J. A. Arnaud

Electronic Letters, january 1975, vol 11, n°1

ABSTRACT

A closed-form expression is obtained for pulse broadening in graded-index fibres with k2(r)=1−r2+ε2r4+…+εnr2n. Pulse broadening for k2(r)=1−r2+0.615r4+70r6 and r<0.1 is 12 times smaller than for square-law fibres if material dispersion is neglected.

LIEN VERS  L’ARTICLE : PULSE BROADENING IN MULTIMODE GRADED-INDEX FIBRES

J. A. Arnaud

Proceedings of the IEEE  (Volume:62 ,  Issue: 11 ), pages 1561 – 1570, Nov. 1974

ABSTRACT

A general theory of optical resonators based on the concept of complex point-eikonal is presented. The analysis is limited to the approximation of Gauss. The modes of resonance of open resonators formed by two spherical mirrors facing each other have been obtained in previous works by fitting the wavefronts of Gaussian beams to the mirror surfaces. This method becomes complicated when the resonator contains focusing elements or dielectric slabs. The approach proposed in this paper is more straightforward than previous approaches dealing with this problem and is applicable to resonators containing anisotropic media. The round-trip point-eikonal is first evaluated on the basis of the conventional laws of Gaussian optics. The presence of apertures with Gaussian transmissivity, and of lasers with quadratic transverse variation of the gain, are accounted for by introducing complex round-trip point-eikonals. The modes ψm(x) of the resonator are obtained from a power series expansion of the Green function of a mode-generating system related to the round-trip point-eikonal S of the resonator. The resonance frequencies and the round-trip losses are given by simple and general formulas. The mode fields are described by Hermite-Gauss functions with complex arguments, explicitly in terms of S. For resonators that do not contain apertures, the wavefronts are the same for all the modes and they are plane at planes of symmetry. In reciprocal resonators, clockwise and counter-clockwise modes have the same losses and resonant frequencies, but different mode pattents. These modes are shown to be mutually adjoint. Adjoint modes, with < ψ†m, ψn> = 0 if m ≠ n, are useful to evaluate the response of optical resonators to incident fields. Results applicable to resonators containing nonorthogonal astigmatic elements are also discussed.

LIEN PAYANT VERS  L’ARTICLE : OPTICAL RESONATORS IN THE APPROXIMATION OF GAUSS

J. A. Arnaud

Bell System Technical Journal, The  (Volume:53 ,  Issue: 8 ), pages 1643 – 1656, Oct. 1974

ABSTRACT

The theory of propagation in a new single-material, single-mode, optical fiber is given. The modes are of the whispering-gallery type, with the propagation taking place along helicoidal paths close to the boundary of a cylindrical dielectric rod. The beams are confined in the azimuthal direction in helicoidal ridges. It is shown that single-mode, low-loss operation is possible if the helix period is of the order of the rod cross-section area divided by the wavelength and the ridge area is of the order of 1 percent of the rod cross-section area for two channels. The rod is supported by helicoidal wings that play a role in the mode-selection mechanism.

LIEN VERS  L’ARTICLE : THEORY OF THE SINGLE-MATERIAL, HELICOIDAL FIBER

J. A. Arnaud

Bell System Technical Journal, The  (Volume:53 ,  Issue: 8 ), pages 1599 – 1618, Oct. 1974

ABSTRACT

A dielectric slab can keep optical beams confined transversely in its plane if it is tapered, with the slab thickness having a maximum along some straight line. When the square of the local wave number of the slab (k2) is a quadratic function of the transverse coordinate (y), the rays in the plane of the slab are sinusoids whose optical length is almost independent of the amplitude. For thin slabs (2d « λ) as well as for thick slabs (2d » λ), pulse spreading is large because the ratio of the local phase to group velocity is strongly dependent on the distance (y) from axis. We show that pulse spreading is almost negligible, however, if the thickness of the slab is properly chosen. For example, if the slab thickness on axis is 2.5 micrometers and the refractive index of the slab is 1 percent higher than that of the surrounding medium, pulse spreading is only 0.05 nanosecond per kilometer at a wavelength of 1 micrometer. Pulses in clad fibers having the same width (0.2 millimeter) and carrying the same number of modes (15) spread 50 times faster. Splicing and matching to injection lasers may be easier with planar fibers than with conventional fibers. Low-dispersion planar fibers are therefore attractive when used in conjunction with sources that are multimoded in one dimension. Closed-form expressions are given for square-law and linear-law profiles.

LIEN VERS  L’ARTICLE : PULSE SPREADING IN MULTIMODE, PLANAR, OPTICAL FIBERS

J. A. Arnaud, A. A. M. Saleh

Applied Optics, vol 13, n°10, october 1974

ABSTRACT

A periodic sequence of layers with alternately high and low refractive indices can guide loosely bound surface waves parallel to the layers. Most of the power flows in free space, and, thus, the losses may be considerably smaller than the bulk losses of the dielectric materials used. Possible applications are briefly discussed.

LIEN VERS  L’ARTICLE : GUIDANCE OF SURFACE WAVES BY MULTILAYER COATINGS

J. A. Arnaud

Microwave Conference, 1974. 4th European, 10-13 Sept. 1974, 410 – 414

PAS D’ABSTRACT

LIEN PAYANT VERS  L’ARTICLE : QUASI-OPTICAL FILTERS

J. A. Arnaud

Bell System Technical Journal, The  (Volume:53 ,  Issue: 7 ), pages 1379 – 1394, Sept. 1974

ABSTRACT

A general method is proposed to evaluate the radiation loss of bent open waveguides. This method consists in evaluating the coupling between the waveguide mode and the whispering-gallery modes that can be associated with the surrounding medium. The expression obtained for a reactive surface coincides with a previous result by Miller and Talanov.1 We investigate in detail the radiation loss of the fundamental (HE11) mode of a dielectric rod coupled to a slab. This arrangement, described in Part II of this article series,2 provides a useful mode-selection technique. The radiation loss is given by a simple closed-form expression. We find that for a wavelength of 1 µm and a rod radius of 5 µm in physical contact with the slab, the bending loss is less than 1 dB/km if the radius of curvature, in the plane of the slab, exceeds 22 mm.

LIEN VERS  L’ARTICLE : TRANSVERSE COUPLING IN FIBER OPTICS PART III : BENDING LOSSES

J. A. Arnaud

Electronics Letters, Volume 10, Issue 14, 11 July 1974, p. 269 – 270

ABSTRACT

Experiments performed in the 50–80 GHz band show that single-mode propagation is possible near the contact line of two thin-wall dielectric tubes. The group delay c/vg, is found to be almost a constant(3·3)from 55 to 75 GHz. Pulsespreading is therefore very low for that structure (< 1·6 ns/km½). These experimental results are in good agreement with a semiclassical theory of propagation.

LIEN VERS  L’ARTICLE : ELECTROMAGNETIC PROPAGATION ALONG CONTACTING DIELECTRIC TUBES

Jacques A. Arnaud, Adel A. Saleh and Joseph T. Ruscio

IEE Transactions on microwave theory and Techniques, Vol MTT-22, n°5, Mai 1974, pp 486-493, 1974

ABSTRACT

Fabry-Perot (FP) resonators working under oblique incidence can be used in the millimeter and far infrared bands as diplexers or channel dropping filters. The response of two-grid Fabry-Perot resonators under Gaussian beam excitation is evaluated by adding the fields of the successive passes of the beam. The results coincide with those obtained from a plane wave expansion of the incident field. Closed form expressions are obtained for the losses due to diffraction walk-off, geometrical walk-off, and mismatch. Excellent agreement is obtained with experiments in the 70-80-GHz band. For a 1-GHz-bandwidth filter, working at an incidence angle of 15 degrees, and an incident beam waist radius of 40 mm, the transmission loss at resonance does not exceed 1 dB. The reflection loss off-resonance is about 0.1 dB. This type of diplexer is particularly useful when used in conjunction with quasioptical guiding systems.

LIEN VERS  L’ARTICLE : WALK OF EFFECTS IN FABRY-PEROT DIPLEXERS

J. A. Arnaud

Bell System Technical Journal, The  (Volume:53 ,  Issue: 4 ), pages 675 – 696, April 1974

ABSTRACT

The number of modes that can propagate without radiation loss in oversized waveguides is sharply reduced if the waveguide is coupled to a structure supporting radiation modes, the loss mechanism being analogous to Cerenkov radiation. The coupling formula derived in Part I1 is used to evaluate the loss for a specific configuration: a reactive surface (e.g., a thin dielectric slab) acting as a waveguide, coupled to a semi-infinite dielectric acting as a mode sink. The method consists in first assuming that the substrate is finite in size and lossy and adding the losses associated with each substrate mode. The substrate dimensions are subsequently made infinite and the dissipation loss is made to vanish. The expression obtained for the radiation loss coincides with an expression obtained by solving the boundary value problem. The method is then applied to the problem of mode selection for dielectric rods coupled to dielectric slabs, which is of particular importance for optical communications and integrated optics. A 2-dB/m radiation loss is calculated for the first higher order mode when the rod radius is 10 µm, λ = 1 µm, n = 1.41, and the rod-to-slab spacing is 0.15 µm.

LIEN VERS  L’ARTICLE : TRANSVERSE COUPLING IN FIBER OPTICS PART II : COUPLING TO MODE SINKS