The textbook used in this module is: Photonics and Laser: An Introduction by R.S. Quimby

Transcription

1 PH 2601: Introduction to Laser Final Examination 2010/2011 The textbook used in this module is: Photonics and Laser: An Introduction by R.S. Quimby By: Yonathan Priambada 1) A)Three elements of laser are: a. The mirrors to provide optical feedback b. The gain medium amplifies the laser light to the desired intensity c. Pumping mechanism supply energy to the system (Page 281) B) High temporal coherence implies long coherence time and long coherence length L C. Applications: holography, light source for high speed communication (page ). High spatial coherence applications: coupling into small cores of single mode fibers, high intensity laser to melt materials, enabling applications such as laser surgery, laser machining. (Page ) C) In three level laser system, the lower laser level is the ground state whereas in the four level laser system, the lower level is still an excited state, and in this level, the atoms decay quickly to the ground state (0). Hence, in four level system, the population inversion can be achieved by fewer number of atoms rose out of the ground state, and subsequently, smaller pump energy is needed. Thus it is easier to achieve lasing and amplification using four level laser system. (note: in population inversion, the upper and lower laser level is 1

2 used for the consideration; in three level laser system it will be 1 and 3 (refer to the image above) whereas in the four level laser system it would be 1 and 2. In three level laser system, the lower laser state is the ground state, which means eventually all the atoms will fall back on to it. Hence the population there is quite large, making population inversion harder to achieve as more atoms need to be pumped up to the excited state to offset the atoms on the ground level) (Page ) D) I) P=0.02W λ=532 nm / = 2.25x10^10 W m 2 ii) P=4x10^26 W r=7x10^8 m B=P/ (4 r 2 ) = 64.9 X10^7 W m 2 Laser light is much brighter than the light of the sun as laser light is highly coherent (spatial) and it is highly directional and thus its brightness is independent with respect to the beam diameter. On the other hand, the sun light, which is not as coherent (spatial), and hence its brightness is dependent on beam diameter, thus the farther it is from the source, the fainter the beam becomes. 2) A) As 2

3 As As well as using Einstein equation relating A and B coefficient (Eq 18 10), we can rewrite the expression for I as: As Hence we can rewrite the expression as Δ Taking the limit z 0, this becomes differential equation: z (Shown) Where is a function of and I is a function of t. Condition necessary to achieve optical amplification is the population inversion must be maintained (N 2 >N 1 ), this can be achieved by continuously pumping in energy into the laser system. 3

4 B) Assuming that is positive and independent of z. I 0 is the intensity at z=0, or in other words, the initial intensity (before the amplification). We are also assuming that the process will not go on indefinitely, as I(z) will reach the infinity value, which is not feasible in real life. (Page 339) C) As z, and assuming that the gain is small so that I<<I s we can rewrite the given expression into: Integrating this expression, we get And thus, the small signal gain can be expressed as (Page 357) 4

5 3) A) Mode frequencies can be expressed as =m(c/ (2nL)) Where m is the mode number, L is the cavity length, n is the refractive index of the medium and c is the speed of light in free space. For λ=632.8 nm, L=0.25 m and n=1, the mode spacing is C/ (2nL) = 6.00x10^8 Hz Mode number m is then m = / 6.00x10^8 = B) is the loss coefficient and is the gain coefficient. I A is the initial intensity. The minimum requirement for lasing is that I B >=I A 5

6 Taking the logarithm to solve for : 4) 90 0 w z z t y y A) I) First, we know that 2z w=mλ, where m is the mode number, and 2z w is the path difference travelled by the light through the etalon. z tn/cos ) (multiplied by n to find its optical path length) w= 2y sin( ) y= t tan( ) 6

7 we can relate with through the law of the refraction: n=sin( )/sin( ), where n is the relative refractive index between the second medium and the first medium. Hence we can rewrite w as w= 2(t tan( )) n sin( ) to find out the path difference 2z w= 2tn/cos( ) 2tn(tan( )sin( ) = 2tn cos( ) =mλ Since λ=c/, =(mc)/(2tn cos( )) And thus the frequency spacing between etalon modes is = c/(2tn cos( )) shown 2) 7

8 Only lasing mode which falls into the range of one of the etalon modes will be available for lasing. Hence we can choose a single longitudinal mode by choosing the appropriate thickness of the etalon as well as adjusting the incident angle B) Bragg reflection, ring laser (Page 387) 8