By Amir Golan

034918714

Table of contents:

1. History............................................................................................................ 3

2. Structure and Properties of organic dyes ....................................................... 4

General Properties of organic dyes ....................................................... 4

Energy levels and rotational spectra ..................................................... 6

Losses and Deactivation of excited molecules ..................................... 9

Examples of typical dyes and their properties .................................... 11

The Coumarine Family: ...................................................................... 11

The Xanthene Family:......................................................................... 13

3. Oscillators and Pumping of Dye Lasers....................................................... 14

Practical pumping arrangements......................................................... 14

Wavelength-selective resonators for dye lasers.................................. 17

4. Solid State Dye Laser................................................................................... 22

5. Gain Analysis of cw dye laser ..................................................................... 24

Analysis at laser threshold .................................................................. 24

Analysis above laser threshold............................................................ 27

6. Application of dye laser ............................................................................... 31

7. Conclusion ................................................................................................... 32

8. References.................................................................................................... 33

2

1. History

Soon after the laser invention in the 1960's the question whether it is possible to

make a laser that could be easily tuned over a large range of frequencies raised. The

answer came not long after, in a shape of an organic dye laser, which made this dream

into a fact. Today tunable organic dye lasers cover the spectrum from near Infra Red to

the ultraviolet.

The first report of dye laser action was in 1966 by Sorokin and Lankard who

observed laser emission from a solution of chloroaluminium pthalocyanine.

Independently Schafer, Schmidt, and volze obtained laser emission for a number of

cyanin-type dyes. Later a few important advances where made by Soffer and McFarland

in 1967 who succeeded in spectrally narrowing and tuning a dye laser by replacing one of

its resonator mirrors with a diffraction grating. This was the first demonstration that a

laser could be easily tuned over a broad spectral range. Over these first years many

different setups where experimented including; flashlight pumping, high intensity laser

pumping and various techniques involving grating and prism resonators. In 1970,

Peterson, Tuccio and Snavely at Kodak Research Laboratories achieved the first

continuous dye laser action using a focused argon laser as a pump.

The uniqueness of these contributions was that they where the first to report of

laser action from a broad, diffuse energy bands rather than a set of discrete energy levels,

that where typical of gas and rare-earth lasers.

3

2. Structure and Properties of organic dyes

General Properties of organic dyes

Organic dyes are a class of colored substances which are useful for their ability

to impart color to other substances, liquid, gaseous or solid. These substances are

characterized by their strong absorption bands between the ultraviolet and the near

infrared. The chemical structure that is unique to all theses materials is an alternating

structure of single and double carbon to carbon bond (conjugate bonds).

C == C – C == C – C

These compound are much too complex to rigorously derive a full quantum

mechanical Hamiltonian that would yield their absorption spectrum. However simple

models have been suggested and have been giving good approximations (Shafer 1977).

On the other hand these approximation that would be discussed later does not help when

it comes to non radiative processes that are, of course, very important for the laser

operation.

The ground state electron configuration is: [He].2s2.2p2, therefore, it consist of

two p electrons each. In a dye molecule structure, the bonds between the carbons are

formed by the σ electrons (the ones that we call "s" in a single atom) they are called π

electrons. These electrons are free to move along the molecule, and in fact they form "π

electron cloud" around the molecule. Since the dye molecules are plain these electrons

actually move inside a planar potential barrier. In most dye molecules the molecule has

either a straight line shape or a zigzag line shape; in any case the molecule is planar. If

we look at a simple zigzag dye molecule we can see the π electron cloud zigzagging

around it (Fig 1a) but if we look at the electron cloud from the side we can see the

electrons are in a one dimensional potential barrier in the length of the molecule (Fig 1b).

4

Figure 1. a.Looking at a simple zigzag dye molecule from above, showing the π electron

cloud zigzagging around it. b. At a side view, we can see that the electrons are in a one

dimensional potential barrier in the length of the molecule.

The energy spectrum will be given from the Hamiltonian, H = p2/2m , therefore,

if we take the length of the molecule to be L then the momentum spectrum will be

pn=ћπn/L where n=1,2,3… Thus we can get the energy spectrum: 222 8mLnhEn = .

According to the Pauli principle, each state can be occupied by two electrons. Thus, if we

have N electrons, at the molecular ground state, the lower 1/2 N states will be occupied

with two electrons each, while all higher states are empty. The absorption of on photon

with energy E = hc/λ raises one electron from an occupied state to an empty one. Hence

we can calculate that the longest wavelength that can be absorbed by the dye corresponds

to a transition from the highest occupied state to the lowest empty state:

==> 1

8max = h

mcλ2

+NL

From this simplified calculation we can calculate the position of the first

absorption band, knowing only the number of the π electrons, N, and what is the length of

the molecule. Dye molecules with different lengths were tested and the results are quite

good, implying that the above approximation is a good basis for further calculations

(Miyazoe and Maeda, Jpn, J. App. Phys. (1970)). Generally the dye molecules are more

complex and cannot be simply calculated from the molecular structure. In such cases

perturbation theory calculation are done and give a more precise calculation.

)1(8 2

2

min +=∆ NmLhE

5

Energy levels and rotational spectra

The characteristic of the dyes energy levels is that they are essentially a wide band

or in other words, a continuum of vibrational and rotational levels. The lowest electronic

level absorption is from the ground state singlet state S0 to the first exited singlet S1. Dyes

exhibit a strong absorption in this transition, and usually it is in the visible range. This

absorption is what gives the dyes their name, this transition is what gives colors to the

objects around as; such as cloth, plastics, plants etc. The figure below shows a diagram of

the energy bands structure of a typical dye molecule, it also shows a basic emission

mechanism, beginning with pumping into the first exited singles state S1, and radiating

back to the ground state note that there are losses to the lowest triplet state T1 from which

there can be further pumping to the next higher triplet state, T2, or down to the ground

state through a radiative (or non-radiative) process. The radiative processes from T1 to the

ground state, S0, is called phosphorescence, but cannot be used for laser emission due to

the strong triplet-triples absorption (the triplet absotption bands are broad and diffuse).

Another reason the triplet state T1 cannot be used for the laser emission is that the

radiative transition from a singlet ground state must end in an excited singlet state. For

this reason the only allowed transitions from the ground state are S0 -> S1 and S0 -> Si

(i=1,2,3…) . By contrast, the transition S0 -> Ti (i=1,2,3…) is spin-forbidden (in such

cases the wave function gets very low values approaching zero).

6

Figure 2. Energy levels diagram (bands) of a typical dye molecule, it's relaxation

pathways and possible deactivation mechanisms.

An important character of the organic dye is that it should have a strong

absorption band as mentioned before, and also a strong fluorescent emission that does not

overlap the absorption range. There are some reasons for weakening the fluorescence

emission one of them is nonradiative processes that compete with the fluorescence

radiation that is essential for the stimulated emission. The second reason for decreasing

the population in the singlet state is absorption of the emitted radiation by the triplet

states, thus inhibiting the laser action. In figure 3 we can see an absorption / emission

spectrum of a typical dye molecule, note the overlap of the fluorescence band and the

triplet-triplet absorption.

7

Figure 3. fluorescence, absorption and triplet-triplet absorption spectrum of the dye

Rhodamine 6G

There are thousand of organic dyes but only a few classes of dyes have the right

band structure that allows them to be relevant for laser action. The next figure (4)

illustrate the different groups of dyes and the spectral range that they cover.

So far no discussion was made regarding the solvent in which the dye is diluted

in. The solvent plays an important role in selecting the wavelength range that the dye is

used for. The reason the solvent has such a major influence is because of solvent-dye

interaction, processes of polarization-depolarization and proton transfer between the

solvent and the dye, change the energy levels considerably. As a result, the fluorescence

shifts to different areas of the spectrum, some times by more than 200nm away. This

means that the same dye with different solvents can be used to cover a large part of the

visible spectrum.

The physical mechanism that allows the dye laser to have such a wide spectral

range is its homogeneous broadening, this broadening is a results of a continuum of

rotational and vibrational states. When the dye is pumped to its first singlet state S1, after

a short time (fast relaxation) the system reach to a thermal equilibrium in this new state

and reaches the ground state (of S1), see figure 2 . From this upper electronic ground state

there is a radiative transition to one of the rovibrational levels on the electronic ground

state. Form that level another rapid transition occurs, this time from the rovibrational

level to the ground state, so the lasing rovibrational level is unoccupied again. Now, if we

introduce a frequency selective device to the optical cavity, we can limit the spectral

width to a very narrow bandwidth, the next chapter will discuss it extensively.

8

Figure 4. Illustrate the different groups of dyes and the spectral range that they cover.

Losses and Deactivation of excited molecules

Some of the ways that allow the dye molecule to reach back to the ground state

without the laser emission have been discussed shortly above, and are mainly through the

triplet states. Over all, the transition can take place from S1 to the ground state and then it

is called fluorescence or from the triplet state, then (if it is a radiative transition) it is

called phosphorescence.

The trivial mechanism that takes the system down to the ground state is of course

the spontaneous radiation with the rate constant of Einstein relation "A" or 1/τsp. Another

possible way for the molecule to reach the ground state directly is the possibility that the

hypersurface of the excited molecule will pass closely enough to the ground state of the

molecule and there will be tunneling through the barrier between them. This is usually

the case when the system is in a vibrational state (hydrogen vibration). (fig 5) This

process is termed "internal conversion" and has the rate kSG

9

Mol

ecul

ar

Internal

Distance between H and the rest

Figure 5. Tunneling between upper and ground state (internal conversion)

The internal conversion between S2 and higher exited states to S1 is usually very

fast, taking place in less then 10-11 sec. This is the reason why the fluorescence spectra

of dyes generally des not depend on the excitation wavelength. There are a few

exceptions in which the dye molecule is lasing directly from the second triplet state, S2

(e.g. azulene and its derivatives). In these molecules, the transition between S1 to the

ground state is extremely fast. (also seen in fig 2),

The radiationless transition from an excited singlet state to a triplet state can be

induced by internal perturbations like spin-orbit coupling and substances containing

nuclei with high atomic number, as well as by external perturbations like reactions with

the solvent. These radiationless transitions are termed "intersystem crossing" and have

the rate kST.

The quantum yield of fluorescence, φf, is then defined as the ration between the

radiative and non-radiative transition rates: φf = (1/τsp) / (1/τsp+ kSG + kST)

10

Examples of typical dyes and their properties

The Coumarine Family:

A group of widely used laser dyes emitting in the green-blue region of the

spectrum are derived from coumarine by substitution with an amino or hydroxyl group in

one of the 7 possible positions on the molecule.

Figure 6. The two mesomeric forms of the basic Coumarine dye.

Some members of this class rank among the most efficient laser dyes known

today. Their usefulness is mainly due to the marked change in basicity that occurs upon

optical excitation which causes a shift of the fluorescence to longer wavelength, a

property that can be used to achieve a wide tuning range.

The molecule can take two typical mesomeric forms (A and B) where in the

electronic ground state the π-electron distribution closely resembles type A. On the

ground state there is just a small amount of type B (the polar form). The amount of the

mesomer B controls the lower wavelength cutoff of the absorption band since when type

A and B meet they connect to one another and form a longer chain similar to the

symmetrical canine dye. In this case the positive charge at the N atom in form B is

stabilized, for instance, by electron-donating alkyl groups.

Figure 7. The symmetrical canine dye

A good way to stabilize form B, and therefore increase its concentration is by

using a polar solvent, the higher the polarization of the solvent, the higher the

11

concentration of the B form. In the table below we can see that in the case of Coumarine

102 when diluted in NMP (N-methyl-pyrrolidinone) which is a non-polar solvent the

absorption maximum is 383 nm whereas in HFIP (hexafluoroisopropanol) which is a

polar solvent the maximum absorption shifts to 418 nm. This influence sometimes does

the opposite depending on the specific hydrogen combinations, (see for example in

Coumarine 120).

Figure 8. Various derivatives of the Coumaine Family.

When not in a highly polar solvent (most cases), on the electronic ground state S0

the coumarine is mostly in its A form (the π-electron distribution resembles type A).

After optical excitation, in the first excited singlet state S1, the majority of the molecules

are in their polar form, B. Therefore on optical excitation the static electron dipole

moment increases, and a major rearrangement of the surrounding solvent molecules takes

place immediately after excitation. Thus the energy of the excited state is markedly

lowered before light emission occurs. This is the reason for the large energy difference

between absorption and fluorescence (Stockes shift) in the Coumarine derivatives.

Another method to shift even further the fluorescence band is to use acidic solvents. In

such cases even a small amount of acid the spectrum considerably.

12

Figure 9. Absorption spectrum and the fluorescence band with and without acid solution

The Xanthene Family:

Another Classical dye family are the Xanthene group, this group devides into two

main branches, the rhodamines and the fluorescein. This family of dyes cover the

wavelength region from 500nm to 700nm and are generally very efficient. Unlike the

cuomarines from above, this group is soluble in water, a fact that gives them great

advantage, over other dye. Another important advantage is the fact that they are relatively

very easy to manufacture, without complicated purifications, unlike most other dyes.

The π-electron distribution of the xanthene dyes can be described approximately

by the two identical mesomeric structures, A and B.

Figure 10. The two identical mesomeric structures.

Unlike the Cumarine dyes, forms A and B have the same weight, and thus in the

xanthene dyesthere is no static dipole moment parallel to the long axis of the molecule in

either ground or excited state. Figure 3, in the previous chapter, shows the absorption

spectrum and the fluorescence band.

13

3. Oscillators and Pumping of Dye Lasers

Practical pumping arrangements

There are several pumping methods available that are currently in use in dye

lasers. Various methods are being applied for different laser setups.

Grating

Figure 11. Various pumping schemes, in green is the pumping laser and the red is the

output laser.

The above figure shows some of the methods that are in use to achive practical

pumping, in most cases however the pumping beam gets totally absorbed in the dye and

does not proceed after the dye chamber. This absorption is of course a result of Beer's

law:

dNaeII −= 0

Where

I is the transmitted light

I0 is the incident light

a the molar extinction coefficient [1/cm]

N the concentration [mole / liter]

d the thickness of the absorbing layer [cm]

Fabri-

Perot Ethalon

C

ylindrical

D

D

14

This paper will focus on two of the most popular arrangements, a and b, which are

both very simple and are widely used. The two examples below are actually amplifiers

but demonstrate the use of these configurations.

In figure (11a) we can see that the laser beam hit the dye solution directly and

gets absorbed completely, while in the perpendicular direction the new laser beam is

emitted. This apparatus exists in the most advance dye lasers today, for example the ND

6000 form Continuum company (operates also here in BGU). In the photo below, figure

(12a), we can see the actual dye solution in the chamber and further below, figure (12a),

the result of the emitted laser beam as it strikes a sensitive paper. Note the shape of the

beam that clearly shows Beer's absorption from right to left across the cell.

The other apparatus uses the technique sown on figure (11b). In this method the

pumping laser beam is first expanded and the focused along a horizontal line using a

cylinderal lens, While the dye solution circulates inside a long tube. The advantage of the

cylinderal lens is that it spread the intense of the pumping laser over a wider area. In

many cases, this is done because the excitation beam might be too intense for the dye to

bear, and will brake apart some of the dye molecules instead of being used for excitation

only. In many dyes the penetration distance of the pumping beam in the dye solution is

very sort and this method overcomes this disadvantage by spreading the beam along a

wide area of the dye solution. This method is being used in a ScanMate dye laser, from

Lambda Physik company. This laser also operated here in BGU and uses the Coumarine

dye that was mentioned before.

15

a.

b.

Figure 12. a. Shows the apparatus in the ND6000 dye laser. b. Shows the output result as

rved on a sensitive paper put in front of the output beam, indicating the absorba

in the dye according to Beer's law.

obse nce

16

Wavelength-selective resonators for dye lasers

Until now, it was demonstrated how a laser can have a wide spectral range, as

explain

n any of

idth.

ation.

imination.

istributed feedback.

The f into an

appara s

Figure 13. a rotating grating

n

(α=β) r

α. Where m is the order, λ is the wavelength, d is the grating constant ,

α is the

ed before the laser operates by taking the system from the first excited singlet

state to some rovibrational level on the electronic ground state, so that the laser

wavelength is the wavelength correspond to this energy gap but can vary betwee

the lower rovibrational levels (see figure 2 above). In order to select only one specific

transition, a wavelength-selective resonator is needed. This will ensure also the

possibility to attain both fine tuning and simultaneous attainment of narrow linew

There are many different ways to reach this goal:

1. Resonators with spatial wavelength separ

2. Resonators with interfrometric wavelength discr

3. Resonators with rotational dispersion.

4. Resonators with wavelength-selective d

irst wavelength-selective resonator in the list above was first put

tu in 1967 by Soffer and McFarland, they replaced one of the mirrors of the

resonator by a plane optical grating in Littrow mounting. This arrangement is shown

below in Fig 13.

Mirror Active medium

A simple frequency selective resonator with

Consider the grating equation mλ = d(sinα+sinβ) , which for autocollimatio

educes to

mλ = 2d sin

angle of diffraction from the normal to the grating, and β, is the angle of

incidence. From this equation we can derive the angular dispersion of the grating:

αλα

cos2ddmd

=

17

If the dye laser has a beam divergence angle of ∆α, the passive spectral width of

this arrangement would be:

ααλ ∆=∆2cos2d

From the above equation we can see that the spectral resolution is linearly

proportional to the spatial divergence, therefore if we could minimize the spatial

e only

me of the solutions to this problem are using a

Figure 14.

with stripes of different height, plastic is the most common material. B. An ordinary

mirror before the grating (Figure 15

Figure 15. d before the grating to lower the intensity that hit the

grating and lower the output bandwidth.

Mirro

divergence by any optical means, we will increase the spectral resolution of the dye laser.

High quality gratings can have up to 95% efficiency, however most gratings achiev

65%, but in any case the losses due to the grating are small in comparison to the losses of

the rest of the system.

The primary disadvantage of the grating is the reflecting metal film which may be

damaged by high intensity laser beam. So

telescope to enlarge the beams dimensions or a grating substitute made from honorifically

produced bleached transmission gratings.(Kogelink et al. 1970) (figure 14).

M

A. Holografically bleached grating, consist of high refracting index material

grating with metal stripes.

Another way to prevent the burning of the grating is to use a bandwidth selective

)

r-Grating combination

Active

Output

mirror

n ≈ n >

Bandwidth mirror is place

18

This scheme not only reduces the power incident on the grating to a few percent

been without the mirror, but also significantlyof what it would have reduces the laser

thresho

use

sms in the laser cavity (Yamaguchi et al, 1968). The relatively small

angular

in

ld; this is because the mirror-grating combination acts as a high reflectivity

resonant reflector for the tuned wavelength. This scheme was reported to reduce the

threshold by a factor of two and to lower the bandwidth by a factor of three over the

of grating only.

Another way for tuning and spectral narrowing of the dye laser can be achieved

by on or more pri

dispersion of a single prism is sufficient to isolate one of several sharp lines in

gas lasers, for example, where this method has long been used. When flashlamp is used

the dye laser, one prism is not enough and then multiple-prism arrangements have to be

used. A mathematical analysis of such prism array can be easily done, with the notation

of (Fig 16) we can see that we have α=2i-β and r = β/2 so that :

Figure 16. Ray analysis of a simple prism.

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ +

=

2sin2

2cos

β

βα

αµ

dd

Since it is better to work near the Brewster angle where dα/dµ = 2, the angular

dispersion of the prism is:

λµ

λα

dd

dd 2=

Therefore, if we use an array of n prisms all autocollimated, (figure 17) with a dye

laser of beam divergence ∆α, then the passive spectral width is:

λµαλ

ddn4∆

=∆

19

Figure 17. An array of 6 autocollimated prisms, and a dye tube, The tuning is done by

changing the wedge in the upper element.

achieving a small spectr avity one or more

fabri-P

s spatially spread to the different wavelengths

and the the

wn

radiation equations:

s law.

The second kind of resonator mentioned above is especially well suited for

al bandwidth and is done by inserting the c

erot ethalons or interference filters.

The fourth kind is the one that is most widely used, the basic idea is very

simple, using a grating the dye laser beam i

n using a rotating mirror only the selected wavelength is reflected back into

cavity. This method achieves a very narrow bandwidth since the feedback beam acts in

the resonator as it would in an amplifier, hence reducing the bandwidth and any other

fluorescence.

The narrowing of the band width in an amplifier arrangement can be easily sho

from the basic lg

wweII )(

0)( = From Beer'

lg we )( The definition oww I

IG

0

)()( == f the gain.

lwe ) We want to find the wiglg

w

w

eGG (

00

22)(

)21(

=== dth in half maximum, for this

example we can use the natural line shape: 22

0

20 )2/( wgg ∆⋅

=

From the above equality,

)( )2/()( wwww ∆+−

lglg

wee )(0

= , we can find the new line width (after 2

substituting g(w) in)

20

2ln2

0 −lg

see that as long as g0 >>1 the new line with is much narrower:

wwamp ∆<<∆

avoid burning it with high energy pulses, the beam hits the grating at a very low angle,

and thus spread over a large area of the grating and then reflected back onto the dye cell.

See figure 18. The first two figures (a and b) ar

Figure 18.

the ScanMate respectively. c, t showing an example of the

mirror-grating combination in the re

ln)(2 0∆

=∆=−⇒wwww amp

We can now

As seen in the figures below, in order to enlarge the gratings efficiency, and to

e drawing of the beam's optical path in the

two dye lasers discussed above, the Continuum ND6000 and the Lambda Physik

ScanMate respectively. Figure 18c, is taken form a Continuum OPO laser but showing an

example of the mirror-grating combination in the resonator (I will not discuss the OPO

laser in this work, but the mirror-grating combination, is the same in both cases).

sonator as in the Moya setting.

a. ScanMate b. ND6000 – Moya setting

c. Mirror-grating combination in an OPO resonator.

a and b are drawing of the beam's optical path in the dye lasers ND6000 and

is taken form an OPO laser bu

21

4. Solid State Dye Laser

solid matrices containing laser dyes is an attractive alternative The use of to the

conventional liquid dye solutions. The first solid-state dye lasers where reported in the

late 1960's by Soffer and Mcfarland, and Peterson and Snavely. They demonstrated

stimulated emission from polymeric martices doped with organic dyes. However work

on solid-state dye lasers was not pursued for over a decade due to low lasing efficiencies

and fast photodegradation of the dye. In recent years, significant breakthroughs have been

achieved in the development of practical tunable solid state dye lasers. The solid state dye

lasers have several advantages over the traditional liquid dye lasers. Along with the ease

of handling, these lasers posses commercial advantage because of the low cost of

production and the safety of operation. Other technical advantages are compactness,

manageability, versatility, lack of flammability and lack of toxicity. The flow fluctuations

and the solvent evaporation is considerably reduced in the case of solid state dye lasers.

There are several materials which have been used as solid hosts for laser dyes

such as polymers, porous glasses, organically modified silicates or silicate nano-

composites, and polycom glass (a combination of polymer and sol-gel). In general, the

solid host materials suitable for use in solid state dye lasers should have the following

requirements. They should be highly transparent to the pump and laser wavelengths and

of course they should have high photochemical stability. Polymer based systems have

limitations such as a low damage threshold of the host material and limited lifetimes. The

main reason for the destruction of the host is the fact that polymers are poor thermal

conductors and thus tend to heat up quickly without the ability to lose the heat. The silica

matrix has thermooptical constants that are better by two orders of magnitude. However

these materials have optical inhomogenities, which can affect the laser performance.

The photostability of the dye doped solid materials depend on the inter-

molecular and intra-molecular interactions of the dye molecule with the surrounding

chemically active molecules such as the polymer macromolecule end groups, unreacted

monomers, absorbed atmospheric oxygen molecules and another dye molecule. In

general there are three accepted reasons for degradation of the dye molecule:

22

1. Photodeactivation from the excited state caused by chemical oxidation

2. Formation of dimers that absorbs irradiation without any fluorescence.

n of

the dye because of the low therm

on

reaction.

3. Thermal destruction.

Dye doped solid-state laser materials have low quantum efficiency and limited

useful operation time. The low quantum efficiency is mainly due to photo destructio

dye molecules as mentioned above. The mobility and the concentration of the dye

molecules are the important factors that decide the probability of the photodeactivation

reaction. Different methods are used to decrease the mobility of the dye molecules and to

reduce the rate of destructive collisions and diffusion out of the active area. The main

method is by inserting low molecular weight additives, such as different alcohols and

phenyl derivatives. their purpose is both to fill free volumes in the polymer host and to

improve the thermal conductivity thus preventing the dye from moving and achieving

better cooling for the active medium.

Another reason for the degradation of dye molecules is thermal destruction of

al conductivity of the polymer host. Since the polymer

host is transparent to the pump radiation, the excited dye molecules heats up the host

through non-radiative thermal relaxation.

Due to recent developments of new and improved host materials with higher

laser damage threshold and longer lifetimes, there is a lot of research in this field

recently. For example, the efficiency of the PMMA based rhodamine 6G chloride dye

was improved from 14% to 28% by the addition of ethyl alcohol-carbonic acid ether

mixture into the PMMA. (PMMA ( polymethylmethacrylsate) - is a clear color comm

plastic)

23

5. Gain Analysis of cw dye laser

Analysis at laser thresh

e

ye molecules in the ground state of S0.

old Many aspects of the performance of the dye laser can be understood from an

analysis in terms of rate equations. In the treatment which follows the rate equation

approach developed by Snavely (1969) and Peterson (1971) will be followed for th

description of the dye laser at threshold. The effects of system parameters upon tuning

and threshold will be examined.

The transition from the vibrational state to the ground state, both in the ground

singlet levels and in the excited electronic levels is very fast. Thus the molecules in the

system can be found essentially in one of the three states: N0,N1, and NT

N0 – the concentration of the d

N1 – the concentration of the dye molecules in S1 level

NT – the concentration of the dye molecules in T1 or any other triplet level

I(λ,z) – the intensity of the lasing mode

The rate at which the intensity increase along the z axis can be written as:

lossstimtotal dzdI

dzdI

dzdI

⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

the losses part is devided in to two main losses the losses to the upper singlet

state S1 to S2 and the losses to the triplet state (S1 to T1) and from there further up in the

triplet le

⎜⎛⎝ 2

41

8

vels (T1 to Tn). In order to get the expression for the stimulated emission we can

use the identity:

dtdI

cn

dzdt

dtdI

dzdI

=⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

where n is the refractive index and c the speed of light. From this expression we

can write the explicit expression for stimulated emission as derived by Yariv (1967):

( ) ( )IIcnEN

dzdI

em λσπτ

λλ==⎟

⎠⎞

24

Where ( )λE is the spontaneous emission line shape function, so that

( ) φλλ =∫ dE0

∞

the fluorescence quantum yield. τ is the observed fluorescence decay time

for spontaneous emission.

The losses to the higher singlet levels and to the triplet levels can be similarly

expressed as ( )λσααα

NIdzdI

−=⎟⎠⎞

⎜⎝⎛ , where α is the relevant level.

When we put in these expressions we get:

( ) ( ) ( )[ ]υσυσυσ TTSem NNNIdzdI

−−= 01

Now, if we define the gain of the active medium as: ⎞⎛ dI1 ( ) ⎟⎠

⎜⎝

=dzI

λ

g for the

finite r round trip gain:

g

after integrating over a round trip through the active medium accountin

eflectance R1(λ) and R2(λ) of the mirrors, yields G(λ), the

( ) ( ) ( ) ( ) ( )[ ] ( ) ( )( )λλλσλσλσλλ 2101 ln2 RRLNNNdzgG TTSem +−−== ∫ 2L

At the laser threshold where G(λ)=0 we get:

( ) ( ) ( ) ( ) ( )( ) 0ln2 2101 =−−− λλλσλσλσ RR1

LNNN TTSem

Knowing the transition rate between the first excited singlet state and the triplet

lifetime τT, and assuming a steady state situation, we can express the equilibrium

population of T1 by means of N1:

TSTT kNN τ⋅= 1

As mentioned in the introduction to this section, the transition from the

vibrational state to the ground state, both in the ground singlet levels and in the excited

levels is very fast. Thus the molecules in the system can be found only in one of the three

states: N0,N1, and NT . Therefore we can use the relation

TNNNN ++= 01

If we define the part in the gain expression that deals with the mirrors as:

( )21ln21 RRL

r =

25

We can write the expression for the total gain at threshold, as:

10 TTSTSem

] 0=−−− rNkN STTSTem σστσ

[ ] ( ) 011 −− NkN TTSTem σστσ

01 =−−−= rkNNNG στσσ

[ 01

using TNNNN ++= 01 =−−− rNN ST

[ ] 01 =−−++− STSSTSTTSTem NrkkN στσστσσ using again TSTT kNN τ⋅= 1

)[ ] 01 (0 =−−−++ STSTem k ST NrN σσ σττσ

From the last equation we can find the minimal relation for the population

inversion:

( ) ⎥⎦⎤

⎢⎣⎡ +

−++=

Nr

PNN

TTTemN 010

1 1σσσσσ

0σ

If we define the long denominator as ( ) em Pσσυγ ++≡ 0 ( )TTT σστ −01 we can write the

minimal population inversion for lasing as:

( ) ⎥⎦⎢⎣+=⎟

⎠⎜⎝ NN 0

min

1 συγ

A good example of the above derivation is a simulation done by B.B. Snav

⎤⎡⎞⎛ rN 1

ely

(1968) with data take from numerous experimental works that where done at that time on

Rhodamine 6G. The values used are:

[ ] [ ] [ ] 9.0,10*65.,10*2.0,10*05.0 216216216 ==== TSTemTS kandcmcmcm τσσσ

The next figure (Figure 19) shows a three dimensional diagram of the relation

betwee

calculated population inversion ratio of 0.03 was very

close to the experimentally measured.

1

n the ratio r/N and the wavelength vs. the critical population inversion ratio,

N1c/N. In the experiment done, the value for r/N was approximately 10-19 and the

wavelength was set at 580nm. The

26

Figure 19. The figure shows a three dimensional diagram of the relation between the ratio

1c

Analysis above laser threshold When the population inversion is smaller than the threshold there is , of course,

no lasin re

the population of the excited level, is dependent of the location on the z axis, N1

,and alo

d

irror

eam, which has a different spot size (wp0).

Last assumption is that the only transverse mode in the resonator is the TEM00.

Since the intensity is dependent by the position on the z axis, we shall distinguish

forward going rays, I+(r,z), form backward going waves I-(r,z), and will follow the sketch

(Fig 20 ) below.

r/N and the wavelength vs. the critical population inversion ratio, N /N

g in the system. However, above threshold, some of the assumptions taken befo

are no longer valid, thus, new assumptions must be made in order to calculate the lasing

parameters above threshold:

ng the radial distance from the z axis, N1(r,z).

The shape of the resonator is known, and in this case we shall assume forwar

spherical mirror with curvature in the length of the resonator (R2) and a flat back m

(R1), so that al z=0 the spot size is minimal (w0) and has a flat front. We shall assume

these conditions also for the pumping b

27

Z=L Z=0

Figure 20. Geometry of the cw laser considered in the analysis

cribes the gain per unit length on the z axis is

defined

The intensity differential, which des

(derived from the above formulas) as:

dzzrNIzrdI )(),(),( 1 υγ±± =

The gain on a round trip along the z axis (r~0) is therefore:

( )∫+d

dzzNRR )(),0( υγ0

121

The relation between the pumping intensity and

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 2

22

0

the occupation of the first excited

singlet state is given by: ( ) τσ ppump NzrItrN 01 ),(, =

Were σp denotes the cross section for absorption of the pumping photon

previously denoted σS(λ). The intensity of the pumping beam in TEM00 is therefore:

⎥⎦⎢⎣ ⋅⎟⎠

⎜⎝

=sec

),( 2cme

whczrI

ppp α

Where αp is the confocal parameter of the pumping beam and is defined as:

pwπ 202 ⋅ 2

⎤⎡⎟⎞

⎜⎛

−

)0(4 002

22

photonswp pw

r

p

pλpα ≡

41)(p

ppzwzwα

and P0(o) is the radiation power at z=0 of the pumping

laser (in watts). Since every photon absorbed in a molecule at the ground state excites it

to S1, we can write the gain expression using the ground state population and the

pumping laser power:

R1

R2

I--

rZ

I+

2wpo

2wo

28

∫ +=

−d zNpp

p

p

zeN

hcP

Gp

02

02

0 41)0(4 0σσα

αγτ

A more compact definition can be given by:

) ∫ +=

−u z

zrdzevv dNu pσ0= and

ppNv ασ021

=

this happens when the absorption distance is small relatively to t

r the αp parameter.

Until now, the calculation was done sol

laser. A continent way to treat the rays is given by Snavely (

LL

pp

L

p

ww

qαλαλ

ππ

== 2

2

0

0

The total gain is of course also dependent on this q parameter. An experimental

result g

Where the subscript L and p denotes the output laser and the pumping laser

respectively

ives the following approximation:

( )q

GGqG

+≅

1, 0

0

In order to get the most important parameter in the laser action, inout PP , we shall

assume some assumptions that correspond to most systems:

The xcited populatio

(corresponds to TEM ).

Saturation of the ground state absorption can be neglected.

e n distribution perpendicular to the z-axis is Gaussian

00

The active medium is short relative to the αp, αL confocal parameters.

From the above assumptions the output result is

),()0(4

0 vuFhc

PG

p

p

αγτ

=

Where (uF ,0

22 ,

The prime conclusion we can derive from this expression, is that in order to

achieve maximal molecular gain from a given pumping intensity, the dye cell should be

placed at z=0, where the pumping beam waist is minimal, and it has a flat front. The

maxim ove integral is unity, and it reach that when u and v component

are maximal, he cells

length o

ely on the z axis, but in a realistic

calculation we must take into account a finite, and not necessarily small spot size of the

output 1968):

al value of the ab

29

( ) [ ] ( )thppp

L ppqLNspl

LNP −

+−=

200

1exp σ

q

σ

Where Pth is the threshold pumping power and spl are all the single pass losses.

The outcome of these vast assumptions is that the output laser power is linearly

dependent on the pumping power. This approximation was first done by Pike (1971), and

the graph below shows the result for different q parameters, the ratio between the two

beams spot sizes. We can see also th parameter has a significant role both in the

output

at the q

power and in the lasing threshold power.

Figure 21. Calculated dependence of dye laser output upon excitation power. The curves

illustrate the dependence of laser threshold and slope efficiency for different q

param aists

(Pike, 1971).

eters, the ratio of the areas of the laser and excitation beams at the beams w

30

6. Application of dye laser

n wide parts of the spectrum with a very

narrow bandwidth resolution (down to 0.01 wavenumber), got a significant advances.

Another area that contributed both to atomic and molecular dynamics was the use

of the ability of the non-linear frequency mixing to be combined with the ability to tune

the laser over a wide bandwidth of frequencies, now not only in the original dye laser

output wavelength. This method is implied in both lasers I mentioned in the previous

chapters, the ND6000, and the ScanMate. In the former, after the tuned frequency was

chosen and amplified, in the 600nm area, it is mixed with another photon of constant

frequency in the IR and together has the ability to scan over a wide bandwidth in the UV.

doubl

s

This wide range of frequencies ed in many other fields that where

previously impossible to be finely controlled. In physical chemistry they are used in

investigating the processes of photoionization and photodissociation, and thus reveal

many aspects on the molecular and atomic dynamics. These methods are of course

applied in biology and various medical applications.

One such medical application is the improvement of facial acne scars (Astler et al.

2003)and many other skin conditions by radiating the skin with pulsed dye laser. Many

experiments and conventional treatments are already taking place and are mentioned in

many magazines of the American and the European Academy of Dermatology.

Since the first development and the beginning of commercial dye-laser

manufacturing, many of the research objectives that where present at that time got a

significant boost. Some of which are absorption spectroscopy and saturation

spectroscopy, which due to the new ability to sca

A similar method is applied in the ScanMate where an output wavelength of ~480nm is

ed by a BBO crystal and again, gains the ability to be finely tuned over a wide

pectrum in the UV and not only the visible range.

can now be us

31

7. Conclusion

is paper I have covered the basic character of the physics of dye molecules

their en as made

ined

constru

e

n

er the use of dye-based lasers.

In th

ergy bands and the way they can be used for lasing. Further emphasis w

of how these fluorescent dyes can be put into compact resonators and easily be comb

in experimental and commercial applications.

Another topic that was extensively covered was the actual methods that exist

today in building efficient dye laser resonators and amplifiers. Beside the physical

ction of the dye laser and the effective ways to build, operate and tune such laser,

an analytical analysis was made to the effects of system parameters upon tuning and

threshold.

Even though most of the research work on dye lasers was made in the 70's and

80's of the last century, the applications of these tunable lasers have not yet reached its

full potential, as we still see to day many new applications in biology, medicine and th

general industry.

As mentioned in chapter four, there is still active research in the subject of solid

state dye laser, that in the day they will be stable enough to be used intensively both i

duration and in output power, will extend even furth

32

8. References

9(1), 47 (1978).

4. F. P

rexhage, laser focus 9(3), 35, (1973a).

9. Lam

electronics 3rd ed. , California Inst. Tech. (1985).

13. S. S

15. H. Kogelink, A. Dienes, Appl. Phys Lett. 16,(1970)

16. Yamaguchi et al, J. Appl. Phys.8 (1969)

17. H. A. Pike Ph.D. thesis , Ann Arbor, Mich. USA (1971)

18. Sorokin and Lankard , Phys. Rev. 186 (1969)

19. B.B. McFarland Appl. Phys. Lett. 10, (1967)

20. T.S. Astler, T.O. McMeekin, American Academy of Dermatology, 35 (1996)

1. B. B. Snavely, O.G. Peterson, Appl. Phys. Lett. 12 (1968)

2. B.B. Snavely, Continous-Wave Dye Lazer I, in Topics in Appl. Phys. vol (1), (1989).

3. C. A. Moore, C. D. Decker, J. Appl. Phys. 4

. Schafer, Appl. Phys. , B39, 1, (1986).

5. F. P. Schafer, Topics in App. Phys. ,vol (1), (1989).

6. H. J. Baving et al. , Appl Phys. B29, 19, (1982).

7. K. H. Drexhage, IEEE J. Qe-10, 695 (1974).

8. K. H. D

da physik, data sheet.

10. R. Gvishi, Ph. D. thesis, Hebrew university, Jerusalem (1993).

11. T. F. Johnston et al. , Appl. Optics 21(13), 2307 (1982).

12. Yariv, optical

ingh, V.R. Kanetkar, G. Sridhar, V. Muthuswamy, K. Raja, J. of Luminescence

101 (2003)

14. Miyazoe and Maeda, Jpn, J. App. Phys. (1970)

33