Chapter 3 The Wideband Tunable Gaussian-Shaped Spectral Filters
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.
38
References
[1] A. Unterhuber, B. Povazay, K. Bizheva, B. Hermann, H. Sattmann, A. Stingl, T.
Le, M. Seefeld, R. Menzel, M. Preusser, H. Budka, Ch. Schubert, H. Reitsamer, P.K. Ahnelt, J.E. Morgan, A. Cowey, W. Drexler, “Advances in broad bandwidth light sources for ultrahigh resolution optical coherence tomography,” Phys. Med.
Biol., vol. 49, 1235, (2004).
[2] S.K. Dubey, D.S. Mehta, A. Anand, C. Shakher, “Simultaneous topography and tomography of latent fingerprints using full-field swept-source optical coherence tomography,” J. Opt. A: Pure Appl. Opt., vol. 10, 015307, (2008).
[3] K. Grieve, G. Moneron, A. Dubois, J. Gargasson, C. Boccara, “Ultrahigh resolution ex vivo ocular imaging using ultrashort acquisition time en face optical coherence tomography,” J. Opt. A: Pure Appl. Opt., vol. 7, 368, (2005).
[4] H.S. Djie, C.E. Dimas, D.N. Wang, B.S. Ooi, J.C.M. Hwang, G.T. Dang, W.H.
Chang, “InGaAs/GaAs quantum-dot superluminescent diode for optical sensor and imaging,” IEEE Sens. J., vol. 7, 251,(2007).
[5] B.E. Bouma, G.J. Tearney, Handbook of Optical Coherence Tomography, Marcel Dekker, New York, 2002 (Chapters 2, 3, and 7).
[6] G. Contestabile, R. Proietti, N. Calabretta, M. Presi, A. D’Errico, E. Ciaramella,
“Simultaneous demodulation and clock-recovery of 40-Gb/s NRZ-DPSK signals using a multiwavelength Gaussian filter,” IEEE Photon. Technol. Lett., vol. 20, 791, (2008).
[7] A. Chong, W.H. Renninger, F.W. Wise, “Environmentally stable all-normal dispersion femtosecond fiber laser”, Opt. Lett., vol. 33, 1071, (2008).
[8] A. D’Errico, “WDM-DPSK detection by means of frequency-periodic Gaussian filtering,” Electron. Lett., vol. 42, 112, (2006).
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[9] I.C.M. Littler, M. Rochette, B.J. Eggleton, “Adjustable bandwidth dispersionless bandpass FBG optical filter,” Opt. Express, vol. 13, 3397, (2005).
[10] L. Scolari, T.T. Alkeskjold, A. Bjarklev, “Gaussian filtering with tapered liquid crystal photonic bandgap fibers,” in: Proc. of LEOS 2006, ThN3, 2006.
[11] Kuei-Chu Hsu, Nan-Kuang Chen, Sen-Yih Chou, Shien-Kuei Liaw, Yinchieh Lai, and Sien Chi, “Wideband tunable Gaussian-shaped spectral filters based on dispersion engineering,” Opt. Fiber Technol., vol. 15, 373, 2009.
[12] N.K. Chen, K.C. Hsu, S. Chi, Y. Lai, “Tunable Er3+-doped fiber amplifiers covering S and C+L bands over 1490–1610 nm based on discrete fundamental-mode cutoff filters,” Opt. Lett., vol. 31, 2842, (2006).
[13] N.K. Chen, S. Chi, “Novel local liquid-core single-mode fiber for dispersion engineering using submicron tapered fiber,” in: Proc. of OFC 2007, JThA5, 2007.
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Chapter 4
The Supercontinuum Generation in a Tapered Fiber
4.1 Introduction
Generation of broadband supercontinuum (SC) has many practical applications [1], and supercontinuum in the literatures is mainly generated in microstructure fibers [2]-[4] as well as photonic nanowires [5]-[7]. Microstructure fibers are good candidates to generate supercontinuum due to the unique waveguide structure that can manipulate the dispersion characteristics and efficiently generate the nonlinear effects, but they often require high cost and special design. For supercontinuum generation in photonic nanowires, a sufficient length and high-index contrast of submicrometer-diameter wires is needed to obtain long interaction length to generate wideband spectra. However, the fabrication of long submicrometer wires was tough by use of simple tapering techniques, and these long tapered fibers are brittle for high-power handling. Recently, the supercontinuum generation and nonlinear phenomenon from planer waveguide is promising for all-optical circuits, and the waveguide design for managing the dispersion becomes important topic because it greatly affects the nonlinear response [8]-[10]. To understand how the waveguide design influences the nonlinear effect can simply start from conventional tapered fiber,
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and the discussion of the spectral broadening mainly considering the group velocity dispersion inside the taper waist [11]-[18]. The theoretical study on the influence of taper transition region is often neglected because its relative lower efficiency of nonlinear process compared to the waist region. In recent year, some researchers have noted that must simulate the whole region of a tapered fiber for fairly represent the comprehensive propagation characteristics.
In this chapter, by properly tuning the center wavelength of femtosecond Ti:sapphire laser launched into the home-made tapered fiber, relatively wide spectra from above 400 nm to below 1200 nm can be experimentally observed. The tapered fiber is 1 µm in diameter and only 1-cm in length. Creating a model discusses the femtosecond pulse propagation through the whole region of a tapered fiber theoretically and using split-step FFT method to numerically study the characteristics of supercontinuum generation in tapered fiber. Furthermore, it discusses the transition region of a tapered fiber with different shape that will induce phase chirped and exert a strong influence on the supercontinuum generation.
4.2 Experiment Setup and Results
In this experiment, a simple fiber tapering technique is used to produce low-loss 1-µm-diameter wires from a standard single-mode fiber (SMF-28). The fiber pulling setup consists of a hydrogen torch and two computer controlled linear stages [19]-[20].
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
42
elongate the fiber and the flame starts scanning back and forth to enlarge the effective heating-zone. This process ensures that the flame uniformly heats each section of the fiber being tapered in each cycle of scanning. The parameters for the fiber pulling system, such as speed, acceleration, fiber tension and position of the flame, were optimized to yield a uniform waist of about 1-µm in diameter and 1-cm in length. The diameter of the waist is measured around 1 µm, the length of the waist is around 10 mm, and the transition zone has an exponential shape with the length of 45 mm, as shown in Fig. 4-1.
Fig. 4-1. Schematic diagram of the taper fiber structure.
Fig. 4-2. Experimental setup of the supercontinuum generation.
To generate the supercontinuum spectra, the excitation pulses are coming from a tunable femtosecond Ti:sapphire laser (Tsunami, spectral physics inc.), whose center wavelength can be tuned from 700 nm to 900 nm, as shown in Fig. 4-2. Launching 82 MHz and 80 fs pulses into the tapered fiber, the coupling efficiency of the entire
43
tapered fiber is about 40%. The tapered fiber remains about 45-mm-long standard single-mode on each side that causes substantial dispersion when the pulse propagating through. In order to compensate the normal dispersion from the standard optical fiber, a prism pairs with separation about 20 cm is used to provide the anomalous dispersion. Then an optical spectral analyzer (Ando, AQ 6315) is used to measure the generated spectra.
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.
Supercontinuum can be generated by properly tuning the center wavelength of Ti:sapphire laser. Using the 1-µm-diameter tapered fiber and choosing the center wavelengths of 830 nm, the generated spectra at different exciting powers are shown in Fig. 4-3. Notice that the second harmonic wave (around 415 nm) can be generated due to destroy of the centosymmetric. At lower pump power (100 mW to 250 mW), the spectrum is broaden initially due to the self-phase modulation (SPM). As pumping power increases (400 mW to 500 mW), the extension of generated spectra in the
44
Raman scattering. Increasing the pump power (>500 mW) will slow down the extension of generated spectra in the longer wavelength edge. Nevertheless, the generated power in short wavelength becomes strong due to the four waves mixing.
The output pattern and the spanning spectra after the prism are also shown the inset of Fig. 4-3. The spectral bandwidth ∆λ defined at the detuning wavelength with intensity of -20 dB to that at peak wavelength is around 190 nm at 400 mW input power, and 430 nm at 700 mW input power.
4.3 Simulation and Discussion
Numerical simulations are carried out to explain the experimental observations.
There are numerous numerical simulation studies on supercontinuum generation in tapered fibers, and typically supercontinuum generation in a biconical tapered fiber is theoretically investigated using nonlinear Schrödinger equation as numerical model [13]-[19]. The nonlinear Schrödinger equation can be expressed as
( ) ( ) ( )
where A is the amplitude of the pulse envelope, α is the absorption coefficient, t is the time, and z is the propagation axis along the fiber. The βn are nth-order dispersion coefficients, and ω0 is the carrier frequency of the pulse. The nonlinear parameter is defined as γ = n2ω0/cAeff, where n2 is nonlinear-index coefficient and Aeff is the effective mode area. The left-hand side of Eq. 1 represents the linear terms and the
45
right-hand side represents nonlinear terms. The first moment of the nonlinear response function is defined as
( ) (
1 R) ( )
R R( )
R t = − f δ t + f h t (4.2)
where fR, that be estimated to be about 0.18, represents the fractional contribution of the delayed Raman response to nonlinear polarization PNL, δ(t) represents the delta
Fig. 4-4. (a) Effective mode area and (b) nonlinear parameter versus the waist of the tapered fiber at 830 nm.
0 20 40 60 80 100 120 140
46
We used symmetrized split-step Fourier algorithm to solve this nonlinear system numerically. The waist region of the tapered fiber is 10-mm-long with a uniform diameter of 1-µm. The transition region is 45 mm at each side. The fiber parameters adopt Corning SMF-28 specification. The effective core area Aeff is given by
( ( ) )
where F(r) is the amplitude of the electric field for the fundamental mode at a radius r from the axis of the fiber. In our simulation, Aeff and nonlinear parameter γ is individually plotted against the diameter of the tapered fiber at the wavelength of 830 nm, as shown in Figs. 4-4(a) and (b). The Aeff is getting smaller as the cladding being thinner when the fiber diameter is larger than 35.8 µm; at this region the power is confined by the fiber core. However, the tapered fiber being thinner than 35.8 µm, the core leaves a large amount of light guided outside the core and the Aeff begins to nonlinear parameter than untapered fiber. The nonlinear parameter increases rapidly as the fiber diameter thinner than 13.4 µm. Finally, the 1 µm-diameter waist area, the nonlinear parameter γ is 54.86 W-1km-1 which is approximately 25 times larger than that at the untapered region, thus exhibits large nonlinear effects to contribute to intense nonlinear processes.
47
The refractive index of the standard single-mode fiber is obtained using Sellmeier formula, and the propagation constant β is derived by solving the eigen-value equation. Expand β in a Taylor series about the pump frequency that obtain the n-order dispersion coefficients. The zero-, first, second, and third order dispersion coefficients βj are plotted in Figs. 4-5(a)-(d). At the waist region, negative second dispersion coefficient (β2<0) denote anomalous dispersion, which favors soliton formation and also benefits generation of octave-spanning white light.
However, the β2 is positive when the fiber diameter is larger than 2.6 µm, and becomes negative with the zero dispersion cross point located at the fiber diameter being 2.6 µm, as can be seen from Fig. 4-5(c). The β2 has maximum value when the fiber diameter is 11.5 µm. This dispersion variation indicates pulse propagation behavior can be greatly influenced by the sign of the dispersion in the transition region of the tapered fiber, which will be discussed in the next section.
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(a) (b)
(c) (d)
Fig. 4-5. (a)-(d) the dispersion coefficients versus the diameter of the tapered fiber at 830 nm.
Figures 4-6 show the simulation results of supercontinuum spectra for light propagates in the tapered fiber under different average powers using the hyperbolic secant pulses with a center wavelength of 830nm and repetition rate of 82 MHz.
Owing to the inaccuracy measured the geometric parameters of the tapered fiber and the coupling efficiency of the entire tapered fiber, there are slightly different between the simulation results and experiment results. However, the generated spectra broadens when the launch power increases, and the long wavelength grows faster than the short wavelength region, which agrees well with the experimental observation as shown in Fig. 4-6. The spectral bandwidth ∆λ defined at the detuning wavelength
Fiber diameter (µm) 49000 20 40 60 80 100 120
4950
49
with intensity of -20 dB to that at peak wavelength is around 180 nm at 400 mW input power in the simulation result, which agrees well with the experimental results in Fig.
4-6.
Fig 4-6. Simulation results of generated spectra at different pump powers using 1-µm-diameter fiber tapers with different launched pump powers.
The evolutions of the spectral intensity and the time domain pulse shape along the whole region of the tapered fiber are plotted in Fig. 4-7 for investigating the processes of the supercontinuum generation. The color from red to blue represents the intensity from strong to weak and the vertical white lines denote the boundary of the waist region. During the input transition region, the spectrum is slightly broadening but the time domain pulse shape is broadening obviously consequent on the interaction of the linear dispersion. The spectrum spread quickly in the waist region where the nonlinearity is 25 times larger than that at the untapered region and the stimulated Raman scattering play significant roles therefore its spectrum is asymmetrical. In the time domain, the pulse width gradually narrows in the waist region because of anomalous dispersion; however in the end of the waist region the pulse is splitting from the nonlinearity and anomalous dispersion interaction. In the
400 600 800 1000 1200
50
subsequent output transition region, the pulse split into several group when the transition region is in anomalous dispersion regime; however, those sub-pulse cross the zero dispersion point and reach normal dispersion regime, they broaden with propagation direction.
(a)
(b) 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.
Many previous studies assume that the effect of nonlinearity in taper transition region is much smaller than that in the waist region, thus it can be neglected when the numerical simulation is performed. However, according to our result of numerical simulation, the nonlinear effect in taper transition region apparently influences the spectral broadening so that it cannot be ignore. The red line in Fig. 4-8(a) accounts
0 20 40 60 80 100
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both the linear and nonlinear effect in the transition of the taper fiber, while the blue line represents the numerical result considering only the nonlinear effect in the taper transition region. According to Fig. 4-8, the effect of nonlinearity narrows the spectral broadening range and suppresses the blue-shift. To analyze the importance of the nonlinear effect in taper transition region in another viewpoint, the induced frequency chirp when the pulse propagates through the first taper transition region is calculated, as shown in Fig. 4-8(b). Due to the normal-dispersion regime in the taper transition region, the frequency chirp induced by the nonlinear effect and the linear dispersion cannot cancel each other, on the contrary, spectral broadening range degrades as a result of the frequency chirp enhancement due to the nonlinear effect. The pulse shape in time domain is displayed in Fig. 4-8(c). The nonlinear effect in taper transition region broadens the pulse width since the individual frequency chirp induced by the normal-dispersion and the nonlinear effect has the same sign. The broaden pulse width at the exit of the first taper transition lowers the capacity of the supercontinuum generation when the pulse propagates along the following waist region.
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(a)
(b)
(c) 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.
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investigate the influence on supercontinuum generation. Assume the shape of the fiber taper is linear tapered and exponential tapered, and the calculated broadening spectra are respectively shown in Fig. 4-9(a). The blue line presents the linear tapered shape, while the red line shown the exponential tapered shape. It can be shown in the Figure that the spectral broadening for linear tapered shape is narrower than that of the exponential tapered shape. The corresponding frequency chirp and pulse width in time-domain when the pulse propagates through these two different shapes of taper transition region are shown in Figs. 4-9(b) and 4-9(c). Owning to different shapes of taper fiber, the amount and ratio of normal-dispersion, anomalous-dispersion, and nonlinear effect slightly vary when pulse propagates in taper transition region. The exponential tapered shape contains the larger pulse width and lower peak power than that of the linear tapered shape, therefore, the supercontinuum generation efficiency decreases when propagating in the following waist region.
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(a)
(b)
(c) Fig. 4-9. (a)Spectral broadening, (b)frequency chirp when pulse launching into the fiber waist under different shapes of the fiber taper.
From above discussion, the amount of frequency chirp of the pulse when it launches into the fiber waist can greatly change the supercontinuum generation spectrum. Therefore, the normalized optical field associated with incident pulse takes
400 600 800 1000 1200 1400
55
the form
( )
220 0
0, sec exp
2
T iCT
U T h
T T
= −
, (4.5)
The dispersion effect in fiber taper is too complicated to totally compensate by simply adopting conventional dispersion compensation methods. However, the adjustment on the value C can partially compensate the pulse broadening result due to the pulse propagation in taper transition. Figure 4-10(a) presents the supercontinuum generation result using a chirped pulse with C=-1 launched into the fiber taper. The red line in Fig. 4-10(a) is the result for launching an unchirped pulse, and the blue line is the chirped pulse. The spectral broadening range is wider and the efficiency of supercontinuum generation if higher for launching an unchirped pulse rather than launching a chirped pulse. Figures 4-10(b) and 4-10(c) individually plot the frequency chirp and the pulse width in time domain corresponding to a chirp and an unchirp pulse propagation the input of the fiber waist. Because the pulse propagates in the first taper transition experiences mainly normal-dispersion (β2>0), the initially pulse-width narrowing stage in time domain can be observed for the propagation of the chirped pulse with C=-1.
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(a)
(b)
(c) 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.
4.4 Conclusions
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Supercontinuum generation from 1-µm tapered fiber using the 80 fs Ti:sapphire laser excitation is demonstrated experimentally and studied theoretically. By properly choosing the exciting wavelength, relatively wide spectra is observed from near UV to near IR only using 1-cm long and 1-µm-diameter optical tapered fiber. Besides, exciting power can be greatly lower down for wide spectra generation extended to near UV by properly connecting two fiber tapers. Split-step FFT method is investigated numerically in order to analyze the spectral response of supercontinuum generation phenomenon corresponding to the wavelength dependent loss occurred at transition region of the tapered fiber. The simulation results agree with the experimental results, and shows that the dispersion and nonlinear effects at transition region of the tapered fiber greatly influences the broaden spectrum shape. The theoretical result indicates that the zero dispersion cross point located at 2.6 µm so that the pulse width and peak power of the excited pulse is dramatically changed when propagates in transition region, which in term apparently affects the supercontinuum generation spectrum. Hopefully the simulation results in this work provide a helpful viewpoint to analyze the supercontinuum generation in typical tapered fibers.
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References
[1] G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources,” J. Opt.
Soc. Am. B, vol. 24, 1771, (2007).
Soc. Am. B, vol. 24, 1771, (2007).