Tài liệu Fabrication and investigation on microsphere laser based on er-doped silica glass

VIETNAM NATIONAL UNIVERSITY OF HANOI COLLEGE OF TECHNOLOGY HOANG QUANG HUNG FABRICATION AND INVESTIGATION ON MICROSPHERE LASER BASED ON ER-DOPED SILICA GLASS Major: Nano Materials and Devices Index: M ASTER THESIS SUPERVISOR Ass. Prof. Dr. PHAM VAN HOI Hanoi - 2005 Contents A c k n o w le d g e m e n ts In tro d u ctio n .............................................................................................................................. 1 Chapter 1: M icrosphere C a v ity ..........................................................................................4 1.1. Introduction............................................................................................................... 4 1.2. Optical modes o f a dielectric s p h e re .................................................................. 4 1.3. Intensity distribution for a microsphere W G M ................................................ 5 1.4. Asymptotic solutions...............................................................................................6 1.5. Eccentricity sp littin g ............................................................................................... 8 1.6. Loss mechanisms in a m icrosphere................................................................... 10 1.6.1. Intrinsic material loss................................................................................. 11 1.6.2. W hispering gallery l o s s ............................................................................ 11 1.7. Mode volum e o f m icrospheres............................................................................13 Chapter 2: Tapered optical fiber c o u p lin g ................................................................... 15 2.1. Introduction............................................................................................................. 15 1.6.3. Prism s................................................................................................................ 16 1.6.4. Planar structures.......................................................................................... 17 2.2. Evanescent coupling to microspheres using tapered optical fibers........ 17 2.2.1. Optical properties o f tapered optical fib e rs ......................................... 18 2.2.2. Mathematical description o f the waveguide-resonator coupling ju nctio n........................................................................................................... 2 0 2.2.3. Cavity-buildup factor................................................................................... 22 2.3. P h ase-m atch ing .....................................................................................................22 2.4. Extension to backscattering.................................................................................26 Chapter 3: M icrosphere laser based on Er-doped silica g la s s ............................ 29 3.1. Materials using for Microsphere lasers............................................................ 29 3.2. Fabrication o f m icrospheres.............................................................................31 3.3. Pumping and collecting techniques using half-taper coupling................. 33 3.4. Experiment setup................................................................................................... 34 3.5. Experiment results................................................................................................. 36 3.5.1. Caculations o f W GM spectra..................................................................... 36 3.5.2. ASE spectra and threshold laser a c tio n ..................................................40 3.5.3. Forward and backward scattering em issions......................................... 44 3.5.4. Optical power o f W G M .............................................................................. 45 Sum ary...................................................................................................................................48 Publications Reference In tro d u ctio n Introduction Ultrahigh-quality-factors possessing whispering-gallery £ » 1 0 8, dielectric modes (WGMs) microcavity have been resonators investigated intensively for the last decade. Cavity quality factors (Q factors) as high as 8 . 10J [26,19], along with small mode volumes, have been essential driving forces for fundamental research areas such as cavity quantum electrodynamics, nonlinear optics, biosensing, and microscale lasers. Braginsky and Ilchenko [26] realized that the whispering-gallery modes o f dielectric silica microspheres had the potential to experimentally exhibit extremely long photon storage times, exceeding a microsecond. This allowed the realization o f low threshold optical micro- cavity effects, such as lasing and nonlinear wave generation [19]. Furthermore, the low optical loss o f silica microcavities allows the creation o f lasers with submicrowatt thresholds [21]. Before the use o f ultra-high-Q microresonators for photonics applications could advance, the problem o f efficient excitation and extraction o f optical energy from these structures needed to be solved. M ost previous studies o f silica microspheres used glass prisms and free-space laser beams to excite the cavity. While this method is relatively efficient, the true advantages o f these structures could not be realized, due to both the inability to obtain complete power transfer into the cavity and to extract the optical energy in a manner convenient to further manipulation. In 1997, Birks et al. presented a paper which described the coupling between a fiber taper and a silica microsphere [6 ]. They showed that it was possible to efficiently couple into a microsphere. Vahala et al. then realized that this coupling method should in principle allow near perfect coupling efficiency both into and out of a silica microresonator, while the ability to create near lossless tapers allows significant advantages in fiber compatibility. However, the taper coupling technique requires the advance on experiment technique and matters. For initial study on microsphere cavity, we use the half - taper coupling to pump and extract the emission from spheres. Although this method is not suitable to investigate into advanced problems of microcavities, it can ■*. v 'v v •<>’ s <- v hT ■<.'-' HOANG QUANG HUNG 1 v s." ’•Cs! v ‘V \ \ 'v ’v < 's! hJ< < -v."s."•vv 'C -v.'xj \ •*.’< < "v xj < v 'v -"v.'hJ•<•<•<.’xj < -v'■* College o! Technology _ VRUI} In tro d u ctio n bring out a visual view and can achieve good enough results for studying microsphere lasers. In addition. Materials for micro lasers, which should have the fundamental o f optical transmission and act as the active media, are so plentiful including the semiconductor materials, rare-earths or semiconductor nanocrystals doped dielectric or polym er materials. Rare-earths or semiconductor nanocrystals doped dielectric or polym er materials are presently developed in the Institute o f Materials (IMS), VAST. This is a favorable condition to investigate on fiber optic devices, especially for active microsphere devices. The thesis focuses on: S Fabrication o f microspheres from Er-doped silica glass fibers and bulk materials. S D eveloping excitation for and extraction emission from microspheres techniques S Studying on optical characteristics o f laser operation o f Er- doped microspheres Thesis outline: • Chapter 1 describes microsphere cavity with the general optical properties. Some numerical calculations are also represented in this chapter. • Chapter 2 begins with the introduction o f microcavity coupling techniques. Then, optical properties o f tapered fibers are described. Finally, optical coupling between microspheres and fiber tapers is theoretically investigated in terms o f coupling junction and phasematching condition. A suggestion for fabrication o f fiber taper and fiber half-taper is also shown. HOANG QUANG HUNG 2 College o! Technology _ VRU.ft In tro d u ctio n • Chapter 3 discusses the fabrication o f microsphere based on Erdoped silica glass. The results, observed calculatedly and experimentally from these spheres, are shown on the chapter. Finally, I present a brief summary and suggestion for the following studies on microphere laser based on Er-doped silica glass. *>."S ^ ^ "V M' 'v 'V 'V - s < 'V '«v’ 'C HOANG QUANG HƯNG 's.‘"v 'V 'V "V 'V 'V 'V 'S.’ 'S . 'V "V- (1.7) o / - l n ~~~r 3 For the microspheres considered in this thesis, the resonance wavelength is located in the 1550-nm telecommunication band. 1.5. Eccentricity splitting In an ideal sphere the optical modes possess a 21 + 1 degeneracy with respect to the azimuthal mode number m. This can be understood by using classical ray optical interpretation, in which the optical modes with same 1 , but different m, orbit around the equatorial plane by reflecting alternating from the lower to the upper hemisphere (and vice-versa), thereby taking different excursions away from the equator. The wavevector associated with this trajectory ( 18 ) = and the projection onto the equatorial plane (i.e. the propagation constant) is given I M = i r The modes with low m take paths closer to the poles, and their longer path is compensated by a reduced number o f reflections at the dielectric-air interface to complete one revolution. The so called fundamental modes, m = 1 correspond to motion close to the equatorial plane (with an angle Q -l/l12 ). Due to the invariable presence o f imperfection, a microsphere will deviate from exact spherical shape, which will remove the degeneracy in path-length. If the shape deformation is weak, the new resonance frequencies can be calculated using perturbation theory. Assuming a prolate or oblate spheroidal perturbation HOANG QƯANG HUNG 8 College OĨ Technology _ M icrosphere C avity A y\/\^ /\A y V ' - i.e. the sphere is either flattened or elongated along the axis perpendicular to the propagation plane (equator - the perturbed spheroid boundary along the polar coordinate near the equator would follow roughly the expression R(e) = R + A R 9 2 where R (1.10) is the change in radius. After substitution and processing the variational expression, we finally get for the change in the wavevector k LA R Ak = ( l - m + ~ ) — 2 R (1.11) For two consecutive polar modes A(l-m)=\, we first find A kspm = A R / R' , and then finally for the wavelength difference (1.12) 2/r R- Figure 1.3: Calculated values o f resonant wavelength splitting for the polar mode number / = 590. The diameter o f the sphere is 100 |um HOANG QƯANG HUNG 9 College QĨ Technology _ VHỈH} M icrosphere C avity The polar-mode resonant wavelength split is now directly related to the prolate or oblate eccentricity o f the sphere. Figure 1.3 shows calculated values o f resonant wavelength splitting for the polar mode number / = 590 o f a microsphere with the diameter o f 1.6. 100 pm. Loss mechanisms in a microsphere Due to the presence o f loss mechanisms such as material absorption, scattering losses or tunnel losses, the optical modes o f a resonator are dissipative in character ("leaky") and are referred to as "quasi-modes"[19]. Quasi-modes are distinct to their loss-less counterparts (modes). The extent to which dissipation is present in a resonant system is commonly expressed by the Quality-factor or Qfactor o f the mode, which is defined by the energy storage time normalized with respect to the period o f oscillation: (1.13) In this equation w is the resonance frequency, Estored is the energy contained in the resonant system, and I\iiss is the dissipated power. The above definition extends beyond the domain o f electromagnetism, and is also used to characterize mechanical or electrical oscillators. Equivalently, in the case o f optical microcavities the optical Q-factor describes the photon lifetime o f a mode. In the case o f a microsphere, the total Q-factor is comprised o f several loss contributions [Ilchenko]: intrinsic material absorption, scattering losses (both intrinsic, as well as inherent to the surface o f the cavity), surface absorption losses (e.g. due to the presence o f adsorbed water), whispering gallery loss (or tunnel loss) and external coupling losses to a "useful" external mode (such as a prism or a waveguide): Qul - Qmh + Q.Jan +Qsurf + Qji + QwGM HOANG QƯANG HUNG 10 (1.14) College OĨ Technology _ VHỈITị M icrosphere C avity In the following sections the limits imposed by the different mechanisms are briefly reviewed and analyzed, for the case o f silica microspheres involved in this work. 1.6.1. Intrinsic material loss Silica has a large transparency window and exhibits low absorption losses. The minimum loss occurs at 1.55 ^m, f°r which it has become the operating wavelength for fiber-optic telecommunications. The loss at 1.55 |_un is 0.2dB/km and is equally comprised o f absorption loss and loss due to Rayleigh scattering, which translates into an absorption limited Q of: Q‘*s A.a 2.92x10 10 (1.15) Absorption limited Q-factors have indeed be observed in large diameter (>200 |im ) microspheres [4]. 1.6.2. Wh ispering gallery loss The optical inodes within a microsphere are confined by continuous total internal reflection at the dielectric cavity-air interface. However, it is a general property that total internal reflection at a curved interface is incomplete, and leads to a transmitted wave, which for the case o f a resonator causes loss o f optical energy[5]. This loss mechanism is called whispering-gallery loss, and is due to tunneling o f the photons out o f their bound states. This tunneling process can be understood by drawing an analog to the quantum mechanical treatment of a 1-D particle in a central potential. An approximate analytic formula for the whispering-gallery loss o f a spherical, homogeneous dielectric resonator has first been derived by Weinstein [42], by expanding the characteristic equation and allowing the wave-vector to be complex. The result o f this approach (extended here to include one more term in the perturbation expansion) is only valid in the limit / > > 1 . A A A A l'A A A A A A A A A A a' a' a A À i A A A A A A A A A A A A i i HOANG QƯANG HUNG A A A A A A A A A A A A A A A A A A A A A A 11 A A Ằ A A A ¿ A A A i A i A A A -l A A A A A A i College OĨ Technology _ VHETTj M icrosphere C avity 111I-2Ả /;/ - r I- 2Ắ:; / y/r2 - iV 1) 2 e27 (1.16) Where m is the relative index o f refraction, t°n is the Airy function zero and: cas\ tf/T1(/ »)-/ Tn,= (1.17) +p /77" /77 ' / +I 2 (1.18) 2 V 5 6 7 8 y 9 10 11 S phere d ia m e te r Figure 1.4: Whispering gallery loss versus microsphere radius for a polar mode number corresponding to a resonant wavelength of 1550 nm for a fundamental WGM. For R > 12 nm, Q> 108 can be maintained. The expression reveals however the important result o f the exponential dependence o f Quality factor on polar mode number Q wgm ~ e2'■Therefore the Q-factor exhibits a strong dependence on sphere diameter. For small polar mode HOANG QUANG HUNG12 College QĨ Technology _ VRỈHị M icrosphere C avity numbers, the above expression is not precise and higher accuracy can be obtained by solving the characteristic equation numerically (iteratively). The Q-factor obtained by this method is plotted in figure 1.4 as a function o f microsphere radius for the experimentally relevant wavelength range o f 1550 nm. As can be seen, a Q-value o f >10x is maintained in the case of R > 12|im. 1.7. M ode volume of microspheres In many applications, not only temporal confinement o f light (i.e. the Q- factor), but also the extend to which the light is spatially confined is an important performance parameter. Several definitions o f mode volume can be encountered in literature, and are discussed in this section. The most common definition of mode volume is related to the definition of the energy density o f the optical mode. 6000 T" I -------- 1 + O TE TM > ► i _=3 ! OỈ “O o 5Ì ; s .............. .......... ........ ¥ Í* $ i ; 50 B0 * 1000 f .............. ^ỳ & t ... * 10 .. 20 « * > * 4 — J __ ___ 30 i , 40 ------ 70 ----- i _________ 30 90 100 S p h e re d ia m e te r (urn) Figure 1.5: Calculated mode volume for a microsphere as a function of diameter. The polar mode number I was chosen to be consistent with a resonant near 1550 nm. HOANG QUANG HUNG 13 College OĨ Technology _ VTỈOĨ? M icrosphere C avity It is defined as the equivalent volume, the mode occupies if the energy density was distributed homogeneously throughout the mode volume, at the peak value: ™Ár)+m,Ảr) =z;zEE+-— BB (1-19) _ j(w, {r)+rnm(r))dv ^ Je(j {rf c^ r y ^ = J 7 - T T ...... 7-W= - '7 ^ . (1-20) 2ụ 2 m a x iVm c, (\ / •/ ) + (m/')V) m I a x \ The mode volumes using these formulas can be well approximated by: [1.02 Du/6(A/n)1/f' Vm.spi,e,e =i j o S D 11/ 6 ^ / / ; ) 776 A Ầ X X Ằ X X X À X Ằ x~Á À X A X Ằ ~ x ~ í~ x i X X x~X X i X i J, X X X X Ằ~x~Ằ X X i Ầ A~x~ X A A A i A A A A jTX i i HOANG QUANG HUNG 14 TE TM X X X n ° ' 21) ’l J ỉ Y ỉ Y Ũ A Ũ V Ũ ỉ i V i V i ù l Y l 1 College QĨ Technology _ VRmị Tapered optical fib er coupling . A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A AA A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A ^ I Chapter 2: Tapered optical fiber coupling 2.1. Introduction The study o f the optical properties o f ultra-high-Q (UHQ) microcavities requires the ability to optically excite and probe the resonator. Furthermore, the investigation o f the full potential of UHQ structures to realize high performance devices, such as low-loss passive elements and low-threshold active elements such as nonlinear sources, requires an ability to both efficiently excite the modes o f the cavity and to efficiently extract optical energy from the cavity. There are several commonly used techniques to couple optical microcavities. These fall into two classes: phase-matched and non-phase-matched techniques. O f the two, phase-matched schemes offer a dramatic advantage in terms o f coupling efficiency both into and out-of the cavity, relegating non-phase-matched schemes (o f which free-space illumination is the sole member) to systems where experimental limitations and/or simplicity is coupled with a sufficient excitation power and detection margin such that the gross inefficiency is tolerable. Additionally, precise characterization o f the properties o f optical microcavities is extremely difficult for broad illumination schemes, as multiple whispering gallery modes (W GM's) are excited spatially, and the emission is detected in a radial fan o f energy from the perimeter. For these reasons, 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 [4], possess the advantage o f free-space illumination/emission simplicity along with the ability to phase-match, thus in principle allowing high efficiency. However, as the effect o f this coupling method on the intrinsic cavity properties is unclear, I will focus on evanescent coupling methods, especially the fiber taper coupling method. A~ x~ x~ A A A V i Ai A x~ x ~ x~ x~ Á~Ầ X a V a A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A J A A A A A A A A A A A A A A HOANG QƯANG HUNG15 X Ấ Ầ À Á Á Ầ X X X College OĨ Technology _ VHUI) A~Ă A Á i X A A À Ẩ Tapered optical fib e r coupling 2.1.1. Prisms Up until about the mid-90's, prism coupling was the sole technique used to phase-match UHQ microspheres. Prism coupling consists o f a laser beam which undergoes total internal reflection in a prism, such that the external evanescent field o f the beam at the reflection region overlaps the whispering-gallery-mode field o f the optical resonator (Figure 2.1). This method is inherently exible, allowing phase-matching by changing the incident angle o f the input beam (as long as the angle still satisfies the total internal reflection condition), and observation o f optical energy which has interacted with the resonator at the prism output. It is possible both to excite individual resonances and to observe them through a spatially resolved output spectrum [12]. While this m ethod is wellproven and exible, it has a couple drawbacks. First, the coupler is bulky, which while somewhat desirable from a stability standpoint (intrinsic actuation o f the coupler can have a profound effect on the coupling properties o f fiber-tapers), negates most o f the practical advantages o f micron-scale devices. Furthermore, integration with chip-based cavities is, while possible, relatively difficult. Figure 2.1: Prism coupling with microspheres However, in simplistic terms, what happens is that the optical energy in the cavity radiates in a cone centered around the optimal phase-m atching angle (which is determined by the m ode o f interest). This cone thus contains a spread of modes with slightly different k-vectors. The consequence o f this is that although the input beam (to a good degree) and the resonator m ode are single ả a a a ằ a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a HOANG QUANG HƯNG XX X Ấ X X X í X Ầ Ằ X X Ấ X i Ấ X 16 x~Á X i À À A X X Ằ À X À x ~A X X X X X À À Ằ Ấ X X X Ằ Ằ College oĩ Technology _ VĨỈỈỈĨÌ Tapered optical fib er coupling A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A / i A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A / * mode, the output beam is not. Thus experiments where modal purity o f the output energy is desirable are not readily studied using this approach (as manifested by the inability to observe true critical coupling, where all optical energy is coupled into the resonator). Additionally, this fact combined with the limited ability to spatially mode-match the resonator may have played a role in the relatively few experimental observations o f nonlinear optical effects in microspheres (besides thermal nonlinear effects), which are easily observable using tapered fiber đ a couplers. 2.1.2. ; H O C O u O C G IA HA N Ọl Tín t h ư v i ệ n tr u n g tẩm t h ô n g P lanar structures One o f the main advantages o f planar waveguides is the ready integration with planar lightwave circuitry. Thus the ability to use planar waveguides to couple to UHQ microresonators would facilitate integration o f these structures with additional functionality. The use o f planar waveguide couplers has been around for many years, with the technology mature. Typically, these waveguides are used in a simple rectangular or ridge waveguide configuration. For the most part, these waveguides have only been applied to relatively low Q microresonator structures, mostly as a result o f the lack o f suitable UHQ cavities. 2.2. Evanescent coupling to microspheres using tapered optical fibers By the bringing evanescent field region in close proximity to a silica microsphere, evanescent coupling can be achieved. A particularly suitable method is that a fiber is drawn into a thin filament, and the evanescent field o f the fiber is brought to overlap with the sphere. The particular advantage o f this method is threefold. First, tapered optical fibers can be made with low-loss. Secondarily, tapered optical fibers allow highly efficient excitation o f WGM, with negligible parasitically induced losses (such as scattering). In addition they allow not only excitation but also extraction o f cavity fields through the same taper. Thirdly, the tapered optical fibers have small transverse dimensions. a V Ũ i íY íV ìV a Y a V a Y iV ìY » ũ l Y i i X x ~x Ằ i X X HOANG QUANG HUNG X X i. Ằ~x X X X Ầ i X Ằ Ằ Ằ i i X Ằ X X X 17 x~ x~ Ằ A i X Ằ X Ằ Ằ Ấ X Ằ Ằ Ằ X X X Ấ i Ằ AẰ X X Ằ X X College oĩ Technology _ VRmị