Mapping WGMs of erbium doped glass microsphere using near-field optical probe

Vietnam national university, HanoiCollege of Technology Ho Duc Vinh Mapping WGMs of Erbium doped glass microsphere using Near-field optical probe Mapping WGMs of Erbium doped glass micro

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Vietnam national university, Hanoi

College of Technology

Ho Duc Vinh

Mapping WGMs of Erbium doped glass microsphere using

Near-field optical probe

Mapping WGMs of Erbium doped glass microsphere using

Near-field optical probe

Master thesis Supervisor: Dr Tran Thi Tam

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2 CHAPTER I: MORPHOLOGY DEPENDENT RESONANCES

3 CHAPTER II: COUPLING MICROSPHERES WGMs BASED ON NEAR-FIELD OPTICS

4 CHAPTER III: FABRICATION OF MICROSPHERE AND TAPER FIBER

5 CHAPTER IV: EXPERIMENTS AND RESULTS

CONCLUSION

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Chapter 1 Morphology Dependent Resonances

chapter 1: Morphology Dependent Resonances

(MDRs-WGMs) 1.1 Dielectric Microsphere - A simple Model of WGMs:

Microspheres act as high Q resonators in optical regime The curved surface

of a microshere leads to efficient confinement of light waves The light wavestotally reflect at the surface and propagate along the circumference If they round inphase, resonant standing waves are produced near the surface Such resonances arecalled "morphology dependent resonances (MDRs)" because the resonancefrequencies strongly depend on the size parameter

λ

πa

are often called "Whispering Gallery Modes (WGMs)" The WGMs are namedbecause of the similarity with acoustic waves traveling around the inside wall of agallery Early this century, L.Rayleigh [46] first observed and analyzed the

"whispers" propagating around the dome of St.Catherine's cathedral in England

Optical processes associated with WGMs have been studied extensively in recentyears [45]

corresponding to TE (transverse electric) and TM (transverse magnetic) modes TEand TM modes have no radial components of electric and magnetic fields,respectively These integers distinguish intensity distribution of the resonant modeinside a microsphere (a simple model system of Micro resonators) The order

spatial distribution of the mode For the perfect sphere, modes of WGMs are

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1.1.1 Ray and Wave Optics Approach:

The most intuitive picture describing the optical resonances of microsphere isbased upon ray and wave optics

* Ray optics:

be exponentially small This simple geometric picture leads to the concept of

occur (Figure 1.1 b).This condition translates into

2

( )

a n

λπ

ω

c inc θ

θ > Inphase

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In terms of which the resonance condition is

k is the wave number If this ray strikes the surface at near-glancing incidence

2 ( / ( ))

as the angular momentum in the usual sense

the z-component of the angular momentum of the mode is (see Figure 1.2)

2

degeneracy) The degeneracy is partially lifted when the cavity is axisymmetrically(along the z-axis) deformed from sphericity For such distortions the integer values

modes are independent of the circulation direction (clockwise or counterclockwise)[49] Highly accurate measurements of the clockwise and counterclockwise

couples the two counter propagating modes [47]

Geometrical interpretation of light interaction with a microsphere has severallimitations:

- It cannot explain escape of light from a WGM (for perfect spheres), andhence the characteristic leakage rates cannot be calculated

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- Geometric optics provides no possibility for incident light to couple into aWGM.

- The polarization of light is not taken into account

- The radial character of the optical modes cannot be determined bygeometrical optics [7]

* Wave optics:

The proper description of the system should reply on Maxwell’s equations,

(∇ × )− 2 ( ) = 0

×

i.e., the system is spherically symmetric The transverse electric (TE) modes arecharacterized by

waves are then described by a scalar equation [19]

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1.1.2 Lorenz-Mie Theory:

A complete description of the interaction of light with a dielectric is given byelectromagnetic theory which is solved basically in wave optics above The sphericalgeometry suggests expanding the fields in terms of vector spherical harmonics

Characteristic equations for the WGMs are derived by requiring continuity of thetangential components of both the electric and magnetic fields at the boundary ofthe dielectric sphere and the surrounding medium Internal intensity distributionsare determined by expanding the incident wave (plane-wave of focused beam),internal field, and external field, all in terms of vector spherical harmonics and againimposing appropriate boundary conditions

Figure 1.2: The resonant light wave propagates along the great circle whose normal

The WGMs of a microsphere are analyzed by the localization principle andthe Generalized Lorenz-Mie Theory (GLMT) [36, 34, 51] Therefore, each WGM is

which are described above and are summarized here:

electric field distribution in the radial direction

degrees in the angular distribution of the energy of the WGM

+ Each mode WGM of the microsphere also has an azimuthal angular

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However, for sphere, WGMs differing only in azimuthal mode number haveidentical resonance frequencies.

The characteristic eigenvalue equations for the natural resonant frequencies

of dielectric microsphere have been solved in homogeneous surroundings WGMscorrespond to solutions of these characteristic equations of the electromagneticfields in the presence of a sphere The characteristic equations are obtained byexpanding the fields in vector spherical harmonics and then matching the tangentialcomponents of the electric and magnetic fields at the surface of the sphere Noincident field is assumed in deriving the characteristic equations [17]

For modes having no radial component of the magnetic field (transversemagnetic or TM modes) the characteristic equation is,

( ) ( ) ( ( ) )

(1.14)The characteristic equations are independent of the incident field In equation

functions of the first kind, respectively The prime (‘) denotes differentiation withrespect to the argument The transcendental equation is satisfied only by a discrete

The elastically scattered field can be written as an expansion of vector

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plane wave incident on a dielectric microsphere The scattered field becomes infinite

Fig 2.3: Three light waves; the linearly polarized incident plane wave, the sphericalwave inside the sphere and the spherical wave scattered by the sphere

' '

The WGMs of the microsphere occur at the zeros of the denominators (or

the modes are virtual when the resonance frequencies are complex

+ The real part of the pole frequency is close to real resonance frequency[19]

+ The imaginary part of the pole frequency determines the linewidth of theresonance [37]

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Fora fixed radius, the WGMs have l values that are bound by x< <l n( )ω x

[28] (see equation 1.3), where the upper limit is the maximum number ofwavelengths that fit inside the circumference The radial electric field distribution of

mode order becomes, the more the mode distribution goes to inner region [30]

For larger size parameters the first order resonances become narrow while thehigher order resonances heighten and become dominant [8]

The first peaks observed in the spectra are the first-order resonances Thesecond order resonances begin to appear when the size parameter increases due todecreasing the linewidths As the size parameter increases further, the linewidths ofthe first and second order resonances decrease further and third-order resonancesbegin to appear

surrounding lossless medium [23] Thus, equation 1.17 definitions the complexfrequencies at which a dielectric sphere will resonate in one of its natural modes are:

, ,

n n

x a

ω

µε

= l

Based on the Lorenz-Mie theory, the separation between the adjacent peak

λ

∆

2 / 1

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spectral location, separation, and width of WGMs The positions of WGMs areapproximated by [26, 10]:

forms of the Airy function

1.2.2 WGM Separation:

mode positions to determine the approximate sphere size and approximating modenumbers Asymptotic analysis gives:

2 3 2 4 3 ,

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1/ 2

1/ 2 2

Using the vector wave functions, the internal electric fields of a sphere areexpanded as a sum of electric fields (TE modes and one of TM modes) The spatialdistributions of the electric field of TE and TM modes of WGMs are obtained

Figure 1.4 shows the internal intensity distributions in the equatorial plane of

The resonant size parameter is shown in the upper side of each figure Here the

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Figure 1.4 The internal intensity distributions in the equatorial plane for

size parameters are shown in the upper side of each figure

As the mode order increases, number of peaks in the internal intensity profileincreases, corresponding to the mode order, and the highest peak is located at themost inner side in the radial direction An illustration of the angle-averaged radial

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Fig 1.5 (A) Typical illustration of angle-averaged intensity distribution profile

(B) ) Typical illustration of internal-intensity distribution as

l=30, and m=1, 15, and 30 The maximum intensity of each m-mode

sin (m/ )

The dependence of the internal intensity distribution on the azimuthal mode

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1cos ( / )m

sin ( / )m

1sin (15 / 30) 30o

These results are consistent with the qualitative interpretation mentioned in theprevious subsection although the spatial distributions shown in this figure havesomewhat broader structure

1.2.5 Resonator Quality of Microsphere WGMs:

resonance is defined as:

x

ω

ω τω

For frequencies near a WGM, the electric field inside the cavity varies as:

)2exp(

2

)2()(

1

|)(

|

Q E

ωω

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Figure 1.7 The angle average intensity as a function of the normalized radius r/a for

When resonant standing waves grow inside a sphere, the spherical particleacts as a high Q resonator A fraction of the resonant light wave leaks due to thediffractive effect and the quality factor Q of the resonator is limited by thediffractive losses The electric fields of the WGMs extend beyond the particleboundary as evanescent waves The lowest order WGM has the maximum of theinternal distribution at the region nearest the surface of the sphere, and has theshortest penetration depth toward the outer region of the sphere For a given mode

located closest to the surface and the evanescent wave penetrating shortest into the

moves away from the surface, and the evanescent wave penetration into the

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Figure 1.8: The resonance curves for the same WGMs and the sphere as in Fig.1.7

Table.1: The resonance size parameters and the quality factors of TE MDRs

Figure 1.8 shows the resonance curves for the same WGMs and sphere as in

is centered The resonance curve of the lowest order WGM is extremely narrowcompared with the higher order WGMs The quality factor Q of the WGM can bealso defined as:

0

x Q x

=

resonance size parameters and the quality factors of these modes are summarized inTable.1 The lowest order WGM with the same mode number has the highest qualityfactor and is therefore most strongly confined inside the sphere

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Figure 1.9: the resonance curves for the first order TE MDRs with l = 30, 45 and

sphere is 1.4

Table.2: The resonance size parameters and the quality factors of the first

refractive index of the sphere is 1.4 Q increases as the mode number is increased

compared with the lower mode WGMs The resonance size parameters and thequality factors of these modes are summarized in Table.2

On the other hand, one can describe the performance of a resonator element

in terms of its capacity to store energy The quality factor (Q-factor) determines howlong a photon can be stored inside a WGM [18] Therefore the quality (Q) of aresonance is governed by the losses associated with it The observed resonatorquality is the geometric sum of the qualities of each mechanism

coupling observed Q Q Q

1 1

1

0 +

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Alternatively, the observed spectral width is the sum of the widths of all the

s r abs Q Q Q

Q

1 1 1 1

0

+ +

In an optical microsphere WGM resonator, energy storage may be thought of as theretention of individual light rays that have been inserted into the cavity [15] Thevalue of the quality factor roughly equals the number of times a given ray can beexpected to travel around the sphere before succumbing to a loss process In silicamicrospheres, internal loss effects include scattering from surface irregularities,absorption due to molecular resonances, Rayleigh scattering Surface scattering isextremely low, since extremely smooth surfaces can be fabricated Therefore,absorption and Rayleigh scattering dominate the losses [30]

1.2.6 Mode volume of microsphere WGMs:

In many applications, not only temporal confinement of light (i.e the factor), but also the spatial extension to which the light is confined is an importantperformance parameter Several definitions of mode volume can be encountered inliterature, and are discussed in this section The most common definition of modevolume is related to the definition of the energy density of the optical mode

Q-It is defined as the equivalent volume, the mode occupies if the energy densitywas distributed homogeneously throughout the mode volume, at the peak value:

D

TE n

D

V m sphere 11 6 7 6

6 7 6

11

08 1

02 1

/ /

,

/

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Chapter 2: Coupling Microsphere WGMs based on

Near-field Optics 2.1 Introduction of Near-field optics

Near-field optics has developed very rapidly from around the middles 1980safter preliminary trials in the microwave frequency region, as proposed as early as

1928 At the early stages of this development, most technical efforts were devoted torealizing super-high-resolution optical microscopy beyond the diffraction limit

However, the possibility of exploiting the optical near-field, phenomenon ofquasistatic electromagnetic interaction at subwavelength distances betweennanometric particles has opened new ways to nanometric optical science andtechnology, and many applications in the field of nanometric fabrication andmanipulation have been proposed and implemented For optical telecommunicationsystem, near-field optics can demonstrate lots of photonic phenomena such asquantum electrodynamics (QED), CQED… And one of spectacular examples isnear-field interaction of microcavities and tip guide It is my purpose to use a simpleand practical theory so that we can understand easily the fundamental physics of thenear-field in three dimensions and to obtain a general expression for each fieldcomponent which will serve as a guide to more complicated cases This part willshow that the analytic forms of the near-field components around a microsphereproduced by an incident plane wave can be obtained and that the effect of near-fieldcan be evaluated in some applications Comparison of our theory with anexperimental result reported by other authors shows good agreement It will alsoverify that the localization area of the near field is proportional to the size of themicrosphere, and that the field momentum is locally modified by the interferencebetween the near field and the incident field and that the modulation amount isdependent on the size of the sphere, instead of the wavelength of the light Also, Itcould be seen the relationship of Evanescent-field with Near-field optics and thescope of near-field optics in the modern optical telecommunication depictedhereinafter

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Chapter 2 Coupling Microsphere WGMs based on near-field optics

Figure 2.1 Near-field optics and related problems Optical processes areshown in terms of the scales given by the size of the material object and the spatial

extent of the effective field

2.2 Evanescent coupling techniques for optical micro-cavities:

The study of the optical properties of ultra-high-Q (UHQ) microcavitiesrequires the ability to optically excite and probe the resonator Furthermore, theinvestigation of the full potential of UHQ structures to realize high performancedevices, such as low-loss passive elements and low-threshold active elements such

as nonlinear sources, requires an ability to both efficiently excite the modes of thecavity and to efficiently extract optical energy from the cavity There are severalcommonly used techniques to couple optical microcavities These fall into twoclasses: phase-matched and non-phase-matched techniques Of the two, phase-matched schemes offer a dramatic advantage in terms of coupling efficiency bothinto and out-of the cavity, relegating non-phase-matched schemes (of which free-space illumination is the sole member) to systems where experimental limitations

Spatial Extent of Effective Field or Sample-Probe Distance

Propagating Light Wave

Cavity QED

Photon Localiztion

Photon-Light Emission From STM

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and/or simplicity is coupled with a sufficient excitation power and detection marginsuch that the gross inefficiency is tolerable Additionally, precise characterization ofthe properties of optical microcavities is extremely difficult for broad illuminationschemes, as multiple whispering gallery modes (WGM's) are excited spatially, andthe emission is detected in a radial fan of energy from the perimeter For thesereasons, phase-matched couplers are commonly used.

Phase-matched coupling techniques can again be subdivided into two areas,direct and evanescent couplers Direct couplers, such as grating couplers fabricated

on the cavity surface, possess the advantage of free-space illumination/emissionsimplicity along with the ability to phase-match, thus in principle allowing highefficiency However, as the effect of this coupling method on the intrinsic cavityproperties is unclear, thesis focuses on evanescent coupling methods, especially thefiber taper coupling method The fundamental of this theory is more clearly and nowimproved rapidly in research-movements of photonics and nano-technology over theworld A branch of near-field optics, evanescent-field around microcavites -couplers will be analyzed briefly and applied particularly to coupling devices in theexperiments

Figure 2.2 Evanescent field around of microsphere for extracting energy out

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2.2.1 What is evanescent-field?

The optical near-field can be excited whenever light is incident on a surfaceunder the total internal reflection condition It is highly localized at the interface ofthe material and does not propagate away from the surface This localization is lessthan the wavelength of the incident light and probing in this optical near-fieldenables resolution beyond the diffraction limit

with a boundary in this way is governed by Snell’s law, which is defined as

1sin 1 2sin 2

At the boundary, a fraction of the incident light is reflected, while the remainder is

1 2 1

sin

c

n n

leads to total internal reflection

Figure 2.3 Schematic representation of the evanescent-field under the

condition of total internal reflection

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Though no real angle of refraction θ2 exists when 1 90o

c

θ θ< < , the

2 2 2

electric field is given by

( , ) oexp[ ( sin cos )]

equation 2.3 into the equation 2.4 gives

2 2

whose value is in the tens of nanometers Equation 2.5 shows that a surface wave

λλ

θ

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Such a localized surface wave is called and evanescent wave The evanescent

evanescent wave exists is termed the optical near-field or the evanescent field

2.2.2 Methods of coupling

Many applications of microspheres require coupling of light into the WGMsfrom external light sources through evanescent-fields Numerous methods have beendeveloped for the excitation of the WGMs of microsphere resonators as in figure

[16], the tapered fiber coupler [33], and, more recently, the hybrid fiber–prismcoupler [25], and the strip line pedestal anti-resonant reflecting optical waveguide(SPARROW) coupler structure [39]

Figure 2.4 Methods of evanescent-field couplingAmong them, the prism coupler is efficient and tunable, but it uses bulkcomponents required collimation and focusing optics to work with optical fibers

The hybrid fiber–prism makes use of the efficiency of the bulk prism, with theversatility of optical fibers [39] SPARROW coupler structure (Planar structures) isthe introduction of the first wafer-fabricated integrated optical coupling techniquegetting high-Q WGMs in compact integrated circuits [35]

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The use of optical fiber for a coupler means that both the incident wave andany wave that interacts with or is generated from a cavity can be manipulated in anall fiber system using standard components Furthermore, the extremely low loss ofthis transport medium is ideally suited to potential applications of opticalmicrocavities, in particular the generation and transport of quantum states of light.

There are a number of types of fiber-couplers, including side-polished and block couplers [24] The side-polished and half-block couplers, while fiber-based,possess relatively low efficiencies for coupling both into and out of a resonator, inaddition to a high optical loss for energy which does not interact with the cavity

half-However, another type of fiber-coupler, the tapered optical fiber [29], can retain theultra-low loss inherent to optical fiber while possessing very high couplingefficiencies to an optical microresonator In theory and experiments of thesis, It hadbeen chosen a new method, called “ half taper coupler” Here, two half-taperedfibers were used, one for pump into the sphere and another for extracting WGMsand laser signals out of microsphere More experimental details will be discussed inlater sections and the based theories for coupling half-tapered fiber withmicrosphere now is analyzed

2.3 Optical Near-Field Distribution around a Dielectric Microsphere:

A dielectric sphere is an open cavity supporting tunneling leaky waves Theeigenvalues of the exact solution should be complex in order to satisfy the radiationcondition Such solutions, with fields that grow unbounded in the radial direction farfrom the sphere, are difficult to normalize [22] On the other hand, it is only the nearfield, the bound portion of the field, which contributes to coupling with the externalexcitations The field can be written as

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( )

s r

(2.9c)and the coefficients are

λ

, ,m n( , , )rθ φ

The field consists of the following components

defined to range only over positive values)

polynomials are well represented by the Hermite–Gauss functions (Appendix

the polar dependency facilitates the closed-form evaluation of future overlapintegrals

constant parallel to the surface of the sphere The propagation constantparallel the surface of the sphere, but along the equator, is the projection of

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is the effective index and λ is the wavelength Then the range of validity1

m>> indicated in (2.9b) amounts to n( )ω a λ >>1, or that the sphere radiusmust be much larger than the effective wavelength

Figure 2.5 Schematic of the mode propagation constants along the surface of a

sphere, when excited by a side-coupled fiber

s

plane transverse to the effective direction of propagation In my coordinate system,

, ,m n

The characteristic equation which describes the relationship between the

identified as a consequence of separable solutions:

1 Transverse electric (TE) modes, where the electric field is parallel to the

l m n r

Er =θEθ ≡ Ψθ Eφ =E =

2 Transverse magnetic (TM) modes, where the magnetic field is parallel to

l m n r

The

fields of the TM modes, aredetermined by Maxwell’s equations, (see for example, [9]) Matching tangential

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2.4 Fields of a tapered Fiber:

Figure 2.6 Cross-sectional view of the geometry of a tapered fibercoupled to a sphere Near the point of contact between a fiber and sphere, the

sphere curvature is represented by a parabolic profile

A fused tapered fiber is one in which the core and cladding have been heatedand drawn to obtain a narrow waist The waist typically ranges from a few

air-clad glass rod A tapered fiber coupled to a sphere is depicted in figure 2.6 The

2

1 2

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ρ In addition, the global Cartesian coordinates x and y will be used Their origin

is along the fiber axis

The fields of an optical fiber have well known analytic solutions [53] Here

we assume that the fields are linearly polarized and that the radial dependence of thefundamental mode takes the form

J k a N

απ

modified Hankel functions of zero and first order [40] The normalization constant

f

( )

o

The field dependence outside of the core is typically written in terms of themodified Hankel function Here, for ease of manipulation in later integrals, we

exact field at the core boundaries Because this fitting function must agree with boththe exact value and the decay rate at the core boundaries, it proves to be an excellentapproximation for both strongly confined (air clad) and weakly confined modes Thecharacteristic equation used here to determine the fiber mode propagation constant

α

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2.5 Tapered Fiber – Microsphere Coupling:

formulas in this and the following section can be used in a mechanical way to obtain

sphere mode, and the fundamental mode of the fiber Excitation by a tapered fiber isconsidered first

The arrangement of a tapered fiber evanescently side coupled to a sphere is

from the fiber axis The mode numbers of the sphere and the resonant wave vectorare evaluated from the solution to the characteristic equation (2.11) Thepropagation constant of the fiber is found from the characteristic equation (2.15)

With the normalized modes determined, coupled mode theory [20], [6] is invoked toevaluate the interaction strengths The interaction strength between the fiber mode

o

given by the overlap integral

J k a N

απ

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N

minimum separation with the fiber Due to the near parabolic curvature of thesphere at the minimum separation, (see figure 2.10), the interaction decreases with aGaussian dependency away from this point along the length of the fiber Thetransfer of amplitude from the fiber to the sphere per revolution of the mode in the

a a m

By bending the fiber slightly around the sphere, the interaction length can be

equation (2.19)] for instance)

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Chapter 3 Fabrication of Microsphere and tapered fiber

CHAPTER 3: Fabrication of Microsphere and

tapered fiber

3.1 Materials and fabricating methods of microsphere:

3.1.1 Introduction of Erbium doped host glasses for micospheres

a Introduction of materials for active microspheres:

In recent years, multi-component glasses have attracted great interest ashosts for rare-earth ions since they can accommodate larger impurity concentrationsthan silica, and rare-earth doped microcavity lasers have been successfully shownfor practical applications This section will review some recent results of studies inactive doped materials for lasing and extracting WGMs spectra in microsphere

+ A WGM laser utilizing a microsphere made of highly doped erbium

operation in fiber-coupled regime were obtained A bisphere laser system consisting

of two microspheres attached to a single fiber taper also was demonstrated

+ A green-room temperature upconversion laser was demonstrated in a 120

absorbed pump power

+ Experimental results on the realization and spectral characterization of

+ Green lasing having a 4-mW threshold was demonstrated in an doped fluoro-zirconate glass WGM microsphere [21] Periodic narrow peaks of theemission spectra corresponding to the WGMs were observed

erbium-ion-+ An erbium-doped microlaser on silicon operating at a wavelength of 1.5

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[44] The 40 µm diameter toroidal laser WGM was also made using a combination

of erbium ion implantation, photolithography, wet and dry etching, and laser

Single-mode lasing was observed

Moreover, instead of using doped materials, a passive WGM can be coatedwith gain medium For example, erbium-doped sol gel films were applied to thesurface of silica microspheres to create low-threshold WGM lasers [32]

According to the state of the art, experimental results are focused on output

doped PZG glasses With very high-concentrations of Erbium ion dopants (from2,000 ppm to 15,000 ppm) in silica-alumina made in IMS-VAST, the microspheres

- range of microspheres made from PZG glass, section of experiments also paysattention to PZG and fluouride glass samples These samples were made by Physics-Chemical Laboratory of Luminescent Materials, University Claude Bernard Lyon 1

The samples of Erbium doped in various bulk glass-matrices hereinbefore will bestudied about their characteristics Results are rather different particularly not only

in spectra (chapter 4) but also in fabricating (section 3.1.2)

b General features of Erbium doped glass:

v Principle of operation:

Erbium is a rare earth element belonging to the group of the Lanthanides

4f-shell, allowing for different electronic configurations with different energies due tospin-spin and spin-orbit interactions Radiative transitions between most of these

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ground, it occurs a green light emission

When Erbium is incorporated in a solid however, the surrounding materialperturbs the 4f wave functions This has two important consequences Firstly, thehost material can introduce odd-parity character in the Erbium 4f wave functions,making radiative transitions weakly allowed Secondly, the host material causesStark-splitting of the different energy levels, which results in a broadening of theoptical transitions which is basic for the theory of the experiments Figure 3.1(a)

allowed, the cross sections for optical excitation and stimulated emission are quite

states are long, up to approximately 10 milliseconds When Er is excited in one ofits higher lying levels (see Fig 3.1(a)) it rapidly relaxes to lower energy levels viamulti-phonon emission This results in typical excited state lifetimes ranging from 1

multi-phonon emission is unlikely, resulting in lifetimes up to ~20 ms depending on hostmaterial, and efficient emission at 1.54 mm

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v Upconversion :

gain limiting effect such as upconversion, non radiative quenching and excited stateabsorption (ESE) or pump photon Fig 3.1c,d In some host glasses, such as silica, anadded complication is known as the clustering effect That means the nano-scalelocal structure can vary for these glasses, such that clusters of ions can form in oneregion whereas another region might have isolated ions The clustering effect hasbeen shown to lead to cooperative luminescence phenomena and has been evidencedeven at quite low doped levels of rare earth (~ 85 ppm) It has been found, however,that the addition of Al into the host glass composition or modified host glasses canreduce the tendency to clusters which is given more details in two remained sections

of this part

One of nanoscale clustering effect processes is co-operative upconversion In

obtain a certain degree of inversion Co-operative upconversion is possible due tothe presence of a resonant level at twice the energy of the first excited state The co-operative upconversion coefficient depends on the host material, as it is related tothe exact energy level positions, cross sections, the dielectric constant, and thetypical phonon energy of the host material In practice, co-operative upconversion is

v Non-radiative quenching :

non-radiative quenching sites For example, the second overtone of the OH stretch

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correlates with the water content in silica glasses The effect of quenching sitesbecomes more pronounced at high Erbium concentrations, resulting in a reducedpumping efficiency Therefore, care must be taken to synthesize Erbium dopedmaterials that are free of impurities or defects that couple to Erbium

3.1.2 Erbium-doped alumino silicate glasses:

For Erbium doped glass to create microspheres, one of the solutions fordecreasing a short-coming of material due to ion-clusters is to add Al by sol-gelmethods into glass composition Some recent experiments show that the highly-concentrated Er-doped silica-alumina glasses (SiO

2-Al

2O

with optimum Al/Er mole ratio (for example : Al/Er mole ratio is of 10 -11 by [1,2]) have strongest emission with broadened band (up to 60 nm at FWHM) The

the fact that the co-dopant Al

2O

matrix [3] avoiding quenching due to Er-ion pairs or clusters (Fig 3.2)

The main problems which sol-gel method brings in are precise control ofdopant concentration and making possible a low-cost study of a wide range ofinversion concentration

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It is well known that the aluminium co-doping can alleviate the problem ofnanoscale Erbium clusters [11] Moreover, Fig 3.3 indicates an increase of thefluorescence bandwidth with the increase of alumina content [43].

Fig 3.3 Effective bandwidths (absorption and emission) as a function of

The doping solution for materials to fabricate microspheres is alsosignificant One of that is ytterbium co-doping which can significantly enhance

easier than other materials to create microsphere but more difficult to optimizeeffecients in studying spectra of WGMs microspheres The making the pumpingmechanism more efficient [38] is soon demonstrated in the section ZNLAN andPZG host glasses hereinafter

3.1.3 Erbium-doped fluoride and PZG glasses:

Another material solutions for WGMs microsphere used in the experiments

fabrication and WGMs spectra of microspheres

v Er 3+ doped ZBLAN glass:

Heavy metal fluoride glasses (HMFGs) show great promise as fiber opticmaterials With the possibility of far lower attenuation rates than current silica-based materials (as low as 0.001 dB/km, cf 0.2 dB/km for Si-based fibers), the most

(ZBLAN) A perfect ZBLAN fiber could carry light near the theoretical best allowed

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attenuation by matter [56], see Fig 3.4 In addition to its low attenuation, ZBLANprovides a larger spectral window This property is especially important forincreased bandwidth in data transmission applications

Figure 3.4: ZBLAN's attenuation approaches the theoretical minimum allowed

by matter

Given these advantages, why isn't ZBLAN used commercially? The reason isthat amorphous ZBLAN is very difficult to produce ZBLAN will crystallize if it isnot cooled rapidly enough Achieving fast cooling requires that the sample be madewith a high surface area to volume ratio But microspheres offer a good solution tothis issue Due to 40 - 120 m in diameter, they equilibrate very quickly with theirsurroundings, so that very fast temperature changes are possible In addition to thehigher Q values due to lower loss in optical ranges, there is reason to believe thatmicrospheres based on Erbium doped ZBLAN glass can be fabricated to createimproved low threshold green lasers

It is noticeable for fabrication ZBLAN based microsphere, however, thatwater absorption has a far more deteriorative effect in ZBLAN than in Si-basedspheres [31] The following reaction occurs:

Surface scattering in microspheres losses depend largely on two factors:

surface inhomogeneity, which cause diffusive scattering, and surface curvature,which causes a greater fraction of light to be refracted to the outside of the sphere

m

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