Efficiency Curve Key
Selection of a standard Optometrics diffraction grating requires consideration of a number of variables related to the grating's intended use. These are as follows:
DIFFRACTION EFFICIENCY: In general, ruled diffraction gratings have a higher efficiency than holographic diffraction gratings. Applications such as fluorescence excitation and other radiation induced reactions may require a ruled grating (see efficiency curves for comparison). As a rule of thumb, the first order efficiency of a ruled grating decreases by 50% at two thirds and three halves of the blaze wavelength.
BLAZE WAVELENGTH: Ruled diffraction gratings, due to their "sawtooth" groove profile, have a relatively sharp peak around their blaze wavelength while some holographic gratings have a flatter spectral response. Applications centered around a narrow wavelength range could benefit from a ruled grating blazed at that wavelength.
WAVELENGTH RANGE: The spectral range covered by a grating is dependent on the gratings groove spacing and is the same for ruled and holographic gratings with the same grating constant. The maximum wavelength that a grating can diffract is equal to two times the grating period, and this would be achieved when the incident and diffracted light were at ninety degrees to the grating normal.
STRAY LIGHT: For applications such as Raman spectroscopy, as well as many spectrograph, spectrophotometer, and monochromator designs where signal-to-noise is critical, the inherent low stray light of a holographic grating is an advantage.
RESOLVING POWER: There is no difference in resolving power for holographic and ruled diffraction gratings with identical groove spacing. Holographic gratings are, however, available with up to 3600 grooves per mm while Optometrics does not normally rule gratings with more than 1200 grooves per mm.
In the late 1940's, White and Frazer developed the process for precision replication, allowing numerous "replica" gratings to be produced from a single master, either ruled or holographic. It is a procedure that results in the transfer of the three dimensional topography of a master grating to another substrate, allowing reproduction of a master in full relief to extremely close tolerances. This process led to the commercialization of gratings and has resulted in the current widespread use of gratings in spectrometers.
Unless otherwise specified, rectangular gratings are cut with grooves parallel to the short dimension.
A diffraction grating consists of a series of equally spaced parallel grooves formed in a reflective coating deposited on a suitable substrate. The distance between adjacent grooves and the angle the grooves form with respect to the substrate influence both the dispersion and efficiency of a grating. If the wavelength of the incident radiation is much larger than the groove spacing, diffraction will not occur. If the wavelength is much smaller than the groove spacing, the facets of the groove will act as mirrors and, again, no diffraction will take place.
The way in which the grooves are formed separates gratings into two basic types, holographic and ruled. Physically forming grooves into a reflective surface with a diamond mounted on a "ruling engine" produces ruled gratings. Gratings produced from laser constructed interference patterns and a photolithographic process are known as interference or holographic gratings.
Optometrics is one of the few companies that produces both types of master gratings in-house and has full replication facilities and expertise. Ruled and holographic gratings differ in their optical characteristics and each type has advantages for specific applications.
The general grating equation is usually written as: nλ = d(sin i + sin i) where n is the order of diffraction, λ is the diffracted wavelength, d is the grating constant
(the distance between successive grooves), i is the angle of incidence measured from the normal and i' is the angle of diffraction measured from the normal.
For a specific diffracted order (n) and angle of incidence (i), different wavelengths (λ) will have different diffraction angles (i'), separating polychromatic radiation incident on the grating into its constituent wavelengths.
The initial steps in ruling an original or master grating includes the selection of an appropriate substrate, usually glass or copper, polishing the substrate to a high degree of flatness, and coating it with a thin layer of aluminum by vacuum deposition. The ruling of parallel, equally spaced grooves is a slow process that can require several days of set-up and testing prior to the actual ruling. The ruling engine must be able to retrace the exact path of the diamond forming tool on each stroke and to index (advance) the substrate a predetermined amount after each cut. Both groove parallelism and displacement must be controlled with great precision. A series of "test" rulings are made and the grating is checked for efficiency, groove profile and stray light. After each test, a minor mechanical adjustment may have to be made. It can take a week or more of repeated testing to optimize the groove profile for specific optical characteristics. After exhaustive testing, an original grating is ruled on a large substrate. An original grating is obviously very expensive and, consequently, gratings saw only limited use until after the development of the replication process.
Like a ruled grating, the first step in the production of a holographic grating is the selection of an appropriate polished substrate. The substrate for a holographic grating is, however, coated with a photosensitive (photoresist) material rather than the reflective coating used in ruled gratings. The photoresist is exposed by positioning the coated blank between the intersecting beams of monochromatic and coherent light produced by a laser. The intersecting laser beams generate a series of parallel, equally spaced interference fringes whose intensities vary in a sinusoidal pattern. This fringe pattern exposes the resist differentially. Since the solubility of the resist is dependent on its exposure to light, the development process transfers the varying intensities of the interference fringes to the surface of the resist. The substrate is then coated with a reflective material and can be used as is, or replicated by the same process used for ruled originals.
Since holographic gratings are produced optically, groove form and spacing are perfectly consistent. Holographic gratings are, therefore, free from the periodic and random spacing errors responsible for ghosts and stray light in ruled gratings. The result is that holographic gratings generate much less stray light than ruled gratings.
Diffraction grating efficiency is primarily a function of groove shape, angle of incidence, and the reflectance of the coating.
The absolute efficiency of a grating is the percentage of incident monochromatic radiation that is diffracted into the desired order. In contrast, relative efficiency compares the energy diffracted into the desired order with that of a plane mirror coated with the same material as the grating. When comparing grating performance curves, it is important to keep this in mind. A relative efficiency curve will always show higher values than an absolute efficiency curve for the same grating. The efficiency curves in this brochure present absolute efficiency data.
Angle of incidence plays a role in grating performance. Because of the infinite number of configurations that a grating can be used in, a standard geometry is used in the measurement of the gratings. This is the Littrow (or autocollimation) mounting. In this mounting configuration, the diffracted order and wavelength of interest is directed back along the path of the incident light (i=i). The blaze angle of a ruled grating is calculated based on this mounting. This mounting is practical and necessary for laser tuning applications, but most applications will require some deviation between the incident and diffracted beams. Small deviations from the Littrow mounting seldom have an appreciable effect on grating performance other than to limit the maximum wavelength achievable. Unless otherwise stated, all performance curves in this brochure present blazed first order Littrow data.
The grooves of a ruled grating have a sawtooth profile with one side longer than the other. The angle made by a grooves longer side and the plane of the grating is the "blaze angle". Changing the blaze angle concentrates diffracted radiation to a specific region of the spectrum, increasing the efficiency of the grating in that region. The wavelength at which maximum efficiency occurs is the "blaze wavelength."
Holographic diffraction gratings are generally less efficient than ruled gratings because they cannot be blazed in the classical sense. Their sinusoidal shape can, in some instances, be altered to approach the efficiency of a ruled grating. There are also special cases that should be noted, i.e. when the spacing to wavelength ratio is near one, a sinusoidal grating has virtually the same efficiency as a ruled grating. A holographic grating with 1800 g/mm can have the same efficiency at 500 nm as a blazed, ruled grating. In addition, a special process enables Optometrics holographic gratings to achieve a true sawtooth profile peaked at 250 nm, an ideal configuration for UV applications requiring good efficiency with low stray light.
The resolving power of a grating is the product of the diffracted order in which it is used and the number of grooves intercepted by the incident radiation. It can also be expressed in terms of grating width, groove spacing and diffracted angles. The theoretical resolving power of a diffraction grating with N grooves is:
The actual resolving power of a grating depends on the accuracy of the ruling, with 80-90% of theoretical being typical of a high quality ruling.
Resolving power is a property of the grating and is not, like resolution, dependent on the optical and mechanical characteristics of the system in which it is used.
The resolution of an optical system (spectrograph, spectrophotometer, monochromator, etc.), is usually determined by examination of closely spaced absorption or emission lines for adherence to the Raleigh criteria (R = λ/Δλ), depends not only on the grating resolving power but on focal length, slit size, f number, the optical quality of all components and system alignment. The resolution of an optical system is usually much less than the resolving power of the grating.
Angular dispersion of a diffraction grating is a product of the angle of incidence and groove spacing. Angular dispersion can be increased by increasing the angle of incidence or by decreasing the distance between successive grooves. A grating with a large angular dispersion can produce good resolution in a compact optical system.
Angular dispersion is the slope of the curve given by λ = f(i). In autocollimation, the equation for dispersion is given by:
This formula may be used to determine the angular separation of two spectral lines or the bandwidth that will be passed by a slit subtending a given angle at the grating.
For a given set of angles (i,i´) and groove spacing, the grating equation is valid at more than one wavelength, giving rise to several orders of diffracted radiation. The reinforcement (constructive interference) of diffracted radiation from adjacent grooves occurs when a ray is in phase but retarded by a whole integer. The number of orders produced is limited by the groove spacing and the angle of incidence, which obviously cannot exceed 90 degrees. At higher orders, efficiency and free spectral range decrease while angular dispersion increases. Order overlap can be compensated for by the judicious use of sources, detectors and filters and is not a major problem in gratings used in low orders.
Free spectral range is the maximum spectral bandwidth that can be obtained in a specified order without spectral interference (overlap) from adjacent orders. As grating spacing decreases, the free spectral range increases. It decreases with higher orders. If λ1, l2 are lower and upper limits, respectively, of the band of interest, then:
Free spectral range = λ2 — λ1 = λ1/n
Ghosts are defined as spurious spectral lines arising from periodic errors in groove spacing. Interferometrically controlled ruling engines minimize ghosts, while the holographic process eliminates them.
On ruled diffraction gratings, stray light originates from random errors and irregularities of the reflecting surfaces. Holographic diffraction gratings generate less stray light because the optical process which transfers the interference pattern to the photoresist is not subject to mechanical irregularities or inconsistencies.
Gratings are available in several standard square and rectangular sizes ranging from 12.5 mm square up to 50mm square. Larger, and non-standard sizes are available upon request. Unless otherwise specified, rectangular gratings are cut with grooves parallel to the short dimension.
Replicated gratings of all types can be produced on float glass, Pyrex® or Zerodur®. Optometrics carries all three types of substrates in stock, in 3mm, 4mm, 5mm, 6mm, 9.5mm, and 12mm thicknesses. Other materials and thicknesses are available upon request.
Gratings used in the ultraviolet, visible and infrared are normally replicated with an aluminum coating. Aluminum is used rather than silver because it is more resistant to oxidation and has superior reflectance in the ultraviolet. Aluminum averages over 90% reflectance from 200 nm to the far infrared, except in the 750 to 900 nm region where it drops to approximately 85%. When maximum reflectance is required in the near infrared, as is the case with some fiber optic applications, the aluminum coating may be overcoated with gold. Though gold is soft, it is resistant to oxidation and has a reflectance of over 96% in the near infrared and over 98% above 2.0 µ. The reflectance of gold drops substantially below 600 nm and is not recommended for use in the visible or ultraviolet regions.
Dielectric overcoatings such as aluminum magnesium fluoride (AlMgF2) protect aluminum from oxidation, maintaining the original high reflectance of aluminum in the visible and ultraviolet. Gold overcoatings and aluminum magnesium fluoride dielectric coatings must be specified separately when ordering.
While gold overcoating can increase reflectivity, any overcoating may reduce the damage threshold by a factor of two or more.
What are OEM custom size capabilities?
Thicknesses of 2mm, 3mm, 5mm, 6mm, 9.5mm, 12mm and 16mm float glass are routinely available for faster delivery. Sizes in round, rectangular or square shapes as small as 6 mm, up to 90 mm are within Optometrics capabilities, depending upon which grating you have chosen.
What substrate materials are available?
Pyrex and float glass are routinely available as standard materials. However, gratings can generally be replicated on any hard surface such as Zerodur, Fused Silica, Metals and Hard Plastics.
Should I choose float glass or Pyrex?
Your application will generally dictate. The primary advantage of Pyrex is that it has a lower coefficient of thermal expansion and has better thermal stability.
Which way are grooves oriented on a rectangular grating?
Unless otherwise specified, rectangular gratings are cut with grooves parallel to the short dimension.
What types of surface coatings are available?
Bare aluminum offers good visible and infrared performance. AlMgF2 (aluminum magnesium fluoride) is used for enhanced UV performance. Gold is used to increase reflectivity primarily in the near infrared.
Do cosmetic blemishes affect grating performance?
Scratches or other cosmetic defects do not, unless extreme, usually affect optical performance.
Can I clean the grating surface?
The surface of a diffraction grating can be easily damaged by fingerprints, aerosols, moisture or the slightest contact with any abrasive material. Gratings should only be handled when necessary and always held by the sides. Latex gloves or a similar protective coating should be worn to prevent oil from fingers from reaching the grating surface. Any attempt to clean a grating with a solvent voids the Optometrics warranty. No attempt should be made to clean a grating other than blowing off dust with clean, dry air or nitrogen.
Are published efficiency curves based upon actual or theoretical data?
Typical grating efficiency curves published by Optometrics are based upon actual measurements of the gratings Optometrics sells. Efficiency curves available at “View/Download Specific Grating Efficiency Curves” were determined using absolute efficiency criteria. Be careful when comparing the efficiency curves from different manufacturers. Some publish relative efficiency data and relative efficiency curves will always give you a higher efficiency value than an absolute reading. To better understand relative vs absolute efficiency measurements, see “What is the difference between absolute and relative efficiency?” under FAQ for Gratings.
What is the difference between absolute and relative efficiency?
Grating efficiency is typically expressed as either “absolute” efficiency or “relative” efficiency. The absolute efficiency of a grating is the percentage of incident monochromatic radiation on a grating that is diffracted into the desired order. This efficiency is determined by both the groove profile (blaze) and the reflectivity of the grating’s coating. In contrast, relative (or groove) efficiency compares the energy diffracted into the desired order with the energy reflected by a plane mirror coated with the same material as the grating. Be careful when comparing the efficiency curves from different manufacturers. Some publish relative efficiency data and relative efficiency curves will always give you a higher efficiency value than an absolute reading. Efficiency curves published by Optometrics at “View/Download Specific Grating Efficiency Curves” were determined using absolute efficiency criteria.
Can Optometrics manufacture transmission gratings for the Visible range?
Yes. Call, fax or contact Optometrics online for recommendations.
How do the S and P designations correlate to Perpendicular and Parallel polarizations?
S (from the German word "Senkrenkt", meaning right angle) signifies the Perpendicular polarization. The P signifies Parallel polarization.
Why could a gold overcoat lower the damage threshold of an ML grating even though there's less absorption for Gold than Aluminum?
The mechanical characteristics of a gold layer are different than the Aluminum layer. Gold does not adhere well to most materials and, therefore, subjected to high temperatures, it may delaminate.
What is the percent improvement in efficiency obtained by putting a Gold overcoat on an ML grating?
1% absolute efficiency improvement can be expected.
The surface of standard gratings are coated with aluminum or gold and require extreme care when handling. Handling should be done by the edges only. These relatively soft coatings are vulnerable to fingerprints and numerous aerosols. Scratches or other cosmetic defects do not, unless extreme, usually affect optical performance. No attempt to clean a grating should be made without first consulting Optometrics.
Any standard Optometrics grating is available with either P-type or CW-type construction, for higher damage threshold performance.
Damage Thresholds: (no damage threshold minimums apply to gratings with an overcoat)
Standard Replica Gratings:
Pulsed: 350 millijoules/cm2 @ 200 ns
CW: 40 watts/cm2
P-Type Replica Gratings: (pulsed type)
Pulsed: 3.5 joules/cm2 @ 200 ns
CW: 80 watts/cm2
CW-Type Replica Gratings: (for continuous high power applications)
Pulsed: 3.5 joules/cm2 @ 200 ns
CW: 250 watts/cm2
Regardless of size, the additional cost per piece is:
Gold Overcoat (part number AU-3) $60.00
Aluminum Magnesium Fluoride (part number ALMG-3) $55.00
Note: While a gold overcoat can increase reflectivity, any overcoating may reduce the damage threshold by a factor of two or more.
Typical efficiency curves illustrate that, in all cases, orienting the polarization of the E vector (P-Plane) perpendicular to the grooves increases the efficiency over a specific wavelength region. This should be considered when optimizing the figure of merit (Q) of a cavity, particularly when it is polarized by auxiliary components such as Brewster angle windows.
One fine body…