SPIDER

Conventional SPIDER

Spectral Phase Interferometry for Direct Electric-field Reconstruction (SPIDER) is a specific implementation of spectral shearing interferometry for the complete temporal characterization (or more specifically the spectral phase) of ultrashort optical pulses. The basic concept is that two pulse replicas that are delayed in time by an amount $\tau$ and spectrally shifted with respect to each other by an amount $\Omega$ are interfered on a spectrometer. The resulting interferogram (or SPIDERgram) can thus be written as

$S(\omega) = I(\omega) + I(\omega-\Omega) + 2\sqrt{I(\omega)I(\omega-\Omega)}\cos[\phi(\omega)-\phi(\omega-\Omega) + \omega\tau]$,

where I(\omega) = |E(\omega)|^2 is the spectral intensity of the individual pulses and \phi(\omega) is the spectral phase. The time delay results in fringes that are nominally spaced by \delta\omega\sim2\pi/\tau and enables the interferometric term (last term in the equation above), that contain the phase information, to be extracted. For a small spectral shear, it can be understood that the phase of the interferometric term (after removal of the time delay term \omega\tau) is approximately equal to gradient of the spectral phase, scaled by the spectral shear, i.e.

\phi(\omega)-\phi(\omega-\Omega) \sim \Omega\frac{\partial\phi(omega)}{\omega}.

Typically, the size of the spectral shear needs to be a few percent of the pulse bandwidth, or more. For optical pulses, this requires a spectral shear of several terahertz or more, which cannot be achieved by electro-optic modulators. Therefore the spectral shear is generated by upconverting the test pulse with two slightly different monochromatic frequencies, where the difference in their frequencies is equal to the spectral shear. Experimentally, this is achieved by upconverting two time-delayed replicas of the TP with a highly chirped pulse (CP). If the chirp is sufficiently large, then the instantaneous frequency of the CP will be approximately constant over the duration of the TP. Since the two TP replicas are delayed in time, they will upconvert with two slightly different quasi-monochromatic frequencies. The concept is shown below.

Conventional SPIDER concept: The generation of two time-delayed spectralyl sheared pulse replicas via sum-frequency generation between two time-delayed replicas of the test pulse (TP) with a highly chirped pulse (CP) derived from the TP.

SEA-SPIDER

Spatially encoded arrangement (SEA-) SPIDER is a modification of the conventional SPIDER that is suited to the characterization of few-cycle pulses and for measuring space-time coupling. In conventional SPIDER, fringes are generated along the frequency axis, thus requiring a high resolution spectrometer in order to be able to resolve them. For octave spanning pulses, this poses a real challenge: the nonlinear frequency spacing of traditional spectrometers results in a change in the fringe spacing as a function of wavelength, thus requiring a larger delay and thus finer resolution. SEA-SPIDER eliminates this problem by interfering two spatially tilted shear replicas at zero time-delay on the entrance slit of a 2D imaging spectrometer. This can be achieved experimentally by upconverting a single copy of the TP with two spatially tilted chirped pulses (see below). The tilt then results in spatial fringes, instead of spectral fringes. This has the added advantage of not duplicating the TP, and thus ensuring zero added phase (ZAP). This arrangement also enables the spectral shear to be set independantly of the fringes, enabling multi-shearing interferometry for increased accuracy and precision, especially for complex pulses.

SEA-SPIDER concept: The generation of two spatially-tilted spectrally-sheared pulse replicas via sum-frequency generation between a single copy the test pulse (TP) with two tilted highly chirped pulses (CP) derived from the TP.

Another added bonus of SEA-SPIDER is that, for very small or zero space-time coupling, the experimental traces are very intuitive: the contours of the fringes directly map out the gradient of the spectral phase (i.e. the chirp). This can enable a quick optimization of the pulse duration without the need for a full reconstruction. Example interferograms are shown below.

Intuitive SEA-SPIDER interferograms: A pulse shaper was used to add known spectral phase to a pulse before being measured by a SEA-SPIDER. The contours of the fringes (dashed line) map out the spectral phase gradient (i.e. chirp).