I
國
立
交
通
大
學
光電工程研究所
博
士
論
文
應用於檢測技術的光源設計
The Design of the Light Source for Sensing Technology
研 究 生：周森益
指導教授：祁 甡 教授
中
中
中
II
應用於檢測技術的光源設計
The Design of the Light Source for Sensing Technology
研 究 生：周森益 Student：Sen-Yih Chou
指導教授：祁 甡 Advisor：Sien Chi
國立交通大學 電機學院
光電工程研究所
博士論文
A DissertationSubmitted to Department of Photonics and Institute of Electro-Optical Engineering College of Electrical and Computer Engineering
National Chiao Tung University in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy in
Electro-Optical Engineering June 2012
Hsinchu, Taiwan, Republic of China
III
應用於檢測技術的光源設計
應用於檢測技術的光源設計
應用於檢測技術的光源設計
應用於檢測技術的光源設計
學生：周森益 指導教授：祁甡 國立交通大學光電工程研究所博士班摘
要
光學量測技術目前被大量使用在科學研究、工業研發、量產製造及消費性產 品上。光學量測技術的主要原理，為使用一光源投射在待測樣品上，待測樣品改 變投射光源的光學特性，再由偵測器量出被樣品改變後散射或反射光的光學特性。 藉由分析入射與出射光學特性改變，可以量測到待測樣品的特性。因此，檢測技 術所使用之光源將影響最後檢測結果之訊噪比。 a. 熱光效應光錐濾波器：本論文組合錐形光纖及光學匹配液構成高斯濾波器， 並且藉由熱光效應可以調整濾波器的通過頻帶。借由此濾波器可修正 OCT 的寬 頻光源頻譜，並且得到高解析度的生物影像。 b. 超寬頻光源：本論文採用 80fs 的 Ti:sapphire 雷射注入錐形光纖中，產生 400 nm 到 1200 nm 的超寬頻光源。同時採用數值模擬進行超寬頻光源產生過程的動態模 擬，探討注入脈衝初始啾頻如何影響超寬頻光源的產生。 c. 單一縱模雷射光源：單一縱模光纖雷射可被應用於光纖通訊、光纖感測器和 光譜分析等領域。在此論文中採用雙共振環路限制縱模模態，由摻鉺波導放大器、 兩路不等長共振環路及 Fabry-Perot 可調濾波器構成單一縱模光纖雷射。並且討 論此雷射架構的輸出強度、側模抑制比、波長及輸出強度的穩定度。 d. 高動態範圍疊紋干涉術：本論文將提出一種利用面型感光元件(CCD 或 CMOS) 做單次曝光（one-shot）可得到高動態範圍影像之技術。利用此技術可以得到大 範圍且不損失影像細節之高動態影像資料，對此高動態影像進行後續處理，可提 高量測之準確度。
IV
The Design of the Light Source for Sensing Technology
Student: Sen-Yih, Chou Advisors: Dr. Sien Chi
Institute of Electro-Optical Engineering National Chiao-Tung University
ABSTRACT
Optical measurement techniques have been receiving an increasing attention during recent decades. The most important reason is that they work non-intrusively and therefore do not influence the investigated process. The continuing developments in laser, detector, optical fiber and computer technology will further augment the high applicability and versatility of optical measuring techniques. Therefore, it can be expected that optical techniques will continue to gain in importance in many fields of application. However, the procedures of optical measurement techniques include emitted a light signal, this signal modulated by device under test and analyzed the difference of those signal. The purpose of this dissertation is to discuss what is important in optical measurement technology is to adjust the light source suited with this measurement.
V
誌
謝
在這個漫長的旅程中，總是有人適時地伸出援手拉我一把，尤其是我的家人永遠 在背後默默的支持。衷心地感謝所有幫助過我人，謝謝各位。
VI
目
錄
中文摘要...I 英文摘要...II 誌謝...III 目錄...IV 圖目錄...VI Chapter 1 Introduction ... 1
1.1 Overview of Thermo-Optic Tunable Tapered-Fiber Filter ... 1
1.2 Overview of the Wideband Tunable Gaussian-Shaped Spectral Filter ... 1
1.3 Overview of the Supercontinuum Generation in a Tapered Fiber ... 2
1.4 Overview of the Stable and Tunable Fiber Laser ... 2
1.5 Overview of Projection Moiré Profilometry with High-Dynamic Range Image... 3
Chapter 2 Analysis of Thermo-Optic Tunable Dispersion-Engineered Tapered-Fiber Filter ... 4
2.1 Review of Taper-Fiber Filter ... 4
2.2 Fabrication Process and Operation Principle ... 6
2.3 Experimental and Simulation Results ... 9
2.4 Conclusion ... 23
Chapter 3 The Wideband Tunable Gaussian-Shaped Spectral Filters ... 27
3.1 Introduction ... 27
3.2 Simulation and Experiment ... 29
3.3 Conclusions and Summary ... 36
Chapter 4 The Supercontinuum Generation in a Tapered Fiber ... 40
4.1 Introduction ... 40
4.2 Experiment Setup and Results ... 41
VII
4.4 Conclusions ... 56
Chapter 5 The Stable and Tunable Fiber Laser ... 61
5.1 Introduction ... 61
5.2 Experiments and Results ... 62
5.3 Conclusion ... 66
Chapter 6 Projection Moiré Profilometry with High-Dynamic Range Image ... 69
6.1 Introduction ... 69
6.2 Measurement Method ... 71
6.3 Results and Discussion ... 74
6.4 Conclusion ... 78
VIII
圖 目 錄
頁次
Fig. 2-1 (a) Diagram of a tapered-optical-fiber structure with a uniform waist. (b) Schematic diagram of the tapering station used to fabricate the tapered fibers.
7
Fig. 2-2 Material dispersion curves for the original fiber core (GeO2
4.1 mol%), cladding (pure silica), and the index-matching liquids measured at 25, 26, and 27oC, respectively.
8
Fig. 2-3 Experimental and simulated spectral responses of the tunable
short-wavelength-pass fiber filters for (a)ρ = 20μm, (b)ρ = 26μm, and (c)ρ = 40μm at different temperatures.
10
Fig. 2-4 Field distributions along the tapered-fiber filter. (a) When the wavelength (1250 nm) is shorter than the band edge of the filter, the fields are guided over uniform waist and coupled back to the fundamental mode. (b) When the wavelength (1350 nm) is longer than the band edge of the filter, the fields spread out along the uniform waist.
12
Fig. 2-5 (a) Effective index of the fundamental mode versus
wavelength under different waist diameters of tapered fibers surrounded by (a) the air, and (b) the Cargille liquids (nD =
1.456).
14
Fig. 2-6 MFD/waveguide width versus wavelength under different
waist diameters of tapered fibers surrounded by (a) the air, and (b) Cargille liquids (nD = 1.456).
16
Fig. 2-7 Fundamental-mode-field distribution in the tapered waist
under different taper diameters at (a) 1250 nm (guiding wavelength) and (b) 1350 nm (near cutoff wavelength).
18
Fig. 2-8 Simulation results of transmission spectra at different waist diameters of 5, 10, 20, 26, 33, and 40μm, respectively.
18
Fig. 2-9 Transmission spectra associated with different lengths of uniform waist of 2 mm, 10 mm, 20 mm, 30 mm, and 50 mm for ρ = 26μm and 2mm, 10mm, 20mm for ρ=40μm with the taper transition length of 6 mm.
20
Fig. 2-10 Transmission spectra associated with different transition lengths of 3mm, 6mm, and 12mm with the waist length of 18 mm for ρ=26μm.
IX
Fig. 2-11 Transmission spectra of the final optimal design of the short wavelength pass filter. The taper waist diameter is 35μm, the waist length is 30 mm, and the transition length is 6 mm.
22
Fig. 3-1 (a) Refractive index dispersion of silica and Cargille optical liquids. (b) Simulated transmission spectra of the SWPFs at different diameters of tapered waist and the Gaussian fit curve. (c) Simulated transmission spectra of the LWPFs at different diameters of liquid core and the Gaussian fit curves. (d) Simulated transmission spectra of the SWPFs at different lengths of tapered waist.
32
Fig. 3-2 (a) Diagram of a tapered optical fiber (SWPF) with a
uniform waist. (b) Schematic diagram of the tapering station used to fabricate the tapered fibers. (c) Refractive index dispersion curves with different temperature. The solid line depicts the tapered fiber, and the dotted line indicates the index matching liquid with different temperatures. (d) Spectral responses and fitted Gaussian curves of SWPF at different temperatures.
33
Fig. 4-1 Schematic diagram of the taper fiber structure. 42
Fig. 4-2 Experimental setup of the supercontinuum generation. 42
Fig. 4-3 Generated spectra at different pump powers using
1-µm-diameter fiber tapers. The output pattern from the fiber and the dispersed spectra by the prism are shown inset.
43
Fig. 4-4 (a) Effective mode area and (b) nonlinear parameter versus the waist of the tapered fiber at 830 nm.
45
Fig. 4-5 (a)-(d) the dispersion coefficients versus the diameter of the tapered fiber at 830 nm.
48
Fig. 4-6 Simulation results of generated spectra at different pump powers using 1-µm-diameter fiber tapers with different launched pump powers.
49
Fig. 4-7 Simulation results of (a) the spectrum evolved along the tapered fiber and (b) the time domain pulse evolved along the tapered fiber, that the input average power is 400 mW.
X
Fig. 4-8 (a)Spectral broadening, (b)frequency chirp when pulse
launching into the fiber waist, (c)time domain pulse shape when pulse launching into the fiber waist for comparison between the nonlinear effect being neglected and considered.
52
Fig. 4-9 (a)Spectral broadening, (b)frequency chirp when pulse
launching into the fiber waist under different shapes of the fiber taper.
54
Fig. 4-10 (a)Spectral broadening, (b)frequency chirp when pulse launching into the fiber waist (c)time domain pulse shape when pulse launching into the fiber waist for chirped and unchirped pulse.
56
Fig. 5-1 Proposed fiber double-ring laser architecture for SLM
operation
63
Fig. 5-2 Output wavelengths of the proposed fiber laser in an
operating range of 1530 to 1560 nm.
64
Fig. 5-3 Output power and SMSR versus different wavelength for the
proposed laser over the wavelengths of 1530 to 1560 nm.
65
Fig. 5-4 Output wavelength and power variations of the proposed
laser for a lasing wavelength of 1546.5 nm initially and an observing time of 60 minutes.
65
Fig. 5-5 Self-homodyne spectra of the (a) single-ring and (b)
double-ring laser at 1546.5 nm initially
66
Fig. 6-1 The system configuration. 74
Fig. 6-2 The block diagram of a control unit. 74
Fig. 6-3 The captured image and retrieved profile of the traditional fringe projection
76
Fig. 6-4 The captured image and retrieved profile of the regional adjusting fringe projection
1
Chapter 1
Introduction
1.1 Overview of Thermo-Optic Tunable Tapered-Fiber
Filter
Fiber-based filters have attracted considerable research interest due to their compact size and low insertion loss for fiber-optic applications. With the existing technologies, band-pass fiber-based optical filters provide different bandwidths ranging. This dissertation presents a novel and simple wideband and band-width-variable bandpass fiber filter using a tapered standard single-mode fiber covered with Cargille liquids. The thermo-optic tunable short-wavelength-pass tapered-fiber filters based on fundamental-mode cutoff mechanism are realized experimentally and analyzed theoretically. The effects of material and waveguide dispersion are investigated and the optimal tapered fiber structures for attaining high-spectral cutoff slope and high-rejection efficiency are determined.
1.2 Overview of the Wideband Tunable Gaussian-Shaped
Spectral Filter
2
Optical liquids can be used to engineer the dispersion characteristics of fibers by serving as the core or cladding to attain fundamental-mode cutoff effect. The short-pass or long-pass fiber filters are so made and concatenated to achieve widely thermo-optic tunable Gaussian-shaped spectral filters. The proposed wideband tunable Gaussian-shaped spectral filter provides a potential technique in application to high resolution bio-imaging.
1.3 Overview of the Supercontinuum Generation in a
Tapered Fiber
Relatively wide spectral broadening from above 400 nm to below 1200 nm is generated from a tapered fiber by properly tuning the center wavelength of the pumping 80-fs Ti:sapphire laser. The waist of excited tapered fiber is 1 µm in diameter and only 1-cm long. Additionally, numerical simulation considering the dispersion and nonlinear effect at the transition region of the taper fiber is performed to study the generated supercontinuum spectra. The numerical results show that the nonlinear effect inside the taper transition modifies the pulse shape and phase thus greatly influences the spectral broadening, and using a chirped pulse launching can enhance the efficiency of supercontinuum generation.
1.4 Overview of the Stable and Tunable Fiber Laser
3
single-longitudinal-mode (SLM) fiber double-ring laser using an Erbium-doped waveguide amplifier (EDWA), polarization controller (PC), and a fiber Fabry-Perot tunable filter (FFP-TF) into the ring cavity. In addition, the output power, side-mode suppression ratio (SMSR), and the stabilities of power and wavelength of the laser also are investigated.
1.5 Overview of Projection Moiré Profilometry with
High-Dynamic Range Image
As a type of optical measuring apparatus, the charge-coupled diode (CCD) camera provides the capability of increasing the speed of measurement by inspecting an area with only one shot. However, the CCD camera ’ s high-variation range of reflectivity presents an exceptional challenge for the optical measurement established on the surface. The dissertation presents a method that could enable one to acquire an image with a high-dynamic range in one shot without any reduction in spatial resolution. Because of the sufficient signal-to-noise ratio, the method presented could perform the robustness of the phase-retrieving algorithm, and the surface topography could be measured more accurately.
4
Chapter 2
Analysis of Thermo-Optic Tunable
Dispersion-Engineered Tapered-Fiber Filter
2.1 Review of Taper-Fiber Filter
Stronger interaction of the optical evanescent field with the environment has been widely utilized in many fiber-based devices such as the fused-tapered-based fiber filters [1], [2] dispersion-engineering applications [3]–[5] and nanowire sensing applications[6], [7]. The dispersion-engineering techniques manipulate the dispersion characteristics of fiber waveguides to alter the optical properties of fiber devices. In the literatures the theoretical modeling of tapered fibers had been widely developed [8]–[12], the fundamental-mode cutoff effects induced by dispersion-engineering techniques with fiber tapering have not been theoretically investigated yet. The main objective here is thus to theoretically analyze the fundamental-mode cutoff effects and to determine the optimal tapered-fiber structures for achieving low-loss and high-cutoff efficiency. These results should be very crucial for applications such as high-gain low-noise S-band fiber amplifiers [13] and widely tunable S-band fiber lasers [14].
This chapter will present experimental characterization and theoretical simulation results on the studied thermo-optic tunable fused-tapered-fiber filters made
5
by tapering standard single-mode fibers (SMF-28). The tapered fibers are immersed in Cargille liquids for implementing dispersion engineering through the control of material dispersion. The filter becomes cutoff at longer wavelengths due to the reducing refractive index of Cargille liquids below the effective refractive index of the Cargille liquids below the effective refractive index of the fiber waveguide. The propagation loss increases rapidly near the cutoff wavelength, and a sharp short-wavelength-pass optical filtering edge is achieved. To investigate these effects more deeply, the effective index (neff) and the mode field diameter (MFD) of the fundamental mode are calculated and carefully examined in order to understand what determines the filter performance. The numerical beam propagation method (BPM) is then adopted to theoretically simulate the cutoff phenomena and the temperature tuning characteristics of the whole device. Good agreement between the simulation and experimental results has been found. Since the filter performance is also significantly influenced by the whole waveguiding structure, the optimal parameters for the uniform taper diameter, uniform taper length, and taper transition length are investigated by the full BPM simulation for achieving best filter performance. From the simulated spectral responses and the effective dispersion curves, find that the taper-waist diameter greatly affects the MFD, which in turn affects the final dispersion relation and the achievable cutoff slope. The taper length can also affect the cutoff slope, and the transition length has direct impacts on the insertion loss. The obtained theoretical results help to determine the optimal device structures for fabricating efficient short-pass tapered-fiber filters which can be utilized in high performance S-band Er-fiber amplifiers and lasers.
6
2.2 Fabrication Process and Operation Principle
The high-cutoff efficiency of the studied short-pass fiber filter is obtained by locally modifying the material and waveguide dispersion within the uniform taper region. The schematic of the fused-tapered short-pass filter is shown in Fig. 2-1(a). One can describe the structure of a tapered-fiber filter by specifying the transition length (denoted as τ), the uniform waist length (denoted as L0) and the waist diameter
(denoted as ρ). It consists of a transition zone where the diameter is gradually reduced to ρ over a distance τ and then a uniform waist section with the length of L0. The
uniform waist section is immersed within suitable Cargille index-matching liquids. The optical properties of the used Cargille liquids can be summarized as follows. The refractive index nD =1.456, thermo-optic coefficient
4 0
3.74 10
D
dn dT = − × − C, and optical transmittance is 88% at 1300nm, and 80% at 1550nm for 1-cm-long length. The whole device is mounted on a thermoelectric (TE) cooler for temperature control. Those tapered-fiber filters are fabricated by a homemade tapering workstation comprising several modules for fiber pulling, heating, and scanning as illustrated in Fig. 2-1(b). A hydrogen flame head with high-accuracy flow control is set on a three axis stepper motor to precisely control the traveling of the flame over the distance of few centimeters. When the tapering process begins, the pulling motors move outward to pull the heated fiber and the flame simultaneously starts to travel back-and-forth for heating the region to be tapered. The pulling mechanism employs a high-precision stepping motor with a right-and-left-threaded screw to drive two V-groove clampers moving outward in a reverse direction. The clampers bilaterally hold the single-mode fiber for providing a precise pulling stress. By controlling the moving speed of the
7
scanning flame and the pulling clampers, the total elongation length can be varied from 30 to 60 mm, and the corresponding length of the uniform waist is measured to be around 10-25 mm, contingent on the waist diameter. When tapering is finished, the fiber is fixed in a graved U-groove on a quartz substrate and immersed in index-matching liquids. A TE cooler is used to control the liquid temperature to change its refractive index for tuning the cutoff wavelength.
Fig. 2-1. (a) Diagram of a tapered-optical-fiber structure with a uniform waist. (b) Schematic diagram of the tapering station used to fabricate the tapered fibers.
When a single-mode optical fiber is tapered down to few tens micrometer in diameter, the evanescent tail of the mode field spreads out of the fiber cladding and reaches the external environment (Cargille liquids). The size of the Ge-doped core in the tapered zone is so reduced that its waveguiding effects are negligible. Therefore, the pure silica cladding plays as the new core, whereas the external medium serves as the new cladding. The material dispersion curves for the original fiber core (GeO2
4.1 mol%), cladding (pure silica), and the Cargille liquids are plotted in Fig. 2-2 to illustrate their relative relation. On the righthand side of the cross point indicated in
8
Fig. 2-2, the refractive index of the liquids is greater than the index of fiber taper and the total internal reflection of the interface is frustrated. Therefore, the lights cannot be guided in the fiber taper and suffer a great amount of optical loss. On the other hand, the light can be nicely confined in the fiber taper when the wavelength is shorter than the cutoff wavelength. The cutoff wavelength of the short-wavelength-pass filter should be very near the cross point of the two dispersion curves indicated in Fig. 2-2, under the condition that the mode in the tapered region is mainly guided by the original cladding. The temperature shift of the cross point as also indicated in Fig. 2-2 provides an intuitive explanation about the temperature-tuning capability of the tapered-fiber filter.
Fig 2-2. Material dispersion curves for the original fiber core (GeO2 4.1 mol%),
cladding (pure silica), and the index-matching liquids measured at 25, 26, and 27oC, respectively.
It should also be noted that a related but different kind of short-wavelength-pass optical filtering effects can be observed when the tapered fiber waist is in the 100 nm range. [15] The tapered fiber is surrounded by the air, and an abrupt change of the mode field diameter as a function of the optical wavelength can be found. This leads to an abrupt change of optical loss accordingly. However, since no dispersion engineering is used to produce true optical cutoff, the filtering slope and rejection
9
ratio are not as large as the cutoff case studied here.
2.3 Experimental and Simulation Results
Both the experimental and simulated spectral responses of the short-wavelength- pass fiber are displayed in Fig. 2-3 for performance studies and comparison. The solid lines of Fig. 2-3(a)-(c) display the experimental spectral responses of the short-wavelength-pass filter with waist diameters measured to be 20, 26, and 40 μm, respectively. The total elongation lengths are about 30 mm, and the lengths of the uniform waist are measured to be around 18 mm. The larger the waist diameter is, the steeper the cutoff slope can be. Here the cutoff slope (in unit: dB/nm) is defined as the average gradient of the rolloff spectral curve in the linear region from -10 to -30 dB transmission loss. The cutoff slopes are calculated to be -0.54, -1.38, and -2.00 for the cases of ρ = 20µm, ρ = 26µm, and ρ = 40µm, respectively. When ρ = 40µm, the cutoff slope is very sharp, but the rejection efficiency is more limited. The extra loss of less than 2 dB at 1390 nm may result from the absorption of hydroxyl ions which were generated from the hydrogen flame and then diffused into the tapered fiber. The tuning efficiencies of the filter are about 52, 47, and 62 nm/oC for the cases of ρ =
20µm, ρ = 26µm, and ρ = 40µm, respectively. At the guiding wavelengths, the insertion losses of the filters are below 1 dB, 0.5 dB, and 0.3 dB for ρ = 20µm, ρ = 26µm, and ρ = 40µm, respectively. The losses are mainly from the absorption loss of the Cargille liquids and the optical loss due to fiber tapering. The absorption loss caused by the Cargille liquids is estimated to be below 0.2 dB after taking into account the transmittance of the liquids and the evanescent field overlapping effects. The fiber-tapering loss depends on the tapering conditions. In principle, when the
10
tapering transition is slow enough to meet the adiabatic criteria [16], the tapering loss can be made very small. For our cases, the tapering loss is reasonably low but still observable, as can be seen from the above numbers. Even smaller tapering losses should be possible at the cost of increasing the total device length.
Fig. 2-3. Experimental and simulated spectral responses of the tunable
short-wavelength-pass fiber filters for (a)ρ = 20μm, (b)ρ = 26μm, and (c)ρ = 40μm at different temperatures.
11
To further analyze the fundamental-mode cutoff characteristics, numerical simulation by the BPM is performed to study the optical field propagation within the tapered fibers and to predict the filter performance theoretically. The BPM uses the finite difference method to solve the paraxial approximation of the Helmholtz equation with “transparent” boundary conditions [17]. This approach can automatically include the effects of all the guided and radiation modes as well as the mode-coupling and mode-conversion effects. The fiber-taper transition structure is set to be an exponential shape in our simulation. The dotted lines in Fig. 2-3(a)–(c) show the simulated transmission spectra with the temperatures of 25, 26, and 27 oC and the
waist diameters of 20, 26, and 40 μ m, respectively. The cutoff wavelengths gradually shift to longer wavelengths when the temperature increases. Good agreement of the changing trends for the cutoff slopes and rejection efficiencies between the simulated and experimental results has been found. The mismatch of the cutoff wavelengths between the experimental data and simulation results should be due to the uncertainties of the fiber-tapering parameters and the temperature-reading errors in the experiment. Most importantly, the simulation results correctly reproduce the experimental observation that the larger diameter cases have larger cutoff slopes, but will eventually have poorer rejection ratios when ρ is too large (> 40μm). The thermo-optic-tuning efficiency of the filter for ρ=26μm in Fig. 2-3(b) is about 48 nm/oC from BPM simulation, which is also in good agreement with the 47 nm/oC
tuning efficiency from the experimental data.
Based on the facts that the theoretically predicted tuning and cutoff efficiencies agree reasonably with the experimental data, we further utilize the BPM as a reliable simulation tool to investigate the effects of different taper parameters for determining
12
the optimal taper structures.
(a)
(b)
Fig. 2-4. Field distributions along the tapered-fiber filter. (a) When the wavelength (1250 nm) is shorter than the band edge of the filter, the fields are guided over uniform waist and coupled back to the fundamental mode. (b) When the wavelength (1350 nm) is longer than the band edge of the filter, the fields spread out along the uniform waist.
Fig. 2-4(a) and (b) show the simulated field evolution within a tapered fiber with the cutoff wavelength around 1330 nm. The waist diameter ρ is 26 μm, the
F ib e r c ro s s s e c ti o n ( µµµµ m ) Propagation direction (mm) Transition
zone Uniform Waist Transitionzone
1250nm -5 0 5 10 15 20 -200 -150 -100 -50 0 50 100 150 200 F ib e r c ro s s s e c ti o n ( µ m ) Propagation direction (mm) Transition
zone Uniform Waist Transitionzone
1350nm -5 0 5 10 15 20 -200 -150 -100 -50 0 50 100 150 200
13
transition length τis 6 mm, the taper transition angle is around 0.5o , the uniform
waist length L0 is 18 mm, and the temperature is set at 25 oC. In Fig. 2-4(a), when the
propagation wavelength (1250 nm) is shorter than the cutoff wavelength, the fundamental eigenmode of the input SMF is smoothly transformed into the fundamental eigenmode of the uniform tapered waist, propagates through the uniform waist region and then gradually reconverts to the fundamental mode of the output SMF within the second transition distanceτ. The fundamental MFD is larger in the uniform tapered region when compared to that of the SMF-28. On the other hand, Fig. 2-4(b) shows the case when the propagation wavelength (now 1350 nm) is longer than the cutoff wavelength. The optical field quickly disperses away within the first taper transition region as well as the uniform waist region due to the higher refractive index of the surrounding liquids. Only a very small fraction of the optical field can be coupled back to the fundamental mode of the output SMF. In this way, huge optical losses are induced for wavelengths longer than the cutoff wavelength.
14 (a)
(b)
Fig. 2-5. (a) Effective index of the fundamental mode versus wavelength under different waist diameters of tapered fibers surrounded by (a) the air, and (b) the Cargille liquids (nD = 1.456).
The material dispersion of the surrounding medium can significantly modifies the dispersion curve of the propagation mode due to the stronger overlap with the evanescent field spread out of the taper waist. To analyze how the surrounding material affects the dispersion properties of the fused-tapered fiber, the effective index of fundamental mode is calculated under different waist diameters of tapered fibers surrounded by the air and the Cargille liquids(nD = 1.456) . The results are plotted in
15
cladding (pure silica), and the Cargille liquids are also plotted for easy comparison. The index difference of the pure silica and the air is so large that the optical field is strongly confined when the tapered fiber is surrounded by the air. Thus, the dispersion curves of the fundamental mode have almost the same slope (⁄ 1.2
10ିହ /nm) with that of the pure silica when ρ>20μm. The effective mode index is
lower than those of the pure silica and Ge-doped core because parts of the optical mode field are now in the air. When the waist diameter gets smaller than 5 μm, the dispersion curve of the fundamental mode becomes more wavelength dependent. This is because now a larger fraction of the mode field is in the air. The slopes of the dispersion curves in Fig. 2-5(b) are calculated to be -0.55×10-5, -0.87×10-5, -0.94×10-5,
-1.07×10-5, and -1.14×10-5 for ρ=10μm, ρ=20μm, ρ=26μm, ρ=33μm, and
ρ=40μm, respectively. In contrast, the slopes of the modal dispersion curves for
tapered fibers immersed in the Cargille liquids are slightly flatter than those in the air, which indicates that the effective mode index of the tapered fiber is indeed modified by the surrounding dispersive liquids. The insect of Fig. 2-5(b) shows the detailed curves near the cutoff wavelength when the tapered fibers are immersed in the Cargille liquids. The cross points between the dispersion curves of the tapered fibers and the surrounding liquids exactly determine the cutoff wavelength, which will shift to longer wavelengths as the waist diameter increases. When the optical wavelength is near the cross point, the optical field quickly spreads out of the tapered fibers and large optical losses are induced. Intuitively the cross angle between the two intersected dispersion curves determines the cutoff slope. A suitable surrounding material which can produce a larger intersection angle is thus a key for achieving high-cutoff efficiency.
16 (a)
(b)
Fig. 2-6. MFD/waveguide width versus wavelength under different waist diameters of tapered fibers surrounded by (a) the air, and (b) Cargille liquids (nD
= 1.456).
Fig. 2-6(a) and (b) plot the ratio of the 1/e MFD to the waveguide width (waist diameter of the tapered fiber) as a function of the optical wavelength. When the tapered fiber is surrounded by the air, the optical field is strongly confined inside the tapered fiber and thus the width ratio is almost flat with respect to the optical wavelength for the waist diameters considered here. In contrast from Fig. 2-6(b) it is obvious that a larger fraction of the optical field spreads out of the tapered fiber when it is surrounded by the Cargille liquids due to the small index difference. As the waist
17
diameter is getting smaller, the width ratio gets larger. When the waist diameter is smaller than 10 µm, the optical fields will largely spread out of the tapered waveguide region and will experience higher losses even at guided wavelengths. When the waist diameter is between 20 µm and 26 µm, the width ratio curves exhibit a significant turning point between the guided region and the unguided region, as shown in Fig. 2-6(b). When the waist diameter is larger than 40 µm, the cutoff wavelength is shifted toward the longer wavelengths, and the optical field is more strongly confined in the waveguide. The dispersion-engineered effects can also be seen from the wavelength dependence of the MFD. Fig. 2-7(a) and (b) show the mode field distribution of the fundamental mode in the tapered waist under different taper diameters. Two optical wavelengths at 1250 nm (guiding) and 1350 nm (near cutoff) are used as the examples to illustrate the difference. The field is strongly confined in the tapered region for the guiding wavelengths when ρ > 20µm. As the waist diameter gets smaller than 10 µm, the field spreads out of the tapered fiber region and larger losses at the guiding wavelengths are produced. Near the cutoff wavelength in Fig. 2-7(b), the field extends more widely into the Cargille liquids due to the weak guiding condition. Thus, the loss becomes huge and the short-wavelength-pass band edge is formed. Moreover, the larger taper diameters (ρ > 33µm) can confine the fields more tightly than the smaller ones even near the cutoff wavelength.
18 -80 -60 -40 -20 0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0 N o rm al iz ed f ie ld a m p li tu d e Transverse length (µm) ρ=5µm ρ=10µm ρ=20µm ρ=26µm ρ=33µm ρ=40µm (a) -80 -60 -40 -20 0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0 N o rm al iz ed f ie ld a m p li tu d e Transverse length (µm) ρ=5µm ρ=10µm ρ=20µm ρ=26µm ρ=33µm ρ=40µm (b)
Fig. 2-7. Fundamental-mode-field distribution in the tapered waist under different taper diameters at (a) 1250 nm (guiding wavelength) and (b) 1350 nm (near cutoff wavelength).
1250 1300 1350 1400 1450 -60 -50 -40 -30 -20 -10 0 T ra n sm is si o n ( d B ) Wavelength (nm) ρ=5µm ρ=10µm ρ=20µm ρ=26µm ρ=33µm ρ=40µm ρ=45µm ρ=60µm
Fig. 2-8. Simulation results of transmission spectra at different waist diameters of 5, 10, 20, 26, 33, and 40μm, respectively.
19
Fig. 2-8 shows the simulated transmission spectra of the fiber taper with the waist diameter of 5, 10, 20, 26, 33, 45, and 60 µm, respectively. The fiber transition length τ is 6 mm, the uniform waist length L0 is 18 mm, and the temperature is at
25oC. The spectral cutoff responses are not the same for different waist diameters.
Note that as the waist diameter increases, the band edge is steeper. The cutoff slopes are calculated to be -0.38, -0.79, -1.14, -1.68, and -2.01 for ρ = 10µm, ρ = 20µm, ρ = 26µm, ρ = 33µm, and ρ = 40µm, respectively. The band-edge shifts to the longer wavelengths as the diameter increases. The cutoff characteristics in Fig. 2-8 can be described by the waveguide dispersion behavior with different waist diameters. The optical field intensely spreads out into the Cargille liquids when the waist diameter is getting small. The ratio of the optical field distributed in the waveguide with respect to that in the Cargille liquids is strongly decisive to the effective index of the mode field. When the diameter is less than 10µm, the waist is too thin to confine the optical field. Furthermore, when the waist diameter is getting thinner, most optical field extends into the Cargille liquids, the wave-guiding ability is weaker, and thus the transmission loss becomes larger. The simulation results indicate that the larger the waist diameter is, the steeper the filter cutoff slope can be. However, when the waist diameter is larger than 40µm, the achievable spectral contrast (or rejection efficiency) is more limited due to the stronger mode confinement. The short-wavelength-pass bend edge disappears when the tapered waist is larger than 60µm. All the wavelengths are now strongly confined in the Ge-doped fiber core. Thus, the optimal waist diameter for fused-tapered SMFs to produce a sharp short-wavelength-pass band edge should be somewhere between 33µm and 40µm.
Table 2-I lists the cutoff slopes and dispersion slopes for the waist diameters of 5, 10, 20, 26, 33, and 40µm, respectively. When the waist diameter is larger, the
20
dispersion slopes are larger and the cutoff slopes are steeper. It also can be clearly seen that steeper cutoff slopes are associated with larger cross angles between the dispersion curves of the tapered fibers and the surrounding liquids. The good agreement of the cutoff slopes from experimental and simulated results confirms that the simulation can help predict the filter performance.
TABLE 2-I
THE CUTOFF SLOPES AND DISPERSION SLOPES FOR DIFFERENT WAIST DIAMETERS OF TAPER FILTERS IMMERSED IN CARGILLE LIQUID Taper diameter Dispersion slope Δneff / nm (×10-5) Cutoff slope dB / nm 10 µm -0.55 -0.38(simulation) 20 µm -0.87 -0.79(simulation), -0.54(experimental) 26 µm -0.94 -1.14(simulation), -1.38(experimental) 33 µm -1.07 -1.68(simulation) 40 µm -1.14 -2.01(simulation), -2.00(experimental) 1250 1300 1350 1400 1450 -60 -50 -40 -30 -20 -10 0 ρ= 40µm T ra n sm is si o n l o ss ( d B ) Wavelength (nm) L0=2mm L0=10mm L0=20mm L0=30mm L0=50mm ρ =26µm
Fig. 2-9. Transmission spectra associated with different lengths of uniform waist of 2 mm, 10 mm, 20 mm, 30 mm, and 50 mm for ρ = 26μm and 2mm, 10mm, 20mm for ρ=40μm with the taper transition length of 6 mm.
21
on the cutoff slope of the filter’s band edge. The simulation is performed under the assumption that the temperature is 25oC, the fiber taper waist diameter and the waist
length are ρ = 26 and 40µm, respectively, and the transition length is τ = 6mm. The tapers have the waist length of 2, 10, 20, 30, and 50 mm for ρ = 26µm and the waist length of 2, 10, 20 mm for ρ = 40µm, respectively. It can be seen that the longer length leads to a steeper band edge for ρ = 26µm. When the waist length is shorter than 30 mm, the cutoff slopes of the band edge significantly increase with the waist length. Since the optical loss is proportional to the taper length, it is not surprised that longer taper length causes higher cutoff loss and thus provides a sharper cutoff slope. However, when the waist length is longer than 30 mm, the cutoff slopes become saturated. For ρ = 40µm, the length of the uniform waist not only influences the cutoff slopes but also affects the rejection efficiencies. The rejection efficiency relies on the sufficient cutoff loss of long taper length. At ρ = 40µm, the optical field is more confined in the tapered waist, and thus the optical cutoff loss is more limited. Since the simulation results indicate that the longer the taper length is, the steeper the filter cutoff slope can be, the optimal waist length for fused-tapered SMF-28 should be at least larger than 20 mm.
To further investigate how the waveguide structure influences the cutoff slopes and optical losses, the taper transition length is varied from 3 mm (taper transition angle around 1.0o ), 6 mm (taper transition angle around 0.5o ), to 12 mm (taper
transition angle around 0.2o ). The tapered fiber has a fiber taper waist diameter ρ =
26µm and the waist length L0 = 18mm. The obtained spectral responses are shown in
Fig. 2-10. The smaller filter transmission losses in the shorter wavelength side indicate that longer taper transition length can more guarantee low-loss conversion from the SMF-28 region to the taper region. At guiding wavelengths, the insertion
22
loss of the filter is below 1.1 dB, 0.3 dB, and 0.01 dB for the cases of τ = 3mm, 6 mm, and 12 mm. The loss difference for guided wavelengths can be as high as 1 dB between τ = 3 and τ = 12mm. The optimal design of the ratio between the taper transition length to the taper diameter should be at least larger than 6 mm/26 µm (i.e., the transition angle of the fiber structure should be less than 0.5o). Based on the above
theoretical analyses, the optimal design parameters for the taper waist diameter, waist length, and transition length should be somewhere around 26–40µm, 30 mm, and 6 mm, respectively. 1250 1300 1350 1400 1450 -60 -50 -40 -30 -20 -10 0 T ra n sm is si o n ( d B ) Wavelength (nm) τ=3mm τ=6mm τ=12mm
Fig. 2-10. Transmission spectra associated with different transition lengths of 3mm, 6mm, and 12mm with the waist length of 18 mm for ρ=26μm.
1250 1300 1350 1400 1450 -80 -70 -60 -50 -40 -30 -20 -10 0 T ra n sm is si o n ( d B ) Wavelength (nm)
Fig. 11. Transmission spectra of the final optimal design of the short wavelength pass filter. The taper waist diameter is 35μm, the waist length is 30 mm, and the transition length is 6 mm.
23
As the final verification, we set the taper waist diameter, waist length, and transition length to be 35µm, 30mm, and 6mm, respectively, and perform the BPM simulation. The calculated spectral response is shown in Fig. 2-11. The rejection efficiency is as high as 70dB, the cutoff slope is as high as -2.4dB/nm, and the insertion loss is less than 0.3dB. These results indicate the performance improvement that can be expected by carefully adjusting the device parameters.
The aim of this work investigated the influences of the taper length, taper diameter, and transition length on the spectral cutoff slope and rejection ratio of the tapered-fiber filter. The optimization is not absolute in the sense that additional constrains need to be considered. For example, the total length of the device cannot be too long for the ease of practical fabrication. Through this kind of optimization, we can know how much performance improvement can be expected by practically adjusting the device parameters. The Cargille liquids provide a cost-effective, simple, and fast way to implement the fundamental-mode cutoff mechanism.
2.4 Conclusion
In summary, a new type of thermo-optic tunable short-wavelength-pass fiber filters based on fiber tapering and dispersion engineering has been demonstrated experimentally and analyzed theoretically. Good agreements between the BPM simulation and experimental results are achieved. The effects of material dispersion and waveguide dispersion characteristics have been investigated by examining the spectral response as well as the changing trends of the MFD and the effective mode index. An optimized tapered fiber filter structure that can attain high-cutoff efficiency has been suggested based on the obtained theoretical simulation results. It finds for
24
SMF-28 raw fibers, the uniform tapered waist diameter should be around 35µm, the uniform tapered-waist length should be greater than 30 mm, and the tapered-transition length should be greater than 6 mm. With such an optimized structure, the cutoff slope can be as high as -2.4dB/nm, the rejection efficiency can be as high as 70dB, and the fundamental mode-coupling loss is below 0.3dB. In principle, if different choices of raw fibers can be used, it is possible that the performance can be even more optimized. The analyses presented in the present work should be helpful for developing inline tapered fiber filters based on the dispersion-engineered fundamental-mode cutoff mechanism.
25
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Chapter 3
The Wideband Tunable Gaussian-Shaped
Spectral Filters
3.1 Introduction
Broadband light sources with high spectral power density are important for high resolution optical coherence tomography (OCT) in cellular or tissue bio-imaging [1]– [3]. The broadband light source with a smooth Gaussian power spectrum is advantageous to achieve low speckle noise, generating from the mutually coherent scattering photons from biological tissues. Echo free OCT imaging can be obtained since a non-Gaussian-spectrum light source will significantly distort the OCT axial point spread function [4] ,[5]. For non-Gaussian-spectrum light sources, the spectral modulation can cause echoes entering the axial point spread function, and the non-exponentially decay tails can cause the blindness of the weak reflection signals [5] to degrade the imaging. A Gaussian filter is usually required to shape the broadband light source into a Gaussian-spectral profile and to stabilize the output wavelengths. Gaussian-spectral filters are also widely used in various areas besides broadband light source imaging applications. For example, these filters are employed in the fiber laser cavity to shape the spectral profile of the laser output lights or in the optical communication systems to stabilize the system operation [6] – [8]. So far, the
28
proposed Gaussian filters were made of a linear temperature gradient chirped fiber Bragg grating [9] or a large mode area photonic crystal fiber (PCF) filled with high index liquid crystal (LC) in the holey cladding [10]. However, the typical passband bandwidth of the fiber Bragg grating may be too narrow to be used for the practical OCT systems and for the PCF fibers, the tuning efficiency is not very high due to the low temperature gradient of LC. The use of LC would also introduce extra birefringence for the guiding lights. Moreover, the Gaussian-shaped spectrum can only be obtained at certain fixed temperatures of LC and the bandwidth is not tunable. In this chapter, it proposes a new type of widely tunable Gaussian shaped spectral filters by concatenating a short-wavelength-pass filter (SWPF) and a long-wavelength-pass filter (LWPF). The falling (rising) spectral curve of the SWPF (LWPF) is dispersion-engineered to fit the right (left) wing of the Gaussian profile through carefully adjusting the material and waveguide dispersions. For short-wavelength-pass filter, the refractive index dispersion (RID) discrepancy between the optical liquid and silica tapered fiber is so large that the total internal reflection (TIR) criteria can only be satisfied at the wavelengths shorter than the cutoff point and the widely tunable short-pass filters are achieved accordingly. The tuning range is at least wider than 400 nm (1250–1650 nm) with a tuning efficiency higher than 50nm/oC and the filtering efficiency (slope of falling curve) can be
maintained when the cutoff wavelength is tuning far away from the origin [11], [12]. Based on the same principle, a local liquid-core single-mode fiber was used to achieve widely tunable long-pass filters [13] and finally a bandpass filter with a wide tuning bandwidth can be made by concatenating one short-pass and one long-pass filters. The spectral envelope of the bandpass filter can be further engineered to fit the Gaussian profile based on the modification of the waveguide dispersion determined
29
by the fiber diameter and the modification of the interaction length. Consequently, based on the material and waveguide dispersion engineering achieves a widely tunable broadband all-fiber Gaussian-shaped spectral filter by concatenating a short-wavelength-pass filter and a long-wavelength-pass filter. Preliminary experimental and theoretical results show that the generated Gaussian-spectral lights can have a spectral contrast ratio higher than 40 dB, which should be useful for the OCT bio-imaging applications.
3.2 Simulation and Experiment
To achieve spectral Gaussian filters operating over 1250 – 1650nm, a long-wavelength-pass filter with a rising Gaussian-shaped cut-on curve at the shorter wavelength side and a short-wavelength-pass filter with a falling Gaussian shaped cutoff curve at the longer wavelength side are discretely employed. The refractive index dispersion curves for the various Cargille liquids (Cargille index-matching liquid with the index nD = 1.456 and the thermo-optic coefficient ⁄ 3.74 10ିସ/) and the fused silica glass are shown in Fig. 3-1(a). The liquids
have a flatter refractive index dispersion slope than fused silica due to their lower phonon energies [13]. In Fig. 3-1(a), the cross point of the refractive index dispersion curves of the silica and optical liquid (nD = 1.456) are labeled by P. From the two
refractive index dispersion curves, in the left-hand side of P point short-wavelength-pass filters can be achieved when the fused silica and optical liquid respectively plays as the core and cladding [12]. Light guiding is only satisfied for the wavelengths shorter than the P point but frustrated at other side of P point and thus great amounts of optical losses are introduce there. On the contrary, in the right-hand
30
side of P point long-wavelength-pass filters can be realized when the roles played by the fused silica and optical liquid are reversed [13]. The cross angle θ between the two refractive index dispersion curves decides the filtering efficiency and a larger θ can more clearly discriminate the passband and stopband wavelengths and gives rise to a sharper rising or falling curve for the filters. A very sharp rising or falling curve is crucial for the fiber-optic communication systems to clearly separate the desired and unwanted signals but may not be suitable for the low coherence tomography imaging systems in which a broadband Gaussian light source is required to obtain high quality images. A broadband Gaussian spectrum naturally comes along with slowly varying rising and falling spectral curves and therefore the spectral envelope of the bandpass filter must be further adjusted. The adjustments of the slope for rising and falling curves of filters can not only be done by engineering the material dispersion, namely the use of suitable liquids, but also by engineering the waveguide dispersion, namely the modification of the fiber structure. It can reshape the rising and falling curves to fit the Gaussian profile by selecting suitable diameter of tapered waist D, length of tapered waist LW, and length of tapered transition LT. The cutoff and cut-on curves of
the short-wavelength-pass filters and long-wavelength-pass filters are numerically simulated by adopting the beam propagation method (BPM) to determine the optimal waveguide structures for an ideal Gaussian-shaped spectrum and some experimental results are demonstrated to show the thermo-optic tuning ability. Further optimized can be taken in the future to attain better Gaussian-shaped spectral filtering function.
Numerical simulation using the beam propagation method (BPM) is performed to theoretically analyze the fundamental mode cutoff characteristics and study the optical field propagation within the tapered region of the standard single-mode fibers. The fiber taper transition structure is set to be an exponential shape, and a
31
fundamental fiber mode is launched into the transition region to estimate the mode coupling and mode conversion effects along the fiber taper with dispersive liquids surrounded. The fundamental eigenmode of the input SMF fiber is smoothly transformed into the fundamental eigenmode of the uniform taper waist, and the field propagates through the uniform waist region and then gradually re-converts to the fundamental mode of the output SMF within the second transition zone. The fundamental modes corresponding to wavelengths with 10-nm separation are sequentially launched into the tapered fiber, and the output optical powers normalized to the input powers are estimated as transmission loss. BPM simulations with different taper parameters for short-wavelength-pass filters and long-wavelength-pass filters are respectively performed for determining the optimal taper structures to yield the half part of the spectral Gaussian shape. The simulated transmission spectra of the short-wavelength-pass filter and long-wavelength-pass filter are respectively shown in Fig. 3-1(b) and (c) with the key parameters indicated. In Fig. 3-1(b), when D gradually goes down toward 10µm, the slopes of the falling curves get flatter since the waveguide dispersion only dominates the net dispersion at smaller D. Thus a smaller D can make the shorter wavelengths more lossy. The curve of D = 10µm can fit the Gaussian profile quite well and the attenuation can be as high as 80dB. When this Gaussian fit falling curve combined with its mirror image to form a complete Gaussian profile, a broadband Gaussian signal with strong spectral contrast can be generated.
32 0.6 0.8 1.0 1.2 1.4 1.6 1.8 1.435 1.440 1.445 1.450 1.455 1.460 + (silica cladding) + (liquid cladding) θ ∆n P (silica core) (liquid core) LWPF SWPF Cargille liquids (nD) 1.464 1.462 1.460 1.458 1.456 1.454 1.452 1.450 1.448 silica R e fr a c ti v e i n d e x Wavelength (µm) 1.446 (a) θ ∆n 1.25 1.30 1.35 1.40 1.45 -80 -60 -40 -20 0 T ra n sm is si o n ( d B ) Wavelength (µm) D = 40 um D = 26 um D = 20 um D = 10 um D = 10 um (Gaussian fit) L W = 18 mm L T= 6 mm (b) 1 .2 5 1 .3 0 1 . 3 5 1 . 4 0 1 . 4 5 - 4 0 - 3 0 - 2 0 - 1 0 0 T ra n sm is si o n ( d B ) W a v e le n g th (µm) D = 1 0 µm , LW = 1 8 m m D = 9 .2 µm , LW = 1 0 m m ( w it h S T F in c o r e ) D = 9 .2 µm , L W = 2 0 m m ( w it h S T F in c o r e ) D = 9 .2 µm , LW = 2 0 m m ( w it h S T F in c o r e ) ( G a u s s i a n f i t) D = 8 .2 µm , LW = 3 0 m m D = 8 .2 µm , LW = 3 0 m m ( G a u s s i a n f it ) ( c ) 1 .2 5 1 .3 0 1 .3 5 1 .4 0 1 .4 5 - 6 0 - 4 0 - 2 0 0 D = 1 0 µm LT = 6 m m L W = 1 0 m m L W = 1 8 m m L W = 3 0 m m T ra n sm is si o n ( d B ) W a v e l e n g t h (µm) L W = 1 0 m m L W = 1 8 m m L W = 3 0 m m D = 2 6 µm LT = 6 m m ( d )
Fig. 3-1. (a) Refractive index dispersion of silica and Cargille optical liquids. (b) Simulated transmission spectra of the SWPFs at different diameters of tapered waist and the Gaussian fit curve. (c) Simulated transmission spectra of the LWPFs at different diameters of liquid core and the Gaussian fit curves. (d) Simulated transmission spectra of the SWPFs at different lengths of tapered waist.
For the long-wavelength-pass filters, the fabrication method is by stretching a borosilicate capillary with a threaded submicron tapered fiber inside, until the inner diameter of the capillary decreases to a few micrometers. The stretched capillary with a submicron tapered fiber inside is then infiltrated with optical liquids to act as a new core, and long-wavelength-pass filters can thus be achieved. The mode fields of the guiding lights are strongly extended to the outside of submicron tapered filter and tightly overlapped with optical liquids. The dispersion of the guiding lights can be strongly changed by the local liquid-core/borosilicate-cladding structure [13]. In Fig. 3-1(c), a submicron tapered fiber with a liquid-core diameter D of 950 nm [13] is also simulated to engineer the dispersion for the best Gaussian fit. The slope of the rising curve and the attenuation for long-wavelength-pass filters are flatter and smaller than
33
that of short-wavelength-pass filters. This is because even when the long-wavelength-pass filter and short-wavelength-pass filter are using the same silica and optical liquid to produce the same θ and the same index difference Δn near P point in Fig. 3-1(a), the mode field distribution is larger at the longer wavelength side for the long-wavelength-pass filters and thus the poor confinement leads to a flatter cut-on curve and smaller spectral contrast. However, a longer LW can be utilized to
achieve a shaper cut-on curve for Gaussian fitting and, from Fig. 3-1(c), the rising curves of the long-wavelength-pass filters can also fit the desired Gaussian profiles. Simulated transmission spectra of the short-wavelength-pass filters at different length of tapered waist are also shown in Fig. 3-1(d). The adjustment of LW can also help to
fit the Gaussian profile for the cases of smaller D.
(a) (b)
(c)
Fig. 3-2. (a) Diagram of a tapered optical fiber (SWPF) with a uniform waist. (b) Schematic diagram of the tapering station used to fabricate the tapered fibers. (c) Refractive index dispersion curves with different temperature. The solid line depicts the tapered fiber, and the dotted line indicates the index matching liquid with different temperatures. (d) Spectral responses and fitted Gaussian curves of SWPF at different temperatures.
34
The spectral Gaussian filter can be achieved by combining a rising-Gaussian cut-on curve from the short-wavelength-pass filter and a falling-Gaussian cutoff curve from the long-wavelength-pass filter. To generate the falling-Gaussian cutoff curve, Fig. 3-2(a) shows the waveguide structure of the short-wavelength-pass filter. It consists of a transmission zone, where the fiber diameter gradually reduced over the distance, and a uniform-waist section in the middle. The fused–tapered fiber is immersed with index-matching liquids, and the optimal D is around 10µm by simulation, seen from Fig. 3-1(b). The total elongation length is about 30 mm, and the length of the uniform waist is measured to be around 18 mm. The tapered fiber filter fabricated by our homemade tapering workstation which integrates several parts including the pulling mechanism, heating system, scanning mechanism, and real-time monitor system, as has been shown in Fig. 3-2(b). A hydrogen flame with stabilized flow control set on a three-axis stepper motor forms the main part of the heating system and scanning mechanism. This setup allows precise positioning of the flame and the flame is allowed to scan over a large heating-zone. When the tapering process begins, the pulling motors move outward to elongate the fiber and the flame starts simultaneous zigzag scanning to enlarge the effective heating-zone. This process ensures that the flame heats identically each section of the fiber being tapered in each cycle of scanning. As long as the heating-zone can be controlled precisely, the length of the uniform waist of the tapered fiber is controllable. The pulling mechanism has two high-precision stepper motors with simultaneous start/stop design and drives two V-groove holders that can mount a single-mode fiber and provide a constant stress. One end of the single-mode fiber is connected to superluminescent diodes (SLD) and the other end is connected to a photo-detector (PD) to form a real-time monitoring
35
system, which can help determine the best stop-point for the stretching procedure. When finishing tapering, the fiber is fixed in a U-groove on a quartz substrate and then immersed in index-matching liquid. A TE-cooler is used to control the liquid temperature to change its refraction index and the cutoff wavelength turns out to be tunable. When a single-mode optical fiber is tapered to tens of micrometers in diameter, the evanescent waves spread out into the cladding and reach the external environment and the size of the core in the tapered zone is so reduced that its waveguiding effects are negligible. Therefore, the cladding plays the role of core and the external medium plays the role of cladding. Fig. 3-2(c) shows the refractive index dispersion curves of the index-matching liquid (red) and tapered fiber (blue) at different temperatures. At the right side of the cross point (λc), the refraction index of the liquid is greater than the index of fiber taper and the total internal reflection is frustrated. Therefore the lights cannot be guided in the fiber taper and suffer great amount of optical losses. On the other hand, the light can be confined in fiber taper when the wavelength is located at the left-hand side of the cross point. The cutoff wavelength of a short-wavelength-pass filter approximately locates at the cross point. As the temperature increases, the refractive index of the surrounding liquid decreases. Heating up the liquid causes the dispersion curve shift downward and the cross point will move to longer wavelengths. By heating up or cooling down the liquid (temperature changes from T to T + ΔT), we can continuously tune the band-edge wavelength, as shown in Fig. 3-2(c). The gray line in Fig. 3-2(d) is the initial cutoff curve of the tapered fiber immersed in optical liquid at room temperature (RT) and the liquid is then heated up by a 175W infrared lamp which is located 20 cm away from the tapered fiber. When the liquid is respectively heated up by the infrared lamp with an increment of 5 s for each run time, three different falling curves are obtained as
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shown in Fig. 3-2(d), with their slopes getting flatter and flatter. The P point of the short-wavelength-pass filter moves to longer wavelengths with increasing temperature so that the passband bandwidth becomes wider. The achieved spectral contrast is higher than 40 dB for all curves, which is advantageous for practical applications. The cutoff curves become slowly falling down since the waveguide dispersion significantly dominates the dispersion when D decreases to be less than 10µm. The optical field strongly spread out into the optical liquid and becomes less dispersive. The falling curves are individually Gaussian-fitted and the Gaussian fit curves are also displayed as dotted lines shown in Fig. 3-2(d), where in particular the experimental data of the pink line can fit the Gaussian profile and the simulation results excellently well. In principle, the long-pass filter based on liquid-core fiber [13] can also produce Gaussian-shaped curves as predicted in Fig. 3-1(c). Consequently, the concatenated Gaussian-shaped bandpass filter will be widely tunable ascribing to the high thermo-optic coefficient of optical liquids [13]. The wideband tunable Gaussian-shaped spectral filter can be further optimized by carefully considering both material dispersion and waveguide dispersion. The proposed spectral filter provides a potential technique in application to high resolution bio-imaging.
3.3 Conclusions and Summary
This chapter has proposed a new method of achieving widely tunable all-fiber broadband Gaussian-shaped spectral filters by concatenating thermo-optic tunable short-pass and long-pass filters. The material and waveguide dispersions are both employed to vary the spectral envelope of short-wavelength-pass filters and long-wavelength-pass filters to respectively fit the right and left wings of the desired
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Gaussian profile. The achieved spectral contrast can be higher than 40 dB and the filter still keeps Gaussian-shaped during thermo-tuning process. This kind of widely tunable Gaussian filters should be advantageous for optical coherence tomography (OCT) bio-imaging systems using broadband light sources.
