Photonic crystal optics: Manipulate and guiding light using dispersion surfaces
Group velocity
Energy transport velocity
r r Vg = Ve
Vg = ∇ krω r r S nkr (r ) Ve = U nkr (r ) Gradient of the constant frequency surfaces governs the flow of light in photonic crystals
Notami, PRB 62, 10696 (2000)
2D hexagonal Photonic crystal: Left (vanishing small index contrast): A: Transmitted beam B: Diffracted beam Point C: superprism effect: propagation angle sensitive to incident angle and wavelength Right (stronger contrast): Beam A forbidden by gap opening Apparent negative refraction
Constant frequency surface is usually isotropic near band top close to a band gap: It becomes meaningful to talk about a refractive index
Effective refractive index is meaningful here (Snell law holds) Note that it can be negative and less than 1.
Negative refraction using photonic crystals
• Top of negative group velocity band (Folded up bands) can have a “negative” refractive index, but typically |n|
which is the equation of a straight line of slope +a+, (the + and - signs ...... dielectric tensor E, for example) is a quadratic surface (an ellipsoid) defined by [Fig.
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A. The Ray Equation ..... Equation (1.2-2) is usually written in the form ...... trial solution is suitable provided that h satisfies the quadratic algebraic equation.
Certain materials change their optical properties when subjected to an electric field. This is caused by forces that distort the positions, orientations, or shapes of ...
The transfer function and impulse-response function of the free-space ... wavefronts of the wave to the periodic pattern of the harmonic function in the z = 0 ...... Fourier transform G(v,) a sinc(N, 'j2v ) exp( jr,:) (see Table A.l-1 in Appendix A)
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Section 18.3 is devoted to the electro-optic properties of liquid crystals. ... which, in turn, initiates an electro-optic effect that alters the optical properties of the.
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contains three bands- ultraviolet (10 to 390 nm), visible (390 to 760 nm), and .... The optical intensity I(r, t), defined as the optical power per unit area (units of ...... If the central frequency v. is 5 x 10 l4 Hz (corresponding to A = 0.6 pm),
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ray optics is the limit of wave optics when the wavelength is infinitesimally short. However, the ... This chapter begins with the postulates of wave optics (Sec. 2.1). ..... surfaces of these components will be ignored, since it cannot be properly a
They must satisfy the paraxial Helmholtz equation derived in Sec. 2.2C. ...... matrix of a SELFOC graded-index slab with quadratic refractive index (see Sec.
The wave equation, which is the basis of wave optics, is embedded in the structure of electromagnetic ...... carried to the quadratic term. The temporal dispersion ...
Although such beams are easily obstructed or scattered by various objects, this form of free-space transmission of light is the basis of most optical systems.
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