Broadband electro-optic frequency comb generation in a lithium niobate microring resonator.

Optical frequency combs consist of equally spaced discrete optical frequency components and are essential tools for optical communication, precision metrology, timing and spectroscopy1-9. At present, combs with wide spectra are usually generated by mode-locked lasers10 or dispersion-engineered resonators with third-order Kerr nonlinearity11. An alternative method of comb production uses electro-optic (EO) phase modulation in a resonator with strong second-order nonlinearity, resulting in combs with excellent stability and controllability12-14. Previous EO combs, however, have been limited to narrow widths by a weak EO interaction strength and a lack of dispersion engineering in free-space systems. Here we overcome these limitations by realizing an integrated EO comb generator in a thin-film lithium niobate photonic platform that features a large EO response, ultralow optical loss and highly co-localized microwave and optical fields15, while enabling dispersion engineering. Our measured EO comb spans more frequencies than the entire telecommunications L-band (over 900 comb lines spaced about 10 gigahertz apart), and we show that future dispersion engineering can enable octave-spanning combs. Furthermore, we demonstrate the high tolerance of our comb generator to modulation frequency detuning, with frequency spacing finely controllable over seven orders of magnitude (10 hertz to 100 megahertz), and we use this feature to generate dual-frequency combs in a single resonator. Our results show that integrated EO comb generators are capable of generating wide and stable comb spectra. Their excellent reconfigurability is a powerful complement to integrated Kerr combs, enabling applications ranging from spectroscopy16 to optical communications8.

Effect of atmospheric anisoplanatism on earth-to-satellite time transfer over laser communication links.

The need for an accurate time reference on orbiting platforms motivates study of time transfer via free-space optical communication links. The impact of atmospheric turbulence on earth-to-satellite optical time transfer has not been fully characterized, however. We analyze limits to two-way laser time transfer accuracy posed by anisoplanatic non-reciprocity between uplink and downlink. We show that despite limited reciprocity, two-way time transfer can still achieve sub-picosecond accuracy in realistic propagation scenarios over a single satellite visibility period.

Direct-detection mode-division multiplexing in modal basis using phase retrieval.

Mode-division multiplexing (MDM) can increase the capacity of direct-detection short-reach systems in proportion to the number of modes employed. MDM requires compensation of modal crosstalk at a transmitter or receiver by the multi-input multi-output (MIMO) signal processing. We show that the channel estimation required for the MIMO processing in a basis of modes can be expressed as a phase retrieval problem. We propose three techniques for the estimation: sparse training sequences, convex optimization (CO) and alternating minimization. We demonstrate the superior performance of the CO technique.

Design of flexible multi-mode fiber endoscope.

Multi-mode fiber (MMF) endoscopes are extremely thin and have higher spatial resolution than conventional endoscopes; however, all current MMF endoscope designs require either that the MMF remain rigid during insertion and imaging or that the orientation of the MMF be known. This limits their possible medical applications. We describe an MMF endoscope design that allows the MMF to be arbitrarily bent as it is maneuvered to the target site prior to imaging. This is achieved by the addition of a partial reflector to the distal end of the MMF, which allows measurement of the mode coupling in the MMF using the reflected light arriving at the proximal end of the MMF. This measurement can be performed while the distal end of the endoscope is not directly accessible, as when the endoscope is being maneuvered. We simulate imaging through such a flexible MMF endoscope, where the MMF is step-index with 1588 spatial modes, and obtain an image even after the mode coupling matrix of the MMF is altered randomly, corresponding to an unknown bending of the MMF.

Noise-reduction algorithms for optimization-based imaging through multi-mode fiber.

Three modifications are shown to improve resolution and reduce noise amplification in endoscopic imaging through multi-mode fiber using optimization-based reconstruction (OBR). First, random sampling patterns are replaced by sampling patterns designed to have more nearly equal singular values. Second, the OBR algorithm uses a point-spread function based on the estimated spatial frequency spectrum of the object. Third, the OBR algorithm gives less weight to modes having smaller singular values. In simulations for a step-index fiber supporting 522 spatial modes, the modifications yield a 20% reduction in image error (l(2) norm) in the noiseless case, and a further 33% reduction in image error at a 22-dB shot noise-limited SNR as compared to the original method using random sampling patterns and OBR.

Optical network scaling: roles of spectral and spatial aggregation.

As the bit rates of routed data streams exceed the throughput of single wavelength-division multiplexing channels, spectral and spatial traffic aggregation become essential for optical network scaling. These aggregation techniques reduce network routing complexity by increasing spectral efficiency to decrease the number of fibers, and by increasing switching granularity to decrease the number of switching components. Spectral aggregation yields a modest decrease in the number of fibers but a substantial decrease in the number of switching components. Spatial aggregation yields a substantial decrease in both the number of fibers and the number of switching components. To quantify routing complexity reduction, we analyze the number of multi-cast and wavelength-selective switches required in a colorless, directionless and contentionless reconfigurable optical add-drop multiplexer architecture. Traffic aggregation has two potential drawbacks: reduced routing power and increased switching component size.

Diversity-multiplexing tradeoff in mode-division multiplexing.

The capacity of mode-division multiplexing (MDM) systems is limited, for a given outage probability, by mode-dependent loss (MDL) and gain. Modal degrees of freedom may be exploited to increase transmission rate (multiplexing gain) or lower outage probability (diversity gain), but there is a fundamental tradeoff between the achievable multiplexing and diversity gains. In this Letter, we present the diversity-multiplexing tradeoff in MDM systems for the first time, studying the impact of signal-to-noise ratio, MDL, and frequency diversity order on the tradeoff in the strong-mode-coupling regime.

Resolution limits for imaging through multi-mode fiber.

We experimentally demonstrate endoscopic imaging through a multi-mode fiber (MMF) in which the number of resolvable image features approaches four times the number of spatial modes per polarization propagating in the fiber. In our method, a sequence of random field patterns is input to the fiber, generating a sequence of random intensity patterns at the output, which are used to sample an object. Reflected power values are returned through the fiber and linear optimization is used to reconstruct an image. The factor-of-four resolution enhancement is due to mixing of modes by the squaring inherent in field-to-intensity conversion. The incoherent point-spread function (PSF) at the center of the fiber output plane is an Airy disk equivalent to the coherent PSF of a conventional diffraction-limited imaging system having a numerical aperture twice that of the fiber. All previous methods for imaging through MMF can only resolve a number of features equal to the number of modes. Most of these methods use localized intensity patterns for sampling the object and use local image reconstruction.

Effect of fog on free-space optical links employing imaging receivers.

We analyze free-space optical links employing imaging receivers in the presence of misalignment and atmospheric effects, such as haze, fog or rain. We present a detailed propagation model based on the radiative transfer equation. We also compare the relative importance of two mechanisms by which these effects degrade link performance: signal attenuation and image blooming. We show that image blooming dominates over attenuation, except under medium-to-heavy fog conditions.

Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling.

We develop a method for synthesis of a desired intensity profile at the output of a multimode fiber (MMF) with random mode coupling by controlling the input field distribution using a spatial light modulator (SLM) whose complex reflectance is piecewise constant over a set of disjoint blocks. Depending on the application, the desired intensity profile may be known or unknown a priori. We pose the problem as optimization of an objective function quantifying, and derive a theoretical lower bound on the achievable objective function. We present an adaptive sequential coordinate ascent (SCA) algorithm for controlling the SLM, which does not require characterizing the full transfer characteristic of the MMF, and which converges to near the lower bound after one pass over the SLM blocks. This algorithm is faster than optimizations based on genetic algorithms or random assignment of SLM phases. We present simulated and experimental results applying the algorithm to forming spots of light at a MMF output, and describe how the algorithm can be applied to imaging.

Population Pharmacokinetic-B Cell Modeling for Ofatumumab in Patients with Relapsing Multiple Sclerosis.

BACKGROUND: Ofatumumab, a fully human anti-CD20 monoclonal antibody indicated for the treatment of relapsing forms of multiple sclerosis (RMS), binds to a unique conformational epitope, thereby depleting B cells very efficiently and allowing subcutaneous administration at lower doses. OBJECTIVES: The aims were to characterize the relationship between ofatumumab concentration and B cell levels, including the effect of covariates such as body weight, age, or baseline B cell count, and use simulations to confirm the chosen therapeutic dose. METHODS: Graphical and regression analyses previously performed based on data from a dose-range finding study provided the B cell depletion target used in the present work. All available adult phase 2/3 data for ofatumumab in RMS patients were pooled to develop a population pharmacokinetics (PK)-B cell count model, using nonlinear mixed-effects modeling. The population PK-B cell model was used to simulate B cell depletion and repletion times and the effect of covariates on PK and B cell metrics, as well as the dose response across a range of subcutaneous ofatumumab monthly doses. RESULTS: The final PK-B cell model was developed using data from 1486 patients. The predetermined B cell target was best achieved and sustained with the 20-mg dose regimen, with median B cell count reaching 8 cells/µL in 11 days and negligible repletion between doses. Only weight had a significant effect on PK, which did not translate into any clinically relevant effect on B cell levels. CONCLUSION: The PK-B cell modeling confirms the dose chosen for the licensed ofatumumab regimen and demonstrates no requirement for dose adjustment based on adult patient characteristics.

Mode-dependent loss and gain: statistics and effect on mode-division multiplexing.

In multimode fiber transmission systems, mode-dependent loss and gain (collectively referred to as MDL) pose fundamental performance limitations. In the regime of strong mode coupling, the statistics of MDL (expressed in decibels or log power gain units) can be described by the eigenvalue distribution of zero-trace Gaussian unitary ensemble in the small-MDL region that is expected to be of interest for practical long-haul transmission. Information-theoretic channel capacities of mode-division-multiplexed systems in the presence of MDL are studied, including average and outage capacities, with and without channel state information.

Experimental demonstration of two methods for controlling the group delay in a system with photonic-crystal resonators coupled to a waveguide.

We measure the group delay in an on-chip photonic-crystal device with two resonators side coupled to a waveguide. We demonstrate that such a group delay can be controlled by tuning either the propagation phase of the waveguide or the frequency of the resonators.

Efficiency of complex modulation methods in coherent free-space optical links.

We study the performance of various binary and nonbinary modulation methods applied to coherent laser communication through the turbulent atmosphere. We compare the spectral efficiencies and SNR efficiencies of complex modulations, and consider options for atmospheric compensation, including phase correction and diversity combining techniques. Our analysis shows that high communication rates require receivers with good sensitivity along with some technique to mitigate the effect of atmospheric fading.

Capacity of coherent free-space optical links using atmospheric compensation techniques.

We analyze the ergodic capacity and epsilon-outage capacity of coherent optical links through the turbulent atmosphere. We consider the effects of log-normal amplitude fluctuations and Gaussian phase fluctuations, in addition to local oscillator shot noise, for both passive receivers and those employing active modal compensation of wavefront phase distortion. We study the effect of various parameters, including the ratio of receiver aperture diameter to wavefront coherence diameter, the strength of the scintillation index, and the number of modes compensated.

Capacity of coherent free-space optical links using diversity-combining techniques.

We study the performance of diversity combining techniques applied to synchronous laser communication through the turbulent atmosphere. We assume that a single information-bearing signal is transmitted over two or more statistically independent fading channels, and that the multiple replicas are combined at the receiver to improve detection efficiency. We consider the effects of log-normal amplitude fluctuations and Gaussian phase fluctuations, in addition to local oscillator shot noise. We study the effect of various parameters, including the ratio of receiver aperture diameter to wavefront coherence diameter, the scintillation index, and the number of independent diversity branches combined at the receiver. We consider both maximal-ratio combining (MRC) and selective combining (SC) diversity schemes. We derive expressions for the outage Shannon capacity, thus placing upper bounds on the spectral efficiency achievable using these techniques.

Coherent detection in optical fiber systems.

The drive for higher performance in optical fiber systems has renewed interest in coherent detection. We review detection methods, including noncoherent, differentially coherent, and coherent detection, as well as a hybrid method. We compare modulation methods encoding information in various degrees of freedom (DOF). Polarization-multiplexed quadrature-amplitude modulation maximizes spectral efficiency and power efficiency, by utilizing all four available DOF, the two field quadratures in the two polarizations. Dual-polarization homodyne or heterodyne downconversion are linear processes that can fully recover the received signal field in these four DOF. When downconverted signals are sampled at the Nyquist rate, compensation of transmission impairments can be performed using digital signal processing (DSP). Linear impairments, including chromatic dispersion and polarization-mode dispersion, can be compensated quasi-exactly using finite impulse response filters. Some nonlinear impairments, such as intra-channel four-wave mixing and nonlinear phase noise, can be compensated partially. Carrier phase recovery can be performed using feedforward methods, even when phase-locked loops may fail due to delay constraints. DSP-based compensation enables a receiver to adapt to time-varying impairments, and facilitates use of advanced forward-error-correction codes. We discuss both single- and multi-carrier system implementations. For a given modulation format, using coherent detection, they offer fundamentally the same spectral efficiency and power efficiency, but may differ in practice, because of different impairments and implementation details. With anticipated advances in analog-to-digital converters and integrated circuit technology, DSP-based coherent receivers at bit rates up to 100 Gbit/s should become practical within the next few years.

Principal modes in multimode waveguides.

We generalize the concept of principal states of polarization and prove the existence of principal modes in multimode waveguides. Principal modes do not suffer from modal dispersion to first order of frequency variation and form orthogonal bases at both the input and the output ends of the waveguide. We show that principal modes are generally different from eigenmodes, even in uniform waveguides, unlike the special case of a single-mode fiber with uniform birefringence. The difference is most pronounced when different eigenmodes possess similar group velocities and when their field patterns vary as a function of frequency. This work may provide a new basis for analysis and control of dispersion in multimode fiber systems.

Compensation for multimode fiber dispersion by adaptive optics.

Adaptive optics is used to compensate for modal dispersion in digital transmission through multimode fiber (MMF). At the transmitter, a spatial light modulator (SLM) controls the launched field pattern. An estimate of intersymbol interference (ISI) caused by modal dispersion is formed at the receiver and fed back to the transmitter, where the SLM is adjusted to minimize ISI. Error-free transmission of 10 Gbit/s non-return-to-zero signals through standard 50 microm graded-index MMFs up to 11.1 km long is demonstrated. It is shown that a single SLM can compensate for modal dispersion across a 600 GHz bandwidth.

Minimization of acquisition time in short-range free-space optical communication.

We consider short-range (1-3-km) free-space optical communication between moving parties when covertness is the overriding system performance requirement. To maximize covertness, it is critical to minimize the time required for the acquisition phase, during which the party initiating contact must conduct a broad-field scan and so risks revealing his position. Assuming an elliptical Gaussian beam profile, we show how to optimize the beam divergence angles, scan speed, and design of the raster scan pattern so as to minimize acquisition time. In this optimization, several constraints are considered, including signal-to-noise ratio, required for accurate bearing detection and reliable decoding; limited receiver bandwidth; limited scanner speed; and beam divergence as limited by the scanner mirror dimensions. The effects of atmospheric turbulence are also discussed.