Physics 200 Class #1 Outline - DePaul University



Physics 200 Class #19 Notes November 9, 2005

• Review of Class #18 Notes

• “Laser Physics”

• Holography

• Course Evaluations

• Final Exam Reminder: Wednesday, November 16th, regular class time

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Review of deBroglie theory of electron orbitals

[pic]

This is an important conceptual point for two reasons:

1. electrons fit into concepts of quantum mechanics: angular momentum is quantized

mvr = n h/2π, when you see the integer n (n=0,1,2,...) you're dealing with quantum mechanics.

2. electrons behave like waves.

This can be extended to other particles, and all objects really! We all are both particles and waves.

You can get photons to interfere and diffract and ...

So too you can get electrons to interfere and diffract and ... [pic]

And neutrons...

[pic]

And ...

Today:

We will get to a discussion of holography. Since this is most easily done with lasers, we will start with a short discussion of what lasers are and how they work.

Light Amplification by Stimulated Emission of Radiation

Properties

1. High degree of Spatial Coherence. All of the waves are exactly in phase with one another. We can observe an interference pattern by placing two slits in the laser beam.

2. The light is very nearly monochromatic (single color). Temporal coherence

3. Very small divergence. All of the light is essentially traveling in the same direction.

4. All waves have the same polarization

5. The beam is extremely intense.

How do we achieve this?

I Stimulated Emission (Einstein 1917)

Three types of transition:

1. Absorption - atom absorbs a photon and gains energy (it's excited) (electron moves to a higher level)

2. Spontaneous emission - electron moves to a lower level and a photon is emitted, all by itself

3. Stimulated Emission (induced emission) - a photon (photon A) goes by an excited atom/molecule with the same energy as the atom would emit if it de-excited. The atom/molecule thinks this is a great idea and de-excites, emitting a photon (photon B) that has the same energy as the one that gave it the good idea (photon A).

[pic]

h ν is what we write as hf. The Greek letter nu (ν) is sometimes used for frequency.

II We need a metastable state

IIa.

Let's first look at the simple picture of a hydrogen atom with three possible states:

[pic]

using En = [pic]

A photon can be absorbed and the electron can go from state 1 to state 3. The energy is change is:

E1 - E3 ’ −13.6 − (−1.51) ’ −13.6 + 1.51 ’ −12.1 eV (the negative here means a photon is absorbed)

The atom ends up more excited than it started.

The electron can transition from state 3 to state 2 and a photon is emitted

E3 - E2 ’ −1.51 − (−3.4) ’ −1.51 + 3.4 ’ 1.9 eV

The electron can transition from state 2 to state 1 and a photon is emitted

E2 - E1 ’ −3.4 − (−13.6) ’ −3.4 + 13.6 ’ 10.2 eV

This is a simple picture. Only hydrogen follows the easy En = [pic] relation. The diagram is reasonable though. Photons can be absorbed and bring electrons up several levels. When they deexcite they may emit several photons along the way.

Fluorescence is a good example of a three state system. Many materials absorb UV light and when they deexcite they may emit visible light as part of the deexcitation. This is a great way to see what minerals are composed of. See the example in class.

IIb. Metastable states:

Sometimes electrons don't deexcite so quickly. There may be a long lived level - a "metastable" state. One common example of this is glow in the dark stuff. Light is absorbed and is slowly released from a material. See the example in class.

This property of some materials is useful for making lasers work. By staying in an excited state for a while, we can excite many many atoms/molecules of a material and have them ready for spontaneous emission. The electrons don't have to stay in the excited states of the materials for as long as they do in glow in the dark stickers though. The times in the diagram below are: electron falls from the ordinary excited state in 1x10-8 seconds (10 nanoseconds) and then stays in the metastable excited state for 10-3 seconds (1 millisecond, or 10,000 times longer than the ordinary state).

[pic]

III Population Inversion

We need more atoms in the upper state than in the lower state. This can be accomplished by optical pumping or by collisions.

Example: Three Level Laser

[pic]

[pic]

Practical Lasers

Ruby Laser (pulsed)

[pic]

Four Level Laser (can be continuous)

[pic]

Helium-Neon Laser

[pic]

IV Parallel light

Stimulated emission continues in the same direction as the first photon that started it. That could be in any direction.

In a typical laser, the material that emits the light is between two mirrors. Only the light that travels parallel with the laser tube hits the mirrors head on (perpendicular). It is this light which will bounce back and forth several times causing alot of stimulated emission in that direction.

The trick to getting the light out is to have a mirror on one end that allows just a little bit of light out. If the light that gets out of the laser is bright you can imagine that the light inside the laser is very, very intense.

[pic]

"Because of bouncing back between mirrored ends of a laser cavity, those paths which sustain amplification must pass between the mirrors many times and be very nearly perpendicular to the mirrors. As a result, laser beams are very narrow and do not spread very much."

Now we talk about holograms - which was postponed from the online notes lecture 17

Class demonstration of Holograms

A short lecture on holography (HyperPhysics)

A good web site for review and for a description of holography (some figures from there):



We will spend some time exploring this site.

Another good site is (some figures from there):

holo/book/book.html

Most photographs record just the intensity of the light focused on the film, and the light is focused onto the film to form an image on the film itself.

Holographs instead record the intensity of the light, and the phase of the light. This is the complete information about the light hitting the film. (The word holograph comes from the Greek word holo, meaning whole, so this is a whole picture.) How this works will be discussed, after a brief introduction to how we see 3 dimensionally.

I. Stereoscopic vision - seeing the world with 2 eyes.

A big part of our depth perception is due to looking at things with 2 eyes. Our brains are aware of the relative positions of things in our left and right eye and creates a 3 dimensional interpretation of the world. Look at a scene that has both close and far away things in it. Close one eye and look at the relative position of the objects. Switch eyes and see how the position changes. We just see two different two dimensional images from slightly different angles!

To see how our depth perception is due to stereoscopic vision, close one eye. Hold a pen in one hand. Stretch out your arms in front of you and try to touch the tip of the pen with the tip of your finger (use a finger on the hand not holding the pen, of course). Now try it with both eyes open.

If we can make something appear slightly different from two different angles, we'll see it as 3 dimensional.

II. Transmission holograms

Simple model. For simplicity, let's look at small objects. Then we can extrapolate to larger objects.

[pic]

[pic]

Like standing waves with two point sources. The places in the film plate where there is constructive interference will be brighter, and the film will be more exposed there. When you develop the film the exposed stuff will have a different index of refraction and thus will reflect light. Put a laser where the original "reference" laser was and the light reflects off the pattern in the film and looks like it is coming from the object. Like the object you took a picture of is still there and light is reflecting off of the object itself!

In order to have stable interference fringes - ones that don't move around during the time it takes to expose the film - you need a light source with a very stable frequency. It should also be bright. Lasers fit the bill. We'll use a red HeNe (helium-neon) laser.

[pic]

The very fine pattern which the emulsion assumes is a recording of the wavefronts as they interfere in the emulsion. It is definitely not a direct point to point recording of the image of the object but rather a recording of the interference between the coherent light that hit the object and that which did not.

The interference fringes can be very close together (the wavelength of red light is about 700 nm), so you need a very special high quality film to be able to reproduce this. Regular film may be able to record up to 90 lines per millimeter (Kodak Pan X film) while film designed for holography can resolve up to 3000 lines per millimeter! (AGFA 8E75).

To see a transmission hologram you typically need a laser source put near the original light source.

III Reflection Holograms

[pic]

[pic]

The light from the laser hits the object and reflects back to the film. It is the interaction of the "reference beam" from the laser and the reflected beam from the object that causes interference patterns in the film. These expose the film, and when the film is processed produce little points from which light is scattered. That is, the fringes become little reflectors. Now if light is put where the original laser was, light will bounce off the fringes in the film and it will look like light is coming from the original object. Turn the hologram around and what happens? Try that with your hologram that you make today.

To see a reflection hologram you can use a white light source. This is much easier than seeing a transmission hologram. Your hologram will look red even though you shine white light at it. Why? (Think of thin film interference. The fringes act like thin film interfaces.)

IV Interesting properties

Object reconstructs to its original size, regardless of the size of the plate:

In most cases, the object will reconstruct its original size, regardless of the size of the plate, and the same distance from the film that it was when the hologram was made. The reference reconstruction beam will be focused by the complex hologram lens so that the front of the object appears closer, the back further away, and all the points in between are filled in accordingly. This might sound like a point to point correspondence very much like photography. However, there is a very special difference which makes holograms so wonderful.

[pic]

Break the plate and each piece retains the entire image, just get a restriction of the angle.

I am sure that you have heard that if a hologram is broken or cut up, each small portion contains information about the whole object. This is because the light bouncing from each point on the object is not focused to a point on the film, But is allowed to spread out through space between the object and the film, thus covering a large portion of the film and interfering with the reference beam throughout that whole portion of the film as if each point were a spray of light each with a certain angle of divergence. So that every point is coded into a large area of the hologram. It might be easier to understand with this simple example. Let's say we have a very fine 11 x 14" hologram of a George Washington bust, complete with hat and plume. Two museums want this hologram (there is no other and the bust was destroyed in an earthquake) after much ado they decide to cut the hologram horizontally and exactly through the middle. Each museum then has a representation of the whole bust, unchanged in size but from different angles. It will be easier to understand this if you think of the hologram as a window into a room containing the bust. If the window is made smaller, the object does not shrink. We merely have a narrower angle of view of the object. You would be able to see, for example, the plume, even from the bottom portion of the hologram; however, you may not be able to see the very tiptop of the plume from the reconstructed angle of view of the lower part. This is because the light from that point was not able to spread enough to reach and interfere with the reference beam in the lower extremities of the plate. The holder of the upper portion would not get an especially good look under Washington's chin. One simple remedy would have been to move the object back from the plate and thus give the light more space in which to spread. However, as the object is placed farther back from the film it recedes from your personal three dimensional world.

Hologram size scales with the wavelength

The holographic image scales with the wavelength. This initially caused great excitement because one could imagine making holographic images with x-rays and viewing them with visible light, getting three-dimensional views of things on the scale of molecules. X-ray holograms have yet to be made, and there are practical difficulties with the scaling, but there is still the possibility that this feature of holograms will prove to be of great benefit.

Hologram Scaling with Wavelength

|[pic] |One of the unique properties of holograms is that the size of the viewed image scales |

| |with the wavelength of the viewing light. At left is a view of a hologram of the end |

|[pic] |of a pipe formed with light from a mercury vapor tube. The mercury source has three |

|Experimenters:Bob Gobron, Kiyra Holt, David |prominent wavelengths and you can see three distinct images of different size. |

|Patton |Measuring the relative size of the images compared to the blue image (435.8 nm) gives |

| |1.26 for the green (546.1 nm) and 1.36 for the yellow-orange image (576.9 and 579.1 |

| |nm). The scaling of the wavelengths relative to the blue wavelength gives 1.25 for the|

| |green and an average of 1.33 for the yellow-orange lines, so the image sizes appear to|

| |scale with the wavelength. |

| |[pic] |

| |Mercury spectrum |

| |The lower image shows the same hologram viewed with the mercury source filtered by an |

| |interference filter which transmits only the mercury green line. |

[pic]

The direct viewing of a hologram with mercury light illustrates a unique feature of the blue vision of the human eye compared to that for red and green. Because of distinctions with the blue cones of the eye and a bit of chromatic aberration in the eye, the blue image will look less distinct than the green and orange image. The effect must be viewed directly; the way the image is made in this illustration mixes in enough other colors to remove the effect.

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