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CritPt / Challenge_4_main / High-harmonic generation (HHG) is a nonlinear optical process in which intense…

Problem

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problem description

# Problem setup: High-harmonic generation (HHG) is a nonlinear optical process in which intense laser fields interact with gas-phase atoms or molecules to produce coherent extreme ultraviolet (EUV) radiation. In this setup, a sequence of time-delayed laser pulses are focused into a gas jet to investigate the role of structured light in controlling the HHG process. # Main problem: I create a driving field composed of three temporally identical laser pulses of 800 nm center wavelength, 50 fs FWHM pulse duration, with the peaks of the pulses at t = 0 fs, t = 30 fs, and t = 60 fs, respectively. The first pulse is left circularly polarized and carries an orbital angular momentum (OAM) of ℓ=−1\ell = -1, the second pulse is right circularly polarized and has OAM ℓ=2\ell = 2, and the third pulse is left circularly polarized and has OAM ℓ=1\ell = 1. The pulses are focused, overlapped in space, into a gas jet, and used to drive high-harmonic generation to produce EUV light. Calculate the OAM of the 23rd harmonic order and give the associated helicity σ\sigma (±1\pm 1).
Plain-text mathematical notation (without MathML)

# Problem setup:
High-harmonic generation (HHG) is a nonlinear optical process in which intense laser fields interact with gas-phase atoms or molecules to produce coherent extreme ultraviolet (EUV) radiation. In this setup, a sequence of time-delayed laser pulses are focused into a gas jet to investigate the role of structured light in controlling the HHG process.

# Main problem:

I create a driving field composed of three temporally identical laser pulses of 800 nm center wavelength, 50 fs FWHM pulse duration, with the peaks of the pulses at t = 0 fs, t = 30 fs, and t = 60 fs, respectively. The first pulse is left circularly polarized and carries an orbital angular momentum (OAM) of  ℓ=−1, the second pulse is right circularly polarized and has OAM ℓ=2, and the third pulse is left circularly polarized and has OAM ℓ=1. The pulses are focused, overlapped in space, into a gas jet, and used to drive high-harmonic generation to produce EUV light. Calculate the OAM of the 23rd harmonic order and give the associated helicity σ (±1).
Original LaTeX notation

# Problem setup:
High-harmonic generation (HHG) is a nonlinear optical process in which intense laser fields interact with gas-phase atoms or molecules to produce coherent extreme ultraviolet (EUV) radiation. In this setup, a sequence of time-delayed laser pulses are focused into a gas jet to investigate the role of structured light in controlling the HHG process.

# Main problem:

I create a driving field composed of three temporally identical laser pulses of 800 nm center wavelength, 50 fs FWHM pulse duration, with the peaks of the pulses at t = 0 fs, t = 30 fs, and t = 60 fs, respectively. The first pulse is left circularly polarized and carries an orbital angular momentum (OAM) of  $\ell = -1$, the second pulse is right circularly polarized and has OAM $\ell = 2$, and the third pulse is left circularly polarized and has OAM $\ell = 1$. The pulses are focused, overlapped in space, into a gas jet, and used to drive high-harmonic generation to produce EUV light. Calculate the OAM of the 23rd harmonic order and give the associated helicity $\sigma$ ($\pm 1$).

code template

Code

def answer():
    r"""
    Return the OAM and helicity of the 23rd harmonic order.

    Inputs
    ----------
    None

    Outputs
    ----------
    harmonic_23 : set[tuples[int, int]]
        A set of allowed combinations of OAM and helicity for the 23rd harmonic order, ($\ell$, $\sigma$).
    """

    # ------------------ FILL IN YOUR RESULTS BELOW ------------------
    harmonic_23 = ...
    # ---------------------------------------------------------------

    return harmonic_23

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Source and history

upstream_id / Original problem ID
Challenge_4_main
task_id
4c319585-7cdc-51d0-a3dd-0ff3dff68989
task_key
train--Challenge~5f4~5fmain
task_revision_id
4
config / split
/ train

Official source

initial import