Applications for Holographic Gratings

Wavelength Tuning of Lasers

Holographic gratings are often used for wavelength tuning of lasers. The grating acts as a wavelength selective end mirror inside the laser cavity. There are two basic configurations used, Littrow configuration and Grazing incidence or Littman configuration.

Littrow configuration

The grating is mounted so that light of the desired wavelength is diffracted back along the incident beam, and the wavelength is scanned by rotating the grating. Generally, an intracavity achromatic lens is used, which expands the laser beam to fill a relatively large area of the grating. The zero order diffracted beam can be used as the output laser beam; however, a disadvantage is that the beam will have different directions as the grating is rotated.

Grazing incidence Littman configuration

Fig. 15. Grazing incidence configuration for dye laser tuning.

This configuration is shown schematically in fig.15. The grating is kept fixed at an angle of incidence near 90 degrees, and the wavelength is tuned by rotating a special tuning mirror. No beam expanding lens is needed, and therefore a smaller grating can be used. The large incidence angle implies, however, that the ruled width of the grating has to be considerably greater than the groove length.

The efficiency in grazing incidence may be very high for light polarized perpendicularly to the grating grooves (TM polarization), but is always very low for TE polarization. The dye laser beam will therefore be plane polarized.

Laser Pulse Compression

When a short laser pulse is transmitted through an optical fibre, the pulse will be stretched, or "chirped" due to nonlinear effects (selfphase modulation).The group velocity dispersion in the fibre results in that the front of the pulse will have a longer wavelength than the tall. By using a pair of gratings one can arrange so that the long wave length pulse will 11 travel a longer path than the short wavelength pulse, with the result that, after the grating pair, they arrive at the same time. The grating pair not only compensates for the pulse broadening in the fibre, but makes the pulse even shorter than the input. Up to 90 times compression can be achieved.

Chirped pulse amplification

Very short pulses (100 femtoseconds) can be produced by some types of mode locked lasers. For many applications, these pulses have too low peak power. The technique of chirped pulse amplification (CPA) can be used for amplifying such pulses, to achieve peak powers in the order of Terawatts.

The amplifier is basically a laser crystal inside a resonator. To avoid strong nonlinear effects which would destroy the crystal, the input pulse is stretched in time, so that the peak power is decreased. This chirped pulse is then amplified, and subsequently compressed to obtain a high power pulse with a duration nearly equal to the input pulse.

Fig. 16. Grating pair pulse compressor

Stretching and compression

Both stretching and compressing utilize grating pairs, arranged in subtractive dispersive mode; so that the angular dispersion of the first grating is cancelled by the second grating. Two parallel beams of different wavelengths, incident on the first grating, are still parallel when they leave the second grating, but they have travelled different distances.

A grating pair arranged parallel as in fig.16, will introduce a negative group velocity dispersion, i.e. pulses of long wavelength arrive later than short wave pulses.

Fig. 17. Pulse stretcher

In order to achieve a positive dispersive delay, a more complicated arrangement is necessary. Fig. 17 shows such an arrangement, normally used in the stretcher stage. An afocal lens system (telescope) is inserted between the gratings. The telescope reverses the sign of the angles so that the beams will hit the second grating at the same angle as they leave the first one.

Both stretcher and compressor are normally used in double pass. The advantages are twofold: the dispersion is doubled, and all wavelength components of the beam emerge colinear, not linearly translated as shown in the figure for single pass.

Spectroscopic Instruments

A spectroscopic instrument consists generally of an entrance slit, a collimator, a dispersive element, focusing optics, and sometimes an exit slit. Radiation entering the entrance slit is collected by the collimator, generally a concave mirror.

Fig. 12. Optical layout for three monochromators.

The dispersive element, in this case a grating, deviates the radiation in a direction which depends on the wavelength. The dispersed radiation is focused onto the image plane, where a spectrum (a series of monochromatic images of the entrance slit) is formed.

Monochromators

In a monochromator there is an exit slit, which transmits a narrow portion of the spectrum. The entrance and exit slits are fixed, and the spectrum is scanned by rotating the grating. The grating thus works with a constant angular deviation between the incident and diffracted light. This is true for most types of monochromators, such as the Czerny-Turner, Ebert and Littrow types, see fig. 12.

Fibre Optics

Holographic gratings are well suited for fibre optics applications. By using high frequency gratings, high efficiency can be achieved, and high angular dispersion makes it possible to design small compact instruments. The following example gives a brief description on the preliminary design of a fibre optic demultiplexer.

Fig. 18. Optical layout of a wavelength division demultiplexer.

Example:

Suppose we want to design a grating based wavelength division multiplexer/ demultiplexer (WDM) for wavelengths around 1.3 microns. The channels are separated 10 nm in wavelength, and the different channels should be collected by separate fibres, arranged in an array at the output side of the instrument. We assume that the center to center distance of two consecutive fibres in the array is 0.5 mm.

We choose a grating with 1200 gr/mm, and a mounting where the entrance fibre and exit fibres are well separated by, say, 30 degrees. From equation (6)

we calculate the angle of incidence and diffraction for1.3 microns to 38.9 and 68.9 degrees, respectively.

The inverse linear dispersion should be:

In order to give the desired dispersion, the focal length of the instrument should be:

Raman Spectroscopy and Laser Scattering Experiments

The necessary high resolution is achieved by using large instruments with long focal lengths, where all optical surfaces are of the highest quality. When working very close to a strong spectral line, aberrations of the optical system, and Fraunhofer diffraction from aperture stops may yield considerable stray light. Spectrogon low stray light gratings are manufactured on high optical quality substrates and such a grating will have practically no influence on the optical aberrations. Double or triple spectrometers are frequently used in order to reduce the stray light. Holographic gratings are necessary, since even the best ruled gratings give rise to ghosts, which are orders of magnitude stronger than the spectral peaks to be detected.

It is a simple matter to estimate the stray light level for a given instrument, using stray light curves, as presented in fig. 5. For example, in a 1 meter monochromator with a 10 micron wide and 10 mm high slit, grating C would compared to the incident light yield a stray light level of:

2x10^-4x0.010x10/(1000x1000)=2x10 ^-11 compared to the incident light.

Absorption Spectroscopy

Fig. 14. Stray light in a spectrometer

Absorption spectroscopy is another application where the low stray light of holographic gratings is of great advantage. The stray light level is directly related to the absorbance range of the instrument, the smaller amount of stray light present, the higher absorbance values can be measured.

The light source in absorption spectroscopy is generally a broad band source, and the stray light will therefore consist of a continuum of wavelengths. Each wavelength component of the incident light gives rise to stray light, distributed in a similar way as shown in fig. 5, but centered around the actual wavelength.

The resulting stray light is the sum of all wavelength components, as visualized in fig.14.

A rough estimate of the stray light levels can be obtained from stray light curves such as those in fig. 5, and calculations similar to the following:

1. Consider a monochromator with 250 mm focal length, equipped with the ruled 1200 gr/mm grating of fig.5. Suppose we use a slit which transmits a 1 nm wavelength band. The slit width should then be:
   
   
   
2. A normal slit height would be 10 mm, and the solid angle subtended by the slit is then:
   10x0.3/250² = 4.8x10^-5 steradians.
   
3. For monochromatic illumination (at 633 nm) the stray light transmitted by the slit would be about: 10^-1x4.8x10^-5= 4.8x10^-6 over most of the wavelength interval 400700 nm as seen in fig. 5. For white light illumination in this 300 nm wide interval, we would expect the stray light to be roughly 300 times greater, or about 0.001. So in a spectrometer working under these conditions, we cannot expect to be able to measure a transmittance smaller than 0.001, i.e. an absorbance greater than 3.