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Controlled light and precision measurement

Apparatus · Observation · Inference

Chirped pulse amplification separates energy gain from peak power

Sandbox Physics ·

How did stretching a pulse make a shorter, more energetic output practical?

  1. Broadband seed pulse
  2. Stretch it with dispersion
  3. Amplify the energy
  4. Recompress and measure the pulse
Within its usable bandwidth, the compressor undoes the delay between frequencies. The added energy comes from the amplifier, not the compressor.

Peak power limited how far a pulse could be amplified

A short, energetic pulse crossing an amplifier can build up unwanted nonlinear phase and cause damage. Strickland and Mourou stretched the pulse in time, amplified it and then removed the chirp. The energy gain and the highest peak power therefore came at different stages.

The corrected 1985 paper reports millijoule-level pulses at 1.06 micrometres, 2 picoseconds long. Today’s petawatt systems came later. The University of Rochester’s institutional history cites the corrected paper and traces the work’s later influence.

Sources: [1][3][4]

Bright light changes the glass it crosses

In glass the refractive index rises slightly where light is bright. A bright beam therefore slows its own centre more than its edges, as a lens would, and focuses itself. Each instant of a pulse also picks up extra phase in proportion to its intensity. The frequency then shifts while the pulse passes and the spectrum spreads, which is called self-phase modulation.

Aitchison and colleagues saw both in 1991. They sent 100 fs pulses of 620 nm light into a planar glass guide 5 mm long, where the light could spread only sideways. Near one particular power, beams 22 µm wide left the guide about as narrow as they entered, held by the lens they made, and their spectrum broadened. In bulk glass the light can spread in every direction across the beam, and there the same balance is unstable: a beam above it collapses.

Both effects follow the peak power of the pulse, not its energy. At fixed energy and beam size, a pulse stretched a thousand times has a thousand times less peak power, so while it is amplified it picks up a thousand times less of this phase.

n=n0+n2In=n_0+n_2I

Sources: [6][7]

Stretching makes different frequencies arrive at different times

A pulse with enough bandwidth grows longer when its frequencies are given different group delays. For the original demonstration, Strickland describes broadening and stretching the pulse in a fibre, amplifying it in Nd:glass and compressing it with gratings. Modern CPA systems need not use the same stretcher. When the light frequency sweeps systematically across the pulse in time, the pulse is chirped.

For a Gaussian intensity envelope of fixed shape, the peak power is the pulse energy divided by the full width at half maximum of the intensity, times the factor in the formula below. At fixed energy, doubling the duration halves the peak power. The calculation is an illustration and is not fitted to the original apparatus.

Ppeak=2ln⁡2πEτFWHMP_{\mathrm{peak}}=\frac{2\sqrt{\ln2}}{\sqrt{\pi}}\frac{\mathcal E}{\tau_{\mathrm{FWHM}}}

Sources: [2][1]

Storing excitation is different from stretching a pulse

Another route to a strong burst is to keep a laser cavity lossy while the pump stores energy in excited particles. Reduce the loss, and stimulated emission rapidly drains that population into a pulse. This is Q-switching: the main reservoir before release is excited matter.

CPA starts with a pulse that already exists. It spreads that pulse’s frequencies in time so amplification can add energy at a lower peak intensity, then brings them back together. Storing excitation and stretching a pulse solve different parts of the high-power problem.

Sources: [5][2]

Compression has to correct the spectral phase

Amplification adds energy, and it can also favor some frequencies or shift where their oscillations sit within a cycle. Those shifts are the spectral phase. A compressor that corrects only one delay term may leave higher-order phase, wings in time or satellite pulses. A broad spectrum on its own therefore does not show that the pulse is short.

When the frequency components add in step over a brief interval, they form a short pulse. If their peaks arrive spread out in time, the same broad spectrum can describe a much longer pulse. A time-domain measurement must distinguish those possibilities. An intensity autocorrelation compares a pulse with a delayed copy; it gives a unique duration only with an assumed pulse shape or extra reconstruction information.

Sources: [2]

Stretching does not remove every limit

A stretched pulse still passes through real materials. Gain bandwidth limits the range of frequencies it amplifies well. Amplified spontaneous emission adds unwanted background and consumes gain. Intensity-dependent phase shifts distort the pulse, and optical damage also depends on energy per illuminated area, called fluence. The compressor loses some pulse energy as well.

Compression puts the high-intensity pulse at the end of the system, so the compressor and downstream optics must survive it. The 2018 prize recognized a method for generating intense ultrashort pulses. The first picosecond demonstration, later femtosecond systems and attosecond metrology were separate experimental steps.

Sources: [1][2]

Check both energy and duration at the output

A compression measurement needs both energy and duration at the output. The spectrum and spectral phase explain how the frequencies add up in time; a suitable time-domain measurement tests whether the short pulse actually appeared.

Sources: [2]

Sources and reading notes

We read the abstract and correction note of the corrected paper, a search-indexed passage from Strickland’s lecture and the University of Rochester’s attribution. The full lecture could not be accessed. The pulse-shape calculation here is a modern illustration, kept apart from the reported measurements.

  1. D. Strickland & G. Mourou, Compression of amplified chirped optical pulses, corrected version, Opt.Commun.56,219–221 (1985)

    We read the author abstract and the correction note: millijoule pulses, 2 ps, at 1.06 micrometres. This version corrects a figure printed wrongly in volume 55.

  2. D. Strickland, Generating High-Intensity Ultrashort Optical Pulses (2018), original CPA apparatus passage

    We read an indexed passage by the author: spectral broadening and stretching in fibre, amplification in Nd:glass and compression with gratings. The full lecture’s address returned HTTP 403.

  3. University of Rochester LLE, 1985 timeline

    We read the institution’s attribution and its reference to the corrected paper. Later petawatt operation is not credited to the 1985 demonstration.

  4. Royal Swedish Academy of Sciences, Physics Prize 2018: official award announcement

    We read the official announcement for the two separate contributions: Ashkin’s optical tweezers for biology and Strickland and Mourou’s method of generating pulses. Experimental details come from the original accounts cited.

  5. MIT 6.977, Chapter 4, §4.4: Active and Passive Q-Switching

    Read the storage law, fast-extraction invariant and absorber rate equations in §4.4. The article uses the mechanism, not a historical pulse measurement.

  6. J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel & P. W. E. Smith, Experimental observation of spatial soliton interactions, Opt. Lett. 16, 15–17 (1991)

    We read the full paper: 100 fs pulses at 620 nm in a 5 mm planar glass guide, 22 µm beams trapped near the soliton power, spectral broadening, and the instability of the same balance in bulk media.

  7. V. E. Zakharov & A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34, 62–69 (1972)

    We read the full paper: the intensity-dependent index, the nonlinear Schrödinger equation for a beam that spreads in one direction, its exact soliton solutions as self-made waveguide channels, and self-modulational instability.

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