A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Optical frequency combs provide equidistant frequency markers in the infrared, visible and ultraviolet, and can be used to link an unknown optical frequency to a radio or microwave frequency reference. Since their inception, frequency combs have triggered substantial advances in optical frequency metrology and precision measurements and in applications such as broadband laser-based gas sensing and molecular fingerprinting. Early work generated frequency combs by intra-cavity phase modulation; subsequently, frequency combs have been generated using the comb-like mode structure of mode-locked lasers, whose repetition rate and carrier envelope phase can be stabilized. Here we report a substantially different approach to comb generation, in which equally spaced frequency markers are produced by the interaction between a continuous-wave pump laser of a known frequency with the modes of a monolithic ultra-high-Q microresonator via the Kerr nonlinearity. The intrinsically broadband nature of parametric gain makes it possible to generate discrete comb modes over a 500-nm-wide span (approximately 70 THz) around 1,550 nm without relying on any external spectral broadening. Optical-heterodyne-based measurements reveal that cascaded parametric interactions give rise to an optical frequency comb, overcoming passive cavity dispersion. The uniformity of the mode spacing has been verified to within a relative experimental precision of 7.3 x 10(-18). In contrast to femtosecond mode-locked lasers, this work represents a step towards a monolithic optical frequency comb generator, allowing considerable reduction in size, complexity and power consumption. Moreover, the approach can operate at previously unattainable repetition rates, exceeding 100 GHz, which are useful in applications where access to individual comb modes is required, such as optical waveform synthesis, high capacity telecommunications or astrophysical spectrometer calibration.

Optical frequency comb generation from a monolithic microresonator

The series of precisely spaced, sharp spectral lines that form an optical frequency comb is enabling unprecedented measurement capabilities and new applications in a wide range of topics that include precision spectroscopy, atomic clocks, ultracold gases, and molecular fingerprinting. A new optical frequency comb generation principle has emerged that uses parametric frequency conversion in high resonance quality factor (Q) microresonators. This approach provides access to high repetition rates in the range of 10 to 1000 gigahertz through compact, chip-scale integration, permitting an increased number of comb applications, such as in astronomy, microwave photonics, or telecommunications. We review this emerging area and discuss opportunities that it presents for novel technologies as well as for fundamental science.

http://science.sciencemag.org/content/sci/332/6029/555.full.pdf

Microresonator-Based Optical Frequency Combs

Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

High-harmonic generation by focusing a femtosecond laser onto a gas is a well-known method of producing coherent extreme-ultraviolet (EUV) light. This nonlinear conversion process requires high pulse intensities, greater than 10(13) W cm(-2), which are not directly attainable using only the output power of a femtosecond oscillator. Chirped-pulse amplification enables the pulse intensity to exceed this threshold by incorporating several regenerative and/or multi-pass amplifier cavities in tandem. Intracavity pulse amplification (designed not to reduce the pulse repetition rate) also requires a long cavity. Here we demonstrate a method of high-harmonic generation that requires no extra cavities. This is achieved by exploiting the local field enhancement induced by resonant plasmons within a metallic nanostructure consisting of bow-tie-shaped gold elements on a sapphire substrate. In our experiment, the output beam emitted from a modest femtosecond oscillator (100-kW peak power, 1.3-nJ pulse energy and 10-fs pulse duration) is directly focused onto the nanostructure with a pulse intensity of only 10(11) W cm(-2). The enhancement factor exceeds 20 dB, which is sufficient to produce EUV wavelengths down to 47 nm by injection with an argon gas jet. The method could form the basis for constructing laptop-sized EUV light sources for advanced lithography and high-resolution imaging applications.

High-harmonic generation by resonant plasmon field enhancement

A novel type of Fourier-transform infrared spectrometer (FTIR) is demonstrated. It is based on two Ti:sapphire lasers emitting femtosecond pulse trains with slightly different repetition frequencies. Two mid-infrared beams-derived from those lasers by rectification in GaSe-are superimposed upon a detector to produce purely time-domain interferograms that encode the infrared spectrum. The advantages of this spectrometer compared with the common FTIR include ease of operation (no moving parts), speed of acquisition (100 micros demonstrated), and not-yet-shown collimated long-distance propagation, diffraction-limited microscopic probing, and electronically controllable chemometric factoring. Extending time-domain frequency-comb spectroscopy to lower (terahertz) or higher (visible, ultraviolet) frequencies should be feasible.

Time-domain mid-infrared frequency-comb spectrometer.

Since 1998, the interaction of precision spectroscopy and ultrafast laser science has led to several notable accomplishments. Femtosecond laser optical frequency 'combs' (evenly spaced spectral lines) have revolutionized the measurement of optical frequencies and enabled optical atomic clocks. The same comb techniques have been used to control the waveform of ultrafast laser pulses, which permitted the generation of single attosecond pulses, and have been used in a recently demonstrated 'oscilloscope' for light waves. Here we demonstrate intra-cavity high harmonic generation in the extreme ultraviolet, which promises to lead to another joint frontier of precision spectroscopy and ultrafast science. We have generated coherent extreme ultraviolet radiation at a repetition frequency of more than 100 MHz, a 1,000-fold improvement over previous experiments. At such a repetition rate, the mode spacing of the frequency comb, which is expected to survive the high harmonic generation process, is large enough for high resolution spectroscopy. Additionally, there may be many other applications of such a quasi-continuous compact and coherent extreme ultraviolet source, including extreme ultraviolet holography, microscopy, nanolithography and X-ray atomic clocks.

A frequency comb in the extreme ultraviolet

A femtosecond frequency comb provides a vast number of equidistantly spaced narrow band laser modes that can be simultaneously tuned and frequency calibrated with 15 digit accuracy Our Vernier spectrometer utilizes all of theses modes in a massively parallel manner to rapidly record both absorption and dispersion spectra with a sensitivity that is provided by a high finesse broadband optical resonator and a resolution that is only limited by the frequency comb line width while keeping the required setup simple

Frequency comb Vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra.

A new scheme for stabilizing the carrier-envelope (CE) phase of a few-cycle laser pulse train is demonstrated. Self-phase modulation and difference-frequency generation in a single periodically poled lithium niobate crystal that transmits the main laser beam allows CE phase locking directly in the usable output. The monolithic scheme obviates the need for splitting off a fraction of the laser output for CE phase control, coupling into microstructured fiber, and separation and recombination of spectral components. As a consequence, the output yields 6-fs, 800-nm pulses with an unprecedented degree of short- and long-term reproducibility of the electric field waveform.

http://www2.mpq.mpg.de/~ctg/Papers/Eigene/Fuji_Monolithic_CEP_stab_ol_30_332_(2005).pdf

Monolithic carrier-envelope phase-stabilization scheme

The remarkable precision of frequency-comb (FC) lasers is transferred to the extreme ultraviolet (XUV, wavelengths shorter than 100 nm), a frequency region previously not accessible to these devices. A frequency comb at XUV wavelengths near 51 nm is generated by amplification and coherent up-conversion of a pair of pulses originating from a near-infrared femtosecond FC laser. The phase coherence of the source in the XUV is demonstrated using helium atoms as a ruler and phase detector. Signals in the form of stable Ramsey-like fringes with high contrast are observed when the FC laser is scanned over P states of helium, from which the absolute transition frequency in the XUV can be extracted. This procedure yields a (4)He ionization energy at h×5 945 204 212(6)  MHz, improved by nearly an order of magnitude in accuracy, thus challenging QED calculations of this two-electron system.

/pdf/extreme-ultraviolet-frequency-comb-metrology-1z27l4rp70.pdf

Christoph Gohle

Papers

Time-domain mid-infrared frequency-comb spectrometer.

A frequency comb in the extreme ultraviolet

Frequency comb Vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra.

Monolithic carrier-envelope phase-stabilization scheme

Extreme Ultraviolet Frequency Comb Metrology