Department of Physics

Seminar – 1st Year, 2nd Cycle

Fiber Lasers

Author: Jaka Mur

Advisor: izred. prof. dr. Igor Poberaj

Ljubljana, February 2011

Abstract

Fiber lasers combine gain medium, resonator cavity and mirrors inside an optical fiber.

Offering a wide spectrum of operating light wavelengths, durability of design and high wall-

plug efficiency, fiber lasers are finding use in many applications. This seminar addresses

topics of confining light in an optical fiber, fundamentals of lasing inside a fiber, achieving

high output powers and pulsed operation.

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Contents

1 Introduction ................................................................................................................ 2

2 Optical Fibers ............................................................................................................. 3

2.1 Guided Waves ..................................................................................................... 3

2.2 Numerical Aperture .............................................................................................. 4

3 Fiber Lasers Fundamentals......................................................................................... 5

3.1 Fiber Bragg Grating ............................................................................................. 5

3.2 Rare-Earth Doped Fibers ..................................................................................... 6

3.3 Power Scaling ..................................................................................................... 8

3.4 Pulsed Operation ................................................................................................10

4 Conclusions ..............................................................................................................13

5 Bibliography ..............................................................................................................14

1 Introduction

Fiber optics are made possible by a principle of total refraction, resulting in guiding of light

inside a medium with higher index of refraction than surrounding medium. Swiss physicist

Jean-Daniel Colladon and French physicist Jacques Babinet conducted an experiment of

guiding light inside a thin stream of water in 1842, proving this principle. Unclad optical fibers

were first used in 1930s as a medical instrument used to look inside otherwise inaccessible

parts of the body.

Early fiber optic communications were limited with attenuation inside an optical fiber. First

useful fibers for communications were made in 1970 and had a loss of . Modern

fibers have losses as low as . 1

Fiber lasers are a subtype of solid-state lasers. Optical fibers with different dopants inside

core, mainly rare-earth metal ions, serve as a gain media. Mirrors are needed to form an

optical resonator. Dichroic dielectric mirrors can be used in simple laboratory setups of fiber

lasers but fiber Bragg gratings are used in most industrial products. Fiber lasers are mostly

pumped by one or several diode lasers. 2

Fiber lasers have been demonstrated to span wavelengths of light from below to

above . Sensitivity to environment disturbances is minimal due to compact in-fiber design

resulting in high reliability. Fiber lasers are used in many different applications. High power

continuous-wave single-mode fiber lasers are used for laser cutting and welding of various

metals. Q-switched pulsed lasers are used for maximum precision of drilling or cutting thin

Figure 1: Scheme of a simple fiber laser. 2

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metal sheets. Medical applications in surgery, cosmetic and aesthetic medicine use both

continuous wave and pulsed mode-locked and Q-switched lasers. 3

2 Optical Fibers

An optical fiber is a cylindrical dielectric waveguide composed of an inner core and an outer

cladding. It is made mainly of an optical low-loss material, such as silica glass. Light is

guided in a central core, embedded inside a cladding, made of a material with slightly lower

refraction index than the core. In terms of ray optics, every incident ray on the boundary

between core and cladding at angles greater than critical angle undergoes a total internal

reflection. Those rays are guided through the core without refraction into cladding.

Inside a fiber, light propagates in the form of modes. Each mode travels along the axis of the

waveguide with its characteristic propagation constant and group velocity. Inside a fiber with

small enough core diameter, only a single mode is supported and the fiber is called single-

mode. One of difficulties with controlled light propagation inside a multi-mode fiber is due to

modal dispersion. Different group velocities result in a spread of travel times and a light pulse

traveling through the fiber is broadened. Graded-index multi-mode fibers solve this difficulty.

Rays with greater inclination and therefore longer path also travel faster in areas closer to the

cladding. Travel times of different modes can therefore be equalized. 4

Proper description of light propagation through a fiber requires solving a differential wave

equation in cylindrical geometry. Next section shows most important steps in calculating

electromagnetic field inside an optical fiber.

2.1 Guided Waves

Optical fiber is a dielectric medium with refractive index ( ) where represents radial

distance from the axis of light propagation. Maxwell’s equations in a dielectric medium

without electric currents and charge can be written in Helmholtz’s form for each component

of electric and magnetic field:

( )

where and is wavelength of light in empty space.

Figure 2: Refractive index profile and typical rays in a step-index multi-mode (MMF) and single mode fiber (SMF) and in graded-index multi-mode fiber (GRIN MMF).

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Most fibers are at least almost single mode and guided waves are therefore approximately

transverse electromagnetic (TEM). 4 In a cylindrical coordinate system, Laplace differential

operator becomes

(

)

The guided modes are waves traveling along direction of axis and are periodic in the angle

with period . Therefore, can be substituted with

( ) ( )

where is the propagation constant and is an integer. Helmholtz’s equation with this

substitution yields

( ( )

)

The wave is bound if propagation constant is smaller than the wavenumber in the core

and bigger than the wavenumber in the cladding . 4 This is an example calculated

for step-index fiber with refraction index

( ) {

It is convenient to define

( )

( )

and write Helmholtz’s equation in core and cladding separately:

(

) ( )

(

) ( )

Those equations are well known differential equations whose solutions are the family of

Bessel functions:

( ) { ( )

( )

Large value of describes a rapid decay of the evanescent field in the cladding or

equivalently small penetration. Small value of describes faster oscillation inside the core.

The connection between values and is

(

)

If value grows above the value of right hand side of equation, than becomes imaginary

and modes are no longer guided. This equation defines the number of modes able to

propagate inside a specific fiber.

2.2 Numerical Aperture

Important physical property of an optical fiber is its numerical aperture. A ray incident from air

into fiber becomes guided if it makes an angle with the fiber axis smaller than critical angle.

According to Snell’s law it can be written:

√ ( )

√

where is refractive index of the fiber core and is refractive index of the fiber cladding.

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Angles are shown in Figure 3. With numerical aperture the last equation from chapter can

be written as ( )

. It is convenient to define normalized quantities in relation to

and :

With definition of fiber parameter ( ) equation is true. Parameter

( ) governs the number of modes of the fiber and their propagation constants.

Condition for a wave to be guided becomes in this notation. 4

3 Fiber Lasers Fundamentals

A working laser needs an optical resonator with gain media and a source of energy to excite

electrons in the gain media. Classic design of fiber lasers uses a double clad optical fiber. 5

Pump light is directed into the inner cladding, bouncing inside outer cladding through active

core and is gradually absorbed along fibers length. Laser light is bound inside active core,

serving as a gain media too.

Most robust design of a fiber laser uses reflection from fiber Bragg grating as a mirror, so the

whole laser resonator is made inside a fiber. Another possible design of a fiber-integrated

mirror is a loop mirror. In the next sections I will present fiber Bragg grating design and

properties as well as different dopants and corresponding fiber laser types and working

wavelengths.

3.1 Fiber Bragg Grating

Fiber Bragg grating is a periodical perturbation of refractive index along the fiber length. It is

usually formed by exposing the fiber to intense optical interference pattern made with an

ultraviolet laser. 6 First experimental realization of a Bragg grating was done in 1978 in

Canada.

The magnitude of the refractive index change depends on various factors such as irradiation

wavelength and intensity, core dopant material and different preprocessing methods. Typical

Figure 3: The acceptance angle of a fiber with quantities related to numerical aperture. 4

Figure 4: Scheme of a double-clad optical fiber. 5

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values of refractive index change are in a germanium doped single mode

fiber. 6 Photo induced refractive index change induces anisotropy because of the chosen

direction of irradiation. This anisotropy results in fiber becoming birefringence for light

propagating through the fiber and can be used for fabricating polarization mode converting

devices.

Refractive index perturbation is a periodic structure much like crystal lattice. A narrow band

of the incident optical field is reflected by successive, coherent scattering on index

perturbations. Strongest interaction happens at incident light with wavelength equal to Bragg

wavelength

where is the modal index and is the period of modulation. Modal index is effective

refractive index depending also on light propagation mode. In a general case, index

perturbation takes a sinusoidal form

( ) ( (

))

where the contrast is given with parameter .

Figure 5 shows comparison between theoretically predicted and experimentally measured

transmission spectra of a grating length with grating strength of approximately

. With longer irradiation times the refractive index change becomes larger and

reflection stronger, so approaches . A strongly saturated grating is no longer

sinusoidal, peak and valley index regions are flattened. The incident wave is completely

reflected before reaching the end of the grating and therefore spectrum broadens. As a

result, second order Bragg reflection lines are observed at half the fundamental Bragg

wavelength and other shorter wavelengths for higher order modes. 6

3.2 Rare-Earth Doped Fibers

Fiber lasers are usually based on glass fibers doped with laser-active rare-earth metal ions.

Plastic optical fibers are generally not used due to their high absorption but are also highly

multi-modal, hard to dope and sensitive to high optical intensities. Rare-earth metal ions

absorb pump light at a shorter wavelength than the laser wavelength except in case of

upconversion fiber lasers. This allows light amplification with stimulated emission. Such

Figure 5: Comparison of computed and measured transmission spectra. 6

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doped fibers are called active fibers and are a gain media with high efficiency, mainly

because of strong light confinement.

Choosing the correct chemical composition for the host glass is very important. For example,

mid-infrared lasers cannot be realized in silica fibers due to high absorption for

wavelengths . The chemical composition also influences many physical properties of

the fiber, including the maximum concentration of the dopant ions and the optical transitions

of the rare earth ions. Some glasses are photosensitive, allowing fiber Bragg grating

production with UV light irradiation. Photosensitivity is also depending on dopant ions.

Ion Host glass Emission wavelength

neodymium (Nd3+) silicate and phosphate

ytterbium (Yb3+) silicate

erbium (Er3+) silicate, phosphate and fluoride

thulium (Tm3+) silicate, germanate and fluoride

praseodymium (Pr3+) silicate and fluoride

holmium (Ho3+) silicate and fluorozirconate

Table 1: Most common laser-active ions, typical host glasses and operating wavelengths.

2, 3

Emission wavelengths are limited with the selection of fiber material, but are depending on

energy level distribution in rare-earth metal ions. Appropriate pump light wavelengths are

required for different dopants.

Figure 6 shows different working regimes of absorption, stimulated and spontaneous

emission. In erbium ions single photon excitations by many different light wavelengths are

possible and two different emission wavelengths are shown ( and ). Pump

wavelength is shorter than emission wavelength, meaning that energy of a photon of pump

Figure 6: Energy levels and main transitions in (A) erbium and (B) thulium ions (units: ). 3

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light is higher than in emitted light. Part B shows a fundamentally different working regime.

Energy level distribution in thulium allows multi-photon excitation with wavelength

results in blue emitted light at wavelength through upconversion. This process is

mostly used to govern ultraviolet lasers by pumping them with visible or infrared light.

3.3 Power Scaling

The gain of the laser medium is determined by a product of pump light interaction length with

the medium and pump light intensity. Fibers can be made very long so the decisive product

value is orders of magnitude higher in fibers than in bulk solid state lasers. This results in a

highly efficient operation of fiber lasers. Ytterbium-doped glass fibers are the first choice

when high power levels are considered. If those fibers have less than of quantum

defects, optical-to-optical efficiencies above can be achieved. 5

Double-clad optical fibers provide two waveguides, where inner cladding is highly multimode

and active core is at least almost single mode. Large inner cladding enables pumping by high

power and low brightness diodes. Pump light is then gradually absorbed in the active core

along the fibers length and high power, high brightness laser light is emitted. The drawback

of the double-clad fibers is the reduced effective pump light absorption. Such intensity

distributions in the inner cladding can exist that pump light absorption becomes much less

efficient. Proposed solutions to this problem are D-shaped, rectangular or other active core

geometries that break down the symmetry causing unwanted intensity distribution. 7

The tight confinement of the laser radiation is the main reason for all advantages of fiber

lasers. But in combination with long interaction lengths it enforces nonlinear effects, the main

performance limitation of fiber laser architecture. Silica glass is an amorphous solid material

with a center of inversion, so nonlinear effects depending on second order susceptibility ( )

are nonexistent in silica glass fibers. Here I used the notation from the following equation

describing electric polarization in matter with powers of electric field

( )

( ) ( )

The lowest order nonlinear effects in optical fibers originate from third order susceptibility

( ).

Figure 7: Unmodified double-clad fiber (a) in comparison with enhanced pump absorption geometries: (b) offset core, (c) octagonal, (d) D-shaped, (e) rectangular and (f) flower-shaped fiber.

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First class of nonlinear effects includes an intensity dependent refractive index also known as

the Kerr effect:

( )

( )

where is the intensity of incident light in a medium with refraction index 8 Because of the

Kerr effect light propagating through the fiber experiences a self-induced phase shift. This

phase shift can be neglected in continuous-wave fiber lasers.

Second class of important nonlinear effects results from inelastic scattering processes. Light

transfers part of its energy to the glass host in the form of vibrational excitations. An

important example can be made with light in the wavelength region. A large frequency

shift of is observed as a consequence of stimulated Raman scattering, exciting

optical phonons. Stimulated Brillouin scattering causes a much smaller frequency shift of

due to excitation of acoustic phonons. 5

Nonlinear effects are proportional to a power of the mode-field area, equal or smaller than

, thus an enlargement of the fiber core leads to lessening this unwanted effects. One can

show that a fiber becomes single mode for fiber parameter (introduced in chapter 2.2)

( )

Increasing the size of the fiber core thus leads to multimode regime as √

is limited with fiber production processes. A solution to this problem appeared with micro

structured fibers, also known as photonic crystal fibers. 9

This type of micro structured fibers allows very low numerical aperture values for laser light in

the core ( ) and simultaneously high NA for pump light in inner cladding ( ). 5 This

allows simple direction of pump light into the fiber and nearly diffraction limited laser output.

The inner cladding in a photonic crystal fiber consists of a triangular array of air holes. In

order to obtain a large-area fiber core refractive index step between core and inner cladding

must be minimized. Average refractive index of the cladding is reduced by the holes and

precisely adjusted with the hole size and the hole-to-hole distance.

Figure 8: Typical photonic crystal fiber design scheme and scanning electron microscope image. 7, 9

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Outer cladding must have sufficiently low refractive index in order to maintain high NA for

pump light. Therefore, outer cladding consists mostly of air holes, connected with narrow

silica bridges. Those bridges are substantially thinner than the wavelength of the pump light.

Confinement of the fundamental mode is weak in such fibers due to low NA and because of

that sensitive to the environmental perturbation and bending losses. The fiber gains sufficient

rigidity and mechanical stability with adding a large outer protective layer. Commercially

available fiber lasers go up to power for a continuous wave laser at wavelength

while still having approximately wall-plug efficiency. More about power scaling can be

found in the seminar Power Scaling of Fiber Lasers by Jaka Petelin. 10

3.4 Pulsed Operation

Pulsed laser operation is necessary in material processing applications as well as medical

and biophysical applications. 3 Optical damage threshold is a limitation for high pulse

energies in fiber lasers. Optical damage happens due to high power density in the active

core. Silica glass has an extremely high bulk damage threshold of at

wavelength, but tightly focused pulses can still damage the bulk material. Damage most

easily occurs at the fibers end, where pulse enters air. Damage threshold at the fibers end is

at the same wavelength and it is strongly dependent on the fibers end quality.

Any impurity lowers the damage threshold significantly in comparison with bulk material. 7

Due to this fundamental limitation fiber lasers are usually used for nanosecond pulses with

energies in the millijoule range. Peak power can reach dozens of kilowatts in such pulses.

Conventional nanosecond fiber laser architecture is Q-switched pulses. It uses a passive,

electro-optical or acousto-optical light modulator adjacent to an angle cleaved fiber facet to

avoid parasitic lasing between pulses. 7 Frequencies of active Q-switching are limited with

operating frequencies of controlling electronics. The modulator changes gain inside the laser

resonator, pushing it below the level needed for operation. As the time passes more and

more states are excited and when modulator switches again a powerful pulse of laser light is

emitted.

Greatest advantage of fiber laser systems is its possibility for monolithic design also known

as all-fiber design. Several potential monolithic Q-switched systems have been tested both

passive and active. Most common passive elements are saturable absorbers in the cavity,

designed either with end mirrors and thus making the system essentially monolithic or added

by splicing section of saturable absorber into the fiber. 7 Less common passive pulse

generation methods based on Q-switching include a passive mechanism of distributed

backscattering. 11 A simple design, showed in Figure 9, with an added ring interferometer

produced nanosecond long pulses with a repetition frequency of a few kilohertz.

Figure 9: Simple all-fiber passive Q-switch pulsed fiber laser design sketch. 11

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Using pulse stretching and compressing techniques fiber lasers are capable of producing

ultra-short pulses with energies comparable to energies of nanosecond pulses produced by

those same lasers. Ultra-short pulses and their applications are an area of increasing

interests, because of usability in material processing, biomedical imaging, frequency

conversion, remote sensing and other. Most ultra-short pulse fiber systems are capable of

achieving pulse durations in the picosecond order but average output powers remain modest

due to limitations mentioned at the beginning of this chapter. High-power mode-locked fiber

laser oscillators rely on using external cavities and very large-mode area fibers to achieve

their output powers. Cavities usually take the form of ring resonators containing the gain

medium, polarization control elements and other compensation elements. 7 Traditional bulk

optics are commonly used too, making them less useful as stable all-fiber systems.

In the next part of the seminar I will present a specific pulsed fiber laser design because its

realization integrates a few important fiber laser principles. It is a Q-switched, mode-locked

fiber laser, based on an erbium-doped ring cavity laser and employs a subharmonic cavity

modulation. 12 Figure 10 shows a basic scheme of the experimental setup.

The simplest scheme for a Q-switched mode-locked laser is to combine a passive mode-

locking mechanism with an active Q-switch. It is realized by superimposing a Q-switched

envelope on a continuous train of mode-locked pulses. I have already described the basic

principle of mode-locking in my previous seminar about two-photon processes. 13 The peak

power of pulses generated by Q-switched mode locking is about one order of magnitude

higher than pulses generated by mode locking only in the same optical cavity. 12

Ring resonator cavity annuls the need for mirrors but introduces the need for fiber splitters or

couplers so that pump light can be guided in and output laser light guided out. In this

experiment the erbium-doped fiber was pumped by a laser diode rated at

power. Pump light is combined into fiber with a WDM element and output laser light is

extracted via a coupler, direct of laser light out of the resonator. Silicon based fast

variable optical attenuator is a key piece for Q-switching, modulating cavity losses. It is

connected to a signal generator to precisely control the frequency of operation. Optical

isolator and polarization controller were incorporated into the cavity to insure unidirectional

Figure 10: Experimental setup for a Q-switched, mode-locked laser. 12

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beam oscillation. Tunable bandpass filter was added to determine the lasing wavelength and

also eliminate background amplified spontaneous emission. Some of it is visible in Figure 11

(b) as a slight rise before and after pulse.

Figure 11: Pulse train from a Q-switched mode-locked laser (a) with a single pulse magnification (b).

12

Figure 11 shows experimental results in form of a pulse train. Pulse width is approximately

and pulse repetition period which corresponds to a frequency of .

Operating wavelength was measured to be around . Average power was about

while peak power reached . In Figure 11 the fundamental subharmonic order of

Q-switched frequency is used meaning that all pulses are of the same height. Subharmonic

frequencies are by definition frequencies below the fundamental frequency of an oscillator in

a ratio of , where is an integer. In Figure 12 two higher orders of the subharmonics are

used to demonstrate different pulse train shapes. 12

Figure 12: Different subharmonic orders of Q-switched modulation.

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4 Conclusions

Fiber lasers offer a wide variety of possible uses and have shown great progress in recent

years but are still facing a variety of technical challenges, slowing down the mass

appearance. I will sum some of the most important advantages and disadvantages of fiber

lasers.

Most attractive feature of fiber lasers is their compact rugged design. Most of the simpler

fiber laser systems can be realized using an all-fiber design, meaning that there are only fiber

components used as building blocks of the system. Absence of bulk optical components

makes the system outstandingly resistant to mechanical stress and it is virtually impossible to

misalign an all-fiber setup.

Fiber lasers also have a broad absorption specter so it is not important to precisely stabilize

the pump diode while output laser beam has diffraction-limited quality when using

singlemode or slightly multimode fibers. Particularly well accepted are fiber lasers for difficult

lasing schemes such as upconversion or low gain transitions. The potential for high output

power operation has been successfully demonstrated even at unusual wavelengths where no

other laser alternative is available. Also, fiber lasers are getting cheaper than bulk solid state

lasers even when less optimal configurations of fiber lasers are used such as ultra-short

pulse production.

High intensity in the small active core of fiber lasers lead to strong nonlinear effects in fibers

such as the Kerr effect, even though nonlinear coefficients are low for fused silica. Another

problem is met when considering short or ultra-short pulse generation. High peak powers can

by tight confinement of laser light lead to optical damage to the fiber. Even polarization

control can be an issue in fiber lasers, which leads to necessary use of polarization control

and manipulation elements.

Fiber lasers are a rapidly growing field of research with much potential. Fiber laser products

are already found in industry and research, future products are expected to find use in an

even greater variety of applications.

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5 Bibliography

1. Bates, R. J., Optical Switching and Networking Handbook (McGraw-Hill, 2001).

2. Paschotta, R., Encyclopedia of Laser Physics and Technology, Available at

http://www.rp-photonics.com/ (2012).

3. Duarte, F. J. ed., Tunable Laser Applications, 2nd ed. (CRC Press, 2009).

4. Saleh, B. E. A. & Teich, M. C., Fundamentals of Photonics, 2nd ed. (John Wiley & Sons,

Inc., Hoboken, New Jersey, 2007).

5. Limpert, J. et al., The Rising Power of Fiber Lasers and Amplifiers. IEEE Journal of

Selected Topics in Quantum Electronics 13 (3), 537-545 (2007).

6. Hill, K. O. & Meltz, G., Fiber Bragg Grating Technology Fundamentals and Overview.

Journal of Lightwave Technology 15 (8), 1263-1276 (1997).

7. Bass, M. et al., Handbook of Optics, Volume V, 3rd ed. (McGraw-Hill Professional, 2009).

8. Čopič, M., Fotonika, skripta (Faculty of Mathematics and Physics, University of Ljubljana,

Ljubljana, 2011).

9. Limpert, J. et al., High-power air-clad large-mode-area photonic crystal fiber laser. Optics

Express 11 (7), 818-823 (2003).

10. Petelin, J., Power Scaling of Fiber Lasers, Seminar (Faculty of Mathematics and Physics,

University of Ljubljana, Ljubljana, 2010).

11. Chernikov, S. V., Zhu, Y., Taylor, J. R. & Gapontsev, V. P., Supercontinuum self-Q-

switched ytterbium fiber laser. Optics Letters 22 (5), 298-300 (1997).

12. Chang, Y. M., Lee, J. & Lee, J. H., A Q-switched, mode-locked fiber laser employing

subharmonic cavity modulation. Optics Express 19 (27), 26627-26633 (2011).

13. Mur, J., Dvofotonski procesi, Seminar (Faculty of Mathematics and Physics, University of

Ljubljana, Ljubljana, 2011).