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Adaptive Compression

Ultrashort optical signals are often more convenient to manipulate in the spectral domain than directly in the time domain. The pioneering studies of pulse shaping by Heritage and Weiner at Bellcore in the late 80's demonstrated the power of these frequency domain techniques. We have demonstrated and patented techniques for adaptive pulse compression and shaping of ultrashort pulses. Adaptive compression and shaping is a significant advance in short pulse manipulations: Pulses can be compressed down to their transform limit (or shaped into other desirable shapes) even when there is no prior knowledge of their initial shape or phase structure. Using a global search algorithm, the phases of the spectral components are adjusted until a desired target is achieved. This results not only in forming the desired pulse, but also in an effective measurement of the unknown input pulses.  Adaptive techniques are also expected to prove very useful for coherent control, when there is no complete knowledge of the hamiltonian of the system being controlled. Also see [1-3].

 

Short-Pulse Characterization

Third-Harmonic for Autocorrelation
We demonstrated autocorrelation measurements of short pulses where third harmonic generation replaces the usual SHG. This has two advantages: No need for expensive SHG crystal (THG is generated near the surface of a simple glass plate), and more sensitivity to pulse shape differences. See also our work on THG in nonlinear microscopy. [4]

Shor-pulse characterization in the frequency domain
 The exact temporal phase and amplitude of a short pulse can be retrieved by interfereing its spectrum with that of a known short reference pulse. We developed a technique of Spatial-Spectral interference which is very useful in real time monitoring of short pulse systems. These ideas can also be used to measure dispersion with incoherent broad spectral sources [5-6].

White Light Dispersion Measurements by One and Two-Dimensional Spectral Interference

White light dispersion measurements by one and two-dimensional spectral interference are shown. One-dimensional white light spectral interference measurements allow accurate characterization of dispersion using weak optical fields. Two-dimensional spectral interference allows for real-time measurements since no post-processing is needed, and therefore can be used in situations where the optical properties of the elements under test vary in time. We demonstrate the applicability of the two methods for characterizing dispersive elements such as optical glasses and dielectric coatings.

 

Right - The spatial spectral interference pattern of the signal and reference fields, with no spectral phase distortion. (a) No delay. (b) Delay of 67 fs. Middle - The spatial spectral interference pattern of the signal and the reference fields, when optical glasses were inserted in the signal arm. (a) 3.175 mm of fused silica optical glass. (b) 9.525 mm of fused silica optical glass. Left - The spatial spectral interference pattern of the signal and the reference fields, when the silver mirror of the signal arm of the interferometer was replaced by dielectric mirrors. (a) High reflectance, broad-band dielectric mirror for the 450-700 nm wavelengths. (b) High reflectance dielectric mirror for the 1060 nm wavelength.
 

Vector Solitons

What are the possible polarization states of optical solitons?
Surprisingly, this fundamental question had only partial answers in 1994, when we started this research. The polarization properties of 'long' (several picoseconds) solitons, like those that are considered for communication applications, tend to average out over their characteristic propagation lengths, typically many kilometers.  However, this is not the case for much shorter solitons, like solitons in fiber lasers. We studied theoretically and then experimentally the polarization properties of short (subpicosecond) temporal solitons in optical fibers, and the interactions of solitons with various polarization states. Vector solitons are no longer ideal mathematical solitons, and the interactions between them can lead to energy transfer and polarization transformations. We observed for the first time the phenomenon of polarization instability of solitons in birefringent fibers, and of rotating solitons in isotropic fibers. Short solitons are attractive as bits in all-optical systems, and their interactions could lead to ultrafast logic operations. More importantly, perhaps, is the fact the polarization effects will probably impose the next limit on the rate of communications through optical fibers, hence better understanding of these properties in solitons and other pulses is of major importance.

Rotating Vector Solitary Waves in Isotropic Fibers

The properties of elliptically polarized solitary waves in isotropic optical fibers are investigated. Two families of polarized solitary pulses are identified, but only one of them is shown to be stable. These pulses are charcterized by a fixed polarization pattern that rotates at a constant rate as the pulse propagates down the fiber. The evolution of the polarization of these pulses is important for the operation of short-pulse fiber lasers and other nonlinear devices. [7]

 
Left - A circularly polarized soliton field (solid curve) can support, through cross-phase modulation, two kinds of weak pulse in the orthogonal polarization mode: a symmetric pulse (dotted-dashed curve) and an antisymmetric pulse (dashed curve). All pulses have been calculated with a=1 and normalized to vo=1 for ease of viewing. Right - Rate of ellipse rotation, b-a, for elliptically polarized solitary waves as a function of the ellipticity (ratio of the two ellipse axes) at the center of the pulse. Calculated with a=1. Also shown (dashed curve) is the ellipse rotation for a cw wave with intensity equal to the peak intensity of the soliton.

 
Simulations of propagation of a solitary wave from the antisymmetric branch with a=1, b=0.7572, u(0)=2½, and v'(0)=8/3½. The intensity of the two polarization modes is shown along the propagation distance from z=0 (bottom) to z=50 (top). An instability appears, as a symmetric perturbation grows from noise, that eventually transforms the pulse into a simple elliptically polarized soliton.
 

Polarization Evolution and Polarization Instability of Solitons in a Birefringent Optical Fiber

Ultrashort optical solitons with different states of polarization are used to map the polarization evolution in a fixed section of a weakly birefringent fiber. Soliton polarizaion evolution was compared to linear propagation. A significant change in the polarization behavior between the solitons and linear regime is observed. Although solitons contain a continuum of instantaneous intensities, they transform their polarization as a unit, in contrast to other light pulses which acquire complex polarizaion structures.

 

Trajectories on the Poincare sphere for (a) linear and (b) nonlinear propagation. Linear propagation (S0 ~ 0) is equivalent to rotation of the sphere around the S1 axis, with two stationary points for light polarized along the fast and slow axes S=(S0,0,0). Nonlinear propagation is calculated for S0=10Ic. The fast axis (-S0,0,0) is now unstable, and two new stationary elliptical polarization states are obtained. The separatrix (shown in dashed line) separates the trajectories to 3 families, rotating around the 3 stable points.

 

States of polarization after propagating in a section of birefringent fiber. Input states are 36 linear polarizaion states equally spaced along the Poincaré sphere equator. Output states are shown on the Poncaré spheres and on the S1-S2 plane. (a-d) experimental points; (a'-d') calculations. The lines in all plots are calculated, and describe the transformed equator. (a,b): Linear propagation. Theory and experiment show that input states are rotated by 55o around the S1 axis. (c,d): Soliton propagation. Theoretical points were calculated with S0=10Ic Final states are crowding near the stable slow axis S=(S0,0,0).
States of polarization after propagating in a section of birefringent fiber. Input states are 36 polarizaion states equally spaced along the S1-S3 section of the Poincaré sphere. Output states are shown on (a) the Poincaré sphere, and (b) on the S1-S2 plane. The lines are calculated with S0=4Ic They describe the line to which the circle S1^2+S3^2=S0^2 transforms to.
 

Fiber Lasers

Fiber lasers are attractive sources of ultrashort pulses because of their compact size and compatibility with fiberoptics components and systems.  We have developed a unique type of fiber laser which produces noise bursts. The most important feature of these lasers is their very broad and smooth spectral output. Such broad spectra are important for several techniques of measurements, and indeed this new sources are attracting attention of several laboratories and companies worldwide. The research on this laser is now being continued by M. Horowitz at the Technion [9-11].

   
Publications
  1. “Adaptive Ultrashort Pulse Compression and Shaping”, D. Meshulach, D. Yelin, and Y. Silberberg, Opt. Commun. 138, 345 (1997).
  2. “Adaptive Femtosecond Pulse Compression”, D. Yelin, D. Meshulach and Y. Silberberg, Opt. Lett., 22, 1793 (1997). (Get PDF File)
  3. “Adaptive Real-Time Femtosecond Pulse Shaping”, D. Meshulach, D. Yelin and Y. Silberberg, JOSA B, 15, 1615 (1998). (Get PDF File)
  4. "Measurement of Ultrashort Optical Pulses by Third Harmonic Generation", D. Meshulach, Y. Barad, and Y. Silberberg, J. Opt. Soc. Am. B, 14, 2122 (1997). (Get PDF File)
  5. "Real-Time Spatial-Spectral Interference Measurements of Ultrashort Optical Pulses", D. Meshulach, D. Yelin, and Y. Silberberg, J. Opt. Soc. Am. B, 8, 2095 (1997) (Get PDF File).
  6. "White Light Dispersion Measurements by One and Two-Dimensional Spectral Interference", D. Meshulach, D. Yelin and Y. Silberberg, IEEE Journal of Quantom Electronics 33, 1969 (1997)
  7. "Rotating Vector Solitary Waves in Isotropic Fibers" Y. Silbereberg and Y. Barad Optics Letters 20, 246 (1995)
  8. "Polarization Evolution and Polarization Instability of Solitons in a Birefringent Optical Fiber" Y. Barad and Y.Silberberg Physical Review Letters 78, 3290 (1997)
  9. “Noise-Like Pulses with Broadband Spectrum Generated from an Erbium Doped Fiber Laser”, M. Horowitz, Y. Barad, and Y. Silberberg,  Opt. Lett., 22, 799 (1997). GET PDF FILE
  10. “Nonlinear Filtering of Optical Pulses using Intensity Dependent Polarization Rotation in Birefringent Fibers”, M. Horowitz and Y. Silberberg,  Opt. Lett., 22, 1760 (1997). GET PDF FILE
  11. "Control of Noiselike Pulse Generation in Erbium-Doped Fiber Lasers" M. Horowitz and Y. Silberberg, IEEE Photon. Technol. Lett., 10, 1389 (1998).