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Nonlinear Optics in Crystal Fiber

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Nonlinear Optics in Crystal Fiber Nonlinear Optics in Crystal Fiber Doug Nelson Introduction Since its creation crystal fiber has been explored for various uses. This paper describes several uses involving nonlinear optics as well as the differences between crystal fiber and normal optical fiber that allows us to take advantage of these effects. The nonlinear effects I will describe include stimulated Brillouin scattering, supercontinuum generation, and 2nd and 3rd harmonic generation. Let’s start with what differentiates crystal fiber from ordinary optical fiber. Photonic Crystal Fiber vs. Normal Optical Fiber Crystal fiber and normal optical fiber have many similarities, but differ in some key areas. Where normal fiber relies on an index of refraction difference between the core and cladding materials, crystal fiber uses air holes to create an effective index change. These air holes can either create an effective index change, or if they are spaced properly and have the correct dimensions they can create a photonic band gap that will only guide specific frequencies of light. It is these air holes and their various configurations that make photonic crystal fiber (PCF) useful in nonlinear processes. Also, optical fiber has an effective nonlinearity, given by: In the case of silica fiber, the most common, has a typical value of [1]. In this equation is the frequency of light in the fiber and is the cross sectional area of the core. Figure 1, taken from reference 2 The pictures above show examples of optical fibers. From left to right we have normal optical fiber, effective index photonic crystal fiber, and band gap crystal fiber. Where normal fiber can be designed to guide certain frequencies in a single mode fashion, PCF can be designed to guide an even smaller frequency range with engineered dispersion and a variable core size. Normal fiber cannot be made to guide a small selection of frequencies in single mode and still have core size and dispersion as variables. Since nonlinear optical effects depend on concentrating high powers into a material, PCF is an ideal candidate for many applications. Optical fibers can be made to have core sizes from hundreds of micrometers to hundreds of nanometers. These small sizes grouped with long lengths of optical fiber result in a medium that can confine high power in a small area for long distances. PCF can be designed with a large or small core size and still maintain single mode operation for desired frequencies. While engineering the air holes in a PCF for the core size they can also be configured to help minimize, or maximize, dispersion[1]. Some optical fibers use both an index change and the photonic band gap to guide light. This is useful when you need to guide two different frequencies through a fiber. Also, a second layer of air holes may be used to create a second guiding region surrounding the core. This is useful for coupling pump light into a fiber where seed light is guided through the core. Stimulated Brillouin Scattering in PCF One nonlinear effect in optical fibers is called stimulated Brillouin scattering (SBS). This takes place when photons interact with phonons inside the fiber. In an optical fiber photons scattered by SBS predominantly propagate in a direction opposite of the original photons. So, if you send photons down a fiber to the right, then the SBS will send photons to the left. SBS can be detected at low power levels, but there is a threshold level where its effect begins to increase rapidly. This threshold is dependent on the length of the fiber, the power level of light in the fiber, the size of the core, and many other factors. So it can be seen that by varying the core size, length of the fiber, and the intensity of light the SBS effect can be adjusted. For some applications SBS is desired, but for others it is a harmful effect. In the case of all optical buffering, SBS is the mechanism used to store data. In high power lasers SBS is the mechanism that sends high power light back through sensitive optical systems, often destroying isolators and other expensive components. So, to maximize SBS you would want a small core size, high power, and a long fiber length[3]. This increases the optical and acoustic mode overlap[3]. To minimize SBS you would want a large core size, low power, and a short fiber. This would make the overlap between the optical and acoustic modes shrink. With PCF you can vary the size of your core while maintaining good output quality from the single mode operation. All optical buffering uses SBS to store data. Data is sent in pulses through a PCF which are strong enough to induce SBS. The return signal is delayed and at lower power than the initial data, but this information can still be used. Since the return signal from the SBS is delayed by several nanoseconds this function can act as a buffer[4]. Figure 2, taken from reference 4 In the figure above we can see original data signals in blue and the resulting SBS return signals in red, green, and pink. The different colors represent the return signal at different times. The power of the return signal is given at several time intervals and can be seen to be dropping off as time moves on[4]. Supercontinuum Generation Another nonlinear effect that can take advantage of PCF is supercontinuum generation. This effect is seen when pico and femto second pulses are sent through a fiber with high self phase modulation[5]. Sometimes multiple nonlinear effects are used to generate a broad spectrum from a narrow pulse, such as Raman self frequency shifting, soliton fission, and self phase modulation[6]. PCF shows promise for supercontinuum generation because the chromatic dispersion of the fiber can be engineered by properly arraying the air holes in the fiber. Supercontinuum generation is used in the fields of optical coherence tomography, spectroscopy and optical frequency metrology[7]. It can be used to make broad band light sources and tunable femtosecond sources[8]. Since PCF can be made to guide only specific frequencies, once a supercontinuum is generated a PCF could be attached to the output that would then select one specific frequency from the continuum. This effect in a crystal fiber could also be used to create an endoscope which has a frequency range from the visible to the near infrared that can be used to see the full spectrum response of biological tissue[7]. Figure 3, taken from reference 5 The figure above shows the spectrum produced from a specialty PCF after traveling various distances down the fiber. It can be seen that as the distance traveled increases so does the spectrum, to a point. After two meters the figure shows that the spectrum suffers from losses in the fiber, as can be seen from the difference between the red and black lines[5]. 2nd and 3rd Harmonic Generation In PCF it is possible to phase match for 2nd and 3rd harmonic generation by varying the “pitch” of the air holes[9]. The pitch of the air holes is simply the distance between air holes in certain geometries. A typical value for the pitch is on the order of micrometers. 2nd harmonic generation can be accomplished by using stress rods in PCF. These stress rods harden at a different rate during the fiber draw process creating a strain in the fiber, thus breaking the inversion symmetry of the material. Also, a poling technique can be used to break the inversion symmetry in optical fiber [9]. Figure 4, taken from reference 9 In the figure above the phase matching condition for several ratios of air hole radius (r) to pitch (Λ) are given. Thus, once you know which frequency you want, you can determine your air hole size and pitch. Conclusion PCF is useful for nonlinear effects due to its variable internal structure. Both the core size and dispersion characteristics can be engineered. Several nonlinear effects that have been demonstrated are stimulated Brillouin scattering, supercontinuum generation, and phase matching for 2nd and 3rd harmonic generation. References 1) Anders Bjarklev and Theis P. Hansen, “Passive and active photonic crystal fibres,” Proc. of SPIE Vol. 5950 59500I-1, (2005). 2) Jonathan C. Knight, “Photonic crystal fibres,” Nature, Vol. 424 (2003). 3) J.-C. Beugnot, et all, “Complete experimental characterization of stimulated Brillouin scattering in photonic crystal fiber,”Optics Express, Vol. 15 No. 23, (2007). 4) Yingchun Cao, et all, “An efficient method of all-optical buffering with ultra-small core photonic crystal fibers,” Optics Express Vol. 16 No. 18, (2008). 5) Kudlinski, A. K. George and J. C. Knight, “Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation,” Optics Express Vol. 14 No. 12, (2006). 6) Martijn deSterke, “Supercontinuum generation,” http://www.physics.usyd.edu.au/current/tsp/Martijn_deSterke.pdf, accessed Dec, 2008. 7) Rachel Won, “Bright White Light on Demand,” Nature Photonics Vol. 2 (2008). 8) Lars Grüner-Nielsen, and Bera Pálsdóttir, “Highly nonlinear fibers for very wideband supercontinuum generation,” Proc. of SPIE Vol. 6873 68731B-1, (2008). 9) B´etourn´e, Y. Quiquempois, G. Bouwmans and M. Douay, “Design of a photonic crystal fiber for phase-matched frequency doubling or tripling,” Optics Express Vol. 16 No. 18, (2008). .
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