Cavities, Beams and Modes

Question 1

what are superfluorescent lasers

Answer 1

lasers which can achieve laser action without feedback as the gain is so high

Question 2

what do most lasers require

Answer 2

a feedback mechanism usually achieved by a resonator

Question 3

what does the output coupler do

Answer 3

allows photons to escape the laser cavity to give output

Question 4

what kind of emission initiates laser action

Answer 4

spontaneous

Question 5

what kind of laser emission gives gain

Answer 5

stimulated

Question 6

what doe the high reflectivity mirror in the laser do

Answer 6

gives feedback and more stimulated emission

Question 7

how do we extract the energy from the cavity to form a useful laser beam

Answer 7

one of the cavity mirrors will be highly reflective while the second will be slightly lower to allow some of the light to leak out.
this is the output coupler

Question 8

when is the maximum value of the cavity lifetime (and therefore the lowest possible threshold)

Answer 8

when both mirrors are 100% reflective

Question 9

what is beam walk off

Answer 9

in a two plane mirror cavity, if one of the mirrors is slightly misaligned then a ray propagating will eventually escape
it is a source of cavity loss

Question 10

with the mirrors perfectly aligned what losses still need to be considered

Answer 10

diffraction losses due to the finite aperture of the mirror

Question 11

what is the transverse mode pattern of the light

Answer 11

the intensity distribution of light across the width of the cavity

Question 12

what is a confocal cavity

Answer 12

a laser cavity where the radius of curvature of the mirror equals the length of the cavity
their focal points are coincident with the centre of the resonator

Question 13

what can an optical cavity made from two mirrors be considered equivalent to

Answer 13

a series of mirrors, hence a series of lenses

Question 14

what is the ABCD matrix for a simple lens

Answer 14

(1 0)
(-1/f 1)

Question 15

what is the ABCD matrix for free space propagation

Answer 15

(1 d)
(0 1)

Question 16

for a free space propagation followed by a lens, what is the ABCD matrix

Answer 16

(1 d)
(-1/f 1-d/f)

Question 17

What is one round trip of a laser

Answer 17

the free space propagation followed by the lens, followed by free space propagation, followed by the lens

Question 18

what is the stability criteria for a two mirror cavity

Answer 18

0<= (1-d/R1)(1-d/R2)<=1 where d is the mirror separation and R is the mirror radius of curvature
often written 0<=g1g2<=1

Question 19

what type of waves propagate in a laser cavity

Answer 19

Gaussian

Question 20

what is the beam waist

Answer 20

the position at z=0 where w=wmin=w0

Question 21

what is the rayleigh range

Answer 21

zR is the position where the beam area doubles and the wavefront curvature is at a maximum

Question 22

what is the beam divergence angle

Answer 22

sin(theta)= 𝜆/𝜋𝑤0𝑛 ≈ 𝜆/beam dia

Question 23

in a stable cavity, what is the relationship between the radius of curvature and the curvature of the mirrors

Answer 23

they match

Question 24

what does the transverse mode determine

Answer 24

the spot pattern seen as the laser output

Question 25

what type of beams are normal laser modes

Answer 25

Hermite Gaussian Beams

Question 26

What is the general form for transverse electric modes

Answer 26

TEMmn where m is the number of modes in the x direction and n is the number of modes in the y direction

Question 27

what are hybrid transverse modes

Answer 27

a superposition of two transverse modes

Question 28

what are the determining factors in which mode oscillates

Answer 28

the aperture of the gain medium and the radial dependence of the gain

Question 29

what is the preferred and most efficient mode

Answer 29

TEM00

Question 30

how can we supress higher order modes

Answer 30

using an inactivity aperture

Question 31

what is the intermode spacing (FSR)

Answer 31

c/2d

Question 32

what is the condition for light to form standing waves within the cavity

Answer 32

m 𝜆/2 = L

Question 33

why is the output spectrum a combination of the gain spectrum and the cavity modes

Answer 33

because of broadening, the gain spectrum will give optical gain over a continuous set of wavelengths/frequencies but the resonator only supports feedback at the cavity mode frequencies

Question 34

what is a laser with only one longitudinal mode called and where would it be used

Answer 34

a single longitudinal mode laser high resolution spectroscopy and laser cooling

Question 35

what does the number of cavity modes depend on

Answer 35

the broadening mechanism and the cavity configuration

Question 36

In CW lasers what two things balances the pumping rate

Answer 36

the circulating power and the associated stimulated emission

Question 37

at what condition is the population inversion of a CW laser maintained

Answer 37

threshold conditions with a gain of unity

Question 38

What are the CW conditions

Answer 38

round trip gain is unity CW inversion = threshold inversion

Question 39

in a homogeneously broadened laser, what happens as the population inversion is reduced as radiation intensity builds and stimulated emission reduces

Answer 39

gain reduces at all frequencies and the laser only oscillates at the frequency corresponding to the longitudinal mode closest to the line centre with maximum gain

Question 40

In a steady state homogeneously broadened laser why can it be considered single frequency

Answer 40

in steady state only one longitudinal mode oscillates as no ther modes have enough gain to reach threshold

Question 41

in a standing wave cavity, what are nodes

Answer 41

where the e-field = zero

Question 42

what effect happens at nodes

Answer 42

no gain no photon density no stimulated emission called spatial hole burning laser gain wasted and multiple longitudinal mode oscillation more likely

Question 43

what does spatial hole burning mean for the modes accessing gain

Answer 43

pop inversion untouched by first mode can be accessed by a second with different node positions - both modes access gain and oscillate

Question 44

how to circumnavigate spectral hole burning

Answer 44

travelling wave cavity - ring cavity

Question 45

what is the travelling wave condition

Answer 45

light only goes one way round the cavity using an optical diode

Question 46

how do we create an optical diode

Answer 46

using a Faraday rotator, the faraday effect uses a strong magnetic field to change the polarisation of light passing through a magneto optically active material and prevents unwanted reflections back into laser cavity

Question 47

what is the longitudinal mode spacing

Answer 47

FSR = c/L(roundtrip)