* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PDF
Surface plasmon resonance microscopy wikipedia , lookup
Photonic laser thruster wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Atmospheric optics wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Optical aberration wikipedia , lookup
Ellipsometry wikipedia , lookup
Vibrational analysis with scanning probe microscopy wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
Anti-reflective coating wikipedia , lookup
Retroreflector wikipedia , lookup
3D optical data storage wikipedia , lookup
Nonimaging optics wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Optical coherence tomography wikipedia , lookup
Dispersion staining wikipedia , lookup
Birefringence wikipedia , lookup
Photon scanning microscopy wikipedia , lookup
Optical fiber wikipedia , lookup
Optical tweezers wikipedia , lookup
Optical amplifier wikipedia , lookup
Fiber Bragg grating wikipedia , lookup
Harold Hopkins (physicist) wikipedia , lookup
Passive optical network wikipedia , lookup
Ultrafast laser spectroscopy wikipedia , lookup
Silicon photonics wikipedia , lookup
Nonlinear optics wikipedia , lookup
Article Number: OPTC 00932 DIFFRACTIVE SYSTEMS / Nonlinear Optics in Photonic Crystal Fibers 1 DIFFRACTIVE SYSTEMS Q3 Introduction P0005 Photonic crystal fibers (PCFs) are very similar to normal optical fibers in that they consist of a core surrounded by cladding, such that light is guided within the core of the fiber. The primary difference between PCF and standard optical fibers is that PCFs feature an air-silica cross-section, whereas standard optical fibers have an all-glass cross-section. An electron micrograph of a typical PCF is shown in Figure 1. The air holes extend along the axis of the fiber for its entire length and the core of the fiber is formed by a defect, or missing hole, in the periodic structure. The core is formed of solid glass, whose refractive index is that of pure silica (or whatever other glass is chosen), and the cladding is formed by the air-glass mixture, whose effective refractive index depends on the ratio of air-to-glass, also known as the air-fill fraction, that comprises the structure. The resulting effective-index of the cladding will be lower compared with that of the core and, as such, will provide the refractive index variation necessary to support total internal reflection at the core-cladding boundary, and guide light in a manner similar to that of standard optical fibers. The fiber design (i.e., size, shape, and the air-fill fraction) dictates solutions to Maxwell’s equations for light propagating within the fiber. Valid solutions are referred to as ‘modes’ which propagate along the fiber in a known manner, and have a well-defined shape in the transverse direction (i.e., they have a well-defined transverse mode structure). Nonlinear-optical effects in fibers result from the interaction of optical fields with the glass via the xð3Þ ; or Kerr nonlinearity. The phenomenon of nonlinear refractive index is a manifestation of a light-material interaction mediated by xð3Þ : The magnitudes of the P0010 EL SE VI ER FI R S0005 FS J E Sharping and P Kumar, Department of Electrical and Computer Engineering, Northwestern University, 2145 N Sheridan Road, Evanston, Illinois 60208-3118, USA O q 2004, Elsevier Ltd. All Rights Reserved. O J E Sharping and P Kumar, Northwestern University, Evanston, IL, USA components of the third-order susceptibility tensor in glass, xð3Þ ; are generally quite small compared with the analogous second-order ðxð2Þ Þ terms for materials exhibiting such nonlinearities (e.g., lithium niobate, beta-barium borate (BBO), etc.). The relatively small xð3Þ nonlinearity in optical fibers makes them ideal for wavelength-division multiplexed optical communication where light propagation subject to a minimum of nonlinear effects is critical. Nonlinearity does, however, eventually become an issue in wavelengthdivision multiplexed systems as the launched optical power increases and as the channel spacing decreases. On the other hand, one can utilize nonlinear-optical effects in soliton communication systems and to build useful photonic devices. Despite the weak xð3Þ nonlinearity, the net nonlinear-optical effect in fibers can be large due to the ability to tightly confine intense fields within the core of an optical fiber and maintain the interaction over a long distance as the guided fields propagate through the fiber. The study of nonlinear-fiber optics has benefited P0015 from dramatic improvements in optical fiber and fiber-optic device fabrication. The importance of understanding nonlinear-fiber optics is driven by the need to develop fiber-integrated devices, and also by the need to understand and mitigate the problems that these nonlinearities cause in optical communication systems. PR Nonlinear Optics in Photonic Crystal Fibers ST A0005 Q1 Figure 1 An electron micrograph showing the periodic microstructure of a typical PCF. The core is formed by the ‘missing hole’ in the center of the microstructure. (From Ranka, et al. q2000 Optical Society of America), courtesy of OFS. F0005 Article Number: OPTC 00932 2 DIFFRACTIVE SYSTEMS / Nonlinear Optics in Photonic Crystal Fibers This section introduces the unique linear- and nonlinear-optical properties of PCFs in order to understand the reasons why nonlinear-optical effects are often enhanced in such fibers. These discussions pertain to PCFs which are ‘highly nonlinear’. It is essential to clarify that ‘highly nonlinear’ in this context does not mean that the xð3Þ is any larger than that of standard telecommunication fibers, rather that the effect of this nonlinearity is enhanced due to the fiber’s very small core. Photonic crystal fibers feature a variety of interesting properties. From the standpoint of nonlinear-fiber optics there are four very useful fundamental properties of PCFs: P0030 . a mechanically robust optical fiber can be fabri2 cated with an extremely small core (a few mm ); P0040 P0045 mode over an extremely broad wavelength range (370 nm –1600 nm); . there are new degrees of freedom that allow one to manipulate the fiber’s group-velocity dispersion (GVD) properties; and . many, but not all, PCFs are polarization maintaining as a result of form birefringence present in the core. The fact that small-core PCFs can be fabricated is clear from Figure 1 by taking note of the fact that the center defect region which comprises the core is about 1.7 mm in diameter. Photonic crystal fibers with even smaller cores have been fabricated. FI R P0050 . a fiber can be made to guide in a single transverse where L is the spacing between air holes, l is the wavelength of light, and Vcutoff is the cutoff condition for the PCF. A similar expression for the V parameter is commonly used to understand the modal behavior of standard fibers where larger the V is, the more transverse modes are supported within the fiber. In standard fibers the cutoff condition below which only a single mode can propagate within the core of a fiber is given by Vcutoff , 2:405: In the case of PCFs, a numerical method should be used to determine Vcutoff : Mechanically robust PCFs can be fabricated where the dispersion in neff ðlÞ (i.e., the variation of neff with l) offsets dispersion in nco ðlÞ and compensates for the 2pL=l coefficient in eqn [1]. Therefore, the light within the fiber propagates in a single, Gaussian-like mode because for all wavelengths Veff , Vcutoff : A graph of the variation of Veff with L=l is shown in Figure 2, where d represents the size of an air hole. Conceptually, the effective index model can be P0060 understood by noting that at short wavelengths the mode field is confined well within the all-silica core, but as l increases the mode field extends further into the air-glass cladding and Veff and neff ðlÞ both decrease. ST P0035 F0010 FS P0025 Figure 2 Variation of Veff for different relative hole diameters d =L: The calculation assumes a fiber with an air-glass crosssection where the refractive index of air and glass were taken to be 1 and 1.45, respectively. The dashed line marks Veff ¼ 2:405; the cutoff value for a step-index fiber. (From Birks, et al. q1997 Optical Society of America) O PCF Properties O S0010 PR P0020 Transverse Mode Structure P0055 A widely accepted model used to describe the transverse modal behavior of PCFs is called the effective-index model. The effective-index model can be used to understand why some PCFs are ‘endlessly single mode’, meaning that the fiber guides in a single transverse mode over an exceptionally wide wavelength range (370 nm –1600 nm). In the effectiveindex model, the refractive index of the core, nco ðlÞ; is that of glass, and the refractive index of the cladding, neff ðlÞ; assumes a value in between that of glass and air. In the context of PCFs, one makes a modification to the standard expression describing single-mode behavior in step-index fibers: EL SE VI ER S0015 Veff ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pL nco ðlÞ2 2 neff ðlÞ2 , Vcutoff l ½1 Dispersion in PCF S0020 Other critical differences between PCFs and standard P0065 optical fibers lie in the dispersion properties. When light propagates through a fiber its behavior depends on the light’s optical frequency: Eðt; zÞ ¼ Aðt; zÞei½vt2bðvÞz ½2 Equation [2] describes the mode as it propagates through the fiber. It is decomposed into a slowly varying envelope, Aðt; zÞ; and a rapidly varying exponential component where v is the frequency of Article Number: OPTC 00932 DIFFRACTIVE SYSTEMS / Nonlinear Optics in Photonic Crystal Fibers 3 D [ps/nm km] Total dispersion 0 –10 Waveguide dispersion – 20 1.1 1.2 1.3 1.4 Wavelength [mm] 1.5 1.6 Figure 3 Plots of the theoretical dispersion coefficient, D; as a function of wavelength for a standard optical communication fiber. F0015 O FS the wavelength-dependent mode depends on the properties of the waveguide (i.e., the core size and refractive index contrast between the core and cladding). Empirical models can be used to describe the material, waveguide, and total GVD for standard communication fibers. Such a set of curves are given in Figure 3 where it can be seen that it is possible to have positive, negative, or zero values for D: For historical reasons, the regions where D is negative (b2 is positive) exhibit ‘normal GVD’, while those where D is positive (b2 is negative), exhibit ‘anomalous GVD’. The wavelength corresponding to D ¼ 0 is referred to as the zero-dispersion wavelength ðl0 Þ; which for most silica glass fibers is about 1,300 nm. In contrast with standard optical fibers, where the P0085 waveguide contribution to D is always less than zero, small-core PCFs can be fabricated where the waveguide contribution to GVD is positive and quite large. As such, in PCFs, l0 can be shifted to wavelengths shorter than the intrinsic dispersion zero of glass. Control over the GVD is essential for phase matching certain nonlinear-optical interactions involving light of different colors co-propagating within a fiber. Indeed, several exciting applications of nonlinear optics in PCF require a fiber with a l0 , 800 nm. The GVD is also of great importance when working with pulsed light in PCF, because GVD results in temporal pulse broadening. It also governs pulse temporal walkoff effects, limiting the effective interaction length between pulses of different colors. This new flexibility to manipulate the GVD curve, by varying waveguide design parameters, is a key advantage associated with using PCFs for nonlinear optics. O where bi ¼ di b=dvi : The physical significance of the various bi in eqn [3] are as follows: the phase-fronts of the electric field move at a speed given by v=b0 ¼ vp ; and the envelope, Aðt;zÞ; moves at a group velocity given by 1=b1 : A GVD term, which governs temporal spreading of the envelope, is given by b2 : Higherorder b terms are usually negligible for propagation of pulses of $1 ps duration in optical fibers and are lumped into the category of ‘higher-order chromatic dispersion.’ The notation ‘b2 ’, as defined above, is often used in the literature with dimensions of ps2/nm. However, another expression is frequently used because of its direct relationship to measured quantities. It is straightforward to measure the relative delay, T; between two pulses having different center wavelengths. Choosing a particular wavelength as a reference, one can then measure relative delay as a function of an injected pulse’s center wavelength. The first derivative with respect to l of the relative delay curve gives the GVD according to ! 1 › vg 1 dT 2pc D¼ ¼ ¼ 2 2 b2 ½4 L dl ›l l Material dispersion VI ER FI R P0075 ½3 10 PR 1 bðvÞ ¼ b0 þ b1 ðv 2 v0 Þ þ b2 ðv 2 v0 Þ2 þ ··· 2 20 ST P0070 the mode, t is time, z is the position along the length of the fiber, and bðvÞ is called the mode-propagation constant. The general term used in describing the frequency dependence of b is chromatic dispersion, which includes contributions from the material as well as the waveguide. Other types of dispersion present in optical fibers include multi-modal (arising from multiple guided transverse modes) and polarization-mode dispersion. One way to understand the chromatic dispersion of a mode propagating through an optical fiber is to study the Taylor series expansion of the modepropagation constant, b; about the center frequency of the field, v0 : SE EL P0080 where vg is the group velocity, and L is the length of the fiber under test. The dimensions commonly used for D ps/(nm km). Chromatic dispersion in single-mode optical fibers results from two different wavelength-dependent fiber parameters. The medium itself, glass in this case, has a wavelength-dependent refractive index. This ‘material’ contribution has the same magnitude regardless of the various parameters associated with the waveguide. A second contribution has to do with the design of the optical fiber. This ‘waveguide’ contribution to dispersion arises from the fact that Birefringence in PCF S0025 The core of an optical fiber often exhibits some P0090 amount of anisotropy. The core may be elliptical in form (shape) which leads to a phenomena referred to as form birefringence. Since mode propagation depends on the fiber structure, a fiber with an Article Number: OPTC 00932 4 DIFFRACTIVE SYSTEMS / Nonlinear Optics in Photonic Crystal Fibers P0105 . propagation losses are generally larger in PCFs P0110 . free-space coupling and splicing is difficult and can FI Nonlinear Phenomena P0115 The basic principles determining nonlinear effects in PCF are the same as those for standard optical fibers (00652). It is the new flexibility in PCFs to obtain transverse-modal and GVD behavior different from that of standard optical fibers that makes PCFs truly interesting for nonlinear optics. The relevant nonlinear-optical effects are: self-phase modulation (SPM); cross-phase modulation (CPM); third-harmonic generation (3HG); four-wave mixing (FWM); Raman scattering; and Brillouin scattering. Self-phase modulation (also known as the optical Kerr effect) refers to the self-induced phase shift experienced by an optical field as it propagates through a fiber. It becomes particularly important for the case of pulses of light propagating through optical fibers. In small core PCFs, SPM is enhanced EL SE VI ER S0030 P0120 FS O O P0130 P0135 R than for standard optical fibers; and result in large coupling losses. P0125 PR P0100 due to the high intensity light propagating within the core. Self-phase modulation can lead to substantial spectral broadening of pulsed light propagating along an optical fiber. When a pulse of light experiences normal GVD (i.e., D , 0) as it propagates, the longer-wavelength components travel faster than the shorter-wavelength components. Anomalous GVD (i.e., D . 0) leads to the opposite, short-wavelength components traveling faster than the long-wavelength components. Groupvelocity dispersion generally leads to temporal broadening of pulses as they propagate along a fiber. Under ideal conditions, however, SPM in combination with anomalous GVD, leads to pulses which propagate without any temporal or spectral broadening. These self-sustaining pulses are called ‘optical solitons’. When waves of light having different wavelengths co-propagate along a fiber, CPM can occur. It can be understood as a phase shift induced on one wave, due to the presence of the other wave. Cross-phase modulation also leads to spectral broadening and solitonic pulse propagation. In 3HG and FWM, one or more photons are destroyed and others are created. In 3HG, three ‘fundamental’ photons are destroyed to create one with three times the energy of the fundamental photons. In FWM, two fundamental photons are destroyed while two others are created. While it is straightforward to conserve energy in 3HG and FWM, these interactions must be ‘phase-matched’, meaning that the interacting waves must be made to propagate in-phase over a meaningful length. Such phase-matching conditions need to be carefully considered when studying 3HG and FWM. Nevertheless, 3HG and FWM can be used to obtain frequency shifts and all-optical amplification. In comparison with other types of optical fibers, PCFs are particularly useful for 3HG and FWM applications. The small core of the PCF allows interactions to occur at much lower input power, and the new flexibility associated with the GVD properties permits phase matching in cases which are not possible using standard optical fibers. Finally, the fiber’s endlessly single-mode behavior permits very good transverse mode overlap between interacting waves having widely different center wavelengths (e.g., the fundamental wave and third-harmonic wave in 3HG). Self-phase modulation, CPM, 3HG, and FWM are photon –photon interactions wherein no energy is exchanged with the medium itself. In contrast, Raman scattering and Brillouin scattering result from photon– phonon interactions. The differences between Raman and Brillouin scatterings lie in the energy of the phonons involved and the direction in ST P0095 elliptical core will exhibit mode propagation that depends on the electric field’s polarization with respect to the axes of the elliptical core. As a result of birefringence, the polarization of the mode varies as it propagates through the fiber (unless care is taken to align the polarization of the injected light with respect to the principal axes of the birefringence). Polarization-maintaining (PM) fibers are designed to include birefringence in a particular axis of the fiber. By including a well-defined birefringence throughout the length of a fiber that is larger than that induced by external perturbations, fast and slow axes of the optical fiber are created for all guided wavelengths, giving two orthogonal ‘polarization modes’. If light is injected into one of the polarization modes (i.e., with its linear polarization along one of the axes) it remains linearly polarized along that axis as it propagates along the fiber. The two polarization modes generally have different group velocities, so pulsed light in each mode will take a different amount of time to propagate through a given segment of fiber. Most PCFs exhibit strong birefringence due to a slightly elliptical core combined with a large corecladding index difference, and so they behave similarly to PM fibers. Special care must be taken when working with PCF to be sure that the polarization of the light launched into the fiber is aligned with one of the birefringent axes. In practice, there are a few other features of PCF that are of importance when discussing nonlinearoptic interactions: P0140 Article Number: OPTC 00932 DIFFRACTIVE SYSTEMS / Nonlinear Optics in Photonic Crystal Fibers 5 Figure 4 In supercontinuum generation one observes a broad continuum generated after short pulses of light from a Ti:Sapphire laser propagate through a 75 cm-section of PCF. The spectrum of the input pulse is shown as a dashed curve, while the output is a solid curve. (From Ranka, et al. q2000 Optical Society of America). F0020 ST PR O O FS from an input pulse whose spectral width is only about 10 nm. It is widely accepted that supercontinuum gener- P0160 ation results from a combination of solitonic effects which conspire to generate the broad spectrum. As the pulse propagates through the PCF, high-order solitons are formed which then undergo a ‘fission’ or ‘Cherenkov radiation’ process that blue-shifts energy into the normal dispersion regime. This explanation is consistent with the fact that for efficient supercontinuum generation the injected pulse’s wavelength should be chosen in the anomalous dispersion regime but close to l0 : Under these conditions, solitons are formed and there is a wide phase matching bandwidth for the soliton fission process. Spectral broadening, due to SPM, is common in P0165 standard optical fibers, but what makes this particular experiment interesting is the remarkable width of spectrum generated with a short piece of fiber (,3 m) and with comparatively small optical powers. FI R P0145 which the interactions occur. Raman scattering is an interaction between a photon and an optical – phonon mode of the molecules making up the material. In the case of Raman scattering in glass, the energy shift, associated with molecular vibrational (Raman) modes, corresponds to frequencies of 1 –12 THz. Raman scattering occurs in the forward and backward directions. With pulsed light, stimulated Raman scattering can occur when the lower-frequency spectrum of the pulse overlaps with the spectrum of the Raman resonances excited by the higher-frequency spectrum. When this happens, energy can be efficiently shifted in spectrum towards the peak of the Raman resonance. In the forward direction, this ‘Raman self-frequency shift’ builds up. Additionally, if the Raman self-frequency shift occurs in the presence of anomalous dispersion, a ‘Raman soliton self-frequency shift’ can result. As the injected power is increased, the spectral shift between the injected pulse and the resulting Raman soliton increases. The principal advantage associated with PCF is the ability to generate Raman solitons for a broader range of wavelengths than was previously possible. For Brillouin scattering, interaction with the acoustical phonons results in frequency shifts of about 10 GHz and the interaction only occurs in the backward direction. Brillouin scattering is generally a nuisance in fiber-based devices, leading to intensity noise and other problems. The interesting feature of Brillouin scattering in PCFs is that the threshold intensity where problems begin to occur is higher for PCFs than for standard optical fibers. The higher threshold permits further optimization of fiber-based devices wherein Brillouin scattering limits the performance. Experiment Examples P0150 In the following subsections, a selection of experiments, demonstrating a few of the relevant nonlinearoptical phenomena, are briefly described. VI ER S0035 Supercontinuum Generation P0155 One of the most exciting demonstrations of nonlinear optics in PCF is that of supercontinuum generation. In a typical experiment, 100 femtosecond pulses from a mode-locked Ti:Sapphire laser operating at a wavelength of 800 nm were injected into the PCF. As the injected power was increased, a broad continuum of spectrum was generated from wavelengths of 400 nm up to 1,600 nm. Typical data showing the input and output optical spectra are given in Figure 4, where it can be seen that well over an octave of frequency spectrum is generated EL SE S0040 Optical Switching in PCF S0045 Cross-phase modulation can be used to build an all- P0170 optical switch. Such a switch can be implemented as a three-port device where the output port for a given optical bit (the signal pulse), is determined by the presence of an optical control (the pump pulse). Switching can then be achieved by dividing the signal pulse equally on two arms of an interferometer and injecting the strong pump pulse only on one arm. Because the pump pulse co-propagates with only one of the two signal pulses, there exists an CPM-induced phase difference fNL ¼ 2gPp L at the output of the interferometer, where Pp is the peak power of the pump pulse and L is the interaction length. By varying the intensity of the pump pulses one can vary the Article Number: OPTC 00932 6 DIFFRACTIVE SYSTEMS / Nonlinear Optics in Photonic Crystal Fibers Signal (1546 nm, 2.6 ps) Pump (1537nm,4.9ps) FPC2 FPC3 FPC1 50/50 EDFA TBPF BWDM APC POL Detector PBS Synchronous pump and signal input AL AL Q1 Sagnac loop FS O O magnitude of this phase difference. If a p-phase shift is achieved, one can switch the interference from destructive to constructive, or vice-versa, thus realizing an all-optical switch. Figure 5 shows an experimental setup used to observe switching near 1,550 nm (a similar apparatus using bulk-optic rather than fiber-optic components can be used to conduct experiments near 780 nm). The pump and signal are synchronous few-psduration pulses with a tunable wavelength separation of 5 – 15 nm. The switching characteristics for this implementation are shown in Figure 6. The apparatus has the advantage of requiring short fiber lengths, low switching powers, and allows switching of weak pulses. It demonstrates the feasibility of using nonlinear optics in PCF to perform essential functions in high-speed all-optical processing. ST P0175 Figure 5 Experimental setup used to demonstrate all-optical switching near 1,550 nm. (EDFA, erbium-doped fiber amplifier; BWDM, bandpass wavelength-division multiplexor; PBS, polarization beamsplitter; FPC, fiber polarization controller) (From Sharping, et al. q2002 IEEE). PR F0025 MF (5.8m) F0030 ER FI R Figure 6 Switching curves (open boxes and filled circles), showing the relative power measured in each port of the switch vs. the pump peak power, for experiments conducted near (a) 1,550 nm and (b) 780 nm. The curves accompanying the data are generated from numerical solutions of coupled wave equations for XPM. (From Sharping, et al. q2002 IEEE). Q1 Parametric (Mixing) Processes P0180 The first set of experiments with controlled FWM in a PCF achieved nondegenerate parametric gains over a 30 nm range of pump wavelengths near the l0 of the PCF. The experiments also confirmed the wavelength dependence of the GVD coefficient of the PCF near l0 : Since the dispersion characteristics of these fibers can be adjusted during the fabrication process, the experiments demonstrate the potential for the use of PCFs in broadband parametric amplifiers, wavelength shifters, and other optical communication devices. The experimental setup used to demonstrate phase-matched FWM in PCF is shown in Figure 7. EL SE VI S0050 P0185 Q1 Figure 7 A schematic of the experimental setup used to investigate FWM in PCFs. (From Sharping, et al. q2001 Optical Society of America). F0035 Article Number: OPTC 00932 FS DIFFRACTIVE SYSTEMS / Nonlinear Optics in Photonic Crystal Fibers 7 Figure 8 A typical FWM spectrum observed at the output of the microstructure fiber. The inset shows a spectrum where higher-order cascaded mixing is evident. (From Sharping, et al. q2001 Optical Society of America). . PCFs can support a single transverse mode over ST an extremely broad wavelength range (370 nm – 1600 nm); . PCF design parameters allow one to manipulate the fiber’s GVD properties; and . nonlinear interactions are enhanced due to the polarization maintaining properties of PCFs which result from form birefringence present in the core. R The pump and the input signal are two synchronous pulsed beams having 3 –5 nm wavelength separation with the center wavelength tunable over a 720 – 850 nm range. The maximum peak power of the pump pulses is .12 W: The two synchronous beams are then combined and injected into the PCF. The pump and signal’s optical paths are adjusted to obtain temporal overlap in the PCF and their polarizations are aligned by fiber polarization controllers. Figure 8 shows a typical FWM optical spectrum at the output of a 6.1 m long PCF. Here the strong pump beam and weak signal beam have wavelengths of 753 nm and 758 nm, respectively. The spectrum shows the undepleted pump, the amplified signal, and the generated idler at 747 nm. The spectra in Figure 8 show that large gain is achievable for a pump-to-signal spacing of 5 nm. Gain values of more than 20 (13 dB) were obtained. PR O F0040 O Q1 FI SE VI ER P0190 These four properties combine to allow efficient interactions to occur in PCFs which are either inefficient or not possible at all in standard optical fibers. Conclusion P0195 In summary, the advantages of using photonic crystal fibers for demonstrating nonlinear-fiber optical effects arise from four novel properties: P0200 . the nonlinear coefficient is enhanced in small-core EL S0055 PCFs (core area of a few mm2); See also P0205 P0210 P0215 P0220 S0060 Raman, Brillouin and Parametric Amplifiers: (00663). P0225 Nonlinear Sources: Raman Scattering (00862). Diffractive Systems: EM Theory of Photonic Crystals, 1D, 2D, and 3D Band Structure Calculations (00926). Further Reading Agrawal GP (2000) Nonlinear Fiber Optics, 3rd edn. Academic Press. Birks TA, Knight JC and Russell PStJ (1997) Endlessly single-mode photonic crystal fiber. Optical Letters 22: 961 – 963. Hansryo J, Andrekson PK, Westlund M, Li J and Hedekvist P (2002) Fiber-based optical parametric Q2 Article Number: OPTC 00932 8 DIFFRACTIVE SYSTEMS / Nonlinear Optics in Photonic Crystal Fibers Russell PStJ (2003) Photonic crystal fibers. Science 299: 358 – 362. Sharping JE, Fiorentino M, Coken A, Kumar P and Windele RS (2001) Four-wave mixing in microstructure fiber. Optical Letters 26: 1048– 1050. Shapring JE, Fiorentino M, Kumar P and Windelen RS (2002) All-optical switching based on cross-phase modulation in microstructure fiber. IEEE Photonics Technology Letters 14: 77 – 79. EL SE VI ER FI R ST PR O O FS amplifiers and their applications. IEEE Journal of Selected Topics in Quantum Electronics 8: 506 – 520. Monre TM, Richardson DJ, Broderick NGR and Bennett PJ (2000) Modeling large air fraction holey optical fibers. Journal of Lightwave Technology 18: 50 –56. Ranka JK, Windeler RS and Stentz AJ (2000) Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm. Optical Letters 25: 25– 27.