards or sideways). Under "normal" conditions, the medium responds in a linear manner. That is, the molecules vibrate at the frequency of the incoming light. As the intensity of the light goes up, the molecules are driven much more intensely and so go into a nonlinear stage, this means that the molecules now transmit not only the incoming light but also multiples of the incoming light. The molecules respond as the square of the light field. The substance now exhibits various non-linear effects such as the Kerr effect and the Cotton Mouton effect. These effects also create birefringence and so you now have polarisation effects. In terms of refraction, Snell's Law may no longer apply. In some cases, you may have negative refraction occurring ( http://en.wikipedia.org/wiki/Negative_refraction ). As the laser intensity grows, more and more heat is imparted to the medium. This heat causes transfer of kinetic energy and so causes inter-molecular collisions. In a complex molecule such as gelatin, these inter-molecular collisions will cause new energy levels to appear, also altering the index. On top of all this, you'll get second harmonic generation which will create four wave mixing inside the medium, and, as the intensity goes towards infinity, third harmonic generation to create 8 wave mixing. The whole characteristics of both refraction and diffraction change and the nice tidy interplay of sinusoidal fringes will get an awful lot more complex.

Think of a small paper boat on a lake. If you throw stones near the boat you create waves. These waves will rock the boat at roughly the same frequency as the waves. However, if you throw larger and larger stones at higher frequencies, the boat no longer rocks in response the the wave frequency, but in a much more apparently chaotic way. As the boat rocks more and more wildly, it creates it's own waves, which it then reacts to and creates a more frenzied rocking. Now the boat has gone into second harmonic generation.

Of course, heating effects may (probably will!) destroy the medium long before these non-linear effects start to take place

[BobH]

So after all that physics, the answer still is: "you'll cook the jello".

[Johnfp]

Wow, all this time I thought the delta index of refraction between the air and gelatin was what made a DCG hologram. This I thought was refraction. Now an unbleached silver hologram I would imagine is diffraction. Bleach that same hologram and I thought is was refraction again.

But the entire point I believe of the original question has nothing to do with the physical medium....Tony??? And I guess this is where interpretation comes into play.

So say you have a high DF hologram (say 90%) narrow band.
You blast it with a light source that has infinite intensity.
You start low and turn the knob it gets brighter and brighter
Is there a point where the hologram saturates? In other words is there a point where it no longer able to defract the incoming light?

There is no mention of DCG or any medium for that matter.
We are speaking of infinite intensity, which is impossible.
The question is "is there a point where it no longer able to diffract the incoming light."

This is a question, as I so often ponder, of the nature of light and a diffractive or refractive optic. I belive inbedded in Dinesh's third paragraph is the answer somewhere.


So I ask the same question, which I hope Dinesh will explain in nice simple thoughts, but instead of a hologram, let's use a nice quartz lens. Is there a point where the lens saturates? That is, is there a point where the lens no longer is able to refract the incoming light? Is there a point where a slit can no longer diffract the light?

[Dinesh]

So after all that physics, the answer still is: "you'll cook the jello".

Ahh, the eternal struggle between the theoreticist and the "practical" types!!

Of course, you'll cook the jello, assuming it is jello and we're talking STP! But, what if it's Lithium Niobate? What if it's a magneto-optic film such as MnBi? The actual photosensitive wasn't mentioned in the problem.

The problem, as I read it, isn't what would happen to a real piece of dcg or silver halide as you blasted it with greater and greater power, but, in a theoretical sense, what material changes would occur in any material as you blasted it with more and more laser power from a theoretical point of view.

Now I know that a vast majority of you holographers out there really don't care a whit about theory, simply the practicality of zapping some film in an appropriate manner (beam ratio, polarisation, coherence considerations etc). However, this does beg the question: How do you know? Say you have 3 microwatts hitting your plate at a ratio of 8.34:1, what exposure? Experience tells you that it should be so-and-so, but why? Books and papers tell you it should be so-and-so (ironically, those books and paper are based on the very theory that seems so vilified!), but how do they know? The answer is usually: "because it works!", or "Experience!". So, if you do nothing except that which works based on past experience of doing the same thing over and over again, what price progress? Why, theory! So the cycle renews: Theory suggests an algorithm, the algorithm is followed with no understanding of the theory, the algorithm works and so becomes a de facto methodology. Any mention of the underlying theory is then disregarded, at best, or vilified, at worst. Of course if an "expert" such as an academic or "industry leader" or even a (Gawd help us!) a "PhD" spoke forth on matters theoretical, the "Practical" person promptly cries "Hallelujah!, The gods have spoken!" If Joe Schmo were to delivery theory, it appears tantamount to blasphemy!

No wonder science is seen as a religion, it's correctness based on a belief system and faith dispensed by The High Priests of PhD's and Professors! There's nothing wrong with being a practical holographer, but I do feel that theory is often sneered at, despite the fact that the theory is the underlying reason behind the practical methods. The two must go hand in hand. Ignore one and you stand in a position of the Zen Finger to the Moon

By the way, Bob, I hope this doesn't sound angry in any way. These are interesting questions and I believe there should be debate about them. I suppose it's obvious to all that I have a bee in my bonnet about Pundits and Professors, because I've heard the most atrocious commentary from them which is simply believed with no debate or dissenting voice, simply because they are the Professors and Pundits and are therefore believed. I think that debate is a necessary means of dispensing knowledge and getting different opinions.

[Dinesh]

Wow, all this time I thought the delta index of refraction between the air and gelatin was what made a DCG hologram. This I thought was refraction. Now an unbleached silver hologram I would imagine is diffraction. Bleach that same hologram and I thought is was refraction again

No. The index modulation forms a diffractive structure, from which diffraction occurs. A diffractive structure is a variation of a material property on the order of a few wavelengths. Goodman in "Introduction to Fourier Optics", makes the statement that all propagation of light is a form of diffraction, but I think that's too generalised. Anyway, in holography, this variation is either a variation of optical density - amplitude modulation - or a variation of physical density - phase modulation. In an unbleached hologram, the variation is a variation of dark lines and so it's an amplitude modulated diffractive structure. When you bleach the hologram, you're effectively converting the variation of darkness into a variation of hardness. By an equation known as the Kramer Konig equation, a variation of hardness can be seen as a variation in refractive index, hence bleaching converts an amplitude modulated hologram into a phase modulated hologram. In dcg, you go directly into a phase modulated hologram because the actinic reaction makes the exposed parts harder and so, by Kramers Kong, creates an index modulation.

This is a question, as I so often ponder, of the nature of light and a diffractive or refractive optic. I belive inbedded in Dinesh's third paragraph is the answer somewhere.


So I ask the same question, which I hope Dinesh will explain in nice simple thoughts, but instead of a hologram, let's use a nice quartz lens. Is there a point where the lens saturates? That is, is there a point where the lens no longer is able to refract the incoming light? Is there a point where a slit can no longer diffract the light?

Jeez! You don't ask easy questions, do ya!
Ok, let's try start at the beginning. What is light? No one knows! Einstein, in his 70's, said that he'd spent his entire life trying to understand light and still didn't know! So, moving on to the next best question, how do the properties of light manifest themselves? This we can answer!

Firstly, light does not actually "saturate" in a medium. It's not like a liquid or like dissolving a solute in a solvent, where you can only put in so much and so saturate to the point where you can put no more in. The ability to refract or diffract does not depend on "how much light" there is in any medium.

We start with a form of energy we call the "electric field". This is not electric, in the sense of an electric circuit, but it is an energy field that gives (charged) material objects the propensity to move. Put an electron in an electric field and it'll move because the field has given it the energy to do so. This energy is usually called "potential energy" because it has the potential to cause motion, and is given the unit "volts". The greater is the difference in potential energy between two points, the faster will the material particle move. The important thing here is that the strength of the field is dependent on the potential difference between two points. A field of 10V/meter is stronger than one of 10V/kilometer. This E field also has direction; this means that the electron will move in a specific direction determined by the direction of the E field. Thus the E field can be represented by an arrow. The length of the arrow is given by the value of the field (so many volts/metre) and it's direction is given by the direction that a positive particle will move (this is the opposite direction to the direction an electron will move). So far, all we have is a mathematical structure - the E field - which can manifest itself by causing a real electron to move. If there is no electron, nothing at all, then the E field is a purely mathematical structure with no manifestation.

Now, let this E-field - this arrow - change it's value in a cyclical sense and also reverse it's direction. Let it start at zero, grow in a particular direction at a particular speed to a particular value, then shrink down to zero, then reverse direction, grow, shrink, reverse direction again and repeat. This is an oscillating E field: it grows, shrinks, reverses itself, grows, shrinks etc. This oscillating E field (along with an oscillating magnetic field) is known as electromagnetic radiation, in particular, light. For visible light, this sequence repeats about one hundred thousand billion times a second (10^14). Also, the amount of energy contained in this oscillating E field depends on the square of the strength of the field when at it's maximum - the amplitude. So, an oscillating field that went from zero to 100 V/meter, then reversed and went to -100 V/m, then the amount of energy contained in the field is dependent on 100 squared, or 10,000 J. For example, the amplitude of a 100mJ beam is about 150,000 V/m ~ 10^5 V/m

What causes such a thing to form in the first place? Well, one thing is the motion of a charged particle in the vicinity of other charged particles. If I have an electron near a bunch of other electrons or positively charged particles, and I shake the electron, I create an E field. If I jiggle the electron backwards and forwards (or side-to-side) then I create an oscillating E field. If I jiggle this electron fast enough, let's say one hundred thousand billion times a second, I create light. Now, remember I said that the electric field can only manifest itself by causing motion to a charged particle? So, now you have a chicken-and-egg situation. The oscillating E field from a light beam entering a collection of atoms, which have (negative) electrons surrounding a (positive) nucleus will cause the electrons to move. But, an oscillating electron surrounded by charged particles (the positive nucleus) will generate it's own oscillating E field. So, the light causes motion in the electrons and the moving electrons cause light. So, now you have the original light that caused the electron to move, and the new light caused by the moving electron. If the incoming E field from the light were to oscillate at one hundred thousand billion times a second, then the electron would also move at that rate and the new light would also have the same frequency and so the same colour. The new light thus can, and does, interfere with the original light causing constructive interference in the forward direction and destructive interference in all other directions. So, light propagates through the medium in this way: Light comes into a collection of atoms, the electrons in those atoms vibrate at the same rate and create new light, the new light interferes with the original light and causes another "new" light, but only in the forward direction, which then goes on to hit the next atom and the process continues atom to atom to atom. The electrons act like a vibrating spring fixed at the nucleus at one end and free to vibrate at the other.

I said that the electrons oscillate when hit by an oscillating E field. But, do they oscillate in phase? Does the motion of the electron to-and-fro follow the rise and fall of the E field? No! There is a phase lag between the motion of the electron and the incoming E field. This phase lag causes a retardation in the velocity of the wave going through the medium. The denser the substance, the greater the phase lag and the greater the retardation. So, when a wave goes from a substance of a particular density to one of another density there is a change in retardation and hence a change in the speed of the wave. This effect of light slowing down due to the phase lag of the oscillating electrons is known as refraction. When light along a broad front hits an interface at an angle, the leading edge that first hits the interface changes speed. But, the rest of the wavefront has not hit the interface yet. To maintain continuity, the part of the wavefront that has entered the medium and so is going slower than the rest of the wavefront must bend otherwise you'd destroy the wavefront. So, the light changes direction.

What happens when light hits an aperture? That is, when light hits a "hole" surrounded by matter? The hole transmits the light uninterrupted - it just goes through. However, the light that hits the edges of the hole, the edges of the aperture, causes the electrons in the substance of the aperture to oscillate. These oscillating electrons generate new light in many different directions. So, a plane wavefront hitting an aperture, will, on exiting the aperture, become a diverging wave. What happens if there's another aperture nearby? Then the diverging wave from the one aperture will interfere with the diverging light from the other aperture. This is diffraction. The exact form of the diffracted light, on exiting both apertures, will depend on the amount of divergence from each aperture. What happens if you have thousands of aperture, thousand of very narrow slits? Then each slit will cause incoming light to diverge, the diverging light from all these slits will interfere with light from all the other slits and you'll create a "new" form of light caused by the multiple interferences from all these slits. What happens if these "slits" are all of different shapes - some thin, some fat - curved in different directions. Then light hitting these slits will all recombine in a totally different form because of the numerous multiple interference effects from all these different slits. This is diffraction - the multiple interference effects from multiple slits all recombining due to multiple interference. Can I say: "I want this particular form of light to go into a structure of slits, and then I want that particular form of light to exit these slits caused by multiple interferences from all the slits?" Yes, holography! The "slits" are interference fringes - either fringes of light and dark or fringes of soft and hard.

In answer to Tony's question "what happens if slowly increase the laser power to infinity?", I mentioned that the E field of a 100mW beam is 10^5 V/m. What if the beam were much stronger, say 10^8 or 10^10 V/m? In this case, you're hitting the electrons awfully hard. The electrons are not only out of phase, but also, they're no longer moving in the sinusoidal form of the incoming light. The electrons cannot keep pace with a very strong, high amplitude oscillation. They try, but you're hitting the spring much too violently. The spring creates new harmonics - like an overdriven amp. These new harmonics are known as Second Harmonic Generation (SHG in the literature). As you slowly increase the laser power so the E field gets to 10^12 V/m, 10^15 V/m, 10^20 V/m, you're really hitting the electrons hard! The electron no longer moves at the same rate as the E field. The electron is now said to oscillate in a non-linear manner and you have non-linear effects. Because of various quantum rules, at really high E fields, you may create new energy states and you may create quasi stable states, a laser. The electrons may end up colliding with each other, causing possibly what are called phonon oscillations. When you start getting around 10^50 V/m, gawd alone knows what happens!

[Johnfp]

Brilliant. Very excellent reading and very comprehendible! Thank you for taking the time to explain it that way. Dang, that is some cool stuff.