We explore the spatial profile of the ensemble average of the energy density of eigenchannels of the transmission matrix within random diffusive media using computer simulations and nonperturbative diagrammatic technique. A symmetrical profile with a peak in the middle of the sample is found for the fully transmitting eigenchannel and is shown to be closely related to a position dependent diffusion coefficient of the open media. We show that the average spatial profile of each transmission eigenchannel when normalized by the profile of the completely transmitting eigenchannel depends only upon the value of transmission through the corresponding eigenchannel. A universal expression for the average spatial profile is given in terms of the auxiliary localization lengths determined from transmission eigenvalues and position dependent diffusion coefficient. These lengths were first introduced by Dorokhov to describe the scaling of transmission and conductance through disordered media. Though direct measurement of energy distribution within a scattering medium is generally difficult, we demonstrate in microwave measurements that the integrated energy density stored in the media of each eigenchannel can be determined from the measurements of spectra of the transmission matrix. The derivative of the composite phase of the eigenchannels with respect to the angular frequency yields the contribution to the density of states (DOS) from the individual transmission eigenchannels. This is proportional to integrated energy stored and the dwell time of the transmission eigenchannel. The DOS determined from the transmission eigenchannel is shown to be in good agreement with DOS obtained by analyzing the field spectra into quasi-normal modes of the open medium. These results provide a path towards controlling the energy deposition within a scattering medium.
In response to the optical packaging needs of a rapidly growing silicon photonics market, Chiral Photonics, Inc. (CPI)
has developed a new generation of ultra-dense-channel, bi-directional, all-optical, input/output (I/O) couplers that bridge
the data transport gap between standard optical fibers and photonic integrated circuits. These couplers, called Pitch
Reducing Optical Fiber Arrays (PROFAs), provide a means to simultaneously match both the mode field and channel
spacing (i.e. pitch) between an optical fiber array and a photonic integrated circuit (PIC). Both primary methods for
optically interfacing with PICs, via vertical grating couplers (VGCs) and edge couplers, can be addressed with PROFAs.
PROFAs bring the signal-carrying cores, either multimode or singlemode, of many optical fibers into close proximity
within an all-glass device that can provide low loss coupling to on-chip components, including waveguides, gratings,
detectors and emitters. Two-dimensional (2D) PROFAs offer more than an order of magnitude enhancement in channel
density compared to conventional one-dimensional (1D) fiber arrays. PROFAs can also be used with low vertical profile
solutions that simplify optoelectronic packaging while reducing PIC I/O real estate usage requirements.
PROFA technology is based on a scalable production process for microforming glass preform assemblies as they are
pulled through a small oven. An innovative fiber design, called the “vanishing core,” enables tailoring the mode field
along the length of the PROFA to meet the coupling needs of disparate waveguide technologies, such as fiber and onchip.
Examples of single- and multi-channel couplers fabricated using this technology will be presented.
We have fabricated both pressure and temperature sensors based on chiral fiber gratings that can operate in harsh
environments over wider measurement ranges than conventional fiber Bragg gratings (FBGs). Chiral fiber sensors
are made by twisting one or more standard or custom optical fiber with a noncircular or non-concentric core as they
pass though a miniature heat zone. Because the resulting structures are as stable as the glass material, they can
operate in harsh environments. Excellent temperature stability up to 900°C is found in pure silica chiral fiber
temperature sensors. We developed a correlation algorithm for use with a standard FBG interrogator to accurately
measure the shift in the transmission spectrum as the environment of the sensor changes. We developed a calibration
procedure, which allows the chiral temperature sensor to operate at temperatures from 200 to 900°C with a
maximum difference in temperature reading from a calibrated thermocouple of +/- 2°C. We have fabricated a
transducerless pressure sensor (i.e. no moving parts) operating from 1 atm. (14.7 psi) up to 12 kpsi with a resolution
of 1 psi that can operate at temperatures as high as 700°C.
We have fabricated chiral fiber long-period gratings (CLPGs) for radiation sensing by co-twisting two standard
optical fibers or twisting a single custom optical fibers with nonconcentric core as the fibers pass though a miniature
oven. The wavelength shift of transmission dips in the CLPGs have proven to be much more sensitive to ionizing
radiation than are fiber Bragg gratings. The radiation sensitivity of these CLPGs was investigated in a wide variety
of twisted fibers at the Fraunhofer Institute for Technological Trend Analysis by Henschel <i>et al.</i><sup>7</sup>. Because chiral
fiber gratings do not rely on glass photosensitivity, as is the case for fiber Bragg gratings (FBGs), chiral radiation
sensors can be fabricated from a range of glass combinations selected strictly for their sensitivities to radiation in
different circumstances. The fiber may also be made of glass selected to be radiation insensitive so that the fiber can
be used to sense temperature in high-radiation environments. Radiation-induced shifts of up to 10 nm are observed
in transmission dips of CLPGs for doses of 100 kGy of Co-60 gamma radiation. With such high sensitivity, these
gratings can be used as radiation sensors for doses below 10 Gy. The wavelength shift was found to depend upon the
radiation dose rate. This dependence is found to vary with glass composition. This opens up the possibility of using
two CLPGs to simultaneously measure both the dose and rate of radiation.
We have fabricated a variety of chiral fiber sensors by twisting one or more standard or custom optical fibers with
noncircular or nonconcentric core as they pass though a miniature oven. The resulting structures are as stable as the
glass material and can be produced with helical pitch ranging from microns to hundreds of microns. The polarization
selectivity of the chiral gratings is determined by the geometry of the fiber cross section. Single helix structures are
polarization insensitive, while double helix gratings interact only with a single optical polarization component. Both
single and double helix gratings may function as a fiber long period grating, coupling core and cladding modes or as
a diffraction grating scattering light from the fiber core out of the fiber. The resulting dips in the transmission
spectrum are sensitive to fiber elongation, twist and temperature, and (in the case of the long period gratings) to the
refractive index of the surrounding medium. The suitability of chiral gratings for sensing temperature, elongation,
twist and liquid levels will be discussed. Gratings made of radiation sensitive glass can be used to measure the
cumulative radiation dose, while gratings made of radiation-hardened glass are suitable for stable sensing of the
environment in nuclear power plants. Excellent temperature stability up to 900°C is found in pure silica chiral
diffraction grating sensors.
We propose an in-fiber chiral optical isolator based on chiral fiber polarizer technology and calculate its
performance by incorporating the magnetic field into the scattering matrix. The design will be implemented in a
special preform, which is passed through a miniature heat zone as it is drawn and twisted. The birefringence of the
fiber is controlled by adjusted the diameter of a dual-core optical fiber. By adjusting the twist, the fiber can convert
linear to circular polarization and reject one component of circular polarization. In the novel central portion of the
isolator, the fiber diameter is large. The effective birefringence of the circular central core with high Verdet constant
embedded in an outer core of slightly smaller index of refraction is small. The central potion is a non-reciprocal
polarization converter which passes forward traveling left circularly polarized (LCP) light as LCP, while converting
backward propagating LCP to right circularly polarized (RCP) light. Both polarizations of light traveling backwards
are scattered out of the isolator. Since it is an all-glass structure, we anticipate that the isolator will be able to handle
several watts of power and will be environmentally robust.
Long period fiber gratings couple core and co-propagating cladding modes to produce dips in the transmission
spectrum and have been widely utilized as sensors and filters. We have recently developed a new approach to long
period fiber gratings utilizing optical fibers, which are uniformly twisted at elevated temperatures to produce
double or single helices. Because these fibers are not manufactured by exposing photosensitive glass to patterned
UV illumination, as is the case for traditional fiber Bragg gratings (FBGs) or long period gratings (LPGs), they are
more robust in harsh thermal and chemical environments. Double helix fibers are polarization sensitive and are
fabricated by twisting fiber preforms with high-index noncircular cores while single helix gratings are polarization
insensitive and are created by twisting standard optical fibers with cores that are not perfectly centered. Here, we
present a new approach to single-helix chiral long-period gratings (CLPGs). The CLPG is created in a glassforming
process in which two optical fibers are twisted together to form a helix in the signal fiber as the fibers pass
through a miniature oven. "Dual-twist" CLPGs may be fabricated from any conventional or specialty fiber and
provide reproducible spectra that may be tailored to specific applications.
Chiral fiber gratings are produced in a microforming process in which optical fibers with noncircular or nonconcentric
cores are twisted as they pass though a miniature oven. Periodic glass structures as stable as the glass material itself are
produced with helical pitch that ranges from under a micron to hundreds of microns. The geometry of the fiber cross
section determines the symmetry of the resulting structure which in turn determines its polarization selectivity. Single
helix structures are polarization insensitive while double helix gratings interact only with a single optical polarization.
Both single and double helix gratings may act as a fiber long period grating, coupling the core and cladding modes. The
coupling is manifested in a series of narrow dips in the transmission spectrum. The dip position is sensitive to fiber
elongation, twist and temperature, and to the refractive index of the surrounding medium. The suitability of chiral
gratings for sensing pressure, temperature and liquid levels is investigated. Polarization insensitive single helix silica
glass gratings display excellent stability up to temperatures of 600°C, while a pressure sensor with dynamic range of
nearly 40 dB is demonstrated in polarization selective double helix gratings.
We explore the specific nature of wave propagation in multiple scattering media and examine how this is revealed in
various aspects of the speckle pattern measured at the output surface of an ensemble of disordered media. We present
near-field measurements of the speckle pattern transmitted through random samples in a quasi-one dimensional
geometry. The microwave field -amplitude and phase- is measured as a function of frequency on a grid of points on the
output surface of samples composed of randomly positioned dielectric spheres. The field and intensity correlation
functions versus displacement and frequency shift are measured and reveal non-Gaussian behavior, namely long range
correlation. The widest fluctuations of the phase derivative with frequency are found at low intensity values near a phase
singularity in the transmitted speckle pattern. The position of these phase singularities at which the intensity vanishes is
reconstructed for the entire speckle pattern and followed in space while frequency is shifted.
In this paper, we explore the specific nature of wave propagation in multiple scattering media and examine how this is revealed in various aspects of the speckle pattern measured at the output surface of an ensemble of disordered media. We present near-field measurements of the speckle pattern transmitted through random samples in a quasi-one dimensional geometry. The microwave field--amplitude and phase--is measured as a function of frequency along perpendicular transverse polarizations on a close grid of points on the output surface of samples composed of randomly positioned dielectric spheres. The field spectrum is Fourier transformed to access the temporal evolution of the speckle pattern. The field and intensity correlation functions versus displacement and frequency shift are measured and reveal non-Gaussian behavior, namely long range correlation. The key distributions and correlation functions of the delay time are also measured and compared to calculations, to show the interplay between the delay time and the intensity in the speckle pattern. The widest fluctuations of the phase derivative with frequency are found at low intensity values near a phase singularity in the transmitted speckle pattern. The position of these phase singularities at which the intensity vanishes is reconstructed for the entire speckle pattern.
In this paper, we attempt to find a unified framework in which the statistics of wave propagation in random media can be understood as strengths of scattering and absorption increase. First, we discuss the weak scattering, diffusive limit without absorption. In this limit, the suppression of transmission by weak localization, the distribution of total transmission and the intensity correlation functions with displacement and polarization rotation are all described in terms of the dimensionless conductance so that these effects are explicitly linked. When absorption is introduced, the dimensionless conductance can no longer serve as a fundamental scaling parameter, but the variance of the total transmission is still able to chart the changing statistical character of propagation and localization with sample size. By examining transport at a fixed time following pulsed excitation, the affect of absorption can be removed while the growing impact of localization can be clearly discerned. The functional form of probability distributions of intensity and total transmission and of the spatial and polarization intensity correlation functions in the time domain are the same as in the frequency domain. The connection of mesoscopic fluctuations to localization can be seen in the spectral correlation function of the field, which is the Fourier transform of average pulsed transmission. The spectral field correlation function can be expressed as a product of the correlation function of the field normalized to the average amplitude in a given configuration and of the square root of the total transmission.
We describe the development of fiber chiral gratings and discuss salient similarities and differences from planar chiral structures. Planar chiral structures include cholesteric liquid crystals and structured thin films produced by oblique deposition of dielectric materials on a rotating substrate. These are composed of uniform anisotropic planes with 180 degrees rotation symmetry which rotate uniformly with displacement perpendicular to the planes so that the pitch is equal to twice the period. The sinusoidal modulation of the structure which possesses double-helix symmetry results in a single band gap for co-handed light with the same sense of circular polarization as the handedness of the helical structure. Orthogonally polarized light is freely transmitted. Within the band gap the wavelength in the medium equals the structure pitch. Double-helix symmetry may also be implemented into a fiber geometry by twisting glass optical fiber with noncircular core cross section as it passes through a miniature oven. In addition to the polarization-selective resonant band observed in planar chiral gratings, we observe two additional modes of optical interaction when the pitch exceeds the wavelength in the fiber. In chiral long period gratings, dips in transmission are observed at wavelengths associated with coupling of the core mode and distinct cladding modes mediated by the chiral grating. In chiral intermediate period gratings, a broad scattering band is observed due to scattering out of the fiber into a continuum of states. Gratings with uniform pitch as well as with a specially designed pitch profile can be utilized to produce a variety of polarization selective devices. In addition to describing optical chiral gratings, we describe studies of microwave planar and fiber gratings, which played a key role in the development of optical fiber chiral gratings.
We find that the evolution of an optical polarization along a twisted optical fiber may be spatially synchronized with polarization-selective light scattering. We demonstrate experimentally that linearly polarized light initially oriented along the fast axis of an adiabatically twisted single-mode, polarization-maintaining optical fiber is converted into elliptically and then into circularly polarized light with the same handedness as the chiral structure. As the state of polarization is changing along the length of the fiber, the light is scattered out of the fiber core. By choosing an appropriate twist acceleration profile in custom-made, rectangular-core polarization maintaining fibers, scattering and conversion may be synchronized, allowing the orthogonal polarization to freely propagate through the fiber. When the portion of the fiber with accelerated twist is combined with another fiber segment with decelerated twist, the fiber becomes a broadband, low-insertion-loss, in-fiber, linear polarizer. In this polarizer, the passing component of the incident light oriented along the slow axis, is converted to circularly polarized light of the opposite handedness, and then converted back to linearly polarized light oriented along the same slow axis. While the polarization evolution may be calculated using 1D model of light propagation through a birefringent medium, the calculation of light scattering requires a full 3D calculation.
We have produced chiral fiber Bragg gratings with double-helix symmetry and measured the polarization and wavelength selective transmission properties of these structures. These gratings interact only with circularly polarized light with the same handedness as the grating twist and freely transmit light of the orthogonal polarization. The optical characteristics of chiral fibers are compared to those of planar cholesteric structures. The resonant standing wave at the band edge or at a defect state within the band gap, as well as the evanescent wave within the band gap is comprised of two counterpropagating components of equal amplitude. The electric field vector of such a circularly polarized standing wave does not rotate in time; rather it is linearly polarized in any given plane. The standing wave may be described in terms of the sense of circular polarization of the two counterpropagating components. The wavelength dependence of the angle q between the linearly polarized electromagnetic field and the extraordinary axis, which is constant throughout a long structure, is obtained in a simple calculation. The results are in good agreement with scattering matrix calculations. Resonant chiral gratings are demonstrated for microwave radiation whereas chiral gratings with pitch exceeding the wavelength are demonstrated at optical wavelengths in single-mode glass fibers. The different functionalities of these fibers are discussed.
We show that introducing anisotropy into periodic dielectric structures leads to new optical phenomena as well as to a new approach to a variety of applications. One-dimensional anisotropic structures allow a new type of chiral twist defect resulting in a localized photonic mode with unusual properties. Unlike isotropic layers of alternating index of refraction, where the periodicity can be destroyed only by changing the refractive index or thickness of a layer, a defect can be created in anisotropic media by introducing an additional rotation between consecutive layers. Computer simulations show that introducing an additional rotation in the middle of a sample with cholesteric ordering produces a localized state whose frequency can be tuned from one edge of the photonic stop band to the other by varying the angle of rotation from 0 to 180 degrees. Most of the energy of this mode exists as a circularly polarized standing wave with the same handedness as the structure, independent of the polarization of the exciting wave. This localized mode gives rise to a crossover in the nature of propagation. Below a crossover thickness, the localized mode is excited only by a wave with the same handedness as the structure and exhibits a peak in transmission at the defect frequency. Above the crossover, however, the defect mode can be excited only by the oppositely polarized wave and a resonant peak appears in reflection. Simulations for lengths below the crossover are in agreement with measurements of microwave transmission through stacks of overhead transparencies, ordered in the same way as the molecular layers of a cholesteric liquid crystal. Three types of defect are introduced: (1) an additional 90 degrees rotation, (2) an additional 45 degrees rotation, and (3) a combination of a 45 degrees rotation and a quarter-wavelength separation.
We find a ring structure in the far field of laser radiation emitted from a dye-doped cholesteric liquid crystal (CLC) film. This is a consequence of angular confinement of radiation at the frequency of the mode propagating normal to the molecular layers, which lies closest to the reflection band edge. This is a result of the increase in frequency of the band edge with increasing angle from the normal, which places oblique radiation at the frequency of the band edge for normally propagating radiation inside the photonic gap. As a result, the intensity along the output surface of the film decays exponentially on a length scale that can be much larger than the film thickness. This in turn gives rise to a ring structure in the far field that is similar to Fraunhofer diffraction of a plane wave by an aperture. These results apply not only to CLC films but also to binary layered media.
We present simulations of optical propagation in cholesteric liquid crystal (CLC) films and find a stop band in which the wave is evanescent and the density of states is zero. Sharp structure is found in the calculated transmission spectra near the band edge. This corresponds to enhanced residence times and lower group velocities, as well as to significant enhancements of the energy density and of the density of states within the samples. These simulation are consistent with our measurements of suppressed emission within the stop band and of enhanced emission at the band edge for dye molecules doped into CLCs. We also observe spatially coherent emission from the CLC sample with narrow spectral lines at the edge of the stop band and a distinct threshold behavior for the coherent emission. The results of computer simulations together with observations of emission and lasing demonstrate that the optical properties of CLCs, including laser action at the modes closest to the band edge, are consequences of its band gap structure. The compact nature of these structures and the ease with which they ca be fabricated suggest that they may be useful for producing integrated lasers and photonic devices.