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H F-XC A N GE H F-XC A N GE c u-tr a c k N y bu to k lic Vietnam national university, Hanoi College of Technology d o Ho Duc Vinh Mapping WGMs of Erbium doped glass microsphere using Near-field optical probe Master thesis Supervisor: Dr Tran Thi Tam LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com o c m C m w o d o w w w w w C lic k to bu y N O W ! PD O W ! PD c u-tr a c k c CONTENT INTRODUCTION CHAPTER I: MORPHOLOGY DEPENDENT RESONANCES CHAPTER II: COUPLING MICROSPHERES WGMs BASED ON NEAR-FIELD OPTICS CHAPTER III: FABRICATION OF MICROSPHERE AND TAPER FIBER CHAPTER IV: EXPERIMENTS AND RESULTS CONCLUSION LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! PD O W ! PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Morphology Dependent Resonances Chapter w w w c u-tr a c k c 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 waves totally reflect at the surface and propagate along the circumference If they round in phase, resonant standing waves are produced near the surface Such resonances are called "morphology dependent resonances (MDRs)" because the resonance frequencies strongly depend on the size parameter x = 2π a , (where a is the radius of λ microstructure and λ is the light wavelength) Alternatively , the resonant modes are often called "Whispering Gallery Modes (WGMs)" The WGMs are named because of the similarity with acoustic waves traveling around the inside wall of a gallery 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 recent years [45] WGMs are characterized by three numbers, n, l and m, for both polarizations corresponding to TE (transverse electric) and TM (transverse magnetic) modes TE and TM modes have no radial components of electric and magnetic fields, respectively These integers distinguish intensity distribution of the resonant mode inside a microsphere (a simple model system of Micro resonators) The order number n indicates the number of peaks in the radial intensity distribution inside the sphere and the mode number l is the number of waves of resonant light along the circumference of the sphere The azimuthal mode number m describes azimuthal spatial distribution of the mode For the perfect sphere, modes of WGMs are degenerate in respect to m In this section, firstly, it presents a simple model of WGMs in terms ray and wave optics for a qualitative interpretation Ho Duc Vinh K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Morphology Dependent Resonances Chapter w w w c u-tr a c k c 1.1.1 Ray and Wave Optics Approach: The most intuitive picture describing the optical resonances of microsphere is based upon ray and wave optics * Ray optics: Consider a microsphere with radius a and a refractive index n(ω ) , and a ray of light propagating inside, hitting the surface with angle of incidence θ in (Figure 1.1.a) Inphase θ inc > θ c Figure 1.1 a/ Ray at glancing angle is totally reflected b/ If optical path = integral number of wavelengths, a resonance is formed If θ in > θ c = arcsin(1/ n(ω )) , then total internal reflection occurs Because of spherical symmetry, all subsequent angles of incidence are the same, and the ray is trapped Leakage occurs only through diffractive effects, i.e., because of the finiteness of a / λ , where λ is the wavelength in vacuum The leakage is expected to be exponentially small This simple geometric picture leads to the concept of resonances For large microspheres ( a >> λ ), the trapped ray propagates close to the surface, and traverses a distance ≈ 2π a in one round trip [52] If one round trip exactly equals l wavelengths in the medium (l = integer), then a standing wave can occur (Figure 1.1 b).This condition translates into 2π a ≈ l λ n(ω ) (1.1) A dimensionless size parameter x is defined for this system x= Ho Duc Vinh 2π a λ (1.2) K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Morphology Dependent Resonances Chapter w w w c u-tr a c k c In terms of which the resonance condition is x≈ l n(ω ) (1.3) Consider the ray in Figure 1.1.a as a photon Its momentum is p = h k = h [2π (λ / n(ω ))] (1.4) where p is the momentum of photons, h is the Planck’s constant divided by 2π , and k is the wave number If this ray strikes the surface at near-glancing incidence ( θ in ≈ π ), then the angular momentum, denoted as h l , is h l ≈ a p = a 2π h (λ / n(ω )) (1.5) which is identical to Equation 1.3 The point of this derivation is to identify the integer l , originally introduced as the number of wavelengths in the circumference, as the angular momentum in the usual sense The great-circle orbit of the rays need not be confined to the x-y plane (e.g., the equatorial plane) If the orbit is inclined at an angle θ with respect to the z-axis, the z-component of the angular momentum of the mode is (see Figure 1.2) π m = l cos( − θ ) (1.6) For a perfect sphere, all of the m modes are degenerate (with l +1 degeneracy) The degeneracy is partially lifted when the cavity is axisymmetrically (along the z-axis) deformed from sphericity For such distortions the integer values for m are ± l , ± (l − 1), 0, where the degeneracy remains, because the resonance modes are independent of the circulation direction (clockwise or counterclockwise) [49] Highly accurate measurements of the clockwise and counterclockwise circulating m-mode frequencies reveal a splitting due to internal backscattering, that couples the two counter propagating modes [47] Geometrical interpretation of light interaction with a microsphere has several limitations: - It cannot explain escape of light from a WGM (for perfect spheres), and hence the characteristic leakage rates cannot be calculated Ho Duc Vinh K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Morphology Dependent Resonances Chapter w w w c u-tr a c k c - Geometric optics provides no possibility for incident light to couple into a WGM - The polarization of light is not taken into account - The radial character of the optical modes cannot be determined by geometrical optics [7] * Wave optics: The proper description of the system should reply on Maxwell’s equations, which, for a definite frequency ω and in units where C = 1, is ∇ × (∇ × E ) − ω 2ε (r )E = (1.7) Here we assume that the dielectric constant ε depends only on the radius a, i.e., the system is spherically symmetric The transverse electric (TE) modes are characterized by E ( r ) = Φ lm ( a ) X lm (θ , Φ ) where X lm = l ( l + 1) −1/ (1.8) LYlm is the vector spherical harmonic and L = a × i∇ The waves are then described by a scalar equation [19] l ( l − 1) d 2Φ + ω ε ( a ) − Φ = da a2 (1.9) where the scalar function Φ is related to the radial function of the field as Φ = aφ lm ( a ) (1.10) similarly, the transverse magnetic (TM) modes are characterized by E (r ) = ∇ × φ lm ( a ) X lm ε ( a) (1.11) and is again reducible to a scalar equation [19] d d Φ l ( l + 1) Φ = + ω − da ε ( a ) da ε (a) a2 (1.12) where in this case the scalar function is again given by (1.10) Hence, the radial character of the optical modes could be determined by wave optics Ho Duc Vinh K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Morphology Dependent Resonances Chapter w w w c u-tr a c k c 1.1.2 Lorenz-Mie Theory: A complete description of the interaction of light with a dielectric is given by electromagnetic theory which is solved basically in wave optics above The spherical geometry suggests expanding the fields in terms of vector spherical harmonics Characteristic equations for the WGMs are derived by requiring continuity of the tangential components of both the electric and magnetic fields at the boundary of the dielectric sphere and the surrounding medium Internal intensity distributions are determined by expanding the incident wave (plane-wave of focused beam), internal field, and external field, all in terms of vector spherical harmonics and again imposing appropriate boundary conditions Figure 1.2: The resonant light wave propagates along the great circle whose normal direction is inclined at an angle π − θ with respect to the z-axis The WGMs of a microsphere are analyzed by the localization principle and the Generalized Lorenz-Mie Theory (GLMT) [36, 34, 51] Therefore, each WGM is characterized by a mode order n , a mode number l and an azimuthal mode m, which are described above and are summarized here: + The radial mode order n indicates the number of maxima in the internal electric field distribution in the radial direction + The mode number l gives the number of maxima between 0o and 180o degrees in the angular distribution of the energy of the WGM + Each mode WGM of the microsphere also has an azimuthal angular dependence from 0o and 360o, which is define with an azimuthal mode number m Ho Duc Vinh K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Morphology Dependent Resonances Chapter w w w c u-tr a c k c However, for sphere, WGMs differing only in azimuthal mode number have identical resonance frequencies The characteristic eigenvalue equations for the natural resonant frequencies of dielectric microsphere have been solved in homogeneous surroundings WGMs correspond to solutions of these characteristic equations of the electromagnetic fields in the presence of a sphere The characteristic equations are obtained by expanding the fields in vector spherical harmonics and then matching the tangential components of the electric and magnetic fields at the surface of the sphere No incident field is assumed in deriving the characteristic equations [17] For modes having no radial component of the magnetic field (transverse magnetic or TM modes) the characteristic equation is, [ n(ω ) jl (n(ω ) x)] xhl(1) ( x ) = n (ω ) jl (n(ω ) x) hl(1) ( x) ' where x is the size parameter, x = ' (1.13) 2π a , a is the radius, λ is the wavelength, and λ n(ω ) is the ratio of the refractive index of dielectric microsphere to that of the surrounding medium The characteristic equation for modes having no radial component of the electric field (transverse electric or TE modes) is: [ n(ω ) x jl (n(ω ) x)] ' jl (n(ω ) x) xhl(1) ( x) = (1) hl ( x ) ' (1.14) The characteristic equations are independent of the incident field In equation 1.13 and equation 1.14, jl(x) and hl(1)(x) are the spherical Bessel and the Hankel functions of the first kind, respectively The prime (‘) denotes differentiation with respect to the argument The transcendental equation is satisfied only by a discrete set of characteristic values of the size parameter, xn,l , corresponding to the radial nth root for each angular l The elastically scattered field can be written as an expansion of vector spherical wave functions with TE coefficients (al) and TM coefficients (bl) for a Ho Duc Vinh 10 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Morphology Dependent Resonances Chapter w w w c u-tr a c k c plane wave incident on a dielectric microsphere The scattered field becomes infinite at complex frequencies ω ( n , l ) corresponding to the complex size parameters x(n,l) , at which, al and bl become infinite Fig 2.3: Three light waves; the linearly polarized incident plane wave, the spherical wave inside the sphere and the spherical wave scattered by the sphere al coefficients are associated with TEn,l WGMs specified by: jl ( x) [ n (ω ) x jl ( n(ω ) x ) ] − n (ω ) jl ( n(ω ) x) [ x jl ( x ) ] ' al = ' hl(2) ( x) [ n(ω ) x jl ( n(ω ) x) ] − n (ω ) jl ( n(ω ) x) xhl( 2) ( x) ' ' (1.15) Similarly, bl coefficients are associated with the TMn,l WGMs as specified by equation 1.16, where hl(2) ( x) are the spherical Hankel functions of the second type [6] jl ( x ) [ n(ω ) x jl ( n(ω ) x ) ] − jl ( n(ω ) x) [ x jl ( x ) ] ' bl = ' hl(2) ( x) [ n(ω ) x jl ( n(ω ) x) ] − jl ( n(ω ) x) xhl(2) ( x ) ' ' (1.16) The WGMs of the microsphere occur at the zeros of the denominators (or poles) of al and bl coefficients These complex poles occur at discrete values of the complex size parameter x The modes are radiative for real frequencies, and hence 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 the resonance [37] Ho Duc Vinh 11 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k c For a 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 of wavelengths that fit inside the circumference The radial electric field distribution of the lowest order modes (nth) shows a peak just inside the surface The higher the mode order becomes, the more the mode distribution goes to inner region [30] For larger size parameters the first order resonances become narrow while the higher order resonances heighten and become dominant [8] The first peaks observed in the spectra are the first-order resonances The second order resonances begin to appear when the size parameter increases due to decreasing the linewidths As the size parameter increases further, the linewidths of the first and second order resonances decrease further and third-order resonances begin to appear The natural resonance frequencies associated with the TEn,l and TMn,l modes are given by equation 1.17, where µ is the permeability and ε permittivity of the surrounding lossless medium [23] Thus, equation 1.17 definitions the complex frequencies at which a dielectric sphere will resonate in one of its natural modes are: ω n, l = Mode Density (a.u.) c u-tr a c k lic to k lic C m w w w d o C bu y Morphology Dependent Resonances Chapter w w w xn , l (1.17) a µε ∆λ λ1/ Wavelength Figure 1.3 WGM mode spacing ∆λ and the WGM linewidth λ1/ Based on the Lorenz-Mie theory, the separation between the adjacent peak wavelengths of the same mode order (n) WGMs with subsequent mode numbers Ho Duc Vinh 12 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k c 4.2.2 Spectra results: v WGMs spectra Investigation on WGMs spectra and laser oscillation WGMs spectra reveals the important informations such as quality of micro cavity, ability of emission environment and optical amplifier, optical pump technique for microspheres… Therefore, the first problem mentioned in spectra analysis should be studying WGMs spectra We have implemented experiments and solved this problem by using two types of obtained microspheres: Erbium-Ytterbium doped silica-alumina microspheres (A kind) and Erbium – Ytterbium doped PZG microspheres (B kind) ranged in diameter from 30 µm to 200 µm When pumping these microspheres are strong enough (Ppump > mW at 976 nm into the pumping half-taper), we can see the oscillation of WGMs microspheres in wavelength range from 1500 to 1610 nm The gain spectral region of Erbium doped microspheres exhibits that wavelengths of WGMs microspheres vary widely in the both C-band and L-band, which is utilized in optical telecommunication strongly -66 -67 -68 -69 -70 Amplitude (dBm) c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w -71 -72 -73 -74 -75 -76 -77 -78 -79 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 Wavelenght (nm) Figure 4.15 WGMs spectrum of Erbium microsphere (type A5) Figure 4.15 and 4.16 show different features of WGMs spectra, type A5 and A4 for Erbium-Ytterbium doped silica glass microspheres with diameters D = 150µ m and D = 80µ m , respectively With both of microspheres, it is clear to see visually the up-conversion emission effect of ion Er 3+ in the green wavelength of Ho Duc Vinh 67 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k c 540 nm for pump intensity of mW Depending on types of materials for microsphere, percentage of glass compositions, perfectibility of cavity, intensity and technique of pump and collect WGMs… , it is more difficult to obtain WGMs spectra which we can see distinguishable WGMs WGMs spectrum of type A5 in Figure 4.15 is rather similar to ASE spectrum of typical EDFAs, but it still reveals the groups of WGMs manifold inconsiderably Whereas, with A4 microsphere, we can more clearly observe the WGMs oscillations ranged from 1510 to 1610 nm (figure 4.16), from which laser oscillation appearance is form as a first step at wavelength region of 1560 – 1610 nm -71 -72 -73 -74 Amplitude (dBm) c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w -75 -76 -77 -78 -79 -80 -81 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 Wavelenght (nm) Figure 4.16 WGMs spectrum of Erbium microsphere (type A4) As well as its dependency on Erbium doping ratio, the behaviour of erbium as a gain medium is influenced by the host material Silica glass has a broad infrared transmission spectrum, which can absorb ions erbium up to high concentrations and so provide a promising candidate for a compact optical gain medium These high concentrations have the advantage of allowing efficient pumping, high gain and high efficiency of energy transfer between the ions While, PZG glasses have attractive properties such as high gain, low concentration quenching and low up-conversion losses Figure 4.17 shows the WGMs of Erbium-Ytterbium doped PZG glass microsphere with small doping ratio of Erbium and lower pump power (3 mW) The Ho Duc Vinh 68 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k c peaks of laser oscillation WGMs are exposed evidently and gain region is rather wide and flat The theoretical analysis shows that these series of peaks can be assigned to several families of modes, each of them having the same radial order but different polarizations The WGMs signal could be obtained by forward and backward coupling configuration -70 -71 -72 Amplitude (dBm) -73 -74 -75 -76 -77 -78 -79 -80 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 Wavelength (nm) Figure 4.17 WGMs spectrum of 100 µm B1 microsphere (Erbium-Ytterbium doped PZG glass), with pump power of mW v WGMs as function of pump power: -66 -64 30 mW 20 mW mW -68 -70 30 mW 20 mW mW -66 -68 -72 -70 Amplitude (dBm) Amplitude (dBm) c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w -74 -76 -78 -80 -72 -74 -76 -78 -80 -82 -82 -84 -84 -86 1500 1520 1540 1560 1580 1500 1600 Wavelength (nm) 1520 1540 1560 1580 1600 1620 Wavelength (nm) a) b) Figure 4.18 WGMs spectra as a function of pump power for (a) 150 µm, type A microsphere (b) 100 µm B-microsphere Ho Duc Vinh 69 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w c u-tr a c k c We saw in chapter 3, section 3.1, that the optical spectra of WGMs are directly influenced on the absorption and emission cross sections of any materials for microspheres As a consequence, configurations and intensities of pump power are one of important parameters for investigation WGMs of microspheres The results are summarized in Figure 4.18 for 980 nm pumping of a 150 µm microsphere-A and 100 µm microsphere-B with three levels of pump intensity The WGMs peak at 1530 nm is very sensitive to the pump power Similarly to the behavior of intensity for peaks of 1530 –1560 nm range, the 1600 nm WGMs band is at first rather flat and high As the pump power is increased and the inversion of ions Erbium rises, the 1530 nm and 1560 nm (specially for 1530 nm) catch up with and then surpass the 1600 nm WGM band The reason for this can be understood by characteristics of absorption and emission spectra of ions Erbium in the matrix of host glass, which is analyzed in section 3.1 Attention to WGMs peaks, by increasing the pump power we observed much laser oscillations with higher intensity and the wavelength of lasing peak would be shifted to short range The very high gain in our microspheres may be caused by good taper-microsphere coupling at 980 nm pump and a uniform distribution of ions Erbium in the glass matrix Based on the visually obtained WGMs profiles, the Q value of the microspheres in our experiment is estimated to be more than 10 for (a) and 108 for (b) However, the spectral profile of the WGMs for these results is not really clear, maybe, because of the fact that the chosen tapers are unsuitable and the gaps of microsphere-receiving taper are not optimal These problems will be discussed more hereinafter v WGMs spectra for various distances of probe taper-microsphere: One of the most important purposes of the thesis is mapping WGMs spectra using near-field optical probe (or receiving half-taper) from Erbium doped microspheres based on different host glasses As mentioned, phase condition between microspheres and tapers pointed out in section 2.5 require strictly followed optimal conditions such as homogeneity of materials, parameters of microsphere Ho Duc Vinh 70 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k c and half-tapers, the distance and length of near-field interaction around microsphere and tapers The taper is characterized by a conic geometry and a varying effective index, thus more modes can thus be excited in the sphere which qualitatively justify the large number of lines on the fluorescence spectrum (shown in Figure 4.17) In our experiments, half-tapers for extraction WGMs (probe tapers) should have small sizes of apex, high cone angles, short interactive length and no roughness, obviously, which are suitable with theory and facile to manipulate in experiments As a consequence, two tapers in figure 4.9.d (P1) and figure 4.10 (P2) are chosen to maping WGMs spectra from PZG microsphere with 100 µm of diameters -66 100 nm gap Peaks 200 nm gap Peaks -72 -68 -74 -76 -70 -78 Amplitude (dBm) c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w -72 -80 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1500 1510 1520 1530 1540 a) 1550 1560 1570 1580 1590 1600 1610 b) -64 -64 20 nm gap Peaks 50 nm gap Peaks -66 -66 -68 -68 -70 -70 -72 -72 -74 -74 -76 1500 1510 1520 1530 1540 1550 c) 1560 1570 1580 1590 1600 1610 1525 1530 Wavelength (nm) 1535 1540 1545 1550 1555 1560 1565 1570 1575 d) Figure 4.19 WGMs spectra profile depend on gaps of microsphere-probe taper, with 100 µm B-microsphere and P2-taper, 25 mW of pump power Figure 4.19 reveals that, by varying the gap between the tip of the half taper and the microsphere, the multimode WGMs oscillation can be obtained For every gap value with a fixed pumping power (25 mW) we have received a series of WGMs Ho Duc Vinh 71 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w c u-tr a c k c peaks around 1560 nm The ranges of peaks are not absolutely dependent on the distance of microsphere and probe taper, which presents a discrete characteristic of collection to WGMs, with mainly two series of peaks associated to TE and TM modes Observing the figure 4.19 in turn from (a) to (d), WGMs can be mapped and selected by adjusting the gap When the microsphere is close to the probe taper, only TM modes of low wavelengths oscillate because of the higher losses for TE and higher wavelength modes For larger gaps, TE and TM modes oscillate simultaneously It is obvious that the propagation in the taper, its non constant diameter and consequently variable gap of microsphere and taper (few tens of nanometers), leads a higher peak density and a vague view for observing peaks location versus distances between microsphere and probe taper Besides, when the distance between the pumping half-taper and microsphere is changed and the pump power is fixed, the intensity of green light from microsphere is evidently variable A spectroscopic technique based on the green upconversion fluorescence could be used to compute a loading effective temperature in Erbium doped PZG microsphere and this further should allow us to calibrate the properties of the microsphere WGMs in term of the variation of the refractive index On the other hand, similar to the spectra versus pump power, we have obtained higher levels of amplitude for WGMs peaks for lower gap values The reason for this can be deduced simply that a decrease of microsphere-taper gap resembles a increase of detection ability of the near field surrounding microsphere Focusing on the 1558 nm peak, experimentally, we could demonstrate that the gain of the WGMs signal at this wavelength is a function of microsphere-probe taper gap (figure 4.20) In our experiments for using the P2-taper with pump power of 25 mW, the profile of gain at the 1558 nm wavelength is distinguished for two types of microsphere (PZG microsphere – B3 and silica alumina microsphere – A4) For the former, the gain obtained is rather high (about 15 dB) at the overarched part, since the distance of probe taper far from microsphere is approximately 70 nm Maybe, the WGMs laser oscillation could occur at this distance, however, the mechanical limit of equipment and the vibration of probe taper’s apex are obstacles Ho Duc Vinh 72 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k c in the way of lasing The received gain values for the latter (150 µm A4microsphere) run gradually straight through, which exhibits lower capacity of lasing for this type of microsphere From the other point of view that the overgrown parts of curves locate versus various values of distance, it makes sense that the optimal distance between microsphere and probe taper depends on the suitable sizes of microsphere and probe tapers Extinction in the vicinity of the critical point for phase matching conditions owing to position and size of probe bodes well for application of this WGMs microsphere system as an improved sensing device 16 B3-microsphere A4-microsphere Averaging curves 14 Gain at 1558 nm (dB) c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w 12 10 20 40 60 80 100 120 140 160 180 200 Probe taper - microsphere distance (nm) Figure 4.20 Gain of WGMs signal at 1558 nm as a function of microsphere-probe taper gap, with 25 mW of pump power v Optimal distance for mapping WGMs: As analyzed earlier (section 2.4), ideality for mapping WGMs is defined as amount of power coupled into the desired mode (in this case n = 1) The degree of ideality is determined by the parasitic coupling factor κ (S o ) (equation 2.17.a), κ ( So ) is, in general, a function of the relative position of the taper and microsphere Based on this theoretical groundwork, the dependence of ideality on the gap were investigated (figure 4.21) After calculated results (figure 4.11), the chosen probe- Ho Duc Vinh 73 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k c taper-P2 with 80 nm of apex diameter brings about the value of propagation constant β f for fundamental taper mode about 4.106, from which, coupling parameter κ versus gap on a logarithmic scale is numerically plot in figure 4.21 The obsevation that the critical point data of high ideality is given by the gap where κ = shows that the numerically calculated results were in good agreement with the experimental results corresponding to the figure 4.20 It means that the optimal distance between microsphere and probe taper in this case is about 70 nm under given parameters above 10 Squares fit line 10 10 κ c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w 10 10 10 20 40 60 80 100 120 140 160 180 200 Distance from microsphere (nm) Figure 4.21 Coupling parameter κ versus probe taper – microsphere gap for 100 µm B3-microsphere and P2-probe taper (80 nm of apex) As a consequence, the Q-factor dependence versus probe taper-microsphere distance was calculated from equation 2.19 and plot in figure 4.22 with a confident view From experiments for four PZG microspheres with various ratios of doping sizes, the profiles of data received are rather identical at the condition that pump power is fixed of 25 mW, the wavelength of WGMs signal focused in calculation is 1558 nm Ho Duc Vinh 74 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! 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PD c y bu to k d o m o o c u-tr a c k c 1x10 9x10 8x10 Q-factor c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w 7x10 50 µm - B1 80 µm - B2 100 µm - B3 150 µm - B4 6x10 5x10 4x10 3x10 20 40 60 80 100 120 140 160 180 200 Distance from microsphere (nm) Figure 4.22 Q-factor versus probe taper – microsphere gap for various microspheres For a detailed quantitative analysis of the loss rate due to scattering from the probe taper a numerical analysis that includes the exact shape of the taper and the spatial extent of the modes would be required However, in case of a rather extended whispering gallery mode, it is expected that the loss rate scales with the fraction of the mode volume of the whispering gallery mode, which is disturbed by the probe taper We investigated the limiting case experimentally with a probe of tip diameter smaller than 200 nm Then, we did not observe much influence of the probe taper on the Q-factor, even if the initial Q-factor of the mode was as large as 2.108 The experimental results demonstrate that it is possible to minimize the degradation of the Q-factor of whispering gallery modes by choosing a small tip size and a suitable shape Additionally, in our set-up we are able to control the position of the probe taper in order to achieve an optimum of low scattering loss and high probe signal v Calculation for WGMs spectra: In the experiments, the obtained WGMs spectrum presents a discrete feature which is characteristic of the collection through WGMs, with mainly two series of Ho Duc Vinh 75 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! PD O W ! PD c y bu to k d o m o o c u-tr a c k c peaks associated to the TE and TM modes shown in figure 4.24 It should be to emphasize that for the large gap (150 nm) and high pump power (30 mW), TE and TM modes oscillate simultaneously with high intensites The measured Free spectral range or spacing between modes having same quantum numbers but different polarizations is 3.2 nm close to the calculated value given by equation 1.18 (≈ nm) From this result, one round trip of microspherical resonator quantitatively equals 253 µm followed to the formula L = λ / n ∆λ ( = (1558 µ m)2 / ∗1.5 ∗ (3.2 nm) ) On simple reflection for that the radius range of microsphere used in figure 4.23 is 40 ± µm, the circumference of microsphere is defined about 239ữ285 àm, which covers the experimental result above TM1, 242 -62 TE1, 242 TM1, 240 TM1, 243 -64 Amplitude (dBm) c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w TM1, 236 TM1, 238 TE1, 238 TM1, 241 TE1, 239 -66 TE1, 233 -68 TM1, 240 TE1, 241 ∆λ = 3.2 nm TM1, 244 TM1, 247 TE1, 244 TE TM1, 246 1, 245 TM1, 235 TM1, 248 TE1, 246 TM1, 245 TE1, 249 TE1, 247 TE1, 248 TE1, 232 TM1, 250 TM1, 249 -70 -72 -74 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 Wavelength (nm) Figure 4.23 Calculated WGMs spectra of the 80 µm B3-microsphere Include TE and TM modes with mode order of 1st and polar mode from 230 to 254 and ∆λ = nm between the number set (n, l ) and (n, l +1) Furthermore, the size parameter from which WGMs laser oscillation mode can be selected is used to calculate the polar mode numbers As a result of equation 1.1 in chapter ( l ≈ n(ω ) 2π a / λ ) , these calculations exhibit that for microsphere Ho Duc Vinh 76 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! PD O W ! PD c y bu to k d o m o o c u-tr a c k c with 80 µm of diameter, the polar mode numbers are quite large, in 230÷254 range (shown in figure 4.23 for two types of mode TE and TM) v Emission Ability of WGMs laser oscillation : The threshold of laser action defines the pumping power at which the internal circulating signal energy is zero, another hand, the total gain is equal to the total loss out of the sphere It is known that WGMs signals becomes WGMs lasing mode when the SNR at the interested wavelength of spectrum is over 10 dB and FWHM (full width half maximum) of this signal is ultra narrow (< 0.1 nm) Figure 4.24 demonstrates that we have reached one WGMs lasing mode at 1600.1 nm with 15 dB of gain and the FWHM very close to the theoretical result (0.12 nm) -62 -62 -64 -64 -66 -68 -66 FWHM=0.12 nm -70 -72 -74 -68 -76 -78 Amplitude (dBm) c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w -70 -80 -82 1600.0 Gain = 15 dB 1600.5 -72 -74 -76 -78 -80 -82 -84 -86 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 Wavelength (nm) Figure 4.24 lasing WGMs at 1600.1 nm for 50 µm B3-microsphere using taper B2, 30 mW pump power and 150 nm gap of microsphere-taper Achieved 15 dB of gain and 0.12 nm of FWDM An interesting point in the experiment is that laser operation acts preferentially in the range of 1600 nm around the predicted threshold regime for Ho Duc Vinh 77 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE N N O W ! PD O W ! PD c y bu to k d o m o o c u-tr a c k lic to k lic C m w w w d o C bu y Experiments and Results Chapter w w w c u-tr a c k c PZG microsphere (about 30 mW) The reason for this can be explained by characteristics of absorption and emission cross section of PZG glass, which offers the capacity to build L-band micro lasers However, in many cases, we are only used to get the spectra of typical WGMs oscillation due to the fact that fabricated microsphere still remains imperfect of surface, defects of glass, Erbium ion clusters,… In conclusion, microspherical laser is quite simple in principal of lasing action, but it is very sophisticated and strict in fabrication of equipments, techniques for high coupling, and in materials which are required for studying QED effects (Quantum Electro Dynamic) in quantum dielectric materials and devices Ho Duc Vinh 78 K10N LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com H F-XC A N GE H F-XC A N GE c u-tr a c k N y bu to k lic d o Conclusion q THEORY Give a clear picture of optical process in microsphere: field intensity distribution, resonant location, mode volume, quality factor, and phase matching condition Theoretical models were presented increasingly for microspheres and tapered fibers coupling based on near-field optics The techniques and methods of fabtrication are also analyzed in the conditions of our laboratory Master thesis Mapping WGMs of Erbium doped glass microsphere using Near-field optical probe LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 40 o c m C m w o d o w w w w w C lic k to bu y N O W ! PD O W ! PD c u-tr a c k c H F-XC A N GE H F-XC A N GE c u-tr a c k N y k lic d o 30 µm to 200 µm Erbium doped microspheres over the PZG glasses and silica-alumina glasses ranged are obtained with Fine Fine homogeneous, homogeneous, Eccentricities: Eccentricities: on on the the order order of of 1-2% 1-2% Very low roughness (1 nm: silica-alumina Very low roughness (1 nm: silica-alumina glass glass and and 10 10 nm: nm: PZG PZG glass), glass), very very high high Q Q microsphere microsphere Achieved half-tapers from standard optical fibers using CO2 laser system and heating arc system are produced low low roughness roughness of of surface surface (on (on the the order order 11 nm) nm) 80 80 nm nm in in size size of of apex apex various various shapes shapes and and varying varying cone cone angles angles Meet Meet phase phase matching matching condition condition In our experiments, both configurations (CW and CCW) of using two different probes ones for pumping and extracting WGMs from microspheres were implemented The WGMs spectra were gained with various materials, sizes and experimental conditions The thesis also discussed and analyzed WGMs spectra versus pump powers and distances between microsphere and probe taper The numerically calculated results were in good agreement with the experimental results shows the optimal condition for mapping WGMs of High-Q microspheres Also, we have reached one WGMs lasing mode at 1600.1 nm with 15 dB of gain and 0.12 nm of FWHM 41 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com m w o q EXPERIMENTS - Thesis has obtained some particular results to bu c C m o d o w w w w w C lic k to bu y N O W ! PD O W ! PD c u-tr a c k c H F-XC A N GE H F-XC A N GE c u-tr a c k N y bu to k lic d o The microsphere optical resonator is still an interest not only in optic and photonic studies but also in fabricating micronano materials and devices By the methodology based on mutual relationship between theories and experiments, the thesis have obtained the results as a first steps but it has been fundamental theory and very useful for the purposes of application and researching in future Master thesis Mapping WGMs of Erbium doped glass microsphere using Near-field optical probe LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 42 o c m C m w o d o w w w w w C lic k to bu y N O W ! PD O W ! PD c u-tr a c k c ... in microspheres based on erbium doped glasses using near- field optical probe in our Lab “Micro-nano dielectric materials and devices” I will demonstrate obtained Erbium doped microspheres and near- field. .. Coupling Microsphere WGMs based on near- field optics Chapter w w w Optical Property of Mesoscopic Material System Optical Near Field 10 nm Spatial Extent of Effective Field or Sample -Probe 0.1 nm Distance... 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 for decreasing a short-coming of
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