The Laser

Introduction:

               The purpose of this lab is to understand how the laser works by using Modern Physics, ActivPhysics Online. The general ideas of laser is contributed by three interaction processes between an atom and electromagnetic waves, as well as the energy carried by the photons. The energy difference between the ground state and the excited sate has to be considered, whether the gound state has higher energy or the excited state has higher energy will result in different interaction process between atoms and photons.
               The first interaction process is Aborption, which is the case when the atoms are in their ground states. Therefore, when the photons are inciden to those atoms, the energy carried by the photon will be absorbed by the atoms hence being excited to the higher energy level.
               The second interaction process is called Spontaneous emission, which basically interprets the oppocite concept on the transferring energy to the case of Aborption. In this case, all atoms are inicially in their excited states. Therefore, since the atoms carry higher energy than the ground states, the difference in energy would then emit photons in ramdon directions. Since the photons are emitted in random direction, it interprets that each photon is independent in this case, and it also shows that the emitted light in this process is incoherent.Spontaneous emission alwasy follow the process of Absorption, hence those emitted photons have the same frequency as the one originally absorbed.
               The last interaction process is the Stimulated emission. In this process, the photons are incident to the atoms in the excited states, and the photons are also emitted from the excited states at the same time due to the energy difference between the inicial excited level and the ground level. However, one of the major differences in this case is that the photons are not emitted in random direction. Instead, the photons are emitted and perfectly matched to the incident phtons, with same frequency, direction, phase, and polarization. Therefore, the emitted light in this process in coherent. Basically speaking, the incident photons are jointed with the emitted photons hence creating a amplified radiation, also known as the light amplification.
               If the three basics interaction processes are going to be analyzed further, the concept of pumping has also be considered. Here, the Maxwell-Boltzmann distribution would be discussed. Now the rario of energy for the ground state and the excited state is going to be analyzed by using the Maxwell-Boltzmann distribution. The ration for this two states is described by using the following equation:

Here, the Ni is denoted for the numbers of atom for the excited state, and the N is denoted for the numbers of atom for the ground state. After arranging the equation and calculating the ratio, the result shows that the fraction of atoms above a ground sate is extremely small. In other words, the rate at which energy is absorbed by the ground state atoms is far more than the rate at which energy is emitted by the excited atoms. However, as being illustrated earlier, the Stimulated emission happens only when the atoms are inicially in the excited states, hence in this case, the rate at which energy is emitted by the excited atoms should be increased. It also means that the numbers of atoms in higher-energy state should be increated to that it exceeds the numbers of atoms in lower-energy state. This situation when the rate of energy radiation by stimulating emission exceeds the rate of absorption is called the population inversion.

               Since the spontaneous emission always happens when the atoms are in the excited level, the energy difference will cause the emission happen and make the atoms go to the ground state. However, the basics polulation inversion is to increase the number of atoms in excited state hence having more energy. In order to increase the energy and since the photons are the result of stimulated emission, the emitted light in this process is coherent as mentioned earlier, hence the resulting is much more coherent than the original sources. 

Now we want to verify the concept with the Laser simulation provided by the ActivPhysics.

figure 1.-Absorption

 figure 2.-Spontaneous Emission

 figure 3.- Stimulated Emission

 figure 4.-Laser

figure 5.-Laser

Conclusion:

For the process of Absorption, when the photons are incident to the atoms which are inicitally at ground state and excite then the higher-energy level. From figure 1., it shows that there are atoms being excited by the incident photons. The total input of the photons are six, one photon leaves without exciting any ground-level atom, and two atoms are about to exite atoms or leave without exciting atoms. Therefore, 3 excited atoms plus 2 incident photons plus 1 left photon equal to the total number of input photons. This is also proven by the process of Spontaneous emission, which instead of atoms receiving energy from the photons, those atoms emit energy and go to the ground level. In figure 2., the number for the atoms go to the ground state is 13, and it equals to the number of the photons output 9, plus the numbers of just emitted light 4. In figure 2., it also shows that the emitted lights go random directions. For the Stimulated Emission, in figure 3., the numbers of atom which are left in the excited state is 9, and the numbers for photons output is 2. It equals to the numbers of atoms which go to the ground state. In this process, even the light is emitted, the incident photons re-excite the atoms at the same time. Furthermore, figure 3. also shows that the light goes to the same direction. It happens becuase when the light emitted from the excited level, it is re-excited by the incident phtons at the same time, hence resulting in this coherent emitted light. From the three figures discussed above, it also shows that the only case there is no incident photons is the spontaneous emission, hence it is also the only case which atoms acutally go from higher-energy level to lower-energy level. For the concept of puming, how the photons are incident to the atoms are determined by the number of pumping number. In order to have incident photons to re-excite the atoms resuled from the emitted light, the number of incidents photons is much more when the pumping number is big than when the pummping number is small. It also shows in the figure 4. and figure 5. that larger pumping number is able to keep the number of atoms in excited state. However, the lower pumping number fails to keep the number of atoms in excited state. Hence, with larger pumping number, it would alow the laser to have larger number of atoms in the excited state than in the ground state, thus the laser can have higher energy.

Color and Spectra

Introduction:

The purpose of this experiment is to find the wavelengh of different color for the wavelength spectrum by applying the concept of constructive interference. The idea of the constructive interference is used because when the light source entered the slits, the distance through the upper slits and the distance through the lower slits are the same. Therefore, the wave fronts spread out from the upper slits and the lower slits are in phase. In this case, the upper slits and the lower slits are coherent. Since the width of the slits is much smaller than the distance from the light source to the slits, the equation used for this experiment is:

y_m=Rmλ/d

,so the equation for wavelength is:

λ= y_md/R

here λ is the wavelengh of the color on the spectruem, y_m is the width of the slit, d is the distance from the center to the first dark fridge, and R is the distance between the light source and the slits(linear diffraction grating ). The other method, witch actually has the same concept as the above one can also be applied to get the result of the wavelength. The two similar triangles are used to get the wavelength λ,where

λ/d=D/√(L²+D²)

after the equation is rearrange, the new equation for wavelengh is obtained:

λ= Dxd /√(L²+D²)

here, d is the width of the slits, L is the distace from the light soure to the slits(linear diffraction grating ), D is the distance from the central mexima to the first minima. As a result, it proves that the concept of constructive interference was applied.

The basic appartus for this experiment

Data and Calculations:

Distance from the light source to the grating : 1m			Wavelength Spectrum (nm)
			Violet	Blue	Green	Yellow	Red
			415	472.5	532.5	580	685
White	---------------		Violet	Blue	Green	Yellow	Red
500 lines for 1mm àym=2×10-6			Range(cm)
			18~22.5	22.5~24.2	24.2~27.5	27.5~30	30~38.5
If the wavelength has large difference: λ=mλ+λ0			Distance from light source to the middle of the range(cm)
			20.25	23.35	25.85	28.75	34.25
			Equation λ = dy/L
			Wavelength(nm)
			405	467	517	575	685

 Obtaining Wavelengh Uncertainty by plotting and get the slope:



After Uncertainty Equation was applied:

Wavelength(nm)
415	472.5	532.5	580	685
Wavelength with uncertainty(nm) Slope = 1.0334x
418.5	482.5	534	577	707

In this figure, it shows us that the wavelenght spectrum is formed when we view the light source through the linear diffraction grating

 Now the color of the light source was changed, the hydrogen tube and one unknown tube would be used as the light source and the different wavelengh would also be calculated. The idea of getting different color specturm is that different color has its particular path hence having a particular wavelength. The wavelength for that colar will superimpose in a constructive manner and thus different color would appear.Each path of each color would reinforce itself and also cancel other color's wavelengh at its position. Since the distance from the upper slits is still equal to the distance from the lower slits, it shows that the wave fronts are inphase as discussed earlier.

Data and Calculations:

Hydrogen Tube
Color	Violet	Green	Yellow		Red
Distance from the grating to the light source(cm)	19.9	22.1	27		31.6
Wavelength (nm)	398	442	540		632
	Unknown Gas #4 Tube
Color		Violet		Green	Red
Distance from the grating to the light source(cm)		23.4		27.2	33
Wavelength (nm)		468		544	600
	Actual unknown Gas-Neon
Color	Pink	Blue		Green	Red
Actual Wavelength (nm)	410	434		486	656

Conclusion and Discussion :

Based on the experimental results obtined from the white light, the final wavelenght with applying the uncertainty euation would be within 10 (nm) if the inital experimental result is not close to the actual value enough. Therefore, the results with uncertainty shows that with the concept of constructive interference and the concept of spectrumeter, the results satisfy that when light passes through the linear diffraction grating, the particle emitted by the light reaches its excited level and drops back to the ground level. When it goes back to its ground level, with the energy losing, or the energy being emitted to reach the excited level, it results in having lower energy and hence longer wavelength. Therefore, conclusively, the visible portion of the light (the range for the wavelength of those visible lights ) appears and forms different colors. It is also known as the specturm.  It can also be denoted as the absorption spectrum, which a series of dark lines corresponding to differen length of the wavelengths were constructed with the concept of interference.