An acousto-optic programmable dispersive filter (AOPDF) is a special type of collinear-beam

acousto-optic modulator An acousto-optic modulator (AOM), also called a Bragg cell or an acousto-optic deflector (AOD), uses the acousto-optic effect to diffract and shift the frequency of light using sound waves (usually at radio-frequency). They are used in lasers ...

capable of shaping spectral phase and amplitude of ultrashort laser pulses. AOPDF was invented by

Pierre Tournois Pierre is a masculine given name. It is a French form of the name Peter. Pierre originally meant "rock" or "stone" in French (derived from the Greek word πέτρος (''petros'') meaning "stone, rock", via Latin "petra"). It is a translation ...

. Typically,

quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical ...

crystals are used for the fabrication of the AOPDFs operating in the UV spectral domain, paratellurite crystals are used in the visible and the NIR (up to 4 µm) and calomel in the MIR (3-20 µm). Recently introduced

Lithium niobate Lithium niobate () is a non-naturally-occurring salt consisting of niobium, lithium, and oxygen. Its single crystals are an important material for optical waveguides, mobile phones, piezoelectric sensors, optical modulators and various other line ...

crystals allow for high-repetition rate operation (> 100 kHz) owing to their high acoustic velocity. The AOPDF is also used for the active control of the

carrier-envelope phase The carrier-envelope phase (CEP) or carrier-envelope offset (CEO) phase is an important feature of an ultrashort laser pulse and gains significance with decreasing pulse duration, in a regime where the pulse consists of a few wavelengths. Physica ...

of the few-cycle optical pulses and as a part of pulse-measurement schemes. Although sharing a lot in principle of operation with an ''

acousto-optic tunable filter Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound (or sound in general) through an ultrasonic grating. Introduction Optics has had a v ...

'', the AOPDF should not be confused with it, since in the former the tunable parameter is the

transfer function In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that theoretically models the system's output for each possible input. They are widely used ...

and in the latter it is the

impulse response In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (). More generally, an impulse response is the reac ...

Theory of operation

Traveling acoustic wave induces variations in optical properties thus forming a dynamic volume grating.

Pulse shaping

AOPDF is a programmable spectral filter. From

signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...

point of view, the AOPDF corresponds to a

time-variant A time-variant system is a system whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also change ...

passive linear transversal filter with a programmable

finite impulse response In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of ''finite'' duration, because it settles to zero in finite time. This is in contrast to infinite impulse ...

. Phase and amplitude filtering in the AOPDF is achieved by virtue of birefringent

acousto-optic effect Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound (or sound in general) through an ultrasonic grating. Introduction Optics has ...

and can be represented by a convolution between the amplitude of the input optical signal ''E''_in(t) and a programmable acoustical signal ''S''(t/α) proportional to the electrical signal ''S''(t) applied to the Piezoelectric transducer (made typically from

lithium niobate Lithium niobate () is a non-naturally-occurring salt consisting of niobium, lithium, and oxygen. Its single crystals are an important material for optical waveguides, mobile phones, piezoelectric sensors, optical modulators and various other line ...

). Here, α is a scaling factor equal to the ratio of the speed of sound ''v'' to the speed of light ''c'' times the index difference Δ''n'' between the ordinary and the extraordinary waves taken along the propagation axis in the crystal. In the limit of low diffraction efficiency the AOPDF behaves as a linear filter and the small value of the α (typically 10⁻⁷) allows for the quantitative control of optical signals with frequencies of tens to hundreds of terahertz with electrical signals of tens of megahertz, which are readily produced by commercial waveform generators.

Polarization

Owing to its birefringent nature, the AOPDF is intrinsically polarization-sensitive. Furthermore, polarization of the diffracted wave, created as the result of the interaction between the incident optical wave and the acoustic wave in the crystal, is rotated by 90° with respect to the incident wave polarization. For the single-beam optical input there could be up to 4 beams at the output of the AOPDF: two transmitted (non-diffracted) beams arising from

double refraction Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefringe ...

and (in the presence of a suitable acoustic wave in the crystal) two diffracted beams corresponding to each linear polarization component (ordinary and extraordinary) of the input beam. Typically, an ordinary-polarized beam is used at the input and so, only two beams are observed at the output: an ordinary-polarized transmitted beam and an extraordinary-polarized diffracted beam.

Diffraction efficiency

Spectral intensity of the diffracted wave depends on the spectral intensity of the acoustic wave (which depends, in turn, on the RF power applied to the transducer). Ratio between the diffracted intensity and the input one represents the diffraction efficiency. Maximum diffraction efficiency is limited by nonlinear effects. Linear regime persists up to diffraction efficiencies of about 50% . Total efficiency is altered by Fresnel losses at the input and output faces of the crystal unless

anti-reflection coating An antireflective, antiglare or anti-reflection (AR) coating is a type of optical coating applied to the surface of lenses, other optical elements, and photovoltaic cells to reduce reflection. In typical imaging systems, this improves the eff ...

is used.

Spectral bandwidth

Spectral bandwidth of the AOPDF is defined as a range over which the device can operate. One can distinguish intrinsic bandwidth, which is limited by absorption of the acousto-optic crystal, total device bandwidth, limited by impedance matching between the piezoelectric transducer and the radio-frequency generator, and instantaneous bandwidth defined by maximal simultaneous spectral width diffracted with reasonable efficiency.

References