Investigation of lasing emission effect and optical amplification in the cavity conjuncted with 1D, 2D photonic crystal structures

ctions on photonic devices, including optical amplification by experimental method combined with simulation calculation. On the basis of the PhC research results, coupling the micro- resonant cavity with the PhC structure for laser emission is necessary direction to demonstrate high orientation in integrated photonic devices fabricated technology. To continue developing the research direction of nano and micro-meter photonic structure, towards the application in optical communication and sensors, we choose the thesis topic with title: “Investigation of lasing emission effect and optical amplification in the cavity conjuncted with 1D, 2D photonic crystal structures”. 2. The objectives of the thesis - Research, fabricate Er3+-doped silica glass microspheres with different sizes by arc discharge method; building an experimental system to investigate WGM mode laser emission spectrum in the 4 optical communication wavelength region ~ 1550 nm of some fabricated microspheres. - Design and simulation of integrated structure of silica glass microsphere with 2D-PhC waveguide based on SOI material to study on WGM mode laser emission effect in the optical communication wavelength region ~ 1550 nm. - Design and construct a sensor system for refractive index measurement of some liquids using the FBGs that are integrated into the fiber ring laser configuration without using spectrometer. Research method The thesis uses both simulated and experimental calculation methods. The simulated calculation method was used to determine PBG, waveguided mode, guided-mode resonance, WGM mode and field distribution in the structure of PhC. The experimental method was used to fabricate microspheres, FBG, design and construct laser emission spectrometry system of Er3+-doped silica microspheres coupled with pump source and receiver by the single-mode optical tapered fibers, design and construct liquid sensor system based on FBG integrated in fiber ring laser configuration. 3. The main contents of the thesis: - Overview of photonic crystal and its application in research on laser fabrication. - The research methods. - Calculate and simulate some optical devices using two- dimensional photonic crystal structure. - Study on laser emission effect of microspheres based on Er3+- doped silica glass, photonic devices and its application. Thesis layout 5 The thesis includes the introduction, four chapters of content and the general conclusion. The main contents of the thesis is presented in four chapters. The first chapter presents the concepts, research situation of PhC structure and its application. The second chapter introduces the research methods, including theoretical models of the waveguide - resonator coupling, simulated calculation and experiment. The third chapter presents the results of calculation and simulation of some optical devices using 2D-PhC structure. The fourth chapter presents the results of the emission of microspherical lasers on Er3+-doped silica glass, simulation of the integrated structure of Er3+-doped silica microsphere with 2D-PhC waveguide and some test results of liquid refractive index measurement using PBG elements integrated in fiber ring laser configuration. CHAPTER 1. OVERVIEW OF PHOTONIC CRYSTAL AND ITS APPLICATION IN RESEARCH ON LASER FABRICATION - Introduction to the photonic crystal structure. - Presenting features of 2D-PhC such as photonic band gap, waveguided and wave confinement, guided-mode resonance. - Presentation of the optical processes in spherical micro- resonance cavities: WGM mode of dielectric microspheres, equations of state for modes and microsphere - waveguide coupling methods. - Apply the 1D-PhC structure in fiber optic (FBG) to developing optical sensor. CHAPTER 2. THE RESEARCH METHODS 2.1. The theoretical models of the resonator-waveguide coupling 2.1.1. The theory of resonator - waveguide coupling Mode coupling method has been applied to many physical 6 systems to process the resonant modes or propagating modes. We can choose a simple LC circuit to illustrate the significance of the related physical parameters [94]. - If the loss is small, then: da/dt = joa – (1/o)a (2.10) where a, 1/o are the mode amplitude and the decay rate due to the loss, respectively. - When the resonator is coupled to an external waveguide, due to escaping into the waveguide, equation (2.10) must be modified: da/dt = joa – (1/o + 1/e)a (2.15) where 1/e expresses the additional rate of decay due to escaping power. - In case, the waveguide carries a wave traveling toward the resonator of amplitude s+ due to a source, there will be a coupling of waveguide and resonator so (2.15) must be written: da/dt = joa – (1/o + 1/e)a + ks+ (2.19) where k is a coefficient expressing the degree of coupling between the resonator and the wave s+. We normalize s+ so that 2s = power carried by incident wave; here s+ to designate a wave incident upon the resonator; the reflected wave will be denoted by s-, respectively. - If the source is at frequency , then the response is at the same frequency, from (2.19), that: ja = joa – (1/o + 1/e)a + ks+ from then a = ks+ /[j(-o) + (1/o + 1/e)] (2.20) The relationship between k và e are given by: 2 / ek  (2.28) From (2.19), we have: 7 da/dt = joa – (1/o + 1/e)a + 2 / e s+ (2.29) (2.29) is the equation describing excitation of the resonator mode by an incident wave. 2.1.2. The coupling of a micro-resonator - two waveguides The simple model is shown in Figure 2.4. U, o are the amplitude and frequency of the resonator mode excited in the resonator, respectively. The resonator mode couples to two waveguides () and () and obeys the equation [96]: dU/dt=joU–(1/e +1/e +1/o)U + 2 / e a1 + 2 / e a4 (2.30) where a1 and a4 are the incident waves in the two waveguides, normalized so that 21a and 2 4a are equal to the incident power in the two waveguides; 1/ e and 1/ e are the coupling ratios between the micro-resonator with the two waveguides () and (), respectively; 1/0 is the decay rate due to the loss (radiation and other losses combined). The resonant mode U couples back into the outgoing waves in the waveguides in the clockwises direction: 2 1 2 / eb a U  (2.31) 3 4 2 / eb a U  (2.32) Figure 2.4. Coupled-mode model of resonator with two waveguides 2.1.3. The coupling of the micro-resonator - waveguide when considering backscattering The coupling between a waveguide and a micro-resonant cavity 8 when considering backscattering can be illustrated in Figure 2.5. Figure 2.5. Schematic of the coupling of a micro-resonator with a waveguide when considering backscattering The equations of motion for counter-propagating modes (CCW and CW) that are coupled to one another as well as to a waveguide mode can be described by the couple-mode equations similar to those presented in [96,97]: dacw/dt = j.acw - (1/2)(1/e + 1/o)acw + (j/2)accw + k.s (2.33) daccw/dt = j.accw - (1/2)(1/e + 1/o)accw + (j/2)acw (2.34) here acw and accw are the amplitude of the clockwise and counterclockwise modes of the resonator, respectively; s denotes the input wave, which is selected to excite the CW mode; the scattering rate 1/ describers the mutual coupling of the CW and CCW mode. 2.2. The simulation calculation method 2.2.1. The finite-difference time-domain method (FDTD) FDTD is a method of directly solving the system of Maxwell equations in the time-domain [117,118]. The relationship between the time steps of the FDTD method is as follows: at any point in space, the next value of the electric field E  over time depends on the value of the previous electric field E  and the numerical rota of the local distribution of the magnetic field H  in space [117]. Similarly, for the time-step progression of the magnetic H  . K. Yee proposed the “leap-frog” leap-frogging scheme for the 9 progression over time of E  and H  . The computational processes for E  and H  are illustrated by the flowchart in Figure 2.7. The relationship of E  and H  calculation is as follows: - Calculate the components of E  at a point in space at the time n t . - Calculate the components of H  at that point at the next moment  1/ 2n t  . Figure 2.7. Flowchart illustrating the E  and H  calculation procedures at different times in space With the “leap-frog” algorithm proposed by K. Yee, the E-field value in the space at the specified time is calculated according to the previous electric field value and its four adjacent magnetic field values. The same goes for calculating the value of the magnetic field. 2.2.2. The plane wave expansion methode (PWE) The PWE method has simple manipulation; it is used in the studies of PhC structure [121-123]. The PWE method allows solving the complete wave vector equation of the electromagnetic field, calculates eigenfrequency with standard accuracy and suitable timing, It can be used to calculate the energy band structure of the PhC structure, the transmission spectrum [121,124,125], 2.2.3. The Boundary conditions and convergence of the algorithm There are many different boundary conditions, but the two basic 10 types mentioned are Bloch periodic boundaries and perfectly matched layers PML. The periodic boundary conditions are useful in periodic systems. For periodic boundaries, in a cell of size L, the field components satisfy f(x + L)= f(x) . To simulate open boundary conditions, we need the boundaries to absorb all the waves towards them without reflection. This is done by the PML. 2.3. Fabrication method for silica glass microspheres and FBG 2.3.1. Fabrication of microspheres by arc discharge method The silica and Er3+-doped silica microspheres have been fabricated by us by the arc discharge method on standard telecom fiber and Er3+-doped fiber according to the process: - Peel off the coating at the start of the fiber-optic to a length of  1.0 cm. - Using HF solution to chemically etch peeled optical fiber head with a length of  0.4 cm. - Arc discharge at the start of the optical fiber has been etched. 2.3.2. Fabrication of FBG using photolithography technique Figure 2.9. Diagram of fabrication principle of FBG by interfering mirror system In this thesis, we present only method to fabricated FBG by interferometer system; this is method that we used to make FBG. The 11 wavelength of the UV beam we used is UV = 248 nm and the optical fiber with the SiO2 core is highly doped with GeO2 photosensitive material (14% to 20%). When illuminating UV beam at a certain location of the optical fiber, the structure of GeO2 there is broken. The region that receives high UV intensity, the refractive index increases; the region that receives low UV intensity, the refractive index remains; on that basis, we obtained the FBG structure. Diagram of fabrication principle of FBG is illustrated in Figure 2.9. 2.4. Some experimental configurations to survey laser emission spectra This section presents experimental configurations to survey laser emission spectra based on the coupling of Er3+-doped silica microsphere with the tapered fibers and fiber laser configuration of the liquid sensor system using e-FPG. 2.5. Scanning Electron Microscope (SEM) This section presents the meaning of the SEM method and the general operating principle of the SEM machines. CHAPTER 3. CALCULATE AND SIMULATE SOME THE OPTICAL DEVICES USING 2D-PhC STRUCTURE 3.1. The photonic band gap of 2D-PhC slab structure The structure of the 2D-PhC waveguide is modelled as shown in Figure 3.1: 2D-PhC triangular lattice structure with lattice constant a of air holes of radius r, depth h =220 nm is designed on the dielectric background Si with thickness d = 220 nm and refractive index n1 = 3.48; this lattice is placed on SiO2 substrate with refractive index n2 = 1.44. The PBG simulation was performed using 3D-PWE method, PML boundary conditions are placed above and below the slab (parallel to the structural surface), Bloch periodic boundary 12 conditions are applied according to the periodic directions of the structure, the resolution to perform the simulation is 10 nm. Figure 3.1. The triangular lattice structure of the 2D-PhC slab with lattice constant a of cylindrical air holes of radius r, depth h is designed on the dielectric background Si with thickness d = h = 220 nm In the case of a = 400 nm, r = 100 nm, the result is shown in Figure 3.2. Figure 3.2. Photonic band structure for the 2D-PhC slab even mode Figure 3.2 shows the existence of a complete PBG with even mode and wavelengths in the range from  1369 nm to  1607 nm corresponding to normalized frequencies 0, 2922( / 2 )a c  and 0, 2489( / 2 )a c  . The selected structure has PBG containing wavelengths 1470nm and 1550nm, that means this structure can be used to fabricate waveguide channels with wavelengths 1470nm and 1550nm. 13 3.2. Waveguide in plane using 2D-PhC slab structure Using 2D-PhC slab structure in Figure 3.1 with the selected parameters: a = 400 nm, h = d = 220 nm, r = 100 nm. The PML boundary condition was used and placed around the structure, the resolution to perform the simulation is 10 nm. The source is placed at the input waveguide and behind PML layer, the receiver is placed around the structure and in the PML layer. 3.2.1. W1 waveguide and field distribution in waveguide W1 waveguides are created by filling a row of air holes of the structure as shown in Figure 3.1. To extend the band [132], we reduce the radius of two adjacent rows of air holes with waveguide W1 from r = 100 nm to r1 = 95 nm. Figure 3.7. Dispersion diagram and electric field distribution of the Ey component in the waveguide at wavelength  = 1550 nm By using 3D-PWE method, we get the dispersion diagram, the electric field distribution of the Ey component in the structure at wavelength  = 1550 nm as shown in Figure 3.7. The simulation results show that the selected 2D-PhC structure that conduct wave is good with wavelength  = 1550 nm. 3.2.2. Slotted waveguide and field distribution in waveguide The model of the slotted 2D-PhC waveguide structure is shown in Figure 3.8. The dispersion diagram, the electric field distribution in the 14 structure corresponding to wavelengths  = 1470 nm,  = 1550 nm and the refractive index distribution of the structure was simulated by the 3D-PWE method. Simulation results for the case w = 165 nm, W = 1.18 W1 and w = 125 nm, W = 1.25 W1 are shown in Figure 3.9 and Figure 3.10, respectively. The results showed that the 2D-PhC with the selected parameters has good wave conductivity with  = 1470 nm and 1550 nm. Figure 3.8. Slotted 2D-PhC waveguide structure of triangular lattice Figure 3.9. Dispersion diagram, E-field distribution of the Ey component in the waveguide at  = 1470 nm and refractive index distribution of the structure Figure 3.10. Dispersion diagram, E-field distribution of the Ey component in the waveguide at  = 1550 nm and refractive index distribution of the structure 15 3.3. The optical wave filter based on GMR effect To test and evaluate the wavelength selection of the 2D-PhC slab structure, we perform the investigation, calculation and simulation of the optical wave filters using 2D-PhC slab based on the GMR effect. The characteristics parameters for filter such as resonance wavelength 0, quality factor Q are determined indirectly through using characteristics expression of the Fano spectrum. The simulation results for GMR spectra, field distributions is given by a single lattice structure and two types of dual lattice structures are presented in detail in this section. CHAPTER 4. LASER EMISSION OF MICROSPHERE BASED ON Er3+-DOPED SILICA, PHOTONIC DEVICE AND ITS APPLICATION 4.1. Fabrication results of Er3+-doped silica microsphere Figure 4.3. SEM images of Er3+-doped silica glass microsphere Figure 4.3 shows SEM images of some Er3+-doped silica glass microspheres that we fabricated by arc discharged method. 4.2. Emission spectrum of Er3+-doped silica microsphere laser The emission spectrum of Er3+-doped silica microsphere laser with diameter ∼ 29.7 μm obtained from experiment with a number of different coupling gaps according to two configurations CW and CCW are shown in Figure 4.12-4.14. 16 Figure 4.12. WGM mode emission spectra extracted from Er3+-doped silica microsphere: coupling gap  1.5  0.1 m according to CW configuration Figure 4.13. WGM mode emission spectra extracted from Er3+-doped silica microsphere: coupling gap  1.5  0.1 m according to CCW configuration Figure 4.14. WGM mode emission spectra depends on the coupling gap according to the CW configuration 4.3. Simulate the WGM mode of silica microspheres 4.3.1. WGM mode of microsphere with diameter of 38.5 m This section presents some simulation results of WGM mode of 17 silica microsphere with diameter of 38.5 m on the equatorial plane of the microsphere. 4.3.2. WGM mode of microsphere with diameter of 29.7 m Figure 4.16 shows some simulation results of WGM mode of silica microsphere with diameter of 29.7 m on the equatorial plane of the microsphere. Figure 4.16. Reflection spectrum on the surface of the microsphere (a), E-field magnitude distribution of WGM mode at  = 1551.53 nm with TM mode (b), field distribution of the EZ component at  = 1551.53 nm with TM mode (c) and HZ component at  = 1550.82 nm with TE mode (d) 4.3.3. Calculate quantum mode numbers using numerical method Table 4.1 presents the results about sets of values (l, n) that characterize WGM modes distributed on the equatorial plane of two silica microspheres is calculated by numerical method using approximate expressions from (1.40) to (1.44) [87] and 3D-FDTD simulation method. 18 The Table 4.1 shows that there is a good suitability between one of quantum value sets (l, n) when calculating numerically with set of values (l, n) is determined by 3D-FDFD simulation method. Table 4.1. Sets of values (l, n) are calculated using two different methods Diameter of S (m) Polarization Resonance wavelength (nm) Numerical method 3D-FDTD simulation 38.5 TM 1550.74 (104, 1), (98, 2), (92, 3) (88, 4), (84, 5), (80, 6) (80, 6) 38.5 TE 1549.01 (105, 1), (99, 2), (93, 3) (88, 4), (84, 5), (80, 6) (85, 5) 29.7 TM 1551.53 (79, 1), (73, 2), (68, 3) (64, 4), (61, 5) (64, 4) 29.7 TE 1550.82 (80, 1), (74, 2), (69, 3) (65, 4), (61,5) (66, 4) 4.4. Integrated photonic device based on the coupling of the microsphere with the SOI slotted 2D-PhC waveguides 4.4.1. Design proposal Figure 4.17. Schematic diagram of the intergration of the Er3+-doped silica microsphere and the two SOI slotted PhC waveguides The integrated structure consists of two SOI slotted PhC 19 waveguides coupled with microsphere of 29.7 m in diameter is shown in Figure 4.17. The 2D-PhC waveguide slab is a triangle lattice of cylindrical air holes with lattice constant of a = 400 nm, radius of r = 100 nm, depth of h =220 nm is designed on the dielectric background Si with thickness of d = 220 nm, refractive index of n1 = 3.48. This lattice is placed on SiO2 substrate with refractive index of n2 = 1.44. The waveguide width and the air slot width of input waveguide and output waveguide are W = 1.18 W1, w = 165 nm and W’ = 1.25, W1 w’ = 125 nm, respectively. In order to maintain the WGM modes in the Er3+-doped silica microsphere, an air ring width of   0.9 m has shown to be suitable and the corresponding geometry structure is presented in Figure 4.17. By using 3D-PWE method, we get the dispersion diagram and the electric field distributions of the Ey components with TE mode in the input waveguide and output waveguide at  = 1470 nm and 1550.84 nm as shown in Figure 4.18, respectively. The simulation results show that the 2D-PhC waveguide structure with selected parameters that conduct wave is good with wavelength  = 1470 nm and 1550.84 nm. Figure 4.18. Dispersion diagram and E-field distributions of the Ey components in two waveguides at  = 1470 nm and 1550.84 nm 20 4.4.2. Simulate the characteristic spectrum of integrated photonic device Using 3D-PWE and 3D-FDTD methods with PML boundary conditions are placed around the structure. The WGM mode emissions excitation sources are TE polarized electric dipoles with wavelength in the range 1400 - 1600 nm are placed inside and near the microsphere surface, the selected mesh size for simulation is 10 nm; the Bloch mode source is placed at the input waveguide and behind PML. The simulation results are shown in figure 4.19. The results showed that this integrated system is capable of coupling the Bloch mode of the waveguided with the WGM mode of microsphere. Figure 4.19. Refractive index distribution of the integrated structure based on the coupling of the microsphere with diameter of 29.7 m with the two SOI slotted 2D- PhC waveguides (a) and E-field distributions in the integrated structure (b,c) 21 4.5. The sensor element based on FBG 4.5.1. The sensor equipment uses two FBGs that are integrated into the ring laser configuration The principle schematic of the sensor equipment measuring the liquid refractive index that we have built is shown in figure 4.20. When the laser emission mode is selected by re-FBG and the Bragg reflection wavelength of e-FBG placed in the measuring medium are coincided (re-B = e-B), maximum resonance in the fiber ring laser resonance cavity will occur and photoelectrical signal obtained from photodiode with maximum value. Figure 4.20. The principle diagram of the sensor system 4.5.2. Procedure for measuring the refractive index of the solution - The first step: Construct a wavelength B - temperature calibration curve for re-FBG. - The second step: Construct a wavelength B - refractive index calibration curve for e-FBG based on using standard solutions. - The third step: Place the e-FBG sensor probe in the solution whose refractive index is to be determined, change the imposed temperature on the re-FBG, measure the optical power obtained from the photodiode then plot the optical power - temperature curve. 22 - The fourth step: Determine the imposed temperature on the re- FBG corresponding to the maximum value of optical power. - The fifth step: Based on the reflection wavelength-temperature calibration curve that has constructed for re-FBG to determine the reflection wavelength value corresponding to the temperature found in fourth step. - The sixth step: From reflection wavelength received in fifth step, based on the reflection wavelength - refractive index calibration curve has constructed for e-FBG, we will determine the refractive index of the solution to be measured. 4.5.3. Some experimental results Figure 4.26 displays the experimental results to detect the gasoline RON 92 mixed with Ethanol or Methanol in range of concentration 0% - 14% v/v. The sensitivity of sensor obtained  45 nm/RIU. The limit of detection of measurement is calculated by LOD = /QS [145] and achieved value of  1.5 x 10-4 RIU (S is sensitive of sensor,  is wavelength of sensor signal and Q is quality factor of laser mode. Figure 4.26. Bragg wavelength shift of e-FBG according to the concentration of Ethanol and Methanol in gasoline RON 92 23 Figure 4.27 presents the experimental result to detect Nitrate in range of concentration 0 - 50 ppm. The limit of detection of the measurement is evaluated  4.5 ppm, this limit is close to value that sensor system received by optical spectrum analyzer with high resolution [25]. Figure 4.27. Sự dịch chuyển bước sóng Bragg của e-FBG theo nồng độ Nitrat trong môi trường nước CONCLUSION Some main results that the thesis has achieved: 1. Calculated and simulated some optical devices such as waveguide, optical wave filter using 2D-PhC slab structure by FDTD and PWE methods. 2. Fabricated some Er3+-doped silica microsphere with diameter of  30 m  60 m by arc discharged method. Designed and constructed successfully the experimental system to survey the WGM mode laser emission effect of Er3+-doped silica microsphere, simulated and solved the numerical for quantum v