Photonic Time-Stretch Fieldoscopy

• Photonic time-stretch fieldoscopy is an ultrafast optical measurement technique that exploits group-velocity dispersion and time lenses to capture femtosecond-to-attosecond field events in a single shot.
• The approach integrates electro-optic sampling and nonlinear sum-frequency generation to transform ultrashort pulses into time-stretched replicas, achieving resolutions from ~165 fs down to below 10 fs with PHz bandwidths.
• Advanced dispersion engineering, including OPC-based cancellation of higher-order distortions, enables high signal-to-noise ratios, scalable throughput, and versatile applications in accelerator physics, nonlinear optics, and spectro-microscopy.

Photonic time-stretch fieldoscopy combines ultrafast field-resolved optical measurement with dispersive waveform stretching, enabling single-shot acquisition of broadband electric field transients with ultrahigh temporal resolution. By coupling electro-optic sampling or nonlinear fieldoscopy with precise dispersion engineering and time-lens techniques, this approach transforms femtosecond–attosecond field events into time-stretched waveforms accessible to GHz–THz electronics. This field has evolved from relativistic THz electron bunch diagnostics to near-petahertz (PHz) single-shot field mapping, opening access to dynamic, non-repetitive ultrafast phenomena in accelerator physics, nonlinear optics, condensed matter, and spectro-microscopy.

1. Physical Principles and Theoretical Framework

Photonic time-stretch fieldoscopy (PTF) exploits group-velocity dispersion (GVD) and temporal quadratic phase modulation (the “time lens”) to map ultrafast temporal variations of an optical field into a scaled, slow replica, suitable for real-time digitization. The fundamental group-delay mapping in a dispersive medium is

$t(\omega) = t_0 + \beta_2 L (\omega - \omega_0)$

where $\beta_2$ is the GVD parameter and $L$ the path length. Dispersion linearly stretches an input temporal bandwidth $\Delta \omega$ into temporal aperture $\Delta t \approx |\beta_2| L \Delta \omega$, enabling single-shot access to previously inaccessible timescales (Gommel et al., 3 Dec 2025).

A time lens imposes a quadratic phase $\phi(t) = \frac{1}{2} K t^2$, allowing the temporal equivalent of imaging. Temporal imaging requires

$\frac{1}{D_s} + \frac{1}{D_f} = K$

where $D_s$ and $D_f$ are GDDs before and after the lens ($K$ the time-lens chirp rate). For chirp-free scaling, the telescopic (afocal) two-lens condition is $D_\text{int} = D_f + D_f'$, yielding pure temporal magnification/compression with zero net quadratic chirp (Srivastava et al., 2023).

2. Experimental Architectures and Implementations

(a) Relativistic Beams: Electro-Optic Time-Stretch Fieldoscopy

Bielawski et al. implemented fieldoscopy of relativistic electron bunches by combining a 1030 nm Yb fiber laser, synchronized pulse stitching, 5 mm GaP crystal for electro-optic sampling, and dual-stage fiber dispersion (Treacy compressor plus 2 km single-mode fiber). The time-stretch factor was $M = 1 + D_2/D_1 = 75.8$, yielding an oscilloscope-to-field mapping of 1 ns $\leftrightarrow$ 13.2 ps (Bielawski et al., 2019).

Key implementation details:

• Balanced InGaAs photodetection (20 GHz), LeCroy oscilloscope (30 GHz, 80 Gs/s).
• Bandwidth limited to 380 GHz at the field.
• Effective per-shot time resolution $\sim$ 165 fs at the field, with analog bandwidth corresponding to 5–10 % modulation detectability up to 380 GHz.

(b) Near-Petahertz Bandwidth: Nonlinear Time-Lens Fieldoscopy

Recent work demonstrated PTF using a time-lens-enabled nonlinear sum-frequency generation (SFG) imaging chain, stretching single-cycle electric fields into the picosecond regime. A signal and pump pulse, individually dispersed by $D_s$ and $D_f$ (chosen for $D_s = -D_f$), interact in a $\chi^{(2)}$ crystal, mapping the signal field's ultrafast envelope into a time-stretched SFG that is directly proportional to the field (Gommel et al., 3 Dec 2025). Balanced GHz photodetection or angularly dispersed CMOS sensor readout enables field retrieval.

Detection bandwidths up to $\sim$1 PHz and attosecond-scale time resolution are achievable, contingent on multi-octave chirped pulses and matching dispersive optics.

3. Dispersion Engineering and Aberration Management

PTF system linearity and bandwidth are bounded by higher-order dispersion and aberrations. Traditional DCF or CFBG-based stretchers suffer from 2–5 % third-order (cubic) dispersion distortions over tens of nm. Optical phase conjugation (OPC) schemes leveraging cascaded SMF and DCF (with $\beta_2$, $\beta_3$ coefficients engineered to cancel cubic terms) can achieve pure quadratic GDD:

• $\pm 3400$ ps$^2$ GDD, $D_3 \simeq 0$ over 30 nm, residual nonlinearity $<0.1$ %, $>98$ % aberration removal (Chen et al., 2019).
• Single-shot record of 15,000 resolvable points (2 pm resolution, 30 nm band).

Key formulae for performance: $$N = \frac{\Delta \lambda}{\delta \lambda} \quad \text{with} \quad \delta\lambda \sim \text{2 pm (OPC-corrected)}$$ Linear group-delay mapping is $\kappa = d\tau/d\lambda \approx 2.67$ns/nm.

4. System Performance Characteristics

PTF enables sub-picosecond (down to attosecond) time resolution, with scalable record lengths and frame rates determined by repetition rate, dispersion, and detector bandwidth. Selected performance characteristics:

Architecture	Temporal Res.	Bandwidth at Field	Throughput
THz EOS (Bielawski et al., 2019)	0.9 ps	380 GHz	2.7 MHz (per revolution)
Nonlinear PTF (Gommel et al., 3 Dec 2025)	<10 fs	500 THz–1 PHz	Single-shot; attosecond
OPC-corrected (Chen et al., 2019)	5 ps (2 pm)	30 nm ($>4$ THz)	Up to 20 MHz

Signal-to-noise ratio (SNR) $>10$ up to 380 GHz in THz EOS (Bielawski et al., 2019), $>40$ dB demonstrated for balanced nonlinear detection, dynamic range $>60$ dB is plausible in shot-noise–limited regimes (Gommel et al., 3 Dec 2025).

5. Applications: Ultrafast Dynamics, Imaging, and Spectro-Microscopy

PTF is employed for non-destructive characterization of electron bunch microstructure and microbunching instabilities in storage rings, with MHz single-shot profiles resolving high-frequency modulations and direct correlation with coherent synchrotron radiation (CSR) emission (Bielawski et al., 2019). In time-lens fieldoscopy, petahertz electronics, real-time field mapping of sub-cycle molecular dynamics, and label-free spectro-microscopy of liquids and solids become accessible (Gommel et al., 3 Dec 2025).

Generalizations include:

• 2D and 3D imaging architectures using spectro-temporal encoding or multimode fiber random speckle projection, enabling widefield compressive field mapping at MHz–GHz frame rates (Wang et al., 2018, Jalali et al., 2011).
• Adaptations for fieldoscopy using continuous-wave (CW) diode laser sources to simplify synchronization and reduce system cost, with typical spatial resolutions of $5$–$10\,\mu\text{m}$ at tens–hundreds of MHz line-scan rates (Zhou et al., 2023).

6. Advanced Architectures: Time Lenses and Chirp-Free Scaling

A single time lens induces residual quadratic phase, which distorts amplitude/phase mapping in fieldoscopy. The “time telescope”/afocal two-time-lens configuration achieves chirp-free temporal imaging, described by: $$D_\text{int} = D_f + D_f', \quad M = -\frac{D_f'}{D_f}, \quad A_\text{out}(t) = \frac{1}{\sqrt{M}} A_\text{in}(t/M)$$ where $M$ is magnification, $D_f > 0$, $D_f' < 0$ for erecting (non-inverting) imaging (Srivastava et al., 2023). This structure is critical for faithful mapping of field transients, preserving both amplitude and phase, and is directly compatible with fieldoscopy of non-repetitive, causality-sensitive phenomena.

7. Outlook and Limitations

PTF at petahertz bandwidths faces challenges due to dispersion loss, limited stretchable pulse energy, and trade-offs between aperture, bandwidth, and SNR. OPC-based dispersion compensation, on-chip integration of time lenses, and angularly dispersed CMOS readout are proposed enhancements (Chen et al., 2019, Gommel et al., 3 Dec 2025). A further direction is leveraging machine learning for efficient compressive measurement and reconstruction (Wang et al., 2018).

PTF has demonstrated non-destructive, high-throughput, real-time measurement of ultrafast electric fields, enabling new studies in beam physics, quantum optics, and condensate dynamics. The methodology enables the systematic investigation of dynamic, rare, and irreversible field-driven processes, previously inaccessible to traditional field-averaged or scanning probe approaches.