See details. Buy It Now. Add to cart. Be the first to write a review About this product. About this product Product Information This book provides the theoretical background required for modelling photonic crystals and their optical properties, while presenting the large variety of devices where photonic crystals have found application.
This second edition includes the most recent developments of two-dimensional photonic crystal devices, as well as some of the last results reported on metamaterials. Additional Product Features Number of Volumes. In Photonic Crystals: Towards Nanoscale Photonic Devices, Jean-Michel Lourtioz and his colleagues have come out with an impressive major valume that covers many of the main themes of photonic crystals The English version, thanks to translator Pierre-Noel Favennec, has been worth the wait Overall, Photonic Crystals is an excellent book that can serve as an introductory text and a reference for graduate students and researchers.
The wide covering of corresponding theoretical, model and experimental methods, and also broad spectrum applications of the photonic crystals allow one to recommend this book for students, engineers and specialists studying and working in different regions of nanotechnologies, nanomaterials and related scientific areas. In your cart, save the other item s for later in order to get NextDay delivery. We moved your item s to Saved for Later.
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Tell us if something is incorrect. Add to Cart. Free delivery. Arrives by Thursday, Oct 3. Or get it by Wed, Sep 25 with faster delivery. Pickup not available. About This Item We aim to show you accurate product information. Manufacturers, suppliers and others provide what you see here, and we have not verified it. The upper and lower bands correspond to the even-symmetric and odd-symmetric guided mode, respectively. Figure 3 a shows the calculated TE-like mode photonic band structures of a particular 2D triangular lattice PC slab, where a wide complete PBG is clearly seen.
In the region, light propagation inside the PC is prohibited. When removing one or several rows of air holes in the PC structures, some allowed modes defect states appear within the PBG [ Fig. It has been well established in plenty of literatures that the number of waveguide modes as well as the width of the transmission windows can be controlled by tuning the core width of the line defects. However, waveguides along other directions in the triangular lattice PC were rarely discussed. The air holes are directly drilled by FIB and the lattice constant is nm.
Then we optimize the geometry to improve its transmission characteristics. We shrink the radius r 1 of the air holes in the two nearest-neighboring rows around the waveguide and enlarge the radius r 2 of the air holes in the two second-nearest-neighboring rows, as shown in Fig. The key point is to generate a transport pathway with walls as smooth as possible. We can also obtain the same conclusion from the measured transmission spectra in Figs. Besides, the intensities of the transmission spectra are much higher than the original one.
In the same time, we modify the bend corner geometry by fabricating smaller air holes in the corner to make the guided modes between the two kinds of waveguides matching better. Based on a serial of simulation and experiment tests, we find the best values for r 1 and r 2. Moreover, we have designed an air-bridged silicon PC coupled-cavity waveguides PCCCWs [ 39 ] and mapped its near-field optical distributions at different wavelengths around nm with the scanning near-field optical microscopy SNOM technology.
For PCCCWs, the eigenmodes usually have relatively narrow bandwidth with slow group velocity in the whole band range. Straight yellow lines in Figs. Simulation model a and calculated optical field distributions at b nm; c nm; d nm; e nm; and f nm . The optical intensity distribution patterns are different at and nm, even though both of them mainly appear as a single narrow line along the central PCCCW region with a full width at half maximum FWHM of about nm.
Precisely speaking, the pattern demonstrates a little bit shoulder as a result of mode superposition at nm, since it comprises two eigenmodes. At nm, the calculated result consists well with the experimental one in Fig. In addition, the simulated field distribution patterns of the snake-like profile in the PCCCW section appear deviating greatly from the detected ones at , , and nm.
However, if we calculate the optical field distribution patterns at , , and nm with the even-to-odd amplitude ratios of , , , and , respectively, we can find the simulated results are consistent with the experimental patterns evolving from single-line, to snake-like, and then to double-line structures for the PCCCW section. Combination of the near-field optical detection and theoretical simulation shows that SNOM is an efficient tool to study the optical propagation in the PCCCW and can help to design slow light elements.
Quantum information processing and quantum state manipulation have received great attentions because of their potential revolutionary impact on future network communication. Optical cavities, which can be used to store information, are considered to be one of the most important devices in the quantum communication application. As a result, high- Q optical cavities show great potential application in quantum information.
Among all the optical cavities, 2D PC slab cavities are the best choice because of their simultaneous high- Q and small mode volume characteristics. Moreover, due to the development of nanofabrication technique, multiple high- Q PC slab cavities can be fabricated at the same time on a single slab by the EBL and ICP etching technique.
Once atoms or quantum dots are embedded into the high- Q PC cavities, various quantum phenomena can be demonstrated on chip. Recently, our works on high- Q silicon PC microcavities have achieved great progress after extensive exploration and delicate improvement of nanofabrication techniques and sample processing techniques have been made [ 42 ]. The lattice constant is nm, the radius of cylindrical air hole is nm and the thickness of silicon slab is nm.
After trying hundreds of simulations, we find that the positions of air holes at the edges of the microcavities affect the Q factor dramatically. The electric field pattern of the cavity mode can be tuned to be Gaussian-type by displacing the six air holes outwardly at the edges of the microcavities, and this can increase the quality factor significantly [ 41 , 42 ]. The optimal displacement is found to be 73, 10 and 73 nm for the first, second and third air holes at both edges of the microcavities, which is depicted in Fig.
The maximum quality factor of , [ Fig. Schematics of a the original PC L3 nanocavity and b the optimized nanocavity; c , d show radiation spectra of the original PC L3 nanocavity and the optimized nanocavity, respectively . As can be seen in Fig. The samples are measured by our home-made fiber coupling system as described in the above section.
When the incident wavelength is off-resonant, light cannot couple with the microcavity, leading to strong output. While, at resonance most energy is tunneled into the microcavity, resulting in weak output. For the case of high- Q microcavity, a sharp transmission dip is expected in the transmission spectrum. The lattice constant, radius of cylindrical air hole and the thickness of silicon slab are , and nm, respectively.
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Limited by the fabrication accuracy of 10 nm, the displacement is adjusted to be 80, 20 and 80 nm for the six air holes at both edges of the microcavities. Figure 10 a shows the enlarged view of the cavity region. A sharp and narrow transmission dip is observed at the For the purpose of extracting the quality factor accurately, we finely tune the wavelength between and nm.
The measured spectrum is illustrated in Fig. Nevertheless, there are some deviation between the simulation and experiment. For example, the resonant wavelength is We believe that the deviation is caused by the imperfection of the cylindrical air holes and the actual radius is not exactly the same as the value in simulation. The success of fabricating high- Q silicon PC slab microcavities enables us to investigate various interesting quantum phenomena, such as strong coupling between light and quantum system, quantum information processing technique, single photon source, all-solid quantum manipulation and high-quality biochemistry sensing devices.
The maximum Q value of up to is obtained . Channel drop filters are key components for extraction of light trapped in a point-defect cavity to a neighboring waveguide and they sit on the basis of wave-division multiplexers and demultiplexers. They have great applications in a wide variety of fields, such as photonic integrated circuits, telecommunications, and quantum informatics. Figure 11 a shows the SEM picture of the three ports filter structure [ 43 ].
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The lattice constant of the PC and the radius of the air hole are and nm, respectively. Port 3 is the input waveguide channel, while ports 1 and 2 are two output waveguide channels, respectively. C1 and C2 are two point-defect cavities. The distance between the center of the defect cavity and the neighboring waveguide is 3 rows of holes in the y direction. As seen in Fig. Similarly, those of the C2 cavity are shifted by 20 nm.
The slight shift of air holes is conducive to confine light inside the cavity and leads to a higher quality factor. Meanwhile, the different shifts of the two cavities make the resonant wavelengths slightly different. The experiment results [ Figs. The wavelength spacing of the two cavities is about 1. The full widths at half maximum of the peaks are 1. To estimate the drop efficiency, a reference straight waveguide of the same parameters is positioned near the three-port filter.
Photonic Crystals: Towards Nanoscale Photonic Devices / Edition 2
By keeping the same intensity of input light, the transmission intensities of the reference waveguide and port 1 are 0. It has been well known that structure is the kernel of filter design. Usually, the regulation of microcavity resonant frequency is obtained by changing the size of the cavities. We have proposed a new way to design multi-channel filters by changing the shape of the air holes [ 44 ]. When the shape of the air holes changes from circle to ellipse, two parameters, the ellipticity and the orientation angle of the ellipse, in addition to its size can be further explored and they can have a great influence on localized cavity modes.
Therefore, we can use this for some special purpose. Figure 12 a schematically shows a one-channel PC filter. It is located four rows away from the major channel and is connected with the major channel through an indirect side coupling. Another single-mode waveguide is formed parallel to the cavity and serves as the output signal channel.
Figure 12 b shows an enlarged picture of the filter in the region around the cavity. The sizes of the axes parallel and perpendicular to this orientation are a and b , respectively. To show this point, we design and fabricate a four-channel PC filter by using different cavity parameters as described in Table 1. The SEM picture of the fabricated four-channel filter is displayed in Fig.
Four cavities are located on the two sides of the central linear W1 waveguide. The input signal propagates upwards from the bottom input ridge waveguide. Each cavity is coupled with another W1 waveguide that is connected to a ridge waveguide, which serves as the output signal channel.
The two axes are of size a and b, respectively . The simulation and experimental results of the transmission spectra for the four channels are displayed in Figs. Although significant noise exists, a resonant peak can be clearly found for each channel. The peaks are located at , , , and nm for channels 1, 2, 3, and 4, respectively. The results confirm that the air-hole shape has a great influence on the functionality of the PC filter devices. The elliptical air holes can induce a fine tuning of the resonant wavelength by changing the ellipticity of the elliptical air holes.
We have proposed a type of PC filter using these two kinds of waveguides [ 45 ].
Figure 14 a shows the SEM picture of a four-channel filter structure. Table 2 gives the detailed parameters of the four cavities. The experiment demonstrates that the four resonant peaks are at the wavelengths of , , and nm, as shown in Fig. In spite of the slight shift in the resonant peak toward higher frequency, which we believe is induced by the uncertainties in the fabrication, the experimental results are in fairly good agreement with the simulation results, where the maximum relative deviation of resonant wavelength is within 2 nm.
In our experiment, we also use the CCD camera to directly monitor the transport of infrared signal within the channel-drop filter. The situation of on-resonance and off-resonance can be clearly visualized and distinguished from the CCD camera images. One typical case is shown in Fig. Four cavities are located on the two sides of the input waveguide; b experimental transmission spectra of the four channel filter in linear scale.
A bright spot appears at the end of the output channel when the input wavelength coincides with the resonant wavelength and disappears when it is at off-resonance . In previous sections, we discuss several PC devices, including waveguides, cavities, and channel-drop filters that are built on the silicon 2D PC platform.
As we have mentioned, PC structures possess another important feature: photonic pass bands. In this section we show several example devices that implement the dispersion and refraction properties of PCs at their transmission bands. Figure 15 a shows the typical photonic bands structure of an air-bridge PC slab structure composed of a square-lattice array of air holes etched in silicon slab. The areas labeled in Fig. One effective way to understand and exploit desirable light propagation properties in PC is using the equifrequency surface EFS contours, as shown in Figs. The EFS contours in the red line frame are flat, meaning that this is the self-collimation region.
The reason is that the group velocity, which is parallel to the gradient of the EFS, is pointing in the same direction for all the modes located within the region. This kind of PC structures can be used as the channelless waveguide in integrated optic devices. Figure 15 c shows EFS contours of the second band. Based on the above analysis, we designed and fabricated an air-bridged PC structure that exhibited negative refraction of infrared light [ 46 ].
The structure is schematically shown in Fig. These structures are directly drilled by FIB technique. The lattice constant a of the square array is nm and the diameter of the air hole is nm. We first use 3D FDTD method to simulate the electromagnetic field intensity distribution at wavelength nm. The result is displayed in Fig. We find strong reflection and scattering at the interface between the input waveguide and the PC structure. This is induced by the serious impedance mismatch at the interface, although the high index contrast air-bridged structure can achieve good optical confinement.
To surpass this obstacle, we use a tapered air-holes connection layer at the input surface of PC structure to reduce the reflection and scattering losses. Besides, the reflection or scattering of light at the input interface of the PC is very much reduced. This clearly indicates that the designed tapered interface can reduce the interface impedance mismatch remarkably.
The ordinary way to see the light propagation behavior is to directly observe the pattern of the radiated light from the top of the sample using a conventional microscopy objective and an infrared CCD camera.
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The result is shown in Fig. The light spot at the middle bottom part of the pattern is the radiated light from the input silicon wire waveguide. The big light spot at the center represents the scattered light at the interface between the input wire waveguide and the PC due to impedance mismatch. There is also a small bright spot at the top right corner of the pattern, and it is recognized to result from the radiated light when the negative refraction beam hits the end facet of the PC structure.
Because the TE-like modes are strongly confined guided mode on the silicon slab and the surface fields are nonradiative and evanescent with respect to the vertical direction of the PC slab, the far-field pattern observed and recorded by the ordinary optical microscopy is not able to reveal the detailed process about how the negative refraction beam propagates inside the PC structure unless the scattering of light by roughness and irregularity is sufficiently strong on the beam propagation path.
This is indeed the case for Fig. In fact, the small bright spot could not appear without the intentional introduction of the air slot at the far end of the PC structure. It would not be possible to tell which way the infrared beam would refract if without the aid of this scattering light spot. A probe scans in the vicinity of the surface of the PC structure and records the near-field intensity distribution. The tip has a resolution of about nm, i. The signal is recorded by an infrared single-photon detector, which allows us to capture very weak infrared signals. The probed near field information directly reflects light propagation properties of the TE-like modes for the PC and enables one to visualize the ray trace of the negative refraction light beam because the near field at the surface is an integral part of the modal profile of the confined guided modes that exponentially decay away from the surface of the slab.
The ray trace of the incident light beam along the silicon wire waveguide and its propagation along the negative refraction direction inside the PC structure can be clearly seen. In each picture, the boundary of the PC structure is superimposed as solid lines .
On the other hand, ordinary positive refraction only occurs for TM-like confined modes, so the designed PC structure can behave as an efficient beam splitter in an integrated optical circuit. The high-resolution SNOM technology can greatly help one to directly visualize the ray trace and acquire deeper understanding on various anomalous wave propagation behaviors, such as super-prism, superlensing, self-collimation, and slow light in deliberately designed 2D PC slab structures in the optical wavelengths.
This in turn can help to explore a wider regime of controlling light behaviors on the nanoscale for future basic science and high technology applications. Self-collimation effect is the propagation of light without diffraction along the propagation direction. This phenomenon has been used to construct non-channel waveguides, beam splitters and beam combiners [ 47 , 48 ].
The behaviors of these devices are determined by the performance of the self-collimation effect. Recently we have designed and realized a simple structure composed by a square lattice array of elliptical air-holes where broadband large-angle self-collimation effect is observed for TE-like guided modes in infrared wavelength [ 49 ]. Figure 17 a shows our PC structure formed by a square lattice of elliptical holes.
The calculated TE mode photonic band diagram of the fourth, fifth and sixth bands are shown in Fig. The self-collimation effect can be observed at the gray regions within a broad normalized frequency range 0. The contours are flat at the normalized frequency between 0. This feature indicates that our structure can support self-collimation for incident light beams with large incident angles. For simplicity, we only consider the minimum 0. From the simulation results, we find that the light beam is collimated along the propagation direction for each situation. However, the couple efficiency of the incident light becomes lower and lower with the increase of the incident angle.
These six situations in Fig. A FDTD method is used in the simulations . Here we only show the patterns of the minimum and maximum wavelengths for each incident angle. They demonstrate strong light confinement along the propagation direction for all the situations. The experimental results are in good agreement with FDTD simulations.
We believe that this kind of structure may have potential applications in beam combiners and multiplexers.