Photoelastic modulator
Encyclopedia
A photoelastic modulator (PEM) is an optical device used to modulate the polarization of a light source. The photoelastic effect is used to change the birefringence
of the optical element in the photoelastic modulator.
PEM was first invented by J. Badoz in the 1960s and originally called a "birefringence modulator." It was initially developed for physical measurements including optical rotary dispersion and Faraday rotation, polarimetry
of astronomical objects, strain-induced birefringence, and ellipsometry
. Later developers of the photoelastic modulator include J.C Kemp, S.N Jasperson and S.E Schnatterly.
modulation results in highly sensitive polarization measurements. The fundamental vibration of the optic is along its longest dimension.
proportional to the resulting strain. Photoelastic modulators are resonant devices where the precise oscillation frequency
is determined by the properties of the optical element/transducer assembly. The transducer is tuned to the resonance frequency of the optical element along its long dimension, determined by its length and the speed of sound in the material. A current is then sent through the transducer to vibrate the optical element through stretching and compressing which changes the birefringence of the transparent material. Because of this resonant character, the birefringence of the optical element can be modulated to large amplitudes, but also by the same reason, the operation of a PEM is limited to a single frequency, and most commercial devices manufactured today operate at about 50 kHz
where A is the amplitude of the modulation.
Linearly polarized, monochromatic light impinging at 45 degrees to the optical axis can be though of as the sum of two components, one parallel and one perpendicular to the optical axis of the PEM. The birefringence introduced in the plate will retard one of these components more than the other, that is the PEM acts as a tunable wave plate
. Typically it is adjusted to be either a quarter wave or half wave plate at the peak of the oscillation.
For the quarter wave plate case, the amplitude of oscillation is adjusted so that at the given wavelength one component is alternately retarded and advanced 90 degrees relative to the other, so that the exiting light is alternately right-hand and left-hand circularly polarized at the peaks.
A reference signal is taken from the modulator oscillator and is used to drive a phase-sensitive detector
, the demodulator.
The amplitude of oscillation is adjusted by an external applied voltage that is proportional to the wavelength of the light passing through the modulator.
PEM polarimetry has the advantage that the signal is modulated at a high frequency (and often detected with a lock-in amplifier
), excluding many sources of noise not at the PEM operating frequency and attenuating the white noise by the bandwidth of the lock-in amplifier.
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
of the optical element in the photoelastic modulator.
PEM was first invented by J. Badoz in the 1960s and originally called a "birefringence modulator." It was initially developed for physical measurements including optical rotary dispersion and Faraday rotation, polarimetry
Polarimetry
Polarimetry is the measurement and interpretation of the polarization of transverse waves, most notably electromagnetic waves, such as radio or light waves...
of astronomical objects, strain-induced birefringence, and ellipsometry
Ellipsometry
Ellipsometry is an optical technique for the investigation of the dielectric properties of thin films....
. Later developers of the photoelastic modulator include J.C Kemp, S.N Jasperson and S.E Schnatterly.
Description
The basic design of a photoelastic modulator consists of a piezoelectric transducer and a half wave resonant bar; the bar being a transparent material (now most commonly fused silica). The transducer is tuned to the natural frequency of the bar. This resonanceResonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
modulation results in highly sensitive polarization measurements. The fundamental vibration of the optic is along its longest dimension.
Basic principles
The principle of operation of photoelastic modulators is based on the photoelastic effect, in which a mechanically stressed sample exhibits birefringenceBirefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
proportional to the resulting strain. Photoelastic modulators are resonant devices where the precise oscillation frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
is determined by the properties of the optical element/transducer assembly. The transducer is tuned to the resonance frequency of the optical element along its long dimension, determined by its length and the speed of sound in the material. A current is then sent through the transducer to vibrate the optical element through stretching and compressing which changes the birefringence of the transparent material. Because of this resonant character, the birefringence of the optical element can be modulated to large amplitudes, but also by the same reason, the operation of a PEM is limited to a single frequency, and most commercial devices manufactured today operate at about 50 kHz
Polarization modulation of a light source
This is the most basic application and function of a PEM. In a typical setup, where original light source is linearly polarized at 45 degrees from the optical axis of the PEM, the resulting polarization of light is modulated at the PEM operating frequency f, and for a sinosuidal modulating signal, it can be expressed in Jones matrix formalism as:
where A is the amplitude of the modulation.
Linearly polarized, monochromatic light impinging at 45 degrees to the optical axis can be though of as the sum of two components, one parallel and one perpendicular to the optical axis of the PEM. The birefringence introduced in the plate will retard one of these components more than the other, that is the PEM acts as a tunable wave plate
Wave plate
A wave plate or retarder is an optical device that alters the polarization state of a light wave travelling through it.- Operation :A wave plate works by shifting the phase between two perpendicular polarization components of the light wave. A typical wave plate is simply a birefringent crystal...
. Typically it is adjusted to be either a quarter wave or half wave plate at the peak of the oscillation.
For the quarter wave plate case, the amplitude of oscillation is adjusted so that at the given wavelength one component is alternately retarded and advanced 90 degrees relative to the other, so that the exiting light is alternately right-hand and left-hand circularly polarized at the peaks.
A reference signal is taken from the modulator oscillator and is used to drive a phase-sensitive detector
Lock-in amplifier
A lock-in amplifier is a type of amplifier that can extract a signal with a known carrier wave from an extremely noisy environment . It is essentially a homodyne with an extremely low pass filter...
, the demodulator.
The amplitude of oscillation is adjusted by an external applied voltage that is proportional to the wavelength of the light passing through the modulator.
Polarimetry
A typical polarimetric setup consists of two linear polarizers forming a crossed analyzer setup, an optical sample introducing the change in the polarization of light, and a PEM further modulating the polarization state. The final detected intensities at the fundamental and second harmonic of PEM operating frequency depend on the ellipticity and rotation introduced by the sample.PEM polarimetry has the advantage that the signal is modulated at a high frequency (and often detected with a lock-in amplifier
Lock-in amplifier
A lock-in amplifier is a type of amplifier that can extract a signal with a known carrier wave from an extremely noisy environment . It is essentially a homodyne with an extremely low pass filter...
), excluding many sources of noise not at the PEM operating frequency and attenuating the white noise by the bandwidth of the lock-in amplifier.
See also
- PhotoelasticityPhotoelasticityPhotoelasticity is an experimental method to determine the stress distribution in a material. The method is mostly used in cases where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress...
- Circular dichroismCircular dichroismCircular dichroism refers to the differential absorption of left and right circularly polarized light. This phenomenon was discovered by Jean-Baptiste Biot, Augustin Fresnel, and Aimé Cotton in the first half of the 19th century. It is exhibited in the absorption bands of optically active chiral...
- phase modulator for ellipsometry