Link between the laws of geometrical optics and the radiative transfer equation in media with a spatially varying refractive index

We proposed in a previous paper [J.-M. Tualle, E. Tinet, Opt. Commun. 228 (2003) 33] a modified radiative transfer equation to describe radiative transfer in a medium with a spatially varying refractive index. The present paper is devoted to the demonstration that this equation perfectly works in the non-absorbing/non-scattering limit, what was contested by Martí-López and coworkers [L. Martí-López, J. Bouza-Domínguez, R.A. Martínez-Celorio, J.C. Hebden, Opt. Commun. 266 (2006) 44]. The assertion that this equation would imply a zero divergence of the rays is also commented.     

Femtosecond filamentation in air at low pressures. Part II: Laboratory experiments

We present experimental studies of filamentation of a femtosecond laser pulse in air at low pressures. The evolution of the filament has been studied by measuring along the propagation axis the conductivity and the sub-THz emission from the plasma channel. We show experimentally that the filamentation process occurs at pressures as low as 0.2 atm in agreement with numerical simulations. Experimental and numerical results [A. Couairon, M. Franco, G. Méchain, T. Olivier, B. Prade, A. Mysyrowicz, Opt. Commun., submitted for publication] are compared and the possible sources of discrepancy are discussed.     

Anomalous wave propagation in quasiisotropic media

Based on boundary conditions and dispersion relations, the anomalous propagation of waves incident from regular isotropic media into quasiisotropic media is investigated. It is found that the anomalous negative refraction, anomalous total reflection and oblique total transmission can occur in the interface associated with quasiisotropic media. The Brewster angles of E- and H-polarized waves in quasiisotropic media are also discussed. It is shown that the propagation properties of waves in quasiisotropic media are significantly different from those in isotropic and anisotropic media.     

单轴晶体光轴任意取向时非寻常光的折射规律

在单轴晶体光轴任意取向的情形下 ,应用惠更斯原理导出了非寻常光折射方向的普遍计算公式 ,并给出了确定非寻常光线折射面和折射角的具体解。结合几种熟知的特殊情形进行了简要讨论 ,揭示了文中所得到的折射规律较之斯涅尔定律更具有普遍性 ,从而为光学系统中各类单轴晶体光学元件的应用提供了一个理论依据     

非寻常光的折射规律

在单轴晶体的光轴与入射面平行的情形下用费马原理计算非寻常光光线的折射角，然后就怎样定义非寻常光作些讨论，最后在单轴晶体的光轴任意取向的普遍情形下给出计算非寻常光光线折射方向的公式。     

Comment on “The Imbert-Fedorov shift of paraxial light beams”

Here I argue that Liu and Li [B.-Y. Liu, C.-F. Li, Opt. Commun. 281 (2008) 3427] reproduce calculations of the Imbert-Fedorov transverse shift previously made in a number of other works. However, it has recently been shown that these results are not valid for standard uniformly polarized beams. The corrected values of the Imbert-Fedorov shift were derived in papers [K.Y. Bliokh, Y.P. Bliokh, Phys. Rev. Lett. 96 (2006) 073903; Phys. Rev. E 75 (2007) 066609] and confirmed by recent measurements [O. Hosten, P. Kwiat, Science 319 (2008) 787] with a great accuracy.     

Reflexion und Brechung des Lichtes an optisch einachsigen Medien

Reflection and Refraction of Light in Uniaxial Media The formulae for the amplitude relations for the reflection and refraction of plane monochromatic light waves at a plane interface between an isotropic and an arbitrarily anisotropic medium, derived in an earlier paper by the author, are specialized here to the case of uniaxial media. The incidence both from the isotropic and from the uniaxial medium is dealt with. A series of special cases (normal incidence, optical axis parallel or normal to the plane of incidence, transition from uniaxial to isotropic media a.o.) are considered.     

Amphoteric-like refraction in a two-dimensional photonic crystal

High-index contrast photonic crystals possess an intricate photonic band structure that is responsible for surprising phenomena as the surperprism effect, self-collimation, power splitting or negative refraction. Recently, it was reported that at the interface between an isotropic medium and a uniaxial crystal (or between two uniaxial crystals) a phenomenon known as amphoteric refraction, that is, positive as well as negative refraction, can take place. By means of a equifrequency contours analysis and finite-difference time-domain simulations, we show that a two dimensional photonic crystal can also present amphoteric refraction by properly choosing the lattice orientation and the termination. However, total transmission is difficult to achieve because a Bloch mode is excited inside the photonic crystal and the coupling efficiency from this mode to an external plane wave is lower than one.     

Reply to “Comment on ‘The Imbert-Fedorov shift of paraxial light beams’”

This is a reply to the Comment by Bliokh on our paper that appeared in Opt. Commun. 281 (2008) 3427. After a brief introduction of the representation theory of vector electromagnetic beams advanced in a recent paper, I point out that the Imbert-Fedorov effect is the evidence of the change of the beam parameter Θ and the polarization ellipticity σ caused by the reflection or transmission process in the linear approximation. Then I explain that it is because the linear approximation of the incident beam that we used in our paper had been assumed in previous works that we reproduced their results.     

Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics

Taking into account many developments in fiber optics communications, we propose a higher nonlinear Schrödinger equation (HNLS) with variable coefficients, more general than that in [R. Essiambre, G.P. Agrawal, Opt. Commun. 131 (1996) 274], which governs the propagation of ultrashort pulses in a fiber optics with generic variable dispersion. The study of this equation is performed using the Painlevé test and the zero-curvature method. Also, we prove the equivalence between this equation and its anomalous integrable counterpart (the so-called Sasa-Satsuma equation). Finally, in view of its physical relevance, we present a soliton solution which represents the propagation of ultrashort pulses in a dispersion decreasing fiber.     

A revised controlled deterministic secure quantum communication with five-photon entangled state

A revised controlled deterministic secure quantum communication protocol using five-photon entangled state is proposed. It amends the security loopholes pointed by Qin et al. in [S.J. Qin, Q.Y. Wen, L.M. Meng, F.C. Zhu, Opt. Commun. 282 (2009) 2656] in the original protocol proposed by Xiu et al. in [X.M. Xiu, L. Dong, Y.J. Gao, F. Chi, Opt. Commun. 282 (2009) 333]. The security loopholes are solved by using order rearrangement of transmission photons and two-step security test.     

Polarization-sensitive propagation in an anisotropic metamaterial with double-sheeted hyperboloid dispersion relation

The polarization-sensitive propagation in the anisotropic metamaterial (AMM) with double-sheeted hyperboloid dispersion relation is investigated from a purely wave propagation point of view. We show that TE and TM polarized waves present significantly different characteristics which depend on the polarization. The omnidirectional total reflection and oblique total transmission can occur in the interface associated with the AMM. If appropriate conditions are satisfied, one polarized wave exhibits the total refraction, while the other presents the total reflection. We find that the opposite amphoteric refractions can be realized by rotating the principle axis of AMM, such that one polarized wave performs the negative refraction, while the other undergoes positive refraction. The polarization-sensitive characteristics allow us to construct two types of efficient polarizing beam splitters under certain achievable conditions.     

Reply to the comment on “Light propagation in the Fresnel region - New numerical approach”

The paper is an answer to the comment on the approach for light propagation in the Fresnel region [W. Zhang, W. Huang, Z. Ye, T. Zhao, F. Yu, Opt. Commun. 281 (2008) 3977]. The examples presented in the commented paper entitled “Light propagation in the Fresnel region - New numerical approach” [M. Sypek, Opt. Commun. 116 (1995) 43] were sufficiently rigorous. A quantitative comparison of the results obtained for non-zero padding and zero-padding techniques are included. The divided steps approach which was the major contribution introduced by the modified convolution method could help reduce the aliasing error for the large propagation range, but only with the simultaneous use of the zero-padding technique. In this paper examples are presented. Additional explanations are enclosed.     

单轴晶体中的负折射现象研究

分析了在各向同性介质和单轴晶体界面实现负折射的最佳条件。计算发现,通过调节光轴角和各向异性参量可以使得负折射现象更为明显,获得最佳光轴角和最大入射临界角。各向异性强的晶体实现负折射的入射角范围可能会很大。讨论了单轴晶体中和负折射率介质中的负折射现象的区别：负折射率介质中的负折射是由负的折射率引起的,单轴晶体中是由于各向异性决定的。同时还发现单轴晶体中的能流负折射现象不能实现Pendry在理论上所预言的完美透镜。     

Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis

The propagation of partially polarized and partially coherent beams in uniaxial crystals orthogonal to the optical axis is investigated. The analytical formulae for the elements of the cross-spectral density matrix of partially polarized and partially coherent beams propagating through uniaxial crystals orthogonal to the optical are derived. The numerical results show that the degree of polarization decreases with the increase of the ratio of extraordinary to ordinary refractive indices at a certain propagation distance, and the influence of uniaxial crystals on the degree of coherent is not so evident. And the beams spread more rapidly in the direction parallel to the optical axis than orthogonal to the optical axis in positive crystal with the propagation distance increasing.     

Electromagnetic fields that remain totally polarized under propagation

It is remarked that, in general, a totally polarized field becomes partially polarized at the output of an optical system, even though the field propagates through non-polarizing devices. Two kinds of fields are shown in the present work, which maintain the totally-polarized character at the output of any (deterministic) non-polarizing first-order optical system. This property is satisfied by uniformly totally polarized beams and also by those fields whose electromagnetic degree of coherence [T. Setälä, J. Tervo, A.T. Friberg, Opt. Lett. 29 (2004) 328.] equals 1.     

Optical Ray Movement Inside Dielectric Sphere

The paper presents results of numerical investigations of electromagnetic (optical) ray propagation inside a sphere, made of optically uniaxial crystal. The types of caustics formed by the ray trajectory inside the sphere are cleared up. It has been demonstrated the difference between types of caustics formed by the extraordinary ray trajectory inside the sphere made of optically positive and negative crystals. Results are discussed on the basis of one-to-one mapping of 2D billiard problem inside isotropic region bounded by ellipse onto anisotropic one.     

Optics of anisotropic nanostructures

The analytical formalism of Rokushima and Yamakita [J. Opt. Soc. Am. 73, 901–908 (1983)] treating the Fraunhofer diffraction in planar multilayered anisotropic gratings proved to be a useful introduction to new fundamental and practical situations encountered in laterally structured periodic (both isotropic and anisotropic) multilayer media. These are employed in the spectroscopic ellipsometry for modeling surface roughness and in-depth profiles, as well as in the design of various frequency-selective elements including photonic crystals. The subject forms the basis for the solution of inverse problems in scatterometry of periodic nanostructures including magnetic and magneto-optic recording media. It has no principal limitations as for the frequencies and period to radiation wavelength ratios and may include matter wave diffraction. The aim of the paper is to make this formalism easily accessible to a broader community of students and non-specialists. Many aspects of traditional electromagnetic optics are covered as special cases from a modern and more general point of view, e.g., plane wave propagation in isotropic media, reflection and refraction at interfaces, Fabry-Perot resonator, optics of thin films and multilayers, slab dielectric waveguides, crystal optics, acousto-, electro-, and magneto-optics, diffraction gratings, etc. The formalism is illustrated on a model simulating the diffraction on a ferromagnetic wire grating.     

Overall parameters for the characterization of non-uniformly totally polarized beams

Several overall parameters are introduced to characterize the linear or circular polarization content of a non-uniformly totally polarized beam over the region of its wavefront where the irradiance is significant. These figures of merit are determined from the values of the Stokes parameters. The physical meaning of the proposed parameters is tested by computing some numerical examples, and their measurability is checked by considering non-uniformly totally polarized fields generated after propagation through uniaxial anisotropic materials.